computer ~erief. 107
edited by JAMES
P. BlRK
Arizona sBte "nivers~ty,Tempe, Az 85281
Bits and Pieces, 42 A Computer Interface tor Kinetic Experimentation in Education K.
Westerholm, T. Salml, and R. Hakkaralnen Department of Chemica! Engineering Abo Akademi SF-20500 Turku. Finland T.-E. Malen Department of lnformatlo~Processing Abo Akademi SF-20500 Turku, Finland
On-line analysis and computer-aided experimentation are frequently used in chemicaireaction engineering. The essential features of such an experiment can be sketched as follows: A microcomputer is coupled to an analytical instrument, the reactingmixture is analyzed continuously,and the kinetic parameters are determined hy regression methods. The experimentalist gets the numerical values of the kinetic parameters immediately after the experiment--or even during the experiment-without any manual calculations or any programming effort. At the initial stage of development the microcomputers were not standardized, and the data acquisition was usually performed by dataloggers or voltage meters equipped with AID-converters. The programming language was BASIC. The systems were difficult to update and they were usually not transferable to other laboratories with different microcomputers and different data acquisition systems. Development of high-level structured languages (Pascal, Modula), standardization of microcomputers (IBM PC) and design of efficient I10 boards have changed the situation dramatically. Today i t is possible to write transferable general-purpose software for automatic experiments. There is, however, a risk in using completely automatic
Ouldelines f w AuIhwsof BimacdPiecesappeared In July 1986; me numbw of Bim andPiea,smanuscrIpts is expected to decrease in the Murthe July 1988 and Mach 1989 Issues. BimandPiecssauihors who describe orwrams will make available listma andln mach nereadaole verslons ol their programs Plsspe read each descrnptm caref~llyto determine cornpatlo IV w ~ myour own computing env ronmenl betwe request ng matsrlals tmm any of the aumors. Several programs described in this article and marked as such are available from Project SERAPHIM at $5 per 5'irin. disk. $10 per 3Gin. disk: pmgram listings and other wrinan materials are available for $2 each; $2 domestic or $10 foreign postage and handling is required f w each shipment. Make checks payable lo Prolect SERAPHIM. TO Order. w oet a Proiect SERAPHIM Catalaa. " write to: John W. Moore. Olreclor, Propcl SERAPHIM Depanmenl of Chemlsby. Universl1y 01 W11mn~in-Madl~0n. 1 101 Unwerslry Avenue. Madrron. Wt 53706 (Ra,ect SERAPH M is supponed by hSF Olrectaats lor Sclence and Engineering Education.)
experiments in education: the student can work like an onerator without a deeper understanding of the basic princi'ples of the exercise. T o avoid this we have combined computeraided experimentation with computer-aided education. The result is the software package KINET, which is used in kinetic data sampling,;n determination of rate constants and as an examinator in chemical engineering kinetics. Experimental Setup The exnerimental setuo consists of a chemical reactor.. an analyticai on-line instrument, and a data acquisition system (an 1RM-com~atihle PC and an 110 board). The xoftware is written in ~ b d u l a - 2language ( I ) . The data sampling is based on the programming of the D T 2801 I10 board (Data Translation Inc., Marlborough, MA). This design enables a fast sampling and conversion ofthe voltage signals from the analytical instrument. The details of the data acquisition part of the software are described elsewhere (2). The program can be applied directly to various experimental equipment. We used a glass reactor that operates either continuously (a CSTR) or batchwise, a photometer, and an Olivetti M24 microcomputer in a test reaction, saponification of ethyl acetate. The Structure and the Working Principle of the Sonware The program KINET consists of entrance examination, data acquisition, data analysis, final examination, and report modules. The program structure and the interaction between the different parts are illustrated in Figure 1. The entrance examination; data analysis, and report modules can be entered independently through the main routine. This is necessary because i t is sometimes useful to reanalyze old data or carry out the "experiment" only as a theoretical exercise with simulated d a t a The databases are completely separated from the proeram. The necessarv databases are entrance and final examination questions and answers and the experiment description database. These data are stored in disk files that are created by the teacher.
