Anal. Chem. 1984, 56,261 R-277 R (398) Zeman, A. Schmiertech. Tribol. 1982,29 (2), 55-8. (399) Zeman, S.;Zemanova, E. J. Therm. Anal. 1981, 20 (2), 331-7. (400)Zhou, Lixing: Chen, Shuxia; Gao, Xiuying Huaxue Tongbao 1981, (12), 733-7.
(396) Yuen, H. K.; Mappes, 0. W.; Grote, W. A. Thermochim. Acta 1982,52 (1-3), 143-53. (397) Zaborenko, K. B.; Kapustin, 0. A,; Bryukvin, V. A. Zh. Fir. Khim. 1 ~ 8 2 56 , (e), 1454-8.
Chemometrics Michael F. Delaney Department of Chemistry, Boston University, Boston, Massachusetts 02215
processing. At this same time ANALYTICAL CHIMICA ACTA discontinued its ‘Computer Techniques and Optimization’ issues (IN2, IN17) in favor of publishing these papers in the regular volumes, since chemometrics topics had come to be considered mainstream analytical chemistry. Toward the middle of the period under consideration, an excellent and informative feature began to appear in THIS JOURNAL. Edited, and often written, by Raymond E. Dessy, the ‘A/C Interface’ column has addressed local area networks, operating systems, programming languages, laboratory information managements systems, and analytical robotics (IN7, INS). During the latter half of the period covered by this review it became increasingly obvious that while computer hardware developments continue to be spectacular, the corresponding software is either lacking,secret, or non-existent. As discussed by S. A. Borman (‘Math is Cheaper Than Physics’) (IN5), chemometric techniques, and their corresponding realization in computer software, is the critical link between a dumb instrument and the resulting chemical knowledge. A controversv between instrument manufacturers and instrument users began playing itself out during 1983. The editor of THIS JOURNAL expressed a serious concern reeardine the lack of detail on the aleorithms used bv the m&ufa&rer of a computerized instriment (IN21). Ii was stated that the technological and legal restrictions should be sufficient to protect the manufacturer’s investment in software development. A letter to the editor (IN231 and a FOCUS article (IN6) in THIS JOURNAL discussed the issue from the both the instrument company’s and user’s point of view. The basic user issue is the following: how do I know whether my data is being manipulated properly. The answer is provided by Bruce Kowalski (IN6) who reminds us that “software is just soft electronics, and you don’t have to know exactly what it’s doing, you just have to validate that the software’s performance is correct. This is done in the same way as with any instrument, using standards, calibration, and various other tests. Two important trends in chemometrics are worthy of note. The first is the increasing rate of data production typically found in automated instruments. An example would be the data acquisition rates needed to keep up with the information being generated in a gas chromatography - mass spectrometry experiment (IN14). An instrument is being built which acquires raw data at a rate of 200 megasamples per second. The developments in instrumentation and computer technology will continue to put pressure on information processing resources to meaningfully and efficient extract results from raw data. The second trend is in response to the first. Chemometrics developments and the accompanying realization of these developments as computer software provide the means to convert raw data into information,information into knowledge and finally knowledge into intelligence. Two example papers are from the laboratory of Jack W. Frazer. Interactive graphics were used on the one hand to model experimental data (IN4) so that functional relationships could be defined, plotted, modified and fit to experimental data. The second use of interactive graphics was to facilitate the simulation of systems of chemical reactions so that sufficiently powerful experiments could be designed (IN11).
This is the third Fundamental Review formally named ‘Chemometrics’. This review will continue to provide some degree of organization and critical appraisal of a rapidly developing subdiscipline of Analytical Chemistry. The author considers himself at best a nephew of the Father of Chemometrics, having never had a formal association with Bruce R. Kowalski. With this change of authorship comes a somewhat different perspective on the topic, which will be reflected in the organization and selectivity of the review. The period covered by this review is December 1981 to December 1983 with the focus remaining on the analytical aspects of chemometrics. Continuity with the two previous Chemometrics Reviews (IN15, IN10) is preserved by using a similar classification of sub-sections. Even though the topic is reasonably narrow, an all-encompassing summary has been avoided so that a more selective evaluation of the field can be made. During the course of this review several notable activities have served to establish the importance of chemometrics and to disseminate the developments in this field. A NATO Advanced Study Institute on Chemometrics was held in Italy, bringing together a number of experts and interested individuals for two weeks of intensive interaction. The second conference on ‘Computer-Based Anaytical Chemistry’ (COBAC) was held in Munich in 1982 (IN18, IN25). An ‘International Conference on Chemometrics in Analytical Chemistry’ was held in Petten, The Netherlands, in 1982 (IN3). Also a symposium was held at the 1983 National ACS Meeting in Seattle, on ‘the Role of Chemometrics in Pesticide - Environmental Residue Analytical Determinations’. Much of an issue of ‘Chemical and Engineering News’ concerned the topic, ‘Computers in Chemistry - Managing a Revolution’, which included three articles (IN9, IN13, IN16) discussing computational chemistry, computerized planning of organic syntheses, isomer generation, molecular structure elucidation, and graph theory. An issue of ‘American Laboratory’ was devoted to Information Management (IN1). Also, several new journals were initiated which will probably be of interest to chemometricians ‘Computer Applications in the Laboratory’ (IN12), ‘Journal of Molecular Graphics’ (IN19), ‘Computer Enhanced Spectroscopy’ (IN24)). In as much as we regard chemometrics as the interface between chemistry and mathematics (IN10) it is reasonable to expect new ventures in chemometrics to involve ‘new’ fields of mathematics. One such development is the increasingly extensive use of graph theory for describing and manipulating chemical structures. For this reason we have added a new section, ‘Graph Theory and Structure Handling’. In addition we have added a section ‘Library Searching’ to contain references describing structure elucidation using stored libraries of reference spectra, and have changed the name of the ‘Spectral Analysis’ section to ‘Signal Processing’ to indicate that these techniques for manipulating waveforms includes application to non-spectrometric signals. New Developments. In the beginning of the time period covered by this review the editor of THIS JOURNAL, described ‘computerphobia’, (IN20) and the salvation to those who do not program provided by ‘intelligent programs’ which will program for you. In the same issue, the ‘Editor’s Column’ (IN22) discussed THIS JOURNAL’Smove into the computer age with computerized selection of reviewers and manuscript 0003-2700/84/0356-26 lR$06.50/0
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PERSONAL SUPERMICROCOMPUTERS Next to one’s mind, the most important tool of the chemometrician is his computer. Striking advances in computer technology have continued at an increased pace since the last review. The title of this section was chosen to highlight the two major computer hardware trends. The first is the increasingly common occurence of high performance superminicomputers in laboratory research groups. These 32-bit processors (e.g., VAX-11/730) feature megabytes of memory, tens to hundreds of megabytes of disk storage, and a number of terminal porta. We have found that such a system relieves us of the constraints of the overburdened University system, while providing a much friendlier operating system and user interface. Such a computer facilitates access to the large datasets that are common in chemometrics studies and also provides the capability of receiving data directly from microcomputers associated with laboratory instruments. The second major hardware trend is the use of personal microcomputers for control of laboratory instruments, acquisition of experimental data, and processing of chemical information (BK9). The personal computer can give the scientist sufficient power and capacity for nearly any significant task coupled with the independence and control inherent in a single user system. In addition, many microcomputers can be cajoled into emulating expensive intelligent terminals when connected to larger computer systems. A wide range of instrumental applications of personal computers, microprocessors and calculators have appeared during the period covered by this review (PS9, PS14-18, PS21, PS25-26, PS28, PS30). The interplay between computers and chemometrics is discussed by Belchamber and associates (PS6) using examples of several recently computerized instruments. These ranged from control of a titrator using a microprocessor to complex image processing in computerized tomography. Other applications of computer controlled instruments have appeared in the areas of electrochemistry (PS3-4, PS29, PS32), ion selective electrode potentiometry (PS5), uv-vis spectrometry (PS33),thermogravimetry (PS19), thin-layer chromatography (PS2), size exclusion or gel permeation chromatography (PS20, PS27), liquid chromatography interfaced to infrared spectrometry (PS31), mass spectrometry (PS8, PS37), radioimmuno-assay (PS22), atomic absorption spectrometry (PSl), auger spectrometry (PS7), and laser spectrometry (PS23). As discussed by Dessy (PSll-12), the local area computer network (LAN) is rapidly becoming a routine laboratory tool, just like a balance or a spectrometer. Two noteworthy chemical laboratory networks were discussed by Ziegler (PS34-36) and Duursma et al. (PS13). Both systems take the approach of using the right size computer for the job at hand. The preferred organization is based on a hierarchical structure centered on a large computer (or two) connected to progressively smaller processors, with the specifics tailored to the demands of the corresponding instruments and users. The central computer facilitates large quantitities of storage, significant information processing power, and high performance peripheral devices (plotters, printers, image digitizers). The burden of directly serving the real-time needs of a laboratory instrument is shouldered by microcomputers at the periphery of the network which have nothing better to do than to wait for something to happen in the instrument. A similar approach has been described for electrochemical studies (PS24). This author’s experience has been that a department can go from not knowing what a network is to being critically dependent upon one in a matter of months (PSlO). In any local area network, an organized and coordinated set of commands is desirable. Ziegler et al. (PS38)described an extensive and organized chromatgraphic data processing command language. Nearly any manipulation of chromatographic data and results can be conveniently conducted using sensible instructions. Examples of well-organized and user oriented software for the analytical laboratory such as this are expected to become increasingly important.
EDUCATION AND BOOKS Education. Thomas L. Isenhour, in an ACS Analytical Award address (EDS), discussed the status of academic analytical chemistry, the decay of U.S.science education ‘physics 282R
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without numbers’), and the future of computers in analytical chemistry. He lists Computing as one of Man’s Greatest Inventions, along with Language and Writing, and predicts that intelligent laboratory robots will emerge in the 1980s. This sprited challenge to American scientists to rescue science education from the disasters of the educationists (‘teacher training and driver education’) should be required reading for us all. Chemometrics has reached the state of development warranting its discussion as a subject worthy of a position in an up-to-date chemistry curriculum. Howery and Hirsch (ED7) have considered the role of chemometrics in a university setting. They summarize the historical development of the topic, review the thoughts and views presented at an ACS Symposium on ‘Teaching Chemometrics’, and briefly demonstrate the chemometrics topics of multiple regression analysis, factor analysis, and pattern recognition. The title ‘Teaching Chemometrics’ was also chosen by Vandeginste (ED13) for detailing his thoughts on chemometrics being an integral part of the analytical process. He presents the organization of chemometrics courses at the University of Nijmegan in The Netherlands, which partitions the topics into the areas of sampling, measurement, data processing, result conversion, and organization. It is noted that chemometrics draws upon a wide array of mathematical techniques. Deming and Morgan (ED3) presented a discussion of the benefits of svstematic exDerimenta1 design and the fundamental concepts and teihniques that Gust be taught to analytical chemists. They submit that the quality of experimental results are critically dependent on the intimate relationships between models, measurement processes, and experimental design. Their approach focuses on two fundamental concepts - the sums of squares tree used in the analysis of variance, and the variance - covariance matrix. In addition, an extensive literature survey of the use of sequential simplex optimization is presented, consisting of 189 citations and a cross-reference table. A very useful source of information on the educational aspects of chemometrics and related topics is the Computer Series in the ‘Journal of Chemical Education’, edited by John W. Moore. This series includes long articles, such as the Howery and Hirsch paper mentioned above (ED7) as well as collections of shorter works (‘Bits and Bytes’), such as the interactive function translator described by Henry and Jurs (ED6). During the past two years this series has included descriptions of a course on applications of computers to chemistry (EDg), the balancing chemical equations using matrices on a hand-held calculator (EDl), and the simulation of aqueous equilibria (ED12), as well as gas chromatography (ED14) and NMR spectroscopy (ED4). Information acquisition and processing using computers remains important as a tool of the chemometrician. Discussion of recent developments in automation (ED2), microcomputer electronics (ED@, and instrument interfaces (ED10) have appeared. Books. The number of new chemometrics books continues to be small. This is not surprising since many chemometricians are actively pursuing new advances, rather than restating past successes or assimilating disparate research activities into an organized body of information. There remains no completely suitable text book of chemometrics. The closest would still seem to be the work by Massart, Dijkstra, and Kaufman (BK12). The proceedings of the 6th International Conference on Computers in Chemical Research and Education has been published in book format (BK3). This includes the text of the 17 plenary lectures and abstracts of the 63 poster presentations. Included is a summary of chemical applications of pattern recognition by Varmuza and discussion of networks, information systems, structure elucidation, computerized organic synthesis, molecular modelling, and drug design. An excellent book on the use of cluster analysis in analytical chemistry has been written by Massart and Kaufman (BK13). In addition to being a well-written and clearly detailed overview of this branch of pattern recognition, the related topics of factor analysis and display techniques are also well presented. The book summarizes nearly all previous applications of clustering in analytical chemistry and other sciences. A more narrowly focused book on the clustering of large quantities
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ofdata has been publishes by Zupan (BK17). primarily based on his computational breakthrough for developing tree structured spectral libraries for structure elucidation. A. G. Marshall has edited a comnrehensive b w k which
transform in speamscOpy and Hilb line shape analysis. In addition to chapters describingFourier transform NMR, twdimensional NMR, IR, UV/VIS, ion cyclotron resonance (ICR), nuclear quadrupole resonance (NQR), and microwave spectroscopies, there are also sections concerning spectroelectrochemistry, faradaic admittance measurements,electron spin echo spectroscopy, and dielectric spectroscopy. The third volume in the series 'Physical Methods in Modern Chemical Analysis', edited by Kuwana (BK8). includes a chapter on transform techniques by A. G. Marshall and one on a global optimization strategy of GC separations by R. J. huh. Justice and Isenhour (BK5, BK6) have edited a two volume collection which bring together reprints of important works involving 'Digital Computers in Analytical Chemistry' from 1950 until 1978. The papers are grouped by ?pic afeas, each of which begins with comments by the editors, including pattern recognition, signal processing, data enhancement, information retrieval, and interpretation. Since the last review, books related to chemometrica have appeared concerning modem electronics for scientists (BK10, BK4), calculator programming in chemistry (BK2), laboratory minicomputin (BKl), personal computers in chemistry (BK9). the maiematica of chromatography (BK14),computer chromatography (BK7). and chemical literature topica (BK15, BK16).
STATISTICS Statistid analysis and s t a t k t i d concepts m completely prewde modem analytical chemistry that their u e is often considered routine, and conquently they are poorly applied. A continued evaluation of the application of statistics to chemical analysis appears to be one of the two primary areas of research and discussion since the last review. The second area involves the application of more complex statistical models to chemical data. The abiliQ to perform the extensive calculations neceaeary for use of these statistics is now readily available to chemists due to the proliferation of computers in chemical laboratories. The general advances in electronics, computationalcapacity, and chemical understanding have sparked an explosion of analytical methods. Considerable attention has been given to the evaluation and validation of new methods. A review of the validation process has recently appeared in THIS JOURNAL (ST19).Two comprehensive discussions on the d;.tection and determination of errors in method validation and evaluation studies have appeared (ST2, ST3). In part one, total verification is proposed whereby the errors i n t r o d u d a t every step of the method development and transfer are determined and used to describe the accuracy. sensitivity, selectivity, and precision. Available testa of ruggednew,accuracy, acaeptibility, precision, and collaboration are presented and evaluated. A second paper by the same author (ST3) presents a method for determining the constant and proportional errors in
an analyak. The method k based on a combination of the standard calibration m e , the Youden regression, and the standard additions m e . A new insight into the fundamental relationshi between the Youden regression and the method of StandarJadditions permitted an asmy of the sample to he obtained from the ratio of their respective slopes The systematic errors as a function of peak skew was evaluated hy Delaney (ST4) for four commonly used m a n d peak area measurement methods. The performance of all four methods was seen to degrade as the peak became more asymmetric, however, the Condal-Bosch trapezoidal method was found to maintain acceptable performance, even for severly skewed peaks. In another study, the variance, accuracy, and precision of peak area measurements were determined by the method of squared successivedifferences (SSD) (ST12). Using computer simulated peaks where the true values were known and where the peak shape, size, and noise level could be varied, a series of equations was derived to estimate the peak variance, and subsequently calculate the accuracy and precision of the estimate. The results indicated that the accuracy of the estimate was not significantly affected by the number of data points, the peak area, the peak shape, or noise level. The authors applied the SSD method to isotope dilution gas chromatography mas spectrometry (ST13 ). Results were compared to thoae oitained with other regression techniques. The analysis of complex environmental and biological eamples has received increasin attention recently. Many of the analyses of these samples gave legal and health ramifications and therefore extensive guidelines are evolving which aid the analyst in producing accurate results. The practical and statistical rinciples of environmental analysis were recently reviewei(ST8). A step-by-tep discussion of proper environmental analysis from planning to documentation and reporting is given. An extended discussion of the application of these princi lea to water analysis has also been published (STS).Exampres of various sources of bias, the application of the recommended defmition of 'limit of detection', and the use of control charts are discussed. The statistical limitations of the spike recovery test of method validation were also discussed (S49,ST16). The spike/recovery test is shown to be fairly insensitive to interferents when used near the limit of detection with small spikes. A modified graphical representation of large data sets, which gives greater emphasis to the coherent nature of data taken from homogenous populations. has also been proposed (ST5). An interesting approach to determine whether mussels were collected from polluted water has been done and was based on a combination of principal component analysis (PCA) and a generalized distance function (ST15). Since the number of factors which influence the concentrations of trace metals in water and organisms is great and varies significantly, PCA of each mussel sample was used to determine and eliminate factors associated with natural variability. The probability and confidence that the sample came from poUuted water was then calculated using the distance function. A general discussion of the sources and manifestations of resampling factors in biological systems has appeared (ST7). & + d l y when establishing baseline levels for trace anal-, vanation in presampling conditions has c a d widely varying results for aeemingly similar eamples. The author points out a need to systematically evaluate these factors and to establish standardized procedures. The sources of error in the determination of particulate bound trace elements in aquatic environmenta by atomic absorption spectrometrywere evaluated (ST1). Two common techniques were compared. and several sources of error were identified. The analysisof contamiianta in foods and drugs is another area where legal and health ramifications encourage accurate and precise methodology and technique. Horwitz (ST6) reviewed the present realities of measuring smaller and smaller amounts of material in both simple and complex matricies. As measurements are made a t lower and lower levels, the analyst sacrifices reliability. The attainment of increased reliability as concentrations decreaae is accompanied by increased costa. It is a balance of costa. sensitivity, and significance that must be achieved by analytical laboratories. Analysts have expressed interest in the magnitude of errors introduced to analyses by data aquisition systems, computer mftware, and electronic calculators. The noise introduced by analog-Migital converters, with respect to resolution in ANALYTICAL C K M I S T R Y , VOL. 58. NO. 5. APRIL 1984
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absorbance measurements was examined experimentally (ST11).The measured noise levels were in close agreement with those predicted by theory. The inaccuracies in the calculation of standard deviations by electronic calculator (ST20) and by IBM 4341 computer (ST17) were investigated. Both authors agree that unless properly controlled,round-off errors can introduce significant inaccuracies to calculated results. Several recent papers (ST9, ST14, ST18) discuss the views on accuracy in analytical chemistry, aptly reminding us that precision without accuracy is useless (ST18). A modified definition of the relationship between the terms precision and accuracy has been proposed (ST9). This definition reflects the view that precision is one of the components of accuracy and bias is another. To say that a determination is accurate would mean, by this definition, that the results are both precise and unbiased. Applications of round-robin-tests (ST14) and improved sample handling methods (ST18) towards the goal of improved accuracy have been discussed.
