Anal. Chem. 1993, 65, 2282-2287
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OPSI: A Universal Method for Prediction of 13C-NMR Spectra Based on Optimized Additivity Models Lingran Chent and Wolfgang Robien' Department of Organic Chemistry, University of Vienna, Wiihringer Strasse 38, A-1090 Vienna, Austria
The mathematical basis and the nature of the recently proposed method for optimized prediction of 'W-NMR spectra using increments (OPSI)are discussed. The new strategy of utilizing different parent structures for a given target structure is described. Some examples are given to illustrate the improvement of the accuracy and theextension of the practical application range of the OPSI method utilizing this new strategy. INTRODUCTION In the past three decades, a lot of effort has been directed toward the establishment of various additivity models for different classes of organic compounds. The publication of the first additivity model for calculating 13C-NMRchemical shift values of the simplest organic compounds in 19641has attracted many people to follow the pioneers' way to continue the research on this new topic. Thus the original model has been improved to deal with more complicated alkane compounds2 and those containing heteroatoms and functional group^.^^^ Many other models have also been proposed to handle a wide variety of compounds.5 The prediction of 13CNMR chemical shift values based upon these empirical additivity models has been proven to be very useful for the interpretation of 13C-NMR spectra. Recently, a lot of additivity parameters have been refined and some new parameters have been reported.617 On the other hand, several computer programs based on these models have also been developed in order to avoid manual calculation of chemical shift values,G1l and even the automatic selection of the appropriate additivity models for each carbon atom is possible.12 These well-established models were generated from small sets of reference compounds of very narrow classes, and thus each of them can give a quite accurate prediction of the chemical shift values but only for members of the same class. Therefore, some original models were generalized in order to cover more structures.6 The wide scope of applicability can be achieved by means of replacing missing + On leave from the University of Science and Technology of China, Hefei, Anhui 230026, The People's Republic of China. (1) Grant, D. M.; Paul, E. G. J. Am. Chem. SOC.1964, 86, 2984-90. (2) Lindeman, L. P.; Adams, J. Q. Anal. Chem. 1971,43, 1245-52. (3) Ejchart, A. Org. Magn. Reson. 1980, 13, 368-71. (4) Ejchart, A. Org. Magn. Reson. 1981, 15, 22-4. (5) Pretsch, E.; Clerc, J. T.; Seibl, J.; Simon, W. Tables of Spectral Data for Structure