-
EXAMINATION
ANALYSIS
UI_I ACQUISITION
EXAMiNATlON
Figure 1. me snucture of KINET
Volume 66
Number 10 October 1989
833
Data Analysis
The data analysis module is used for searching the best rate equation and for determination ofthe numerical value of the rate constant by linear and nonlinear regression. The measured signal is transformed to the concentration of the key component (here: A). A very common form of transformation is the linear equation. cA=a.S+B
(1)
where S denotes the primary signal. Equation 1is valid, for example, for photometry and conductometry. The formula (eq 1) is thus a default in the program. The user can also provide his or her own module for other t w e s of transforma;ions or for computation of t i and p fromprimary data (e.g., cell lengths, absorptivities. and initial concentrations in ph~tom&ryj.~ f t e r g e t t i n the ~ concentration data, the user has to choose the rate equation. The simplest rate models (first order, second order, third order, and fractional order) are included in the program. The user can also give his or her own rate model. For a continuously stirred tank reactor the material balance (4) equation of component A reacting in an irreversible reaction is:
This enables a very straightforward determination of the constant (k) by linear regression (5)
F f g m 2. An exampie of
entrance examination.
Entrance Examination The entrance examination module consists of three parts. In the first section general questions concerning reaction kinetics and reaction engineering are asked. Typical topics are the reactor system, the principles of data acquisition, the material balances, the analytical method, and the regression methods in determination of rate constants. The questions are picked up randomly by the computer from the database. ~ns&eralte;nativesare &en; only if the answer ia correct in the first attempt is a point given. Examples of examination questions used in ethyl acetate saponification kinetics are shown in Figure 2. If the examination is not passed, further study of the theory is necessary, and a new set of questions is delivered. After passing this primary examination, the student is allowed to continue to the next stage, where specific information of the experimental performance is -given: initial concentrations, measurement ranges, volumetric flow rates, etc. The answers are numerical. The program continues asking until the correct answer is given b i the user. Data Acquisition After the examination part the program automatically proceeds to data acquisition. The time domain, the sampling interval, and the reactor type are given by the user. The voltaee sienal from the analvtical instrument and the reactor temp&at&e data are collected, displayed graphically on the screen. and stored in a data file. An optional output to a strip chart iecorder is provided. To suppress the effect of measurement noise an internal sampling interval of l s is used, and the signals are smoothed according to a procedure proposed by Savitzky and Golay (3).The method is based on piecewise polynomial regression through equidistant measurements. 834
Journal of Chemical Education
where9 = (COA - CA)/~(CA) and x = f for a tank reactor. For a hatch reactor the integrated material balance equation is
The analytical solutions of the left side of eq 4 are included for simple kinetic models (4). Also, eq 4 is directly suitable for linear regression of type (3):9 = - S d c ~ / f ( c ~and ) x = t. The use of eq 4 implies, however, a nonlinear transformation of primary data, giving a biased estimate of the rate constant. Therefore the numerical value of the constant is imroved by nonlinear regression (5),where c~ is chosen as the dependent variable. The minimum sum of squares is obtaiied by an optimum searching method using the k value from linear regression as a starting point. The search interval is user supplied. A graphical display of the transformed linear plot and the final plot of CA (measured), CA (calculated) vs. time is provided. Statistical F-testing is performed, and the confidence intervals of the parameters are computed. The user (the student) makes the final decision. Therefore, some control questions are asked: is the experimental data sufficient for a reliable determination of the rate constant?, is there a systematic deviation between the experimental and predicted concentrations indicating an improper rate model?; etc. The user is advised to consider severd rite models when he or she enters the data analysis module. An example of the regression procedure is in Figures 3 and 4. The example illustrates the lack of fit of the "false" rate model (first-order reaction) compared to the correct model (second-order reaction) and the improvement of the fit after switching from linear to nonlinear regression in analyzing batch reactor data. Final Examination
After completing the data analysis, the student has topass the final examination. Typical questions concern the correctness of the rate model, the role of the significance test, the meaning of the confidence intervals. These questions are
Figure 3. Uneer regre4sion of rate date. Case: saponification of emyl acetate. where ydenotes the bansformedvariable accading lo eqs 3 and 4.
chosen randomly by the computer from a database. An example of the final examination is shown in Figure 5.