MODELING AND PARAMETER ESTIMATION As discussed in the previous review (INlO), the concepts of Calibration and Resolution overlap considerably with Modeling and Parameter Estimation (curve fitting). Papers dealing with the conversion between measured response and concentration are under Calibration, and those concerned with the overlappingsignals (chromatograms and spectra) are under Resolution. Molecular modeling, in particular structure activity relationships are covered in the Graph Theory and Pattern Recognition section. In this section are the topics of simulation and parameter estimation for analytical data, methods, laboratories, and chemical systems. Modeling for the purpose of estimating the likelihood of peak overlap in chromatography has been the subject of two excellent papers (M07, M024). Rosenthal (M024) used a discrete combinatorial approach. He estimated, for example, that for a 200 component sample mixture 20 of the components would be expected to elute as unresolved multiplets, even in the case of high resolution chromatgraphy. A more elaborate model based on Poisson statistics was presented by Davis and Giddings (M07). They showed that a chromatogram would need to contain peaks during no more than 5% of the run to have a 90% probability that a given component would appear as a isolated peak. One implication of these studies is that even high resoluton chromatography cannot be relied upon to provide pure samples for spectral identification. Nagels et al., in a similar study (M020), simulated chromatograms of complex samples such as plant extracts, in order to estimate the probability that a given quantitative analysis could be performed successfully. After considering 90,000 synthetic chromatograms, they concluded that the number of components present in these types of samples exceeds the peak capacity of any single chromatographic system. Selective sample pre-concentration, multi-dimensional chromatography, or selective detection are suggested to address this difficulty. In addition to the two modelling papers from Frazer’s group which were mentioned in the introduction (IN4, INll), a third (M04) describes the use of the splines-under-tension concept to construct three-dimensional surfaces using non-uniformly spaced data. The algorithm is computationally and storage efficient and allows the experimenter to ad’ust a tension parameter to obtain satisfactory surfaces. A disadvantage is that the surface can make unreasonable excursions in regions of few known data points if the tension parameter is low. Janse and Kateman ( M o l l ) described the operation of an analytical laboratory using principles of information theory, dividing up the problem into three components: the purpose of the analysis, the object being analyzed, and the analytical procedure. Historical information known about the object before analysis reduces the uncertainty and reduces the information needed by the analysis. Queuing simulations were used to study analytical planning strategies and to optimize the information gained. Simulation, One of the main types of model investigations, simulations are preferred when the mathematical description of the model does not readily lend itself to an analytical solution in closed form. This seems to occur most commonly in electrochemistry in which the mathematically tractable experiments are limited in utility while the useful experiments 264R
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are impossible to solve. Digital simulation of the static mercury drop electrode (SMDE) was found to be more rigorous and general than a theoretical relationship based on a modified form of the Cottrell equation (Mol). It was found that the simulation worked well for a stable drop, but a growing or newly formed drop was subject to complex hydrodynamics. Another group (M03) employed Monte Carlo simulation to study electrocrystallization on microelectrodes. Explicit or implicit finite difference simulation has been used to describe double potential step chronoamperometry and linear sweep voltammetry (M015), very rapid chemical reactions coupled to electron transfers (M025), and electrochemistry on ensembles of microelectrodes (M023). Simulation of electrochemicalsystems using a minicomputer was also extensively considered (MOB). Another study (M014) simulated the high precision determination of zinc by complexometric back titration. Schindler and Weaver (M026) presented an novel approach for greatly speeding up a digital simulation of an electrochemical system. The method involves the parallel calculation of the system of interest and of an ideal analog to which an exact solution is available. Deviations in the calculation caused by numerical errors can be detected using the exact solution and used to correct the solution of the non-ideal system. The copolymerization of ethylene and propylene was simulated as a second order Markovian process, with the results used to fit NMR intensities using simplex optimization (M05). The effect of diffusion on heterogeneous copolymerization was considered. A sterling example of the power and capability of a comprehensive numerical simulation is the paper of Jochum and Kowalski (M012) in which both potentiometric and amperometric immobilized enzyme electrodes were accurately described using a coupled two-compartment model. Previous studies of such systems were obliged to make simplifying assumptions concerning the form and the boundary or initial conditions which govern this system of coupled non-linear differential equations. This model was able to handle the effect of stirring, which is usually ignored by assumptions in other simulation approaches, and it was shown that the stirring rate can be used to increase the linear dynamic range of the electrodes. Parameter Estimation. Meyer (M019) has briefly discussed a subtle difference between two derivations of weighted least squares curve fitting methods which becomes important when the model is not well conformed to by the data. Karrer et al. (M013) have disputed the use of least squares parameter estimation for estimating the composition of a sample using mass spectral data. They contend that the random errors in these data are not statistically independent and probably do not have equal variances and covariances. They developed a linear model based on Bayesian statistical methods and applied it to deconvolve overlapping spectra resulting from hydrogen loss and gain brought about by ionmolecule reactions. Non-linear least squares has been used to determine stability constants of coordination compounds (M016). An elaborate program system was described which uses a variety of mathematical methods which was then used to study five non-aqueous metalloporphyrin ligand systems. Several papers have considered the analysis of titration curves (M010) including both potentiometric (M029) and spectrophotometric titrations (M027). Exponential signals are observed in many experiments exhibiting first order kinetics. Two papers have appeared for extracting the parameters of exponential waveforms. Bacon and Demas (M02) have demonstrated that the phase-plane approach performs better than the more common Guggeneim method, especially in cases where a stable noise-free baseline is not attainable. Estimation of the final value of an exponential response using polynomial smoothing has also been considered (M028). This method was accurate even for data collections times shorter than one time constant. This problem was also handled by the iterative log rate method (M06). A more complex kinetic system consisting of simultaneous first-order reactions was studied using a non-linear differential rate method (M021). Following manipulation of the equations which describe the system, a ‘kinetic spectrum’ is obtained in which different reaction components cause different peaks, with heights equal to the reaction rate constant, and areas
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equal to the initial concentrations. The method was used to study the dissociation of copper ions from estuarine humic substances. The ability of complex non-linear least squares to estimate parameters from impedence and admittance data obtained from electronic circuits was studied (M017). The effect of digitization round-off error and normal noise were considered. A pragmatically quite useful approach for graphically estimating a wide array of parameters of skewed chromatographic peaks has been described (M09). These theoretically-based parameters are collectively referred to as ‘Chromatographic Figures of Merit’, and include standard statistical descriptors and other chromatographicallyoriented parameters such as relative system efficiency. Modeling of chromatographic peaks has been performed using the the Edgeworth-Cramer series to approximate theoretically based chromatographic models (M08). A new approach for calculating the pH of a multi-component aqueous solution has been described (M022). The calculations, which are based on an iterative optimization search method called the ‘golden section’ method, are very fast, and suitable for a process control application.
RESOLUTION Resolving a waveform into the contributions from individual components is one of the most important and useful chemometric techniques. The methods can be classified into two groups - those in which assumptions about the system are made (e.g., number or identity of components, line shapes) and those in which no assumptions are made, other than (perhaps) linear system behavior. (In the former case you get back what you assumed, in the latter you get what you get.) Another distinction is whether one has only a single waveform, such as a UV spectrum of a mixture of several compounds, or a series of related waveforms, such as UV spectra scanned across overlapping chromatographic peaks. In this section we will progress from studies were many assumptions are made, to those in which few assumptions are needed. Five statistical functions (gaussian, log-normal, gamma, Weibull, and Littlewood) were evaluated for their ability to deconvolve overlapping chromatgraphic peaks using iterative least squares minimization (RE3). Some functions performed noticeably better than others on certain experimental chromatograms in cases where the function could bend itself into the proper shape. However, the method still suffers from the limitation of having to assume a specific number of sample components. A similar approach was considered by Kralj and Simeon (RE5). Although using solely synthetic data, a much more statistically based study was conducted. Resolution of UV/VIS spectra of methyl viologen cation radical and its dimer was demonstrated by Stargardt and Hawkridge (RE9). They used a previously described iterative least squares minimization procedure based on gaussian and bigaussian waveforms. While the process does resolve a spectrum into peaks, there remains an ambiguity as to whether small components are real or calculational artifacts caused by deviations of the actual peaks from the assumed shape. Quantitative resolution of severely overlapping chromatographic peaks was demonstrated by DAllura and Juvet (RE1) using an iterative solution of a system of non-linear simultaneous equations. The theory for this approach was described earlier (RE6). It is reported that the method is successful if the retention volumes of the peaks differ somewhat (slight shoulders) or even if the retention is identical but the peak shapes differ. For the experiment to be successful, accurate monitoring of the mobile phase flow rate and computer-based corrections were necessary. Resolution of fast fluorescencedecay curves using the phase plane deconvolution technique was studied numerically by Jezequel et al. (RE4). The observed fluorescence decay curves consist of a convolution of the time profile of the excitation flash and the fluorescence signals from the sample components. The phase plane method consists of manipulating the equations which describe the observed curves into a form which allows the lifetime(s) to be extracted by linear least squares analysis. The effect of errors caused by quantization of the experimental signal, noisy data, and scattered light were considered. Rutan and Brown (RE7) used the Kalman filter to deconvolve spectra of metal-ligand complexation systems obtained
using a pulsed photoacoustic spectrometer. They were able to obtain a formation constant for the PrEDTA- complex, even though the complex and free metal spectra are quite similar. The Kalman filter is a recursive linear parameter estimation technique which needs both a reliable model of the chemical system’s dynamics and a model of the measurement process. Inability of the Kalman filter to deconvolve mixtures when the ligand to metal ratio became too high was attributed to deviations between actual and modeled spectra. Deconvolution using Fourier transforms was employed by Wright et al. (REII)to isolate extra-column contributions to band broadening in liquid chromatography. The transfer functions of the extra-column components (injector,detector) were experimentally determined by operating the chromatograph without a column. The extra-column broadening in a conventional chromatogram could then be removed by algebraic manipulation of the Fourier transform of the extracolumn transfer function and the chromatogram itself in the frequency domain. Experimental results were presented to demonstrate the utility of this approach. As expected, the injector was found to be a more important contributor to broadening than the detector, and the contribution from the injector decreased with increasing retention. The approach of plotting dispersion version absorption (DISPA) for a spectral transition has been used by Wang and Marshall (RE10) to detect the occurence of multiple overlapping gaussian signals. Previously this approach had been used exclusively for Lorentzian line shapes. The dispersion spectrum can be obtained from an absorption spectrum using a Hilbert transformation. The DISPA for a Gaussian peak is not the ideal circle obtained for a Lorentzian profile. Conversion of a Gaussian spectrum into a Lorentzian using an appropriate apodization function on the inverse Fourier transformed gaussian spectrum gave inconsistent results. A successful approach was generating the conventional DISPA plot for the Gaussian curve followed by subtracting from each DISPA data point the difference between the DISPA curve for a ‘pure’ Gaussian and a circle. It was then possible to use this ‘reduced’ DISPA plot to detect overlapping gaussian profiles. Experimental verification was demonstrated using ESR spectra. Instrumental and computer technological advances are making experiments which employ multivariate data a routine activity. Examples of this are combinations of chromatography with spectrometry: GC-MS, GC-IR, LC-UV, etc. The ultimate goal of curve resolution would be to be able to determine the number of components in an overlapping chromatographic peak as well as the spectrum and concentration profile of each compound, without assumption regarding peak shape, location, or identity. As discussed in the Factor Analysis section, abstract factor analysis (AFA) can determine the number of components (FA19), target testing factor analysis (TFA) can confirm the presence of a suspected compound (FA19),and rank annihilation factor analysis (RAFA) can quantitate a known component (FA18). Factor analsis alone, however, is incapable of solving the general resolution problem. Self-modelling curve resolution, as demonstrated by Sharaf and Kowalski (RE@comes as close as possible to providing curve resolution of multi-dimensional data without simplifymg assumptions, at least for a system containing two components. The case of GC-MS experiments has been studied, in which a number of mass spectra are measured during the elution of overlapping peaks. The two most important principle eigenvectors obtained from an abstract factor analysis of the raw data matrix are used to form a two dimensional coordinate system. Each normalized raw spectrum is projected onto this space. In the case of a two component peak, these points will lie on a line with the ends of the line correspondingto the most pure spectra measured for each component. The approach then takes advantage of the fact that all the intensities of a real spectrum must be positive. Each end of the line can be extended until the ‘predicted’ spectrum has a negative intensity, corresponding to a physically impossible situation. The spectrum of the pure component should lie somewhere in this extrapolated region. This approach was shown to be successful at complete curve resolution even when the retention of the two compounds was identical, as long as their peak shape and spectra are somewhat different. The effect of noise, baseline drift, and tailing were ANALYTICAL CHEMISTRY, VOL. 56,
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studied. This is currently the most powerful curve resolution approach available. Self-modelling curve resolution has also been to resolve a set of overlapping x-ray photoelectron spectra (RE2).
CALIBRATION Calibration lies near to the heart of nearly every experiment that we, as analytical chemists, would like to perform. Yet, for many years the calibration function has been treated as a black box by the majority of analysts. This is in sharp contrast to the way that we, as scientists and critical analysts, would like to treat any important aspect of our experimentation. Fortunately, the recent literature contains a fair amount of healthy discussion on various aspects of calibration, We hope this discussion will continue as critical awareness grows of the limitations that the need for calibration places on our experiments. The recent papers discussing calibration in analytical chemistry can be roughly separated into three groups. One group deals with the statistical aspects and limitations of calibration functions. Another group addresses new computational tools for calibration in relatively new areas of analysis, particularly multicomponent analysis. The third group deals with special solutions to calibration problems unique to specific types of instrumentation. The statistical aspects of calibration involve consideration of the validity and predictive power of calibration functions. While a paper (CA46) mentioned in the 1982 Chemometrics review (IN10) warned of the unsuitability of the use of correlation coefficients for evaluation of calibration curves, more rigorous approaches (CA45, CA46) are still shunned by many investigators (CA35, CA45). Normal least squares analysis involves the assumption that variance in the response is normally distributed and homoscedastic (homogeneous) (CA4, CA22, CA36). While suitable tests of these assumptions are available in the chemical literature (CA4, CA31) they are often ignored and many data sets have appeared in the literature which violate those assumptions (CA36). In fact heteroscedasticity of variance may be the general case in chemical analysis (CA4, CA36). Robust regression (CA36) is less sensitive to violations of the underlying assumptions of normality and homoscedasticity of variance than normal least squares regression. Alternatively, variances of responses can be estimated by a number of techniques (CA4, CA22, CA30, CA31) and homogenized in a weighted least squares determination. Robust regression (CA36) involves an iterative reweighting of data with an automatic filtering of extreme outliers. Iteration is discontinued when the change in the predicted parameters (slope, intercept) between succesive steps becomes small. Performance equals or exceeds that of normal least squares determinations except in the case where distribution of response variance is ideal. Weighted least squares calculations generally give similar estimations of line parameters to those given by normal least squares calculations (CA4). The predictive power of the calibration function is greatly enhanced when the proper weighting method is chosen (CA4, CA30), particurlarly for trace analysis. Replicate measurements are the most common variance estimators used for weighting (CA31),but a good deal of replication (n > 5) is required for proper usage. A comparison of several variance estimators has been made for isotope dilution GC/MS data (CA31),the squared successive differences (SSD) estimator (ST12) was preferred. An optimal design for assay calibration (CA1) was recently reported. While this design leads to increased redictive performance when standard material is limite$ extreme caution is warranted. This design is applicable only when the method being calibrated has been shown to be robustly linear over the range of interest. Unfortunately the simplicity of the design would certainly lead to abuse by analysts unaware of its theoretical limitations, should ita use become widespread. A good portion of the calibration literature involves definitions of terms such as limit of detection, determination, quantitation etc. to various degrees of statistical rigor. Because a multitude of such definitions exist, authors and manufacturers should clarify by explicit definition the meaning intended when using such terms. The IUPAC definitions (CA48) are a reasonable starting point but they fail to consider uncertainties contributed by estimation of the parameters of 266R
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the calibration function. The definitions of Currie (CA8) are more rigorous and useful, and have recently been applied to both linear tCA33) and non-linear systems (CA39). Advances in the calibration of multicomponent analyses have been led by applications of the generalized standard additions method (GSAM). Recent papers have documented the applicability of GSAM to a number of different problems (CA10, CA13, CAM, CA19, CA49). GSAM has also been extended to allow identification of and correction for interferences and drift in measurements (CA18, CA19). Partial least squares (PLS) techniques (CA25, CA41) have also been useful in the solution of multicomponent problems. PLS can be applied to systems where fewer independent measurements are available than the number of components to be determined. An example of this is PLS-GSAM (CAlO), where either fewer sensors or additions can be used than the number of components to be determined. PLS calibration methods in multivariate analysis have been compared favorably to combined principal components analysis - multiple regression (PC MR) determinations because PLS uses more of the availab e information and can detect samples which do not fit the calibration (CA25). The recursive GSAM (CA47) is uniquely suited to automation. The results are recalculated after each successive standard addition and the experiment is terminated when a pre-determined level of precision has been reached. Another unique tool in the solution of the multicomponent calibration problem involves solving the system in the predictive form C = PR rather than the normal form R = KC (effectivelytreating responce [R] as the independent variable) (CA3, CA27). While the formulation and meaning of the linear system is less intuitively satisfying in this form, the solution is less complex. This approach has been applied to problems involving both real (CA21) and computer simulated (CA3) IR data. Another simplified solution is attained by use of the Gauss-Jordan row reduction (CA14). Further discussion of multicomponent analyses can be found in the Factor Analysis section of this review. A solution to problems associated with calibration of results of Fourier transform spectroscopies is derived from the Gram-Schmidt reconstruction technique (CA42). The quantitative dependence of the reconstruction has been derived and applied (CA42), it allows quantitative information to be extracted from an interferogram without performance of the Fourier transform. Cross correlation is an extension of least squares determination (CA24) which improves the precision of calibration derived from either Gram-Schmidt reconstructed (CA23, CA24) or Fourier transformed (CA26) spectra. A general correction for non-linearity caused by pulse losses due to event overlap was recently reported. The method can applied to any pulse counting detector, as long as true and measured event rates can be measured or estimated (CA37). A number of recent papers have demonstrated the use of either numerical or empirical formulations of non-linear calibration functions encountered in potentiometry (CA11, CA28, CA50) and atomic absorption spectrometry (CA2).
i
SIGNAL PROCESSING Signal processing is an important principle in understanding the operation of analytical instrumentation, and can be broadly defined as any process which refines information contained in a si nal. By this definition much of what analytical chemists cfo is signal processing. Signal processing can lead to the discovery of new modes of operation for existing analytical methods or entirely new methods. The intimate association between computers and instruments is the key to recent developments in analytical signal processing. Computational power, large data storage volume, fast data acquisition, precise instrument control, precise digital measurement and repetition are some of the computer capabilities important for instrumental signal processing. Digital signal processing in the computer improves data quality and makes possible a variety of new methods such as cross polarization and spin echo techniques which produce additional kinds of chemical information (SP12). Some of the inherent capabilities and limitations of an instrument can be described in terms of signal to noise ratio (S/N). Choice of instrumental operating conditions is often crucial for obtaining acceptable S/N. The importance of the
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interaction between signal strength and noise level on detectability in flame atomic absorption spectrometry (AAS) and the use of ensemble averaging as a technique for S/N enhancement in mass spectrometry (MS) are described by Stolzberg (SP17). In this technique analytical wavelength and spectral bandpass are varied while signal strength and noise level are determined and optimized. A theoretical and experimental study of the effect of changing interferometric sampling of gas chromatography - Fourier transform infrared spectrometry (GC/FT-IR) Gram Schmidt reconstructions on peak S/N ratio and relative peak heights has been presented (SP18). The major advantage of the technique is that a chromatogram can be calculated using time-domain interferometric data so that the time consuming Fourier transformation of each acquired data file can be avoided. Although it is necessary to measure raw spectra which have a high signal-to-noise ratio, the extent to which the noise can be reduced in the measuring process is limited. Thus smoothing of raw data becomes increasinglyimportant. Saitou et al. (SP15) have described spline functions which are useful for interpolation and smoothing. The effects of this method on measured spectra were investigated by computer simulation. The possibility of using Akaike’s information criterion to estimate the fitting was also discussed. The application of factor analysis to reduce random noise in FT-IR spectra is described by Gillette and Koenig (SP8). The total information content of the spectra of a series of component mixtures is utilized to reduce the amount of random noise present in an individual spectrum. Speed is frequently a problem when performing real-time digital smoothing on small laboratory computers. Bush discusses several techniques whereby fast single-precision arithmetic can be used for most of the computation while retaining numerical accuracy. Some empirical filters are also described which possess very favorable computational properties (SP3). Jansen and Poulisse have proposed a discretetime digital filter algorithm that estimates abrupt changes in the process values between two runs of samples based on a model describing the process fluctuations (SP10). They have also formulated a modified data-weighting Kalman filter to estimate the state of the batch-type analysis model and to take advantage of the batch-type situation (SP13). A modification of the second degree Savitzky-Golay smoothing filter is suggested which is found to show better S/N behavior than the exceedingly popular Savitzky-Golay filter (SP1). Cross-correlation is a technique developed to enable the detection of both periodic and aperiodic signals that arise in chemical measurement systems. The identification of fluoresence spectra by cross-correlation of the unknown molecular flourescence spectra with that of reference compounds was described by Stadalius and Gold (SP16). The spectra are obtained with conventional instrumentation and then transformed to the time domain by using fast Fourier transform procedures. In another study the application of cross-correlation to S/N enhancement of Gram-Schmidt reconstructed gas chromatograms in GC/FTIR was shown to improve the S/N of chromatographic peaks while maintaining quantitative information about the peak areas and was found to be superior to multibasis vector Gram-Schmidt reconstructions as a S/N enhancement method (CA23). The value of spectral data can sometimes be enhanced by calculation of second or higher derivative. The application of derivative spectroscopy has recently been given added impetus by the widespread availability of microcomputerbased spectrophotometers and by the development of rapid scanning multichannel spectrometers based on the linearphotodiode array. The impact of this new computer-aided approach to analytical spectroscopy on the biomedical sciences is discussed by Fell (SP7). The derivative transformation of signals combined with least squares deconvolution offers a powerful approach to quantitative analysis in biomedical, environmental and industrial applications of spectrometry (SP7). The use of second derivative UV spectrophotometry in the identification of ketones has been described by Meal (SP10). The effect of temperature on the second and fourth derivative amplitudes for benzenoid drugs and the importance of temperature control in the assay of these drugs in pharmaceutical formulations by derivative UV spectrophtometry was investigated by Davidson (SP6). Morelli compared normal and derivative spectrophotometry for the accurate determi-
nation of iron (111)as well as iron (111) / copper (11)mixtures (SP11). Christenson and McGlothlin have used first and second derivative flourescence spectral analysis over the 325-385 nm excitation region to study fluorescent products of metanephrine and catecholamine (SP5). The derivative Auger electron spectra of many metals, alloys and their oxides have been obtained by the conventional modulation technique and analyzed quantitatively (SP2). The application of nonlinear background subtraction as well as derivative and difference techniques to X-ray photoelectron spectroscopy is discussed by Proctor and Sherwood (SP14). The background at any point due to inelastically scattered electrons is assumed to arise from the scattering of electrons of higher kinetic energy and is proportional to the integrated photoelectron intensity to higher kinetic energy. The use of differences for the enhancement of small spectral features is a well known technique. In order to produce meaningful results from a difference, both alignment and normalization have be considered To standardize the difference procedure the spectra under consideration are initially treated identically, oxygen 1s and carbon 1s spectra are taken as models (SP14). Hadamard transform AC Polarography,which makes use of the simple and fast Hadamard algorithm has been compared to its Fourier transform counterpart. The Hadamard transform was found to be a competent alternative and better suited to real-time microprocessor applications (SP4). The only theoretical disadvantage of Hadamard versus Fourier transformation for AC polarography was the possibility of harmonic distortion.
IMAGE ANALYSIS An image can be viewed as a three dimensional plot of spectral intensity represented as a function of two changing variables or as a picture with differing intensities or colors as the third dimension. Images can be acquired and analyzed in more than two dimensions, but these are rather hard to visualize. The medical fields and space sciences have seen a boom in utilization of the techniques of image processing as evidences by advances in computer-aided tomography, NMR imaging, and planetary exploration probes. In this section references will be limited to chemical applications or advances of a general nature. The rapid increase in computer capabilities during the past decade has already been noted. Computer-dependent fields such as image analysis are following a similar groth trend. As computers get faster and smaller and as hardware gets cheaper with the development of inexpensive core memory and array processsors, we anticipate an increase in the application of image processing in analytical chemistry as in other fields. Three dimensional analysis of elemental concentration has been performed with secondary ion mass spectrometric image depth profiling (SIMS-IDP) (IA8). This is described as a five dimensional analysis technique in which the fourth dimension is concentration and fifth dimension is elemental identity. Metal oxide semiconductor (MOS) integrated circuits and ion implant samples are analyzed by means of multiple simultaneous depth profiles and three-dimensional image profiles. To extract meaningful information from the enormous quantities of data a careful choice of display methods is as important as our understanding of the instrumental technique. In the future, three or higher dimensional images are expected to aid in the interpretation and understanding of useful information. Methods to improve signal-to-noise ratio (S/N) and to enhance the details of an image by sharpening the blurred edges have been described (IA9). The utility of various filters for image enhancement have been detailed. Image restoration and image enhancement methods have been tested for their abilities to remove the blurrin effect imposed on the ion scattering spectrometry or SIM8 images by using a scanning ion beam with a finite beam diameter. These methods allow spatial resolution allowing finer detail to be observed and in some cases improved S/N. The techniques studies are of a general nature and should be useful with a variety of surface analytical techniques. Image analysis has been used to study the surface irregularities observed in galvanostatic electrocrystallization (MI-2). The SEM images of electrode deposits and the theoretical surface patterns drawn by computer were compared. (IA2). ANALYTICAL CHEMISTRY, VOL. 56, NO. 5, APRIL 1984
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Biochemically oriented applications of image analysis have included measurin the distribution of certain immunoreactive sites in brain cells i y chemical staining (IA4) and the mapping elemental distrubutions in tissue sections by proton-induced x-ray emission spectrometry (IA7). The development of hardware for acquiring, processing and storing information has progressed to the oint where image analysis has even invaded such a routine laioratory technique as gel electrophoresis (IA6). Optical density patterns of autoradiographs of soybean proteins separated by two dimensional gel electrophoresis were digitized with a homedesigned flatbed densitometer. Data manipulation programs removed background and quantified individual proteins. It was stated that such an automated procedure for analyzing gel electrophoresis plate would be cost effective in laboratories with sufficient sample volume. The distinction between graphics and image manipulation is lessening due to the rapid pace of technolo . An example would be the striking work of Feldmann FA5) in which threedimensional color images of macromolecular models are generated to aid in elucidating the biochemical function of the molecules. The difference between ‘pretty pictures’ and a useful tool is centered on one’s ability to extract useful information from the images. Utilizing images is termed Image Understanding. An extensive review of the concepts and computational realization of image understanding was prepared by Brady (IA3). Examples are presented from a variety of fields both to highlight current capabilities and to summarize the organization of the field.
FACTOR ANALYSIS Factor analysis (FA) has continued to receive much attention as a multivariate analytical technique in the past two years. The developments in FA theory and application has paralleled and in some cases overlapped with that of other chemometric techniques such a8 pattern recognition, curve resolution, and generalized standard addition. In fact, FA is often only one part of a comprehensive data evaluation scheme. The integration of several computational methods into one data processing technique appears to be an important ongoing trend in Chemometrics. This section of the review will concentrate on the advances in the basic FA technique, and will outline applications which were not categorized into other sections of this review. Fundamental. Obtaining the key set of typical vectors (that combination of fewest data columns necessary to describe the factor space) is a primary objective in FA. This can be done using chemical intuition, or by trying all combinations of typical vectors. The latter technique becomes prohibitive when the dimensionality of the data is greater than three. A rapid, automatic method for obtaining the key set of typical vectors has been developed and applied to several chemical problems (FA16). Using the set of rows (or columns) most orthogonal to each other, a key set was rapidly obtained, which compared favorably with other methods using the same data set. The determination of error in factor analyses has also continued to receive attention. Two methods for estimating uncertainties in loading and score matrix values were compared (FA22): the ‘jack-knife’ method and a much faster calculational method based on comparing the reproduced and raw data matricies. Using data sets from a gas-liquid chromato raphy study and a minerology study, the methods were found to give consistant resulta, though neither method was proven optimal, however, the iterative nature of the jack-knife method made it prohibitively slow compared to the calculational method with large data sets. A clarification of the derivation of the calculationalmethod was also reported (pA20). Chromatography. Factor analytical techniques have been extensively applied to analysis of chromatographic data. Identification and resolution of overlapping peaks has mainly involved improved chromatographic conditions and more elaborate detection. Multivariate computational techniques have also shown promise in this area. Using a data matrix consisting of UV spectra measured for collected fractions of an unresolved LC peak (FA18), the number of sample components was determined by abstract FA. The suspected analyte identities were confirmed by target FA, which does not need unique spectral points. Similarly, rank annihilation FA was used to quantitate components in unresolved LC peaks 268R
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(FA17). By performing a series of principal component analyses (PCA) on properly selected mixtures of eluents, the concentration of each component was found independent of the identities of other peak components. Unresolved gas chromatographic peaks of polychlorinated biphenyls (PCBs) were analyzed by Fourier transform infrared spectrometry (FTIR) and the resulting data sets factor analyzed (FA3). The identities and concentrations of components in simple eluting mixtures were readily determined. With Fourier transform infrared detectors for gas chromatography it is often necessary to reconstruct the chromatogram from the interferograms or absorbance spectra. Factor analysis was compared to a Gram-Schmidt algorithm as methods of calculating a set of basis vectors for chromatogram reconstructions (FA19). The factor analysis method was an improvement over the Gram-Schmidt for real time chromatogram reconstruction due to a three- to five-fold decrease in reconstruction computation time. Rank annihilation FA has been extended to three dimensional data matricies (FA1). Excitation spectra, emission spectra, and retention time were combined in LC-fluorescence analyses. Improved accuracy, increased flexibility, and fewer spectral overlap problems were typically observed. Spectrometry. FA has continued to be applied to the study and manipulation of spectra. An algorithm for factor analyzing W absorption spectra was tested with artificial data matricies (FA9). Digital simulation models for algorithm testing in FA were described. The number of pure components and an estimate of random noise in FTIR spectra were determined by FA (SP8). By reconstructing the data matrix using the key set of typical vectors, an improvement in spectral quality was obtained. This procedure was expanded to include reconstruction of the pure component spectra and subsequent library seaching of these spectra for qualitative analysis (FA7). Pure component IR spectra were extracted from mixture spectra with abstract FA (FA8). Use of the cross product of the eigenspectra and a ratio method identified key frequencies in the eigenspectra. Normalization of spectra corrected for differences in scale. Double stage principal component analysis was found to effect discriminant analysis of pyrolysis mass spectra, thus extracting information not available with simple PCA (FA11). Similarly, the interpretation of complex spectra obtained by pyrolysis mass spectrometry was aided by abstract FA (FA26). Early work applying FA to liquid-state NMR data focused on determining the number of physically significant factors which produce solvent shifts of solutes in solution. Solvent effects on the ion pair structure and the charge distribution of indenyllithium in NMR were investigated by PCA followed by multiple regression analysis (FA6). A two component model was developed for predicting solvent shifts. PCA was also applied to solid-state NMR spectra to deduce the number of factors necessary to reproduce the data and the S/N necessary for accurate analysis (FA14). FA of spectrometric data has also been used to study reaction mechanisms (FA4) and to measure stability constants (FA10). Environmental. PCA continues to be used to determine the number of factors in a data matrix from a complex environmental or biological system. Using the concentrations of metals in fractions of stream sediments, and applying factor and statistical analyses, three factors could be identified which accounted for the abundances of elements in a specific sediment sample (FA13). Mineral phases and sources in coal were identified with FA (FA23). Physically meaningful factors effecting element concentrations in atmospheric aerosols were determined by PCA and abstract FA (FA25). The authors note that significant reduction in data set size can be realized with these techniques, which is particularly important with the large environmental data sets. FA was used to determine the sources of airborne particulates (FA12, FA15). A source profile for coal-burning power plant emissions was tentatively identified. FA of X-ray fluorescence data of particulate air samples not only identified four source factors, but also identified two factors caused by instrument and sampling errors (FA5). PCA was found to identify errors present in large data sets from urban aerosol studies (FA21, FA24). A model for the extraction of sympathomimetics from biological materials for subsequent analysis was developed (FA2).FA identified principal system parameters which when
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combined with regression analysis were used to optimize the method.