Conclusions The transferable-equipment and reaction-independent software package KINET has been developed for automatic experiments, determination of kinetic constants and kinetic examination. The combination of computer-aided education to automatic experiments is a powerful way to strengthen the students' knowledge of the most important aspects of chemical engineering kinetics: material balances, statistical analysis, and on-line experimentation. The package saves
the work of the teaching staff, and i t has aroused considerable enthusiasm among the students. A stripped version of the package KINET has been designed for professionals doing kinetic research work. The software is available from the authors. NOtatlon CA
ACA) k
: t
concentration of the key component A rate function in eqs 2 and 4 rate constant generation rate of A measurement signal readion time Volume 66 Number 10 October 1989
1'90P1 P~'ZOPI'10P191W!Pl"JIHdVZ13Saql UOalqal!EAE s! suo!?alnale~asaql JOJ mr4ord a~!suadxau!pua pjasn v ampal raqlo 03 a!? lua!uaAuoa B s! p m smroj OM?aq3JO sdys -uopqar Braua aql lnoqa uo!pmroJn! raqlo sap!nord osp lnq sanbqaa? Bugapom mpaaIom alaqsnn! p w aanpoqu! 01 samas LIUOlou saqaeordda pagaroaql paawnpa arom uo pamq uo!ppapa B inq 'quamom puoq jo mns rolaaa a q moq pala~napaLpma am ramrojuoa qaaa IOJ w a m o m alod!p pqaadxz 'saqBu!mopard Lnanlaa $q+ uo!lamro~uo3 aql uo uo!wmroju! apKord ppoqs luamom alod~ppams +?amam p w 'uo!pmSguoa ,,swrl,, 10 ,,s!a,, a raqqa u! paz!
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pole moment. (Transfer can be either by printing the data file and re-entering the coordinates manually, or more conveniently by a file transfer program). The results, 4.89 D for the "cis", and 1.8 D for the "trans" conformations are realistic, while the energy difference provides a quantitative explanation for the expected predominance of the "trans" form. (The experimental dipole moment is 1.78 D (7).)Requirements for running these programs, an IBM-PC with 512 K memory and an 8087 coprocessor, are not excessive, while SERAPHIM programs themselves are available at nominal cost. Typical time requirements have been 2 h for a given conformation. Although we employed the SERAPHIM programs initially and found them to be useful, we have now switched to a faster and more convenient, although more expensive, program, PCMODEL from Serena Software2 (academic price $200). In addition to the results aiven bv the SERAPHIM disks, this program readily additional information, such as plots of enerw as afunction of rotation about a bond. that permits the student easily to explore the details of conformational changes and rotational barriers. Figure 6 illustrates one type of information that can be displayed. This shows the variation in energy on rotation about the CH3C-OCH3 bond. This program also gives a simple readout of the structural parameters of the conformation. Students find the data input easy and the entire exercise fast enough to permit extension to other molecules in a reasonable time period. This approach provides a useful linkage of experiment to to link thismaterial theorv,as well asa valuableo~~ortunitv further to lecture topics de&ng with molecular conformations and theoretical chemistry. It is important to make clear the approximations and limitations of the calculations to show that they are not a replacement for experiment, but a guide and supplement.
Microcomputer Interfacing Programs Shahrokh Ghaffarl Mount Marly College Yankton. SD 57078 With recent emphasis on computer interfacing and automationof chemical technioues and instruments it is inevitable for chemists, especialliin the field of analytical chemistrv. to overlook the a~plicationof computers and their place in-both underpaduaie teaching and research. To extend the capabilities of our instrumentssuchas DRG Beckman spec6ophotometer and Gow-Mac gas chromatograph and to introduce students to the applications and the advantages of microcomputers in analytical laboratories, Microcomputer Interfacing Programs were developed. These programs are designed to work with most instruments, and required no computer programming or electronic experiences. The package consists of three programs. The first program is desimed to work with spectrophotometers. In the first section-of this program students &e able to scan for sample cell comparinons (in double-beam instrumentr) and/or find the maximum absorbance. Data are plotted on the screen as they are collected and the program finds the wavelength of maximum absorbance (Fig. 7). Then the spectrum and other information can be stored on a disk and/or printed on a printer. Scanning can be done in two ways, automatically or Available from Serena Software, Box 3076, Bloomington, IN '47402.