PATTERN RECOGNITION Interest in pattern recognition among analytical chemists has remained high during the past two years, and the proportion of literature reports which describe pure applications of this approach to diverse data bases seems to be increasing. Two useful survey papers have appeared. Veress (PR38) has published a very readable overview which provides a good introduction to the basic concepts and rationale of pattern recognition. Derde and Massart (PR12), in addition to providing a helpful survey, offer some practical suggestions to those who may be starting out in this area. Several reports have focused attention on the preparation of suitable data sets for analysis by pattern recognition techniques. One electrochemical data base (PR6-7) was prepared according to a fractional factorial design, followed by Fourier transformation of the voltammograms, etc. to obtain features for each electroactive compound. The application of the k-nearest neighbors method revealed which variables from the original experimental design contributed most to successful classification ability. Another report concerned with electrochemical data (PR32-33) discussed the use of deviation pattern recognition for the classification of potentiostatic current-potential curves according to mechanism. Deviation pattern recognition was also used to detect weak acids in the presence of others (PR27) and to determine additional reactants in a kinetic analysis system (PR28). Scaling and feature selection are applied to most data sets in preparation for analysis by pattern recognition techniques. Derde et al. (PR13) have studied the influence of two approaches to scaling or classification with the SIMCA method. The scaling of data within each class rather than across the entire data set was shown to be beneficial for the classification of olive oils according to their geographical origin. Another study (PR2) used selected algorithms from SIMCA to study infrared spectra, and compared several methods for feature selection, scaling and weighting. Feature selection algorithms from ARTHUR were used by Kentgens et al. to determine the most signigicant parameters for the prediction of alloying behavior (PR22). Research concerning structure-activity (PR24) and structure-carcinogenicity (PR29) relationships have used factor analysis to select reduced sets of features, followed by the application of multivariate linear regression. Wold and Dunn (PR42) have discussed the conditions for the applicability of multivariate quantitative structure-activity relationships (QSARs). Their overview of the many pattern recognition techniques which are commonly used in this research is recommended reading for anyone interested in QSARs. Some extensions of the standard model for supervised parametric pattern recognition have been discussed by Habbema (PR18). For example, several suggestions are offered for more complete use of the probabilities assigned by certain classification rules. The supervised parametric technique of linear discriminant analysis (LDA) has been applied in several areas. Tsao and Switzer (PR35-36) applied LDA to a data set containing both Raman and infrared (IR)spectral information for the classification of monosubstituted benzenes according to the atom bonded to the phenyl ring (C, N or 0). Combined IR and Raman features gave better classification than did either when used alone. In another report (PR30), various cigarette types were characterized by gas chromatographic (GC) profiles and studied by LDA, which provided a satisfactory grouping of the cigarette types. A form of discriminant analysis based on double stage principal component analysis (FA17) was shown to yield improved clustering of pyrolysis mass spectral data. Finally, the results of a survey of 300 Dutch analytical laboratories were subjected to LDA (PR37). It was found that 85% of the respondents could be correctly classified as an industrial, clinical or service laboratory on the basis of answers to the survey questions. Several of the supervised non-parametric techniques have continued to receive attention. Coomans and Massart, in a series of papers (PR8-10), discuss alternative k-nearest neighbor (KNN) rules. In place of the usual majority voting rule, a new probabilistic decision rule is formulated which accounts for any size differences between the classes represented in the learning set. The use of a probabilistic rule
allows an estimate of the degree of certainty associated with each classification decision. However, the authors caution that the probabilistic KNN procedure is very approximate in its present form (PR8). Reduction of the training set to generate a condensed nearest neighbor version of the probabilistic technique was also explored (PR10). Willet (PR41) has reported several algorithms for efficiently accomplishing condensed nearest neighbors searching based on the conventional (non-probabilistic) voting rules. The conventional KNN approach was applied with good success for the classification of samples profiled by field desorption (FDMS) and fast atom bombardment (FABMS) mass spectrometry (PR43). Two-dimensional plots based on non-linear mapping as well as principal components analysis (PCA) confirmed good clustering of FDMS urine profiles by sex of the patient, as well as FABMS profiles of Bordeaux and Rhone wines. Another report (PR5)discussed the use of KNN to classify Roman coins according to their original mint on the basis of non-destructive laser-microspectral analysis, with display of the clusters by principal component plots. The linear learning machine (LLM) was used by Ichise et al. to determine weighting5 for an impulse response function in a simultaneous study of linear and non-linear effects in electrode processes (PR19-20). The LLM was but one of many techniques used in a study of acute lymphocyte leukemia (PR34). LDA, KNN and hierarchical clustering were also applied, with all methods showing excellent abilities to distinguish normal subjects from those suffering from leukemia on the basis of liquid chromatographic metabolic profiles. Another study (PR14) applied LLM and non-hierarchical clustering to a library of vapor phase infrared spectra. The effects of scaling and feature selection were illustrated by Karhunen-Loeve mapping. In addition to the previously-mentioned studies involving SIMCA (PR2,PR13), some interesting applications have appeared. Blue mussels were effectively classified according to their source (i.e. pristine or polluted) using capillary GC profiles of naturally occurring components of muscle and gonad tissues (PR23). Volcanic rocks from five islands of the Aeolian Archipelago were examined on the basis of their elemental compositions (PR3). The applicability of chemometric techniques to geochemical problems was judged 'very promising'. The use of ALLOC as an aid to medical decision-making has been studied (PR11). For this application, modification of the classification rule was desired, to reflect the relative risks associated with classifying subjects as healthy or ill. The proposed 'minimum overall risk' rule displaced the boundary between classes to lie closest to the class having the smallest misclassification risk. As an alternative, a boundary zone for doubtful cases was used in place of a boundary line. The use of clinical data for medical decisions was also studied by hierarchical clustering of 'attention function' scores (PR17). These functions were designed to reflect the degree of attention paid to clinical test results, which depends primarily on their deviation from established 'normal' ranges. Clustering of 29 attention function scores for each of 298 samples revealed a number of understandable combinations of tests which tended to receive attention as a group. This study represents a promising and imaginative approach to the understanding of information flow in a hospital setting. Those interested in the use of cluster analysis will be assisted in their efforts by an excellent new book (BK13) by Massart and Kaufman. Hierarchical and non-hierarchical techniques, as well as display methods and numerous examples, are discussed. The explanations and worked-through examples will be particularly useful to newcomers to this area. for those who would like to try some clustering with a microcomputer having as little as 48K of memory, two recent reports concerning successful implementation of a hierarchical divisive approach will be of interest (PR21, PR25). A data set consisting of 15 measurements on each of 53 coal samples was processed in a 96 minute computer run, giving results which compared very favorably to that obtained using the recently described MASLOC program (PR26) on a mainframe computer. Hierarchical agglomerative approaches are most commonly used. An application to the classification of Roman brick and wall fragments has been reported (PR4). on the basis of GC data for a collection of mono-, di-, and tri-functional benzANALYTICAL CHEMISTRY, VOL. 56, NO. 5, APRIL 1984
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ense, a group of 21 stationary phases was found to form three distinct clusters containing polar, non-polar and polyfluorinated materials (PR15-16). Subsequent application of PCA and multivariate regression allowed successful prediction of GC retention behavior for these compounds. In another study, a variety of agglomerative algorithms was used to classify a group of benzenoid compounds (PR1) on the basis of substituents present. Zupan (PR44) has applied a previously-described method for the ’tree structuring’ of spectral libraries by hierarchical clustering to 500 infrared spectra. The clusters formed in the tree were shown to contain similar compounds, each of which could be retrieved quickly and accurately. Willet (PR39) has reported an algorithm which can speed the calculation of inter-object similarities which serves as the first step of many clustering techniques. The algorithm was applied to the calculation of intermolecular similarities based on lists of substructural fragments. Six hierarchical agglomerative (PR40) as well as four hierarchical divisive (PR31) clustering algorithms have been critically compared through their application to eleven data sets which were previously reported in the literature. For the agglomerative approaches, Ward’s algorithm was preferred and the nearest neighbor linkage was shown to perform badly. None of the divisive algorithms was found to give consisently superior performance.
OPTIMIZATION Since the response of many chemical systems is influenced by a variety of experimental variables, optimization is a topic which should be of interest to many chemists. While variables may at times be set on the basis of previous experience, it is frequently necessary to carry out some sort of formal optimization process. Too often this is accomplished by the conventional, but tedious and unreliable, ’one-at-a-time’ approach, which will only achieve an overall optimum if all variables independently influence the response of the system. Several alternative optimization strategies are surveyed in this section, many of which have been discussed in the literature for some time. Recent work has critiqued, formalized, refined and applied these optimization methods. Interest in optimization strategies seems to be increasing, particularly for selected application areas such as liquid chromatography (LC). This may be spurred on in part by the ever-increasing availability of cheap and powerful microcomputers,especially as components of modern analytical instruments. As with other sections of this review, there is an unavoidable overlap between the optimization literature and other subjects. The principles of information theory have much to offer for the development of effective analytical methods, as summarized in a recent review (OP12). Sufficiently predictive models (see Modeling and Parameter Estimation) whether empirical or based on theory can aid in optimization by permitting the effect of any combination of variable settings to be mathematically evaluated. For example, an effective experimental design in conjunction with a fitted response surface can be a very effective approach to optimization of some systems. The optimization of analytical information was the subject of a very readable survey paper by Vandeginste (OP38) which provides a useful overview for newcomers to this area. Tuinstra and coworkers (PA37), in summarizing the findings of a survey of some 300 Dutch industrial, clinical and service laboratories, provide an indication of the (unfortunately) limited extent to which optimization strategies are presently at work. Only 36 of the responding laboratories said they were aware of current optimization strategies, and a mere 5 were actually using these techniques. Tuinstra et al. propose the development of training courses in chemometrics to address the present situation. It would be of great interest to see the results of similar surveys from other countries. Accurate relationships based on theory can provide a powerful basis for optimization,in those cases where a suitably well-developed quantitative theory exists. For example, a theory for kinetically labile complex equilibria in isotachophoresis was used to successfully predict optimal separation conditions for several organic acids (OP25). A recent review by Halasz (OP16) provides a further example. On the basis of established chromatographic principles, the physical parameters required to give a required degree of efficiency in a packed chromatographic column may be specified. A set 270R
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of convenient nomograms aids in ready interpretation of the results of this work. In another study (OP28), the response equations for chemiluminescence analyzers have been used to obtain optimal operating conditions. The predicted dependence of the system response on several variables was verified experimentally. Holler et ai. (OP18) combined simple reaction rate theory with propagation of error theory to predict the optimal measurement times for precisely determining reaction rates. A theoretical basis for optimization of the determination of free plasma ligand concentration has also been reported (OP13). When accurate theoretical relationships are not available, a useful empirical or semi-empirical relationship can often be used to relate the response of a system to a set of input variables. Bartu and Wicar (OP4), for example, used the approximate dependence of retention time and peak width on column temperature in gas chromatography (OP3) to develop a procedure for calculating the optimal termperatureprogrammed separation of a mixture on the basis of data from several isothermal runs. Similarly, Otto and Wegscheider (OP30) combined previously established models for the effect of pH, ionic strength, and methanol content on the LC retention behavior of dibasic compounds into a single semiempirical model. In this way an optimal eluent was found, for which retention times of seven solutes could be predicted to within experimental error. Krupcik et al. used a semi-empirical approach to optimize experimental conditions for the gas chromatographic separation of polychlorobiphenyls (OP25). Schoenmakers and coworkers (OPlO,OP33) have reported a sequential, semi-empirical strategy for the selection of optimal ternary eluents for reversed phase LC. Separations are first conducted in the two binary eluents which can be mixed to generate the ternary eluent of interest. Retention of sample components is then approximated as log-linear with respect to eluent composition, allowing the estimation of the best ternary eluent for the separation of all components. The predicted optimum is then tested, and if necessary the previous linear approximation is adjusted so that a revised prediction can be made. The process is shown to converge quickly to the global optimum. Frequently the dependence of the system response on a set of experimental variables is unknown, in which case a completely empirical optimization strategy is appropriate. The sequential simplex method continues to be the most popular choice among empirical strategies. Recent reports have discussed fundamental improvements of the algorithm as well as application of simplex. The comprehensive bibliography com iled by Deming and Morgan (ED3) reflects the many uses of tfis technique in analytical chemistry. For an excellent introduction to the use of simplex, the recent paper by Leggett (OP27) is recommended. The modified simplex (MS) and controlled weighted centroid simplex (CWC) methods were critically compared (OP1) with the goal of developing a hybrid simplex which would behave as the CWC in regions of steep slope of the response surface, but as the MS near the optimum. The MS was found to out-perform CWC to the extent that development of a hybrid algorithm was abandoned. Another study (OP37) formulated rules to enhance the performance of the supermodified simplex (SMS). Interesting approaches to coping with boundary violations as well as loss of dimensionality were explored. An application of the modified simplex to flow injection analysis (FIA) by Betteridge and coworkers (OP7) provides an instructive example of the inadvisability of using a oneat-a-time approach to optimization for some systems. This group had sufficient patience to conduct a comparison of simplex and the conventional one-at-a-time approach for both four- and five-variable optimization problems. In the latter case, simplex required 37 experiments to reach an optimum similar to that found by the conventional approach after 168 experiments. It should be noted that four cycles of optimizing each variable individually were required to reach the optimum. Completion of a single cycle, as is commonly done, yielded only 68% of the optimal response. Separations by LC have been the subject of several recent applications of simplex (OP5-6, OPll,OP29,OP32, OP39), with the modified simplex algorithm most commonly used. As an aid to deciding when to conclude the optimization
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process Berridge (OP5) inspected the second derivative of the fiial chromatogram to check for peak overlap and the presence of additional components. Belchamber et al. (OP6) used simplex to improve sensitivity in the flow injection analysis of isoprenaline. Other applications of simplex include the preparation of electrodeless discharge lamps (OP34), the quantitative elemental analysis using a capacitively coupled microwave plasma (OP43), the calibration of glass electrodes (CA28) and the ultrasonic extraction of trace elements from collected atmospheric particulates (OP17). During the past review period, a number of authors have been concerned with the proper design of quality criteria for use with simplex as well as other strategies. All optimization procedures require first that the response to be optimized be defined, and that a suitable criterion be found for characterizing the quality of the response with a single number. Only then can a strategy be fruitfully applied. In some cases the desired response takes on a single form such as the level indicated on a meter, and the assessment of response quality is straightforward. A complex response such as a chromatogram is much harder to characterize with a single number, and some compromise between factors such as resolution and total analysis time must be cautiously sought, such that the chemist’s intuitive evaluation is mimiced. Leary et al. (OP26) discuss such a process of compromise in designing a quality criterion for simulataneous multielement analysis using an inductively-coupled plasma spectrometer, in which optimal analysis conditions for one element may not be best for another. A number of quality criteria have been used in the evaluation of LC separations, and more have been recent proposed (OP10-11, OP24, OP33, OP39). Many of these have been critically reviewed by Debets, Doornbos and coworkers (OP8-9,OP41), who found most to suffer from the inability to distinguish the global optimum in the presence of lesser local optima which may exist in complex response surfaces (OP4). In addition, many criteria were found to perform well only when the number of peaks or even the identity of peak was known, a situation which cannot be guaranteed in practice. Wegscheider et al., in another review (OP40), objected to criteria which predicate the success of the optimization process on prior operator experience by requiring estimates of analysis time and/or weighting factors. The performance of several criteria in the presence of various degrees of noise, peak overlap and relative peak intensity indicated that criteria based on Kaiser’s peak separation metric (see OP29,OP41) depended most directly on chromatographic performance. A popular alternative to the simplex method involves the execution of a formal experimental design to generate results which may be mathematically fitted to a resonse surface. The selection of an appropriate quality criterion plays a significant role in generating a useful surface. Glajch and Kirkland (OP14) have recently given a good overview of this approach. A good response surface will usually indicate the location of the global optimum even when local optima are present. However, Nickel and Deming (OP29) recommend that the location of the global optimum be pinpointed by application of the simplex method to a confined region in the vicinity of the apparent optimum. Issaq (OP19) has written a helpful practical discussion of the use of experimental design/surface fit for the selection of optimal quaternary eluents for reversed phase LC. Listings of necessary software are provided. Antle (OP21, Weyland et al. (OP42),and Glajch et al. (OP15) report applications of similary strategies. Jones et al. (OP23) used a similar approach to determine the combination of flow rate and temperature programming rate which would yield optimized column efficiency in capillary gas chromatography. Window diagrams, overlapping resolution maps, or minimum alpha plots (MAPS) provide alternatives for the presentation of system responses. These displays are especially useful when a number of individual responses (e. g., pairwise chromatographic peak resolutions) are expected to contribute to the overall process. Individual response curves or surfaces are overlapped, and attention is paid to the regions in which the worst of the individual responses is locally optimized. Applications of window diagrams (OP20) and MAPS (OP4, OP22,OP31) to LC have continued to appear in the literature. Chemists continue to look to other disciplines in search of fresh approaches to optimization. Smit and Smit (OP35-36) have used the principles of systems theory to consider auto-
Table I. Types of Spectral Information Utilized by Various Computerized Structure Elucidation Systemsa ‘H
projects
MS
IR
I3C
NMR NMR
UV Raman
DENDRAL A125 A125 A18 A125 CASE A120 A120 CHEMICS A116 A116 A116 SEAC A113 AI13 AI1 3 STREC AI11 AI11 AI11 AI11 AI11 AI11 ASSIGNER A129 AI29 A129
cssc
AI21
Characters in table are leading references to recent advances in these systems. a
mated titrimetric procedures. Rules were developed which led to optimized performance. In one case it was possible to determine the minimum number of reagent additions near the endpoint without significant information loss. Vandeginste (OP38) has emphasized the possibility of using models from the field of operations research to solve certain classes of optimization problems. Weyland et al. (OP42) borrowed the operations research technique of non-linear programming in order to minimize a non-linear quality criterion subject to non-linear constraints. The influx of techniques and concepts from these and other disciplies such as control theory is expected to continue.
ARTIFICIAL INTELLIGENCE Several recent reviews have discussed applications of artificial intelligence (AI) to analytical chemistry (AI3, AI13, AI19, AI25). Hippe (AI13) gives a good overview of the status of AI methods in chemistry, along with a clarified working definition of AI and a discussion of the relationship of library searching and pattern recognition methods to AI. Traditionally, AI approaches have been restricted to problems of structure elucidation of molecules from spectral information. While numerous programs (AI131 have been developed and applied to this problem, there are some basic similarities in the strategies each uses. A general (AI13, AI25) AI strategy to the structure elucidation problem involves four steps: (1) INTERPRETATION of spectra to obtain probable substructures. (2) GENERATION of proposed structures containing the probable substructures. (3) PREDICTION of spectra for the proposed structures, (4) RANKING of the proposed structures by comparison of their Dredicted sDectra with the observed mectra. Whiliall of the iurrent AI structure elucidition systems employ some variation of the above strategy, there are marked differences in the way different systems approach each step. Major areas of difference include the type of interpretation algorithm employed (A113), the ways in which the number of possible solutions is reduced and the way in which the user interacts with the system. Some comparisons between the various systems have been made (AI13, AI22). Interpretation algorithms have now been developed and applied to MS, IR, UV, Raman, I3C-NMR, and ‘H-NMR spectra (Table I, AIS, AI11, AI14, AI16, AI21, AI28, AI29). One system has recently been extended to utilize information from two - dimensional 13C-NMR experiments (AIM). GENOA (AI25) is probably the most sophisticated and versatile structure generation program developed to date (AI13). GENOA has been applied to several different problems (AI7, AI18) and can be combined with the program STEREO (AI7, AI25) to give possible stereoisomers of the proposed structures. Development of programs for the interpretation (AI8, AI11, AI16, AI20, AI28, AI29), prediction (AI8, AI20, AI25), and ranking (AI8, AI20, AI25, AI271 of magnetic resonance spectra are among the most recent advances. Prediction of NMR spectra is a separate field in its own right, so there is a wealth of literature available for consultation on this step (A15 and refs. therein). Comparison algorithms for informationally equivalent predicted spectra have been developed only recently (A18, AI20, AI25, AI27). Recent advances have also been reported in methods of distinguishing benzenoid cornANALYTICAL CHEMISTRY, VOL. 56, NO. 5, APRIL 1984
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pounds from those containing isolated double bonds based on IR spectra (AI17) and in methods of generating and storing canonical names for different conformations of a given structure (AI9). At this point in time it is inevitable that AI applications to chemistry will be expanded to new problems. Fusion of AI approaches with process control and optimization methodologies will lead to the development of intelligent process control and intelligent instrumentation. Control systems displaying AI characteristics have already been reported for use in electrochemistry (AI12, AI15, CA27), ICP-AES (CA48), and general process control (AI4, AI124).
GRAPH THEORY AND STRUCTURE HANDLING Being able to manipulate, search, and manage chemical structures is a critical capability for many chemical endeavors. The impact of computer approaches on chemical structure handling has not been as large as in other areas. Chemical compounds are most often used in a pictorial form, which is not as straight forward to accommodate as is more numerical information. However, the need for computerized structure processing outweighs the difficulties. Graph theory (GT) has been found to be increasingly useful in describing chemical structures and relating these structures to others of interest. Because of this feature, graph theory has also been useful in other chemical applications which concern representations of dynamic processes in molecules, intermolecular interactions, and topological correlation of structurally dependent chemical properties. Many of the chemical applications of GT can be traced back to the work of Randic, which continues at a rapid pace (GT21-23). The basis of applying GT to chemistry and chemical structures lies first in the ability to treat the chemist’s twodimensional representation of a chemical structure as a mathematical graph. One of the first ways of treating these two-dimensional representations in a computer legible format was Wiswesser Line Notation, which uses a combination of numerals, letters and puncuation marks to encode the structure. This process is explained in an article by Vollmer (GT28). The ability to treat structures as graphs is most easily seen by viewing at representations of organic molecules as a set of vertices connected by edges. The connected edges form paths through the chemical graph, which are used to characterize the structure. A major use of graph theory is in compound registration - assigning a unique identification number to each substance. Chemical Abstract Service employs the Morgan algorithm for this purpose. Razinger (GT24) has shown that a more fundamental approach based on the number of walks in a molecule can arrive at the same extended connectivity values as Morgan’s algorithm with improved efficiency. The second major use of GT is to discover relationships between chemical structure and chemical or physical properties. The structural descriptors can either characterize the connectivity of the molecule called a toplogical index (TI) or more simply compile the sub-structural features present in the molecule. The most common family of TISis based on the x functions popularized by Kier and Hall (GT18-19). Edward (GT6) related molar volume and heat of vaporization of liquid alkanes to x TIS followed by an explanation based on molecular interactions. It was concluded that the different chi functions weight the contributions from different types of carbon atoms differently, and thus are able to account for the degree of folding of the molecule and their intermolecular interactions. He studied the aqueous solubility of alkanes in a similar fashion (GT7) A method to calculate the gas chromatographic retention indices of polycyclic aromatic compounds has been developed by Whalen-Pedersen and Jurs (GT31). Molecular Connectivity data as well as molecular volume and fragment descriptors were used to describe the structure of the molecules, and to correlated to actual retention data for the compounds. A multiple correlation coefficient of 0.990 was achieved. Jurs’ group has presented similar studies describing the prediction of liquid chromatographic retention indices for polycyclic aromatic hydrocarbons (GT15), and the simulation of carbon-13 NMR spectra (GT26-27). Chromatographicretention correlation and predictions has also been described by Walters 272 R
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(GT29-30) and others (GT14, GT20). Balaban (GT1) has proposed a new TI based on graph distances rather than simple connectivity. This metric was found to be much more highly discriminating than the chi functions having no degeneracies for non-cyclic alkanes until C-12, nor for mono- or bicyclic alkanes up to C-8. Another related consideration is the description of intermolecular similarity. Willet (GT32) reported a fast method for assessing similarity which was based on lists of substructural graph fragments accessed using an inverted file algorithm. While this technique appears to be useful it sidesteps the issue of a chemist’s subjective views on chemical similarity. More esoteric GT studies have employed polyomials (GT4, GT8-9, GT23) and other representations derived from the original graph (GT3) for placing related compounds into useful orders (GT10-12) describe symmetries (GT2, GT21), stabilities (GT22), or relationships with spectra (GT5) and aromaticity (GT17, GT25). Herndon (GT16) has cautioned against the indiscriminant use of one approach which yields imaginary roots of polynomial equations, in some cases, which is not physically justifyable. Increased analytical uses of GT will be predicated upon competent computer software. To this end Figueras (GT13) has written a computer program to aid in interpretations of mass spectra. The program accepts a structure entered with a graphics tablet, creates a fragment pool by cleaving selected bonds in the structure, and recording the mass of the fragment. Input of a mass fragment enables display of all structures with that mass.
LIBRARY SEARCHING Library searching is appearing in the chemometrics review for the first time as a separate section. The types of studies that appear in this section were previously classified as pattern recognition or spectral analysis as well as other topics. However, with the increased activity in this field, witnessed by the number of papers and the number of people utilizing search systems, it is the opinion of this author that the inclusion of a library searching section is warranted. This section will include papers that make use of techniques that one may associate with other areas of chemometrics but whose main focus is directed toward improvements in library searching techniques. The heart of any computerized search system that aids the chemist in structure elucidation by accessing stored libraries is the stored library itself. The method of spectral representation and the quality of the spectra are of paramount importance to the performance of a search system. There has been and still is a lack of quality banks of analytical data. The need for these quality libraries and the reasons for the lack thereof have been outlined (LS12).Clerc (LS3) discusses some of the requirements that spectral data bases must meet in order to be truly useful in everyday applications. Some of the problems and pitfalls of compiling spectral libraries have also been addressed (LS4). The advantages of Fourier transform instruments have led to the development of libraries that consist of some form of interferometric representation. The majority of new studies on spectral representations or spectral reduction in some way utilize time domain spectra. De Haseth and Azarraga (LS5) introduced a search routine for infrared spectra that uses a 100 point segment of interferometer data displaced 60 points from the center burst. Two forms of instrument-dependent information, a phase error and an instrument function were removed from the spectra. In order to reduce storage requirements, the Karhunen-Loeve transform has been used to compress infrared spectra (LS11). A five-fold storage reduction from 185 dimensional to 37 dimensional and a corresponding reduction in search time with no significant loss of information was observed. The reduction of infrared spectra from intensities at 512 wavelengths to 80 complex Fourier coefficients has also been reported (LS14). The concatenation of infrared and mass spectra prior to factor analysis to remove redundant information has been presented by Williams et al. (LS30). GC/FTIR experiments result in the collection of hundreds of interferograms which must be analyzed to determine which were produced by eluting compounds. White et al. (SP18) have found that the optimal portion of an interferogram used as
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a vector for Gram-Schmidt ortho onalization reconstructions is heavily dependent upon the i entity of the mixture components as well as GC/FTIR instrument stability. A factor analysis chromatogram reconstruction method (FA20) which answers this need has been introduced. This method matches the chromatographic sensitivity of the Gram-Schmidt reconstruction procedure while allowing a 3 to 5 fold decrease in reconstruction computing time, thus enhancing its real time uti1ity. If one wants to reduce a spectral representation by using the time domain representation, it might be thought that the original resolution is not important. One study has shown that even for reduced spectral representation the resolution of the original spectra is important. Search vectors calculated from the inverse-transform of higher resolution spectra have been found to be superior for infrared spectra (LS21). In order to optimize the performance of a search system there must be a compromise between speed and retrieval quality. One must try to minimize the storage requirement while still retaining all relevant information. The binary intensity encoded spectrum is one such attempt. While binary intensity encoding of mass spectra is straightforward, binary intensity encoding of other types of spectra such as infrared spectra, where the shapes of the peaks contain useful information, is more difficult. Recently, two new forms of binary encoded infrared spectra have been reported. One form introduced by Warren and Delaney (LS29) makes use of the information contained in the peak width. Encoding the width between 50 and 70 percent of the peak height was shown to be optimal (LS7). The other form was the clipped spectral transform representation (LS21). Here, Fourier coefficients greater than zero are encoded as a one and those less than zero as zero. Clipped spectra composed of vectors starting one point past the center burst performed optimally overall, whereas for chemically similar compounds a displacement of 60 gave improved specificity.The use of 50 Fourier Coefficients was sufficient to maintain nearly optimal performance of clipped vapor phase FTIR representations (LS7). Beyond spectral representation lies another important area of computer-assisted structure elucidation. This area includes methods of organizing and accessing the spectral representations (LS3). The quality and the speed a t which a library search system is capable of functioning is not only dependent on the size of the data base or the size of each record in the data base but on the organization of the data base. Because of the increasing number of known compounds, and thus the corresponding rowth of data banks, Clerc and Szekely raise the question (L84) of whether large, all-encompassing libraries are more functional than smaller libraries with representative compounds. The three main types of organization are sequential, inverted and hierarchical trees. A recent paper by Zupan (LS32) has discussed the advantages and problems of these various types of data base organizations. From a retrieval point of view, the hierarchical tree organization is the most promising new solution, but has not yet received much attention. With a sequential search system, the time needed for the search increases linearly as the number of objects increase. Searching through a binary structured tree takes only log, N comparisons as opposed to N comparisons for the sequential search. Most probably, tree structured libraries are not being used routinely in spectral interpretations because of the large number of computations needed to construct the tree. To build a tree, one needs to compute the similarity between each pair of spectra in the library. Generation of a hierarchical tree by an iterative 3-distances-clustering method saves 10,OOO times the computing effort, as has previously been described by Zupan. This method was somewhat dependent of the order that data was added to the tree. Two methods that take the order-dependent tree and generate an order independent tree have been described (LS6, PR44). The hierarchical infrared tree clusters structurally similar compounds and has a 100 retrieval ability (PR44). This type of organization has functioned well with infrared spectra since the curve shape of the infrared spectrum is correlated to the chemical structure of the compound but has been unsuccessful with mass spectra libraries. After the individual spectra have been represented in a library comes the task of using the information to identify unknown compounds. Clerc and Szekely (LS4) have reviewed
d
the processes used in identifying an unknown spectrum. A discussion of the basic logical comparison functions used to: (1)search for an identical compound; (2) search for partial structures (forward search); and (3) identify spectra of compound mixtures (reverse search) has been given by Kwiatkowski and Riepe (LS16). Various studies have attempted to limit the search time of a particular search system. Razinger et al. (LS23) outlined a system whereby a spectrum is digitized and displayed; peaks are selected and searched one at a time limiting, thus limiting the search set as it goes. Lowry and Huppler (LS19) have described a VPIR system that allows the user to enter a wavelength window and an intensity window in which the peak is required to appear. Subsets obtained in this manner can be combined based on the three logical operations ‘AND’, ‘OR and ‘NOT. Another way to limit the search time is to make use of pre-screen filters. One MS system (LS26) makes use of an extensive pre-screen filter and uses probability of the uniqueness of the m/Z value and the abundance value of the peak. Several different techniques have been utilized to improve the speed and performance of search systems. Tanabe et al. (LS27) evaluated the use of explicitly denoted peak-less areas in their reduced IR representation. A system in which the user can constantly update not only the spectral file but also the inverted files to improve the performance has been described (LS22) A very extensive search system developed by Zippel et al. (LS31) consisted of NMR, IR, and mass spectra combined with a program containing functions for spectral matching and substructure searching. Inverted files, sequential searches and various functions for graphic output were used. A microcomputer-based search system was reported for binary intensity encoded spectra using large IR, 13CNMR and mass spectral data bases (LS28).The authors also showed that a modification of the Grotch distance metric accommodates the possibility of having impurity peaks or mixtures in real samples. Shackelford et al. (LS24) have reported an extensively tested GC MS data system which compares spectra by both probability ased mathching (PBM) and a retention data match with a historical library. Reliability ranking was supplanted by the use of retention data plus another ranking factor. Several search systems have been developed for specific needs. Among them is a system that uses GC FTIR and GC MS spectra for the monitoring of hazar ous wastes (L 10). A retrieval system used for forensic science, which includes MS, Et,GLC, TLC and previous casework data bases has been described (LS1). Another uses a data bank of histological features to aid in the identification of powdered vegetable drugs (LS15). A medical application of library searching has also been described. This method (LS20) uses computerized GC/MS fragmentography to detect anti-inflammatory analgesics and their metabolites in urine after acid hydrolysis. Frevel (LS9) has described a system for identifying power diffraction. To account for the dilute solutions of the real world the author has resorted to a structure-sensitive quasi-invariant criterion which serves to order the powder diffraction standards into various isomorphous groups. Several search systems that use an interpretive approach for identification of structures have been described. An interesting approach for identification of substructures of I3C NMR spectra has been described by Shelly and Munk (LS25). Spectra were stored as connection tables with chemical shifts assigned to each carbon atom. The comparison consists of flagging each carbon atom of a reference structure if its assigned shift, including a tolerance and multiplicity,correspond to a signal in the spectrum of the unknown. The connection table for the reference structure is exhaustively searched for all substructures that contain only flagged carbon atoms and heteroatoms. Reference spectra containing one or more substructures are retrieved by the search. Hippe (LS13) has described an interactive system for identification of IR spectral substructures. The location of peaks is entered by the user and the probability of a functional group’s presence is calculated by a function that includes a weighting factor, a numerical factor and the most probable location. At present the system can identify 32 substructures. Several authors have attempted to use information theory to optimize library search systems. Cleij et al. (LS2) proposed a similarity index that has the form of a significance proba-
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bility, a quantity originating from the general theory of hypothesis testing, and can be calculated from a statistical model of the reproducibility of the quantities used for the comparison. This study resulted in a similarity index which evaluates the differences between unknown and reference data in comparison to the expected differences between sets of data measured for the same compound. A paper (LS17) dealing with optimization of the parameters of library search methods with respect to the spectra library used has been reported. The two methods include (1) weighting of each spectra statement corresponding to its information content and (2) choosing the parameters for the reduction procedure to give the maximum entropy of the library. Domokos et al. (LS8) reported work that improved the retrieval capabilities of SISCOM by introducing a search algorithm tailored to the retrieval of identical compounds or components of the mixture. It involves selection and ranking of the hit list according to the retrieval function. To facilitate estimation of the weightings of the different variables in the retrieval function, pattern recognition algorithms were applied. Stadalius and Gold (SP16) used a partial cross-correlation to initially determine the degree of similarity between unknown and reference spectra. Final identification utilizes complete cross-correlation on only spectra more positive than a rejection factor. Information content and statistical predictors have been used to optimize VPIR spectral representations (LS29). One critical need with respect to optimizing searching performance is to be able to objectively compare spectral representations including different types of spectra and comparison metrics. Kwiatkowski and Riepe (LS18) developed a general method to combine the results of different library search methods to provide one reliable result. The steps include (1)using the relative information entropy of the spectral library used as a weighting factor (2) combine individual hit-list for each spectroscopic method. Delaney et al. (LS7) developed a procedure for the quantitative evaluation of the performance of a library searching system. This technique allows the evaluation of any form of spectral representation of any spectral comparison metric. The approach is applicable to any type of spectrometry used for library searching or to combinations of different types of spectra. The utility of this evaluation has been demonstrated by the quantitative ranking of various binary intensity metrics used to compare VPIR spectra.