Figure 6.
Sueen dlsplay horn the PCMODEL (Serena) program, showing m r g y as a funnlon of mtation about me CH.-OCH. bond.
0
7bO
600
500
400
300
Wavelength (nm) Flwe 7 . Wavelengm scan for (a) sample cell comparison. (b) finding the wavelengm of the maximum absorbance.
manually, from low wavelength to high wavelength or vice versa. Further scanning is possible using the same plot or selecting different conditions. The second part of the program is designed to collect data from the instrument through an A D for a set of standards and unknown(s). Data are collected and saved as both absorbance and percent transmittance. Results are tabulated, and the best fitted line is plotted. Also other statistical information such as slope, least-square line equation, etc., are presented (Table 1). This program is able to calculate the concentration of one or more unknowns using the same set of standards. If more than one unknown is run, average or separate values for concentration of unknowns can be obtained. Table of data, result of calculations, and calibration curve (Fig. 8) are printed on the printer. Also a simple interface circuitry for Spectronic-20 is available in the supplementary material. The second program, which is developed to work with a Gow-Mac gas chromatograph, also can be used with most other chromatographs. This program can be used to obtain a simple chromatog~amfor a single injection or to run atandardlunknown solutions for a quantitative and/or qualitative exoeriment. In the latter case after initializatioa which includes entering the operation conditions, the computer Volume 66
Number 10 October 1989
837
Table 1. Collected Signal, Statldkal, Data, and Concentration of Unknown Wed Jun 29 3:39:22 PM Concernration mg/L
Data t
1 2 3 4
% Transmiitance
1 3 5 10 U n k m ' s slgnal
90 70.3 60.3 30.2
1 S l o p of line = -6.41 Canelallon coefflcimi = -0.993 Yintercept = 93.2 Least-square line: Y = 93.2 (-6.41)X Std. Oev. for residuals = 3.58 Std. Ow. 01 slope = 0.54 Conc. of unk. #1 = 7.96 mg/L
42.2
+
loof
Mn calibration c u r v e
0
0
2.5 5 7.5 Concentration ( m g / ~ )
10 0
2
Time (min)
Flgwe 8. Gallbrationcurve. Tlw unknown is marked wlth "r'
Retention Times, Peak Names, Table 2. Lld ol Peak Hel-, and Operatlon Condnlons 01 Standard Mlxture Solutlon
1.5
I
.5
Figure 9. Chromatagam of (a) s l a M solution. (b) unknown solution overlapped with standard solution. (clunknown solution.
mu D B 03 ~ 3:04:1o Peak X
Height %
PM Rat. Time mln a s
1 2 3 4 5
48 94 80 8 40
0:24 0:32 0:40 1:2 1:7
Outlet temp. = 155 'C Detector temp. = 170 OC BrMg c w e m = 160 mA Gas carrier = He Recording range = 50 mV Sample sire = 1.2 micro L Injection port = B
comp. ~ a m s Memy! a1 Propyl a1 lsobuiyle Namyl ai
Column temp. = 132 'C InJectiontemp. = 160 OC Polarity = Gas flow rate = 65 mLlmin Recording time = 2 mi"
draws axes of the chromatogram and waits for injection of the standard mixture solution. As soon as the injection is completed the computer is activated by pressing the "return"key. After thelast component emerges from the detector and its peak is plotted, the operator has the option of either getting a copy of chromatogram (Fig. 9a) or repeating the process under the same set of conditions or a different set of conditions. Then the computer advises the operator to save the chromatogram for the next step. The peak heights and retention times are printed on the screen, and the opera838
Journal of Chemlcal Education
tor can type in the name of each peak. This information and other operation conditions are run off on the printer (Table 2). Next the unknown mixture solution is injected as described above for standard solution. The unknown chromatogram can be overlapped by a standard chromatogram for identification of unknown peaks (Fig. 9b) or can be plotted seoaratelv. In the former case. after the unknown Deaks are identified the unknown chromatogram is separated from standard (Fie. 9c). In either case the o~eratorcan t . m- e in the name of each peak and run off a printed copy. The third Dromam, . which is designed for a conductivity measuremeni experiment, after the initialization simply collects data from a conductance meter. This program uses a set of standard solutions to plot a calibration cuke and the best fitted line and then measures the conductance of unknown solution(s) and calculates the concentration(s). An Apple IIe microcomputer with 64 K memory was emoloved for this ~roiect.The chart recorder o u t ~ uof t instrument is used t'o iirect signals into a 12-bit-analogue-toed digital converter (. A D .) interface card ( A ~ ~ l i Engineering c;.).To print the screen, a Grappler interface card (0: ange Micro, Inc.) is used in conjunction with an Imagewriter printer (Apple Co.). A Timemaster I1 H.O. card (Applied Engineering Co.) is placed in slot #4 of Apple computer to print the date and time of experiment (optional).