ACKNOWLEDGEMENT Acknowledgement is gratefully made to the National Science Foundation's Information Science and Chemistry Divisions (Grant No. IST-8120255) for partial financial support of the development of this review. The generation and manipulation of the literature data base was facilitated by the RS/ 1-PLUS software, kindly provided by Bolt Berenek and Newman Inc., Cambridge, Massachusetts. I would also like to especially thank the following members of my research group for their invaluable assistance in the preparation of this review: John R. Hallowell Jr., David M. Mauro, Nandini Mouli, Jayaprakash B. Nair, Kathleen M. Pasko, Steven F. Rhode, and F. Vincent Warren Jr. LITERATURE CITED INTRODUCTION (IN1) Amer. Lab. 1983, 15(9),16-127. (IN2) Anal. Chlm. Acta 1981, 133,469. (IN3) Anal. Chim. Acta, 1983, 151, 1-252. (IN4) Balaban, D. J.; Wang, J. L.; Frazer. J. W. Anal. Chem. 1983, 55, 900. (IN5) Borman, S. A. Anal. Chem. 1982, 54, 1379A. (IN6) Borman, S. A. Anal. Chem. 1983, 55, 519A. (IN7) Dessy, R. E. Anal. Chem. 1982, 54, 1167A, 1295A. (IN8) Dessy, R. E. Anal. Chem. 1983, 55, 70A, 277A, 650A, 756A, 883A, 1100A. 1167A, 1232A. (IN9) Fox, J. L. 'Use of Mathematical Tools In Chemlstry Yields Insights', ' Chem. and Eng. News, 1983, 61(19),45. (IN101 Frank, I.E.; Kowalskl, B. R. Anal. Chem. 1982, 54, 232R. l I N l l l Frazer. .~, J. _ W.: Balaban. D. J.: Wano. J. L. Anal. Chem. 1983. 55. 904. i i N l Z j Grant, D. W.'Comp. A k L a b . 1583, I, 1. (IN13) Haggln, J. 'Computers Shift Chemlstry to More Mathematical Basls', Chem. and Eng. News, 1983, 61(19),7. (IN14) Holland, J.; Enke, C. G.; Allison, J.; S t u b J. T.; Plnkston, J. D.; Newcome, B.; Watson, J. T. Anal. Chem. 1983, 55, 997A. (IN15) Kowalskl, B. R. Anal. Chem. 1980, 52, 112R.
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(IN16) Long, A. K.; Rubensteln, S. D.; Joncas, L. J. 'A Computer Program for Organic Synthesis', Chem. andEng. News, 1983, 61(19),22. (IN17) Macdonald, A. M. G.; Pardue, H. L.; Townshend, A.; Clerc, J. T. Anal. Chim. Acta 1982, 134, 1. (IN18) Mallssa, H. 2. Anal. Chem. 1982, 313,449. (IN19) Morffew, A. J. J. Molecclar Graphics 1981, 1, 3. (IN20) Morrison, G. H. Anal. Chem. 1981, 53, 2161. (IN21) Morrlson, G. H. Anal. Chem. 1983, 55, 1. (IN22) Petruzzi, J. M. Anal. Chem. 1981, 53A, 1584. (IN23) Redmond Jr., M. W. Anal. Chem. 1983, 55, 490A. (IN24) Willis, H. Comp. Enhanced Specfrosc. 1983, 1, 1. (IN25) Ziegler, E. 2. Anal. Chem. 1982, 312,465. PERSONAL SUPERMICROCOMPUTERS (PS1) Adams, M. J.; Mitchell, M. C.; Ewen, G. J. Anal. Chim. Acta 1983, 149, 101. (PS2) Alert D.; Ebel S.;Geltz E.; Hocke J. Z. Anal. Chem. 1982, 3 11, 442. (PS3) Anderson, J. E.; Bond, A. M.; Heritage, I.D.; Jones, R. D.; Wallace, G. G. Anal Chem 1982, 54, 1702. (PS4) Andrieu, X.; Merlcam, P.; Astruc, A.; Astruc, M. J. Nectroanal. Chem. 1982, 138, 217. (PS5) Becht U.; Ebel S.;Reyer B. 2. Anal. Chem. 1982, 31 7, 440. (PS6) Belchamber, R. M.; Betterldge, D.; Chow, Y. T.; Sly, T. J.; Wade, A. Anal. Chim. Acta 1983, 150, 115. (PS7) Burrel, M. C.; Kaller, R. S.; Armstrong, N. R. Anal. Chem. 1982, 54, 2511. (PS8) Burstenblnder J.; Luck J.; Szackl W. 2.Anal. Chem. 1981, 309, 325. (PS9) Chornik, B. Rev. Sci. Instrum. 1983, 54, 80. (PS10) Delaney, M. F. in "Computer Science Educatlon for Chemists"; P. Lykos, Ed., Wiley: New York, 1984. (PS11) Dessy, R. E. Anal. Chem. 1983, 54, 1167A. (PS12) Dessy, R. E. Anal. Chem. 1983, 54, 1295A. (PS13) Duursma, R. P. J.; Stelgstra, H.; Logchles, R. G.; Smit, H. C. Anal. Chlm. Acta 1982, 144, 13. (PS14) Ebel S. 2.Anal. Chem. 1982, 373, 452. (PS15) Ebel S.; Hocke J.; Reyer B.; Walter V.; Weldemann E. 2. Anal. Chem. 1982, 311,441. (PS16) Elgass, H.; Martin, R. Comp. Appl. Lab. 1983, I, 66. (PS17) Glles, I.G.; Gore, M. G. Anal. Chem. Acta 1983, 151, 123. (PS18) Gore, M. G.; Glles, I.G. AnalChlm. Acta 1983, 151, 117. (PS19) Henderson, D. E.; DiTaranto, M. B.; Tonkin, W. G.; Ahlgren, D. J.; Gatenby, D. A.; Shum, T. W. Anal. Chem. 1982, 54, 2067. (PS20) Hutchens, D.E.; Hester, R.D. J. Liq. Chromatogr. 1983, 6, 1037. (PS21) Iida, Y. Bunsekl Kagaku 1982, 31,65. (PS22) Klnberger, B. Anal. Chim. Acta 1982, 138,343. (PS23) Langhoff, C. A.; Nugent, W. H.; Novak, M. Anal. Chem. 1982, 54, 1001. (PS24) Ll, C.; Barren, T. H. Jr.; Lunney, D.; Salt, A. Anal. Chim Acta 1982, 134, 167. (PS25) Mangold K.; Schweers B.; Dorenkamper B. 2. Anal. Chem. 1981, 309. - - -, 193. . .- . (PS26) McDonald, D. C.; Nell, R. S. Anal. Chlm. Acta 1982, 138, 145. (PS27) Miller R. L. Int. Lab. 1982, 12, 90. (PS28) Navas, A. A. J. Liq. Chromatogr. 1982, 5, 413. (PS29) Paul, D. W.; Ragway, T. H.; Heineman, W. R . Anal. Chfm. Acta 1983, 146. 125. (PS30)' Price, J. F.; Cooke, S.L.; Baldwin, R. P. Anal. Chem. 1982, 54, 1011. (PS31) Smlth, S. L.; Wilson, C. E. Anal. Chem. 1982, 54, 1439. (PS32) Tkalcec, M.; Grabaric, B. S.; Filipovlc, I. Anal. Chim. Acta 1982, 143, 255. (PS33) Warren. M. W.; Avary, J. P.; Malmstadt, H. V. Anal. Chem. 1982, 54, 1826. (PS34) Zlegler E. 2.Anal. Chem. 1982, 313,463. (PS35) Ziegler E. Anal. Chim. Acta 1983, 147,77. (PS36) Ziegler, E. Trends Anal. Chem. 1983, 2, 148. (PS37) Ziegler, E.; Henneberg, D.; Lenk, H.; Weimann, B.; Wronka, I.Anal. Chim. Acta 1982, 144, 1. (PS38) Zlegler, E.; Welmann, B.; Wronka, I.; Schomburg, G.; Hauslg, U. Anal. Chim. Acta 1983, 147, 91. EDUCATION (EDI) Alberty, R. A. J. Chem. Educ. 1983, 60, 102. (ED2) Anal. Chem. 1982, 54, 567A. (ED3) Demlng, S. N.; Morgan, S . L. Anal. Chlm. Acta 1983, 150, 183. (ED4) Elllson, A. J. Chem. €doc. 1983, 60,1983. (ED5) Enke, C. G.; Crouch, S.R.; Holler, F. J.; Avery, J. P.; Malmstadt, H. V. Anal. Chem. 1982, 54, 307A. (ED6) Henry, D. R.; Jurs, P. C. J. Chem. Educ. 1983, 60,563. (ED7) Howery, D. G.; Hirsch, R. F. J. Chem. Educ. 1983, 60,656. (ED8) Isenhour, T. L. Anal. Chem. 1983, 55, 824A. (ED9) Krugh, W. D.; Brent, W. J. Chem. Educ. 1983, 60,978. (ED10) Liscouskl, J. Anal. Chem. 1982, 54, 849A. (ED1 1) Mallssa H. Z.Anal. Chem. 1982, 313, 449. (ED12) Schilling, J. W. J. Chem. Educ. 1983, 60,43. (ED13) Vandeginste, B. G. M. Anal. Chlm. Acta 1983, 150, 199. (ED14) Whishart, D. M. J. Chem. Educ. 1983, 60,46. BOOKS
(BKI) Bourne, J. B. "Laboratory Minlcomputlng"; Academic Press: New York, 1981. (BK2) Clark, F. "Calculator Programming for Chemlstry and the Life Sciences"; Academlc Press: New York, 1981. (BK3) Heller, S.; Potenzone, R.; Eds. "Computer Applicatlons in Chemistry (Proc. 6th Int. Conf. on Comp. In Chem. Research. and Educ.)"; Elsevier: New York, 1983.
CHEMOMETRICS (BK4) Holler, F. J.; Avery, J. P.; Crouch, S.R.; Enke, G. C. "Experiments in Electronics, Instrumentation, and Microcomputers"; Benjamin Cummlngs: Menio Park, CA, 1982. (BK5) Justice, J. B.; Isenhour, T. L.; Eds., "Digltal Computers In Analytical Chemistry. Part 1"; Academic Press: New York, 1982. (BK6) Justice, J. B.; Isenhour, T. L.; Eds.. "Digital Computers In Analytical Chemistry. Part 2, 1970 - 1978"; Academlc Press: New York, 1982. (BK7) Kaiser R. E.; Rackstraw, A. J. "Computer Chromatography"; Huthig Veriag: New York, 1983. (BK8) Laub, R. J. 'Global Optimization Strategy for Gas-Chromatographic Separations', in Kuwana, T.; Ed. "Physical Methods in Modern Chemical Analysis" voi 3.; Academic Press: New York, 1983 (BK9) Lykos, P.; Ed., "Personal Computers in Chemistry"; Wiley Interscience: New York, 1981. (BKIO) Maimstadt, H. ; Enke, C.; Crouch, S. "Electronics and Instrumentation for Scientists"; Benjamin Cummings: Menlo Park, CA, 1981. (BK11) Marshall, A. G.; Ed., "Fourier, Hadamard, and Hilbert Transforms in Chemistry"; Plenum Press: New York, 1962. (BK12) Massart, D. L.; Dijkstra, A.; Kaufman, L. "Evaluation and Optimization of Laboratory Methods and Analytical Procedures"; Elsevler: New York, 1978. (BK13) Massart, D. L.; Kaufman, L. "The Interpretatlon of Analytical Chemical Data by the Use of Cluster Analysis"; Wiley: New York, 1983. (BK14) Said, A. S. "Theory and Mathematics of Chromatography"; Huthig Verlag: New York, 1981. (BK15) Skolnik, H. "The Literature Matrix of Chemistry"; Wiley: New York, 1982. (BK16) Wolman, Y. "Chemical Information"; Wlley: New York, 1983. (BK17) Zupan, J. "Clusterlng of Large Data Sets"; Wlley: New York, 1982. STATISTICS (STI) Baudo, R.; Gaianti, G.; Varinl, P.G. Analyst 1983, 708,722. (ST2) Cardone, M. J. J. Assoc. Off. Anal. Chem. 1983, 66, 1257. (ST3) Cardone, M. J. J. Assoc. Off. Anal. Chem. 1983, 66, 1283. (ST4) Deianey, M. F. Analyst 1982, 707, 606. (ST5) Herber J. F. M.; Pieters H. J. 2.Anal. Chem. 1982, 377,667. (ST6) Horwitz, W. J. Assoc. Off. Anal. Chem. 1983, 66, 1925. (ST7) Iyengar, V. Anal. Chem. 1982, 54, 554A. (ST8) Keith, L. H.; Crummett, W.; Deegan, J.; Libby, R. A.; Taylor, J. K.; Wentler, G. Anal. Chem. 1983, 55,2210. (ST9) Kirchmer, C. J. Environ. Sci. Techol. 1983, 77, 174A. (ST10) Massart, D. L. Trends Anal. Chem. 1983, 2 (ST11) Miller-Ihil, N. J.; O'Haver, T. C. Anal. Chem. 1982, 54, 2590. (ST12) Moier, G. F.; Delongchamp, R. R.; Mitchurn, R. K. Anal. Chem. 1983, 55,842. (ST13) Moier, G. F.; Delongchamp, R. R.; Korfmacher, W. A.; Pearce, B. A.; Mitchum, R. K. Anal. Chem. 1983, 55, 835. (ST14) Ohis K.; Sommer D. Z. Anal. Chem. 1982, 372, 195. (ST15) Popham, J. D.; D'Aurla, J. M. Environ. Scl. Techno/. 1983, 77, 576. (STl6) Provost, L. P.; Elder, R. S. Am. Lab. 1983, 57. (ST17) Soiberg, H. E. Anal. Chem. 1983, 55, 1611. (ST18) Staats G. Z.Anal. Chem. 1983, 375, 1. (ST19) Taylor, J. Anal. Chem. 1983, 55, 66OA. (ST20) Wanek, P. M.; Whippie, R. E.; Fickles, T. E.; Grant, P. M. Anal. Chem. 1982, 54, 1877. MODELING AND PARAMETER ESTIMATION ( M o l ) Anderson, J. E.; Bond, A. M.; Jones, R. D.; O'Halloran, R. J. J. Nectroanal. Chem. 1981, 730,113. (M02) Bacon, J. R.; Demas, J. N. Anal. Chem. 1983, 55, 653. (M03) Barradas, R. G.; Boag, P. T.; Vandernoot, T. J. J. Electroanal. Chem. 1983, 757, 23. (M04) Brand, H. R.; Frazer, J. W. Anal. Chem. 1982, 54, 414. (M05) Cheng, H. N. Anal. Chem. 1982, 54, 1828. (M06) Christensen, M. K. Anal. Chem. 1983, 55, 2324. (M07) Davis, J. M.; Giddings, J. C. Anal. Chem. 1983, 55,418. (M08) Dondl, F. Anal. Chem. 1982, 54, 473. (MOB) Foiey, J. P.; Dorsey, J. G. Anal. Chem. 1983, 55, 730. (M010) Gordon, W. E. Anal. Chem. 1983, 54, 1595. ( M o l l ) Janse, T. A. H. M.; Kateman, G. Anal. Chim. Acta 1983, 750,219. (M012) Jochum, P.; Kowaiski, B. R. Anal. Chim. Acta 1982, 744, 25. (M013) Karrer, L. M.; Gordon, H. L.; Rothstein, S. M.; Miller, J. M.; Jones, R. B. Anal. Chem. 1983, 55, 1723. (M014) Kucharkowskl, R.; Pietsch B. 2.Anal. Chem. 1983, 374 , 451. (M015) Lasia, A. J. Nectroanal. Chem. 1983, 746, 397. (MOW Leggett, D. J.; Keiiy, S. L.; Shiue, L. R.; Wu, Y. T.; Chang, D.; Kadish. K. M. Talanta 1983. 30. 579. (MOl7) Macdonald, J. R.'; Schoonman, J.; Lehnen, A. P. J. Eiectroanal. Chem. 1982, 737, 77. ( M O W Magno, F.; Bontempeiii, G.; Perosa, D. Anal. Chlm. Acta 1983, 747, 65. (M019) Meyer, E. F. Anal. Chem. 1982, 54, 1878. (M020) Nagels, L. J.; Creten, W. L.; Vanpeperstraete, P. M. Anal. Chem. 1983, 55, 216. (M021) Olson, D. L.; Shuman, M. S. Anal. Chem. 1983, 55, 1103. (M022) Pons, M.; Greffe, J.; Bordet, J. Talanta 1983, 30, 205. (M023) Reiler, H.; Kirowa-Eisner, E.; Gileadi, E. J. Electroanai. Chem. 1982, 738,65. (M024) Rosenthal, D. Anal. Chem. 1982, 54,63. (M025) Ruzic, I. J. Nectroanal. Chem. 1983, 744, 433. (M026) Schindler, E. W.; Weaver, M. J. Anal. Chlm. Acta 1983, 747, 347. (M027) Shrager, R. I.; Hendler R. W. Anal. Chem. 1982, 54, 1147. (M028) Wlillams, G. R.; Tolbert, L. M.; Holler, F. J. Anal. Chem. 1982, 54, 256. (M029) Zuberbuhler, A. D.; Kaden, T. A. Talanta 1982, 29, 201.
RESOLUTION (RE1) D'Allura, N. J.; Juvet Jr., R. S . J. Chromotogr. 1982, 239, 439. (RE2) Gilbert, R . A.; Lieweiiyn, J. A.; Swartz, W. E.; Palmer, J. W. Appl, Spectrosc. 1982, 36, 428. (RE3) Grlmalt, J.; Iturriaga, H.; Tomas, X. Anal. Chim. Acta 1982, 739,155. (RE4) Jezequel, J. Y.; Bouchy, M.; Andre, J. C. Anal. Chem. 1982, 54,2199. (RE5) Krai], 2.; Simeon, VI. Anal. Chim. Acta 1982, 738, 191. (RE6) Lundeen, J. T.; Juvet Jr., R. S. Anal. Chem. 1981, 53, 1389. (RE7) Rutan, S.C.; Brown, S. D. Anal. Chem. 1983, 55, 1707. (RE8) Sharaf, M. A.; Kowalski, B. R. Anal. Chem. 1982, 54, 1291. (RE9) Stargardt, J. F.; Hawkridge, F. M. Anal. Chim. Acta 1983, 746, 1. (RE10) Wang, T.-C. L.; Marshall, A. G. Anal. Chem. 1983, 55,2348. (RE11) Wrlght, N. A.; Villalanti, D. C.; Burke, M. F. Anal. Chem. 1982, 54, 1735. CALIBRATION (CA1) Aarons, L. Analyst 1981, 706, 1249. (CA2) Andrews, J. A. S.;Jowett, J. A. Anal. Chim. Acta 1982, 734,383. (CA3) Brown, C. W.; Lynch, P. F.; Obremski, R . J.; Lavery, D. S. Anal. Chem. 1982, 54, 1472. (CA4) Bubert H; Kiockenkamper R 2.Anal. Chem. 1983, 376, 186. (CA5) Cammann K. Z. Anal. Chem. 1982, 312,515. (CA6) Chu P. K.; Morrison G. H. Anal. Chem. 1982, 54,2111. (CA7) Crouch, S. R.; Kircher, C. C. Anal. Chem. 1983, 55,242. (CAE) Currie, L. A. Anal. Chem. 1968, 40, 586. (CA9) Efstathiou, C. E. Anal. Chim. Acta 1983, 754,41. (CA10) Frank, I. E.; Kalivas, J. H.; Kowalski, B. R. Anal. Chem. 1983, 55, 1800. (CA11) Frazer, J. W.; Balaban, D. J.; Brand, H. R.; Robinson, G. A,; Lanning, S. M. Anal. Chem. 1983, 55, 855. (CA12) Geren, C. R.; Miilett, F. S. Chem. Homed. Env. Instrum. 1982, 72, 125. (CA13) Gerlach, R. W.; Kowalski B. R. Anal. Chim. Acta 1982, 734, 119. (CA14) Honigs, D. E.; Freelin, J. M.; Hieftje, G. M.; Hirschfeid, T. B. Appi. Spectrosc. 1983, 37, 491. (CA15) Iida Y.; Goto K.; Furukawa M BunsekiKagaku 1983, 32,401. (CA16) Inman, E. L.; Voigtman, E; Winefordner, J. D. Appl. Spectrosc. 1982, 36, 99. (CA17) Jensen, S. A.; Munck, L.; Martens, H. Cereal Chem. 1982, 59,477. (CAM) Kalivas, J. H.; Kowaiski, B. R. Anal. Chem. 1981, 53, 2207. (CA19) Kaiivas, J. H.; Kowalskl, B. R. Anal. Chem. 1982, 54, 560. (CA20) Karrer, L. M.; Gordon, H. L.; Rothstein, S. M.; Miller, J. M.; Jones, R. 0. Anal. Chem. 1983, 55, 1723. (CA21) Kisner, J. J.; Brown, C. W.; Kavarnos, G. J. Anal. Chem. 1983, 55, 1703. (CA22) Kurtz D. A. Anal. Chim. Acta 1983, 750, 105. (CA23) Lam, R. B.; Sparks D. T.; Isenhour T. L. Anal. Chem. 1982, 54, 1927. (CA24) Lam, R. B. Appl. Spectrosc. 1983, 37, 567. (CA25) Lindberg, W.; Persson J. A.; Wold S . Anal. Chem. 1983, 55, 643. (CA26) Mann, C. K.; GoieniewskC J. R.; Simandis C. A. Appl. Spectrosc. 1982, 36, 223. (CA27) Maris, M. A.; Brown, C. W.; Lavery, D. S. Anal. Chem. 1983, 55, 1694. (CA28) May, P. M.; Williams, D. R.; Linder, P. W.; Torrington, R. G. Talanta 1982, 29, 249. (CA29) Mills J. C. X-Ray Spectrom. 1982, 7 7, 99. (CA30) Mitchell, D. 0.; Garden J. S. Talanta 1982, 29, 929. (CA31) Moler, 0. F.; Delongchamp, R. R.; Korfmacher, W. A.; Pearce, B. A,; Mitchum, R. K. Anal. Chem. 1983, 55, 835. (CA32) Montag A. Z.Anal. Chem. 1982, 372,96. (CA33) Oppenheimer, L.; Capizzl, T. P.; Weppeiman, R. M.; Mehta H. Anal. Chem. 1983, 55,638. (CA34) Pacholec, F.; Pooie, C.F. Anal. Chem. 1982, 54, 1019. (CA35) Phillips, G. R.; Harrls J. M.; Eyring E. M. Anal. Chem. 1982, 54, 2053. (CA36) Phillips, G. R.; Eyring, E. M. Anal. Chem. 1983, 55, 1134. (CA37) Pliel, J. D.; Courtney, W. J. Anal. Chem. 1982, 54, 417. (CA38) Rand, W. G.; Mukherji, A. K. J. Liq. Chrom. 1982, 5, 841. (CA39) Schwartz, L. M. Anal. Chem. 1983, 55, 1424. (CA40) Schwedt, G. 2.Anal. Chem. 1981, 309,359. (CA41) Sjostrom, M.; Wold, S.; Lindberg, W.; Persson, J.; Martens, H. Anal. Chim. Acta 1983, 750, 61. (CA42) Sparks, D. T.; Lam R. B.; Isenhour, T. L. Anal. Chem. 1982, 54, 1922. (CA43) Svehia, G.; Dickson, E. L. Anal. Chim. Acta 1982, 736, 369. (CA44) Sasagawa, T.; Okuyama, T.; Teller D. J. Chrom. 1982, 240, 329. (CA45) Thompson, M. Analyst 1982, 707, 1169. (CA46) VanArendonk, M. D.; Skogerboe, R. K.; Grant, C. L. Anal. Chem. 1981, 53, 2349. (CA47) Vandeginste, 8.; Kiaessens, J.; Kateman, G. Anal. Chim. Acta 1983, 750,71. (CA48) Wlnefordner, J. D.; Long, G. Anal. Chem. 1983, 55, 712A. Krug, F. J.; Reis, B. F.; Bruns, R. (CA49) Zagatto, E. A. 0.;Jacintho, A. 0.; E.; ArauJo M. C. U. Anal. Chim. Acta 1983, 745, 169. (CA50) Zuberbuhier, A. D.; Kaden, T. A. Talanta 1982, 29, 201. SIGNAL PROCESSING (SP1) Bromba, M. U. A.; Ziegler, H. Anal. Chem. 1983, 55, 1299. (SP2) Burrel, M. C.; Kalier, R. S.;Armstrong N. R. Anal. Chem. 1982, 54, 2511. (SP3) Bush, I. E. Anal. Chem. 1983, 55, 2353. (SP4) Chang, C. C.; de Levie, R. Anal. Chem. 1983, 55,356. (SP5) Christenson, R. H.; McGlothiin C. D. Anal. Chem. 1982, 54, 2015. (SP6) Davidson, A. G. Analyst 1983, 708,728. ANALYTICAL CHEMISTRY, VOL. 56, NO. 5, APRIL 1984
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CHEMOMETRICS (SP7) Fell, A. F. Trends Anal. Chem. 1983, 2, 63. (SP8) Gilette, P.C.; Koenig, J.L. Appl. Spectrosc. 1962, 36, 535. (SP9) Jansen, R. T. P.; Poulisse, H. N. J. Anal. Chim.Acta 1983, 757,441. (SP10) Meal, L. Anal. Chem. 1983, 55, 2448. (SP11) Morelli, B. Analyst 1983, 708, 870. (SP12) Phillips J. B. Trend Anal. Chem. 1982, 7, 163. (SP13) Poulisse, H. N. J.; Jansen, R. T. P. Anal. Chlm. Acta 1983, 757,433. (SP14) Proctor, A.; Sherwood, P. M. A. Anal. Chem. 1982, 54, 13. (SP15) Saitou, N.; Atsuo, I.; Gohshi, Y. Spectrochim. Acta 1983, 38, 1277. (SP16) Stadaiius M. A.; Gold, H. S. Anal. Chem. Ig83, 55, 49. (SP17) Stolzberg, R. J. J. Chem. Ed. 1983, 60, 171. (SPl8) White, R. L.; Giss, G. N.; Brissey, G. M.; Wilkins, C. L. Anal. ch8m. 1983, 55, 998. IMAGE ANALYSIS (IA1) Aogaki, R. J. Nectrochem. SOC. 1982, 729, 2442. (IA2) Aogaki, R. J. Nectrochem. SOC. 1982, 729, 2447. (IA3) Brady, M. Computlng Surveys, 1982, 74, 3. (IA4) Cassell M. D.; Mankovich, N. J.; Gray, T. S.; Williams, T. H. feptldes 1982, 3, 283. (1A5) Feidmann, R. J., in "Computer Applications in Chemistry", Heller, S.; Potenzone, R.; Eds., Elsevier: New York, 1983. (1A6) Hruschka, W. R.; Massie, D. R. and Anderson, J. D., Anal. Chem. 1983, 55, 2345. (IA7) Lindh, U., Anal. Chem. Acta., 1983, 750, 233. (IA8) Patkln, A. J.; Morrison, G. H., Anal. Chem. 1982, 54, 2. (IA9) Vandeginste, B. G. M.; Kowalskl, B. R., Anal. Chem. 1983, 55,557. FACTOR ANALYSIS (FA1) Appellof, C. J.; Davidson, E. R. Anal. Chim. Acta 1983, 746, 9. (FA2) Brandts, P. M.; Maes, R. A. A,; Leferink, J. G.; DeLigny, C. L.; Anal. Chim. Acta. 1982, 735, 85. (FA3) Chen, J. T.; Gardner, A. M. Am. Lab. 1983, 75, 28. (FA4) Crociani, B.; Uguagliati, P.; Belluco, U.; Nicolini, M. J. Chem. SOC. Dalton Trans. 1982, 2303. (FA5) Dattner, S. L.; Jenks, M. froc. Annu. Meet.-Air Poll. Contr. Assoc. *gal. .- - ., 74 . .. (FA6) Eliasson, B.; Johnels, D.; Wold, S.; Edlund, U. Acta. Chem. Scand. Ser. B 1982, b36, 155. (FA7) Gilbert, R. A.; Lleweilyn, J. A.; Swartz, W.E.; Palmer, J.W. Appl. Spectrosc. 1983, 36, 428. (FA8) Gillette, P. C.; Lando, J. B.; Koenig, J. L. Appl. Spectrosc. 1982, 36, 661. (FA9) Gillette, P. C.; Lando, J. 8.; Koenlg, J. L. Anal. Chem. 1983, 55, 630. (FA10) Haidna, U.; Murshak, A. EestlNSV Tead. Akad. Toim. Keem. 1982, 31, 212 (Russian); CA 97, 117691. (FA1 1) Haldna, U.; Murshak, A. festi NSV Tead. Akad. Tolm. Keem. 1883, 32, 47 (Russian); CA 98, 178649. (FA12) Hoogerbrugge, R.; Willig, S. J.; Kistemaker, P. G. Anal. Chem. 1983, 55, 1710. (FA13) Hopke, P. K. Roc. Annu. Meet.-Alr Poll. Conk Assoc. 1981, 74. (FA14) Kelepertzis, A. E.; Karamanou, E.; Poiyzonis, E. Oryktos floutos 1982, 18,23. (FA15) Kormos, D. W.; Waugh, J. S. Anal. Chem. 1983, 55, 633. (FA16) Liu, C. K.; Roscoe, B. A,; Severin, K. G.; Hopke, P. K. Am. Ind. Hyg. Assoc. J. 1982, 43, 314. (FA17) Malinowski, E. R. Anal. Chim. Acta 1982, 734, 129. (FA18) McCue M. and Maiinowski E. R. J. Chromatogr. Sci. 1983, 27, 229. (FA19) McCue, M.; Malinowski, E. R. Applled Spectrosc. 1983, 37, 463. (FA20) Owens, P. M.; Lam, R . B.; Isenhour, T. L. Anal. Chem. 1982, 54, 2344. (FA21) Roscoe, B. A,; Hopke, P. K. Anal. Chim. Acta 1982, 735, 379. (FA22) Roscoe, B. A.; Hopke, P. K. J. Radioanal. Chem. 1982, 70, 483. (FA23) Roscoe, B. A,; Hopke, P. K. Anal. Chim. Acta 1981, 732, 89. (FA24) Roscoe, B. A,; Hopke, P. K. At. Nucl. Meth. FossilEner. Res. 1982, 163. (FA25) Roscoe, B. A.; HoDke, P. K.; Dattner, S.L.; Jenks, J. M. J. Airfollut. Contr. Assoc. 1982, 32, 637. (FA26) Van Espen, P.; Adams, F. Anal. Chlm. Acta 1983, 750, 153. (FA27) Windig, W.; Kistemaker, P. G.; Haverkamp, J. J. Appl. fyrolysls 1982, 3, 199. '
PATTERN RECOGNITION (PR1) Adamson, G.W. ; Bawden, D. J. Chem. Inf. Comput. Sci. 1981, 27, 204. (PR2) Bink, J. C. W. G.; Van't Klooster, H. A. Anal. Chim. Acta 1983, 750, 53.
(PR3) Bisani, M. L.; Faraone, D.; Clernentl, S.; Esbensen, K. H.; Wold, S. Anal. Chim. Acta 1983, 150, 129. (PR4) Biasius, E.; Wagner, H.; Braun, H.; Krumbholtz, R.; Thlmmel, B. Z. Anal. Chem. 1982, 370, 98. (PR5) Borszecki, J.; Inczedy, J.; Gegus, E.; Ovari, F. Z.Anal. Chem. 1983, 374, 410. (PR6) Byers, W. A.; Freiser, B. S.;Perone, S. P. Anal. Chem. 1983, 55,620. (PR7) Byers, W. A.; Perone, S. P. Anal. Chem. 1983, 55, 615. (PR8) Coomans, D.; Massart, D. L. Anal. Chim. Acta 1982, 736, 15. (PR9) Coomans, D.; Massart, D. L. Anal. Chlm. Acta 1982, 738, 153. (PR10) Coomans, D.; Massart, D. L. Anal. Chlm. Acta 1982, 738, 167. (PR11) Coomans, D.; Massart, D. L.; Broeckaert, I. Anal. Chlm. Acta 1982, 734, 139. (PR12) Derde M.P.; Massart D.L. Z.Anal. Chem. 1982, 373, 484. (PR13) Derde, M. P.; Coomans, D.; Massart, D. L. Anal. Chim. Acta 1982, 747, 107. (PR14) Domokos, L.; Frank, I.; Matolcsy, G.; Jalsovszky, G. Anal. Chim. Acta 1983, 754, 181.
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(PR15) Fellous, R.; Lizzani-Cuvelier, L.; Luft, R.; Lafaye De Micheaux, D. Anal. Chlm. Acta 1983, 754, 191 (PR18) Fellous, R.; Lafaye De Micheaux, D.; Lizzani-Cuvelier, L.; Luft, R. Jour. Chromatogr. 1982, 248, 35. (PR17) Goldschmidt, H. M. J.; LeiJten, J. F.;Scholten, M. N. M. Anal. Chim. Acta 1983, 750, 207. (PR18) Habbema, J. D. F. Anal. Chim. Acta 1983, 750, 1. (PR19) Ichise, M.; Kojima, T.; Yamagishi, H. J. flectroanal. Chem. 1983, 747, 97. (PR20) Ichise, M.; Yamagishi, H.; Olhi, H.; Kojima, T. J. Nectroanal. Chem. 1982, 732, 85. (PR21) Kaufman, L.; Pierreux, A.; Rousseeuw, P.; Derde, M. P.;Detaevernier, M. R.; Massart, D. L.; Platbrood, G. Anal. Chlm. Acta 1982, 753, 257. (PR22) Kentgens, A. P. M.; Pijpers, F. W.; Vertogen, G. Anal. Chlm. Acta 1983, 757, 167. (PR23) Kvalheim, 0. M.; Oygard, K.; Grahl-Nielsen, 0. Anal. Chim. Acta 1983, 750, 145. (PR24) Lukovits, I.J. Med. Chem. 1983, 26, 1104. (PR25) Massart, D. L. Trends Anal. Chem. 1983, 2, 171. (PR26) Massart, D. L.; Kaufman, L.; Esbensen, K. H. Anal. Chem. 1983, 54, 911. (PR27) Meites L. Anal. Lett. 1982, 75, 507. (PR28) Meites L. Anal. Lett. 1982, 75, 1149. (PR29) Miyashita, Y.; Takahashi, Y.; Daiba. S.; Abe, H.; Sasaki, S. Anal. Chim. Acta 1982, 743, 35. (PR30) Parrish, M. E.; Good, B. W.; Jeltema, M. A.; Hsu, F. S. Anal. Chim. Acta 1883, 750, 163. (PR31) Rubin, V.; Wiliett, P. Anal. Chlm. Acta 1983, 757, 161. (PR32) Rusling, J. F. Anal. Chem. 1983, 55, 1713. (PR33) Rusllng, J. F. Anal. Chem. 1983, 55, 1719. (PR34) Scoble, H. A,; Fasching, J. L.; Brown, P. R. Anal. Chlm. Acta 1983, 750, 171. (PR35) Tsao, R.; Switzer, W. L. Anal. Chlm. Acta 1982, 734, 111. (PR38) Tsao, R.; Swltzer, W. L. Anal. Chim. Acta 1982, 136, 3. (PR37) Tuinstra, J.; Vlnne, J. V. D.; Doornbos, D. A. Trends Anal. Chef??. 1983, 2(10), v. (PR38) Veress, G. E. Trends Anal. Chem. 1982, 7, 374. (PR39) Willett, P. Anal. Chim. Acta 1982, 738, 339. (PR40) Willett, P. Anal. Chim. Acta 1982, 736, 29. (PR41) Willett, P. J. Chem. Inf. Comp. Scl. 1983, 23, 22. (PR42) Wold, S; Dunn, W.J. J. Chem. Inf. Comp. Scl. 1983, 23, 6. (PR43) van der Greef, J.;Tas, A. C. ; Bouwman, J.; Ten Noever de Brauw, M. Anal. Chim. Acta 1983, 750, 45. (PR44) Zupan, J. Anal. Chim. Acta 1982, 739, 143.