.~~~~~~~~ .
.
~
~
~
~
~
d
+
The program is written in Applesoft Basic language. I t is very easy t o make any changes in these programs in order to work with other interface systems. A free copy of Microcomputer Interfacing Programs may be obtained by writing t o the author. These programs and three sample experiments, ones used to obtain the data presented here, are also available on disk for $12 (including manual).
Searching the Chemical Literature: An Individualized Librarv Exercise using a SERAPHIM
Give at least three names far your compound (i.e., generic, brand name, IUPAC, ete.), and cite the aaurees for yaur information, Give a complete citation for at least one paper on the synthesis of this compound, and attach a photocopy of the CA abstract to your report. Where and how could you get a copy of the paper? Give a complete citation for a paper about the pharmacological activity of this compound. Where could you get a copy? Attach a copy of the ahstract ta yaur report. Using the Science Citation Index (SCn fmd out how many times the pharmacology article was cited in 19M. Give a full citation for at Least one paper that cites the pharmacology article, and attach a photocopy of the SCZ page to your report. (For extracredit, obtain copies of both your cited papers and write a 1-page summary of their contents. Attach the original papers to your report also.)
After a brief library orientation, the students were allowed eight weeks t o comolete the report. . . including timenecessarv f& interlibrary loans to be processed. University of Wisconsin-Parkside The amount of librarv time actuallv spent on a typical 3Kenosha, W153141 page report ranged from about 5 h tb more than 50 h; the average time was between 10 and 15 h. About half the stuOrganic chemistry students are often introduced to the chemical literature through exercises in their laboratory dents worked on the extra credit assignment. The students manuals; these exercises generally consist of a series of unreenjoyed working with the program and worked hard a t getting a compound with "good" activity, then expended serilated questions that briefly expose the students to a large number of chemistrv sources. However, these exercises do ous effort working on a good report. They were especially not really resemble a-true literature seareh, and the students attracted hy the idea of designing their own molecule. In the initial run of this exercise the Design-A-Drug protend to share data, minimizing their actual exposure to the literature. Later courses that require detailed literature gram generated a numher of compounds with no literature references, yet high reported biological activity. The probsearches also need t o review the basics. lem was traced 6 the manner in which the promam calcuSeveral criteria can be established for a better introductory exercise. I t should provide eacb student with a series of lates activity: it is a weighted calculation based on substituent position and structure but is not directly related to auestions about a unioue com~ound.so that students need use the literature i n a manner more consistent with typireported activity. Modifications t o the program were made cal research Droblems. Such individual, but related.. assianthat minimized this problem; we were also able to speed ments would avert the pooling of specific information to student use of the program with code changes that facilitatsolve auestions but would allow the students to help each ed data retention between trials and eliminated timed waits. A few other problems appeared as well. In their eagerness other with general research techniques if necessary and a t the same time would give the students a sense of having a to get a "good" compound, students often duplicated eacb coherent, realistic problem to solve for themselves. ~ o w e v i r , othkr's results; i n s t i c t o r review of the compounds chosen minimized this. Students also sometimes wanted to count the problems assigned should not he too difficultsince these fnr extra credit articles in foreien languages that they could students are just beginning their serious study of chemistry -.