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OPTIMIZATION (OP1) Aberg, F. R.; Gustavsson, A. G. T. Anal. Chlm. Acta 1982, 744, 39. (OP2) Antle, P. E. Chromatographia 1982, 75, 277. (OP3) Bartu, V. J. Chromatogr. 1982, 260, 255. (OP4) Bartu, V.; Wicar, S. Anal. Chim. Acta 1983, 750, 245. (OP5) Berridge, J. C. Chromafogmphla 1982, 76, 172. (OP6) Berridge, J. C. J. Chromatogr. 1982, 244, 1. (OP7) Betteridge, D.; Sly, T. J.; Wade, A. P.; Tiliman, J. E. W. Anal. Chem. 1883. .- - -, 55. - ., 1292 .- . -. (OP8) Debets, H. J. G.; Bajema, B. L.; Doornbos, D. A. Anal. Chim. Acta IQ83. 757. 131. (OPG-Debets. H. J. G.; Weyland, J. W.; Doornbos, D. A. Anal. Chlm. Acta 1983, 750,259. (OPIO) Drouen, A. C. J. H.; Bllllet, H. A. H.; Schoenmakers, P. J.; de Galan, L. Chromatographla 1982, 76, 48. (OP11) Dunn, D. L.; Thompson, R. E. J. Chromatogr. 1983, 264, 264. (OP12) Eckschiager, K.; Stepanek, V. Anal. Chem. 1982, 54, 1115A. (OP13) Gqisler, D.; Ritter, M. Anal. Chem. 1982, 54, 2062. (OP14) Glajch, J. L.; Kirkland, J. J. Anal. Chem. 1983, 55,319A. (OP15) GlaJch, J. L.; Kirkland, J. J.; Snyder, L. R. J. Chromatogr. 1982, 238, 289. (OP16) Halasz, I.; Gorlltz, G. Angew. Chem. Int. Ed. Eng. 1982, 27, 50. (OP17) Harper, S. L.; Wailing, J. F.; Holland, D. M.; Pranger, L. J. Anal. Chem. lG83, 55, 1553. (OP18) Holler, F. J.; Calhoun, R. K.; McClanahan, S. F. Anal. Chem. 1982, 54, 755. (op19) IsSaq, H.J.; Klose, J.R.; McNitt, K.L.; Jaky, J.E.; Muschik, G.M. J. Li9. Chromatogr. 1981, 4, 2091. (OP20) IssiIq, H. J.; Muschik, G. M.; Janinl, G. M. J. Li9. Chromatogr. 1983, 6, 258. (OP21) Jandera, P.; Colin, H.; Guiochon, G. Chromatographia 1982, 76, 132. (OP22) Jones, L. A.; Beaver, R. W.; Schmoeger, T. L. Anal. Chem. 1982, 54, 182. (OP23) Jones, L. A.; Kirby, S. L.; Garganta, C. L.; Gerig, T. M.; Mulik, J. D. Anal. Chem. 1983, 55, 1354. (OP24) Knoll. J. E.; Midgett, M. R. J. Chromatogr. Sci. 1982, 20, 221. (OP25) Krupcik,J.; Mocak, J.; Simova, A.; Garaj, J. J. Chromatogr. 1982,
238, 1. (OP26I Learv. J. J.: Brookes. A. E.: DorrzaDf, A. F.; Goiightly, D. W. Appl. ' spectr. 1682, 38, 37. (OP27) Leggett, D.J. J. Chem. Educ. 1983, 60, 707. (OP28) Mehrabzadeh, A. A.; O'Brlen, R. J.; Hard, T. M. Anal. Chem. 1983, 55 - -, 1660. - ...
(OP29) Nickel, J. H.; Deming, S. N. LC Magaz. 1983, 7, 414. (OP30) btto, M.; Wegscheider, W. J. Chromatogr. 1982, 258, 11. (OP31) Otto,M.; Wegscheider, W. J. Li9. Chromatogr. 1983, 6, 685. (OP32) Sabate, L. G.; Diaz, A. M.; Gasslot, M. M. J. Chromatorg. Sci. 1983, 27, 439. (OP33) Schoenmakers, P. J.; Drouen, A. C. J. H.; Biliiet, H. A. H.; de Galan, L. Chromatographia 1982, 75,688. (OP34) Seltzer, M. D.; Michel, R. G. Anal. Chem. lQ83, 55, 1817.
CHEMOMETRICS (OP35) Smit, J. C.; Smit, H. C. Anal. Chlm. Acta 1982, 143, 45. (OP36) Sm%,J. C.; Smit, H. C.; Steigstra, H.; Hannema, U. Anal. Chim. Acta 1982, 143,79. (OP37) van der Wiel, P. F. A.; Maasen, R.; Kateman, G. Anal. Chlm. Acta 1983, 153,83. (OP38) Vandeginste, B. G. M. Trends Anal. Chem. 1982, 1, 210. (OP39) Wegscheider, W.; Lankmayr, E. P.; Budna, K. W. Chromatographia 1982, 15, 498. (OP40) Wegschelder, W.; Lankmayr, E. P.; Otto,M. Anal. Chlm. Acta 1983, 150,87. (OP41) Weyland, J. W.; Bruins, C. H. P.; Debets, H. J. G.; Balema, B. L.; Doornbos, D. A. Anal. Chlm. Acta 1983, 153,93. (OP42) Weyland, J. W.; Rolink, H.; Doornbos, D. A. J. Chromatogr. 1982, 247, 221. (OP43) Wunsch G.; Czech N.; Hegenberg G. 2. Anal. Chem. 1982, 310,62. ARTIFICIAL INTELLIQENCE (AI1) Abe, H.; Fujlwara, I.; Nkhimura, T.; Okuyama, T.; Kida, T.; Sasaki, S. Comput. Enhanced Spectrosc. 1983, 1. 55. (AI2) Adler 6.; Derendyaev B. G. In.Slb. Otd. Akad. Nauk SSSR 1982, 85 (Russian); CA 98,52969. (A13) Adler 6.; Herrmann A,; Sorkau E.; Valentin M. 2. Chem. W83, 23, 95 (German); CA 98, 197110. (AI4) Azhogin V. V.; Zgurovskii M. 2.; Rudenki S. S. Khlm. Techno/. 1982, 31 (Russian); CA 96, 182474. (AI5) $rumby, S. Magn. Reson. Rev. 1983, 8, 1. (AI6) Campell A. N.; Hollister V. F.; Duda R. 0.; Hart P. E. Sclence 1982, 217, 927. (AI7) Djerassl C.; Smith D. H.; Crandell C. W. Pure Appl. Chem. 1982, 54, 2425. (AI8) Egll H.; Smlth D. H.; Djerassi C. Helv. Chim. Acta 1982, 65, 1898. (A19) Feila, A. L.; Nourse, J. G.; Smith D. H. J. Chem. Comp. Scl. 1983, 23, 43. (AIIO) Gerlanter, H.; Bhagwat, S. S.; Larsen, D. L.; Miller, G. A. Anal. Chem. Symp. Ser. 15(Comp. Appl. Chem.), 35. (AI11) Gribov, L. A.; Elyashberg, M. E.; Koldashov, V. N.; Pletnjov, I.V. Anal. Chim. Acta 1983, 148, 159. (AI12) He, P.; Avery, J. P.; Faulkner, L. R. Anal. Cbem. 1982, 54, 1313A. (AI13) Hippe 2. Anal. Chlm. Acta 1983, 150, 11. (AI14) Hippe 2.; Hippe R.; Duiiban J. 2. Anal. Chem. 1082, 311, 440. (AI15) Ichise, M.; Yamagishl, H.; Olhl, H.; Kojima, T. J. Elect. Anal. Chem. 1982, 132, 85. (AI16) Ishlda, Y.; Ooshima, T.; Saito, K.; Sasaki S. Bunseki Kagaku 1983, 32, 148. (AII7) Ishida, Y.; Ooshima, T.; Salto, K.; Sasaki S. BunseklKagaku 1983, 32, 184 (AI18) Lindley, M. R.; Shoolery, J. N.; Smlth, D. H.; Djerassl, C. Org. Mag. Reson. 1983, 21,405. (AII9) Marsili M. Chim. Ind. (Milan) 1082, 64, 722. (AI20) Munk M. E.; Shelly C. A.; Woodruff H. 6.; Trulson M. 0. Z. Anal. Chem. W82, 313, 473. (AI21) Nakayama, T.; Fugiwara, Y. Gov. Rep. Announce. Index (U.S.) 1982, 82,5207 CA 98,62718. (AI22) - - -Sasaki .- - - S.; Hanai, S. Kagaku to Kogyu 1982, 35, 21I (Japanese); CA 99. - - , -21582. - - -. (AI23) Sasaki, S.; Abe H. Anal. Chem. Symp. Ser. 1983, 15(Comp. Appl. Chem.), 185. (AI24) Slnichkin D. N. Ref. Zh. Frz. 1982, 7, 631V (Russlan); CA 97, 129857. (A125) Smith, D. H.; Gray, N. A. B.; Nourse, C. W. Anal. Chlm. Acta 1981, 133,471. (AI26) Szalontai, G.; Recsey, 2.; Cspao, 2. Anal. Chim. Acta 1982, 140, 309. (AI27) Szalontal, G.; Recsey, 2.; Cspao, 2. Acta Chlm. Scl. Hung. 1982, 111, 239 (English); CA 98, 142885. (AI28) Szaiontal, G.; Recsey, 2.; Cspao, 2. Acta Chlm. Scl. Hung. 1982, 11 I, 249 (English); CA 98, 142886. QRAPHTHEORY (GT1) Balaban, A. T. Chem. Phys. Lett. 1982, 89,399. (GT2) Balasubramanian, K. Int. J. Quantum Chem. 1882, 21,411. (GT3) Balasubramanian, K. Int J. Quantum Chem. 1982, 21, 581. (GT4) Balasubramanian, K. Theoret. Chim. Acta 1082, 61,307. (GT5) Bonchev, D.; Mekenyan, 0. Chem. Phys. Lett 1983, 98, 134. (GT6) Edward, J. T. Can. J. Chem. 1982, 60, 480.
(GT7) Edward, J. T. Can. J. Chem. 1982, 60, 2573. (GT8) El-Basll, S. Cbem. Phys. Lett. 1982, 89, 145. (GT9) El-Basll, S.; Gutman, I.Chem. Phys. Lett. 1983, 94, 188. (GTIO) El-Basil, S. Int. J. Quantum Chem. 1982, 21, 771. (GT11) El-Basil, S. Int. J. Quantum Chem. 1982, 21, 779. (GT12) El-Basll, S. Int J. Quantum Chem. 1982, 21, 793. (GT13) Figueras, J. Anal. Chim. Acta 1983, 146,29. (GT14) Hanai, T.; Tran, K. C.; Hubert, J. J. Chromatogr. 1982, 239, 385. (GT15) Hasan, M. N.; Jurs, P. C. Anal. Chem. 1983, 55, 263. (GT16) Herndon, W. C. J. Am. Chem. SOC. 1882, 104, 3541. (GT17) Ilic, P.; Mohar, 6.; Knop, J. V.; Juric, A.; Trinajstic, N. J. Heterocyclic Chem. 1982, 19,625. (GT18) Kler, L. 6.; Hall. L. H. J. Pharm. Scl. 1981, 70,583. (GTl9) Kler, L. 8.; Hall. L. H. "Molecular Connectlvity in Chemistry", Academic: New Ywk, 1976. (GT20) Morishita, F.; Murakita, H.; Takemura, Y.; Kojima, T. J. Chromafogr. 1982, 239,483. (GT21) Randic, M.; Katovic, V. Int. J. Quantum Chem. 1982, 21,647. (GT22) Randic, M. J. Phys. Chem. 1982, 86,3970. (GT23) Randic, M. Theoret. Chim. Acta 1983, 62,485. (GT24) Razlnger, M. Theoret. Chlm. Acta 1982, 61,581. (GT25) Shawaii, A. S.; Parkanyi, C.; Herndon, W. C. J. Org. Chem. 1982, 47, 734. (GT26) Small, G. MI.; Jurs, P. C. Anal. Chem. 1983, 55, 1121. (GT27) Small, G. W.; Jurs, P. C. Anal. Chem. 1983, 55, 1128. (GT28) Vollmer, J. J. J. Chem. Educ. 1983, 60, 192. (GT29) Walters, F. H. Anal. Left. 1882, 15A, 1031. (GT30) Walters, F. H. Anal. Lett. 1982, M A , 421. (GT31) Whalen-Pedersen, E. K.; Jurs, P. C. Anal. Chem. Ig81, 53, 2184. (GT32) Willett, P. Anal. Chim. Acta 1982, 138,339. LIBRARY SEARCHING (LSI) Brown, C. Trends Anal. Chem. 1983, 2, 125. (LS2) Cieij, P.; van't Klooster, A.; van Houwelingen, J. C. Anal. Chem. Acta 1983, 150, 23. (LS3) Clerc, J. T. Z.Anal. Chem. 1983, 313,480. (LS4) Clerc, J. T.; Szekely, G. Trends Anal. Chem. 1983, 2, 50. (LS5) de Haseth, J. A. Anal. Cbem. 1981, 53, 2292. (LS8) Delaney, M. F. Anal. Chem. 1981, 53, 2354. (LS7) Delaney, M. F.; Warren Jr., F. V.; Hallowell Jr., J. R. Anal. Chem. 1083, 55, 1925. (LS8) Domokos, L.; Henneberg, D.; Weimann, B. Anal. Chem. Acta 1983, 150, 37. (LS9) Frevel L. K. Anal. Chem. 1982, 54, 691. (LSIO) Gurka, D. F.; Betowskl, L. D. Anal. Chem. 1982, 54, 1819. (LS11) Hangac, G.; Weiboldt, R. C.; Lam, R. B.; Isenhour, T. L. Appl. Spectrosc. 1982, 36, 40. (LS12) Helier, S. R.; Potenzone, Jr., R. Trends Anal. Chem. 1983, 2, 218. (LS13) Hippe, 2. Trends Anal. Chem. 1983, 2, 240. (LS14) Janezic M.; Zupan J. Z.Anal. Chem. 1982, 311,444. (LS15) Jolllffe, G. H.; Jolllffe, G. 0. Trends Anal. Chem.. 1983, 2, 28. (LS16) Kwiatkowskl, J.; Riepe, W. Anal. Chem. Acta 1982, 735, 285. (LS17) Kwiatkoswki, J.; Riepe, W. Anal. Chem. Acta 1982, 135, 293. (LS18) Kwlatkowski, J.; Riepe, W. Anal. Chem. Acta 1982, 135,381. (LS19) Lowry, S. R.; Huppler, D. A. Anal. Chem. 1883, 55, 1288. (LS20) Maurer H.; Pfleger K. ;Z. Anal. Chem. 1983, 374, 586. (LS21) Owens, P. M.; Isenhour, T. L. Anal. Chem. 1983, 55, 1548. (Ls22) Razinger M.; Penca M.; Zupan J.; Janezic M. ;Z.Anal. Chem. lg82, 3 11, 445. (LS23) Razinger M.; Penca M.; Zupan J.; Janezlc M. Z.Anal. Chem. 1982, 313,444. (LS24) Shackelford, W. M.; Cline, D. M.; Faas, L.; Kurth, G. Anal. Chem. Acta 1983, 146, 15. (LS25) Shelley, C. A.; Munk, M. E. Anal. Chem. 1982, 54, 516. (LS26) Shindo, J.; Yasuhara, A.; Ito, H.; Mizoguchl, T. Chem. Lett. 1982, 4, 521. (LS28) Tanabe, K.; Tamura, T.; Hiraishi, J.; Saeki, S.Bunseki Kagaku 1982, 31,27 (Japan); CA 99, 168200. (LS29) Uthman, A. P.; Koontz, J. P.; Hinderliter-Smith, J.; Woodward, W. S.; Reilley, C. N. Anal. Chem. 1982, 54, 1772. (LS30) Warren Jr., F. V.; Delaney, M. F. Appl. Spectrosc. 1983, 37, 177. (LS31) Williams, S. S.; Lam, R. B.; Isenhour, T. L. Anal. Chem. 1983, 55, 1117. (LS32) Zippel, M.; Mowitz, J.; Kohier, I.; Opferkuch, H. J. And. Chem. Acta 1982, 140, 123. (LS33) Zupan J. 2.Anal. Chem. 1982, 313,466.
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