~~-~~~~ and have not previously been exposed to the chemical literanot read, but the student summary (not a parrot-of the English abstract) was required for any extra credit. ture a t all. This paper reports an individualized literature exercise Evaluation of the student work was based on complete and reasonable answers to the questions, judged with referthat fulfills these criteria and has been used successfullv for ence to the photocopied materials included. Summaries for several classes of organic chemistry laboratory student;. Molecules for each r e w r t were generated bv the students extra credit could usually he evaluated in comparison with themselves, using the SERAPHIM provam f ) e s i g n - a - ~ r u ~ the abstract of the paper in question and were counted less (SERAPHIM Disk 1H 701). 1)esip.n-a-Druginvestigates the heavily if they merely copied an ahstract or other sections of pharmacological activity of a nu&er of tricyclic aniidepresa paper. Writing style, grammar, spelling, and effort were molecule sants by allowinp.the operacor to build up also given some weight. - a specific The has been found narticularlv suitable for an on a tricyclic base; variations in substituents can be made a t - -- - exercise - -- five different positions, and for each specific molecule made organic chemistry course since i t relates t o organic synthesis of comnounds relevant t o the "real world" and allows the the program returns a calculated biological activity. Thus student t o relate biological activity t o molecular structure. the operator can examine a large number of molecules for activity and build up a body of information from which Copies of the program can be obtained from the author, structur+activity relationships can be determined. For this along with a more detailed discussion and a list of successful library exercise, each student was required to use the proreferences. gram to design a molecule for investigation that had an activity of a t least 75 on the program's rating scale of 1-100. This activity was chosen in order to minimize false starts for the students; the hope was that any compound with activity Huckel Molecular Orbitals that great would be a well-known, easily found compound John J. Farrell and Harry H. Haddon with commercial application and many references. Franklin and Marshall College The students were asked to answer nine questions about Lancaster, PA 17604 their compounds: G. Lynn Carlson and Erlk Womeldorl
tb
What is the structure of your pharmacologically active compound? What type of biological activity does it have? What is the correct numbering system for the ring system in your compound? What is the CA registry number far this compound?
Program Huckel Molecular Orbitals (Version 2.3) calculates energy eigenvalues, eigenvectors, pi-electron charge densities, and pi-electron bond orders for conjugated and aromatic molecules using the assumptions of simple Huckel molecular orbital (HMO) theory. Each of these parameters Volume 66
Number 10 October 1989
839
pyrrole
r&&&m
LQmmts
6 File Edit Windows
Remonanceslrurture
d
Carbon atom
Nitrogen stam Oxygen atom Fluorine atom chlorine atom Emmine stom Sulfur atom Pseudoatom for carbon i n methyl grow Pseudoatom for hydrogens I n methyl group Single bond Double bond
ErarerTool ( f o r deleting atoms and bonds) Figure 11. Th. resonance structure window palette contains symbols for atoms, bonds, and an eraset tool. Figure 10. me resonance struchre window for pynole.
pyrrole Secular M a t r i n ZEzES
is useful for some chemical nurDose: (1) to oredict sites of electrophilic and nucleophilic attack, (2) to-estimate bond t of free radical strengths and bond lengths, (3)to ~ r e d i csites attack, and (4) to estimate oxidation and reduction potentials. For a discussion of the assumptions-and some insight into how breathtaking approximations can lead to useful results-refer to A. Streitwieser (8)and J. P. Lowe (9). The program can be used bv anvone who can draw the resonance k ~ c t u r efor a moleche. it is best suited for students in junior-level and senior-level chemistrv courses who are being introduced (or have been introduced) to HMO theory. Entering the Resonance Structure
A window is used to enter the resonance structure of the molecule. The resonance structure window has a grid of hexagonally spaced dots marking the locations where atoms and bonds can be entered. Alone the left side of the window is a MacDraw-like palette to select the type of atom or bond to be entered (see Fie. " 10). . The nalette svmbols are described in Figure 11. When the pointer is outside the content part of the window, it is an arrow pointer. When the pointer is within the window, its shape depends on the tool last chosen in the palette (atom, circle; bond, cross hair; eraser, hollow square). Atoms are entered in the resonance structure window by clicking the desired atom type (in the palette) and moving the pointer (circle) to an empty atom position (dot) within the window grid. Clicking an atom position depcsits an atom at that position. Atoms of the same type can be entered at other nositions without clickine the nalette. Bonds are entered in a similar fashion. to& are'numbered as they are entered. The number of ni electrons is automaticallv calculated by the program. he resonance structure and tienumber of pi electrons can be edited easily. The Secular Matrlx
Program HMO automatically assigns standard values for the Coulomh and bond integral parameters (including heteroatoms and methyl groups) to theappropriate locations in the secular matrix. The secular matrix is displayed as an array with the rows and columns designated hy-numerals (representing theatom numbers) to the left and on topof the arrav (see . Fie. 12). The matrixelements lCoulomb and bond parameters) appear as decimal numbers, n.n. The programassiened narameters can be chaneed bv double-clickine anv ma&x eiement and typing the new vkue or by any 2 tce usual Macintosh editing techniques. When an element in row i and column j of the secular matrix is changed by the user the element in row i and column i is changed - automatitally by the application.
.
840
u
.
Journal of Chemical Education
1 1 2 / 0.8 0.8 / 0.0 " 0.0, . . " " a1 I .o ..-I.--. 0.0 i0.0 0.8 /O.O
1.5
2
i 3
1 0.0 1 1.0
1 0.0 /
1.0 10.0
1 4 ;!j !O.O 1 0.8 jo.0 1 0.0 / 1.0 :10.0 --10.0 / 1 .o f.((-f.((f.((.-C.---11.0 10.0
-
Q Figwe 12. The secular matrix window fapynole.
Results
The results of the HMO calculations made by the program HMO are displayed in a results window. The results can he printed and they incude the following: the resonance structure (without the grid); the secular matrix; energy eigenvalues, Ei = a n.nnnnS; molecular orbitals, q i = cilml + cam2 . . . c;.*,; charge densities; charges; bond orders.
+ +
+
System Requirements and Avallabllity
Program HMO can he used with a Macintosh 512K, 512K Enhanced, MacPlus, or SE, it cannot be used with a Macintosh 128K. It is a stand-alone application; that is, the user does not need BASIC. Pascal, or anv other nromam. It takes the program a few seconds to calcuiate th;res>lts for small molecules (four atoms) and about 5 min for large ones (25 atoms). The application can handle up to 32 atoms. Printing can be directed to an imagewriter, Laserwriter, or Apple Talk Imagewriter. The application can be purchased from Kinko's Academic Courseware Exchange (4141State Street, Santa Barbara, CA 93110, or 800-235-6919,800-292-6640 in California, 805-967-0192 outside the United States for $20 current price). Literature Cited
1. Wirth. N.Pmnmmingin Modulo-2Spd r: Heidelberg. 1985. 2. Ma1en.T.-E. DT28Hondler. ~sers'Cuide%~kademi: 1987. 3. Savitzky, A.; Golay, M. J. E. A m 1 Chem. 1964.36.1627. I. ~sse,~.~.~homieal~eoetor~~sipipfor~r~r~r~r~r~r~hnrs: wilcy:~ew~ork.19~9:vo1.1. 5. Freuod, a. J.; Minton, F. D.Rsgression Methods; Dekker: NeaVork, 1919. 6. Matthew, 0. P. Ezpwimnfal Physical Chemistry: Clamdon: Oxford, 1985: p 18% Shoemaher,D.P.;Garlsnd,C.W.: Steinfield.J. I. Erperimants inPhyaicolCkmistry, 3rdd.; McCma-Hid: New York, 1976 7. Wo1f.R. L.:Grans, W.J.Z.Phyaik.Chem. 193l,BI4,305. 8. Stmitwieer, A. Moleeulor Orbital Theory /or Orgonic Chemist,; Wiley: New Yark. IQC, 9. Lowe, J. P. @anturn Chemistry:Academic: NeaYork. 1978. 10. Lcvine, I. N. Quantum Chomistry;Allyn and &on: Boaton, 1983: p 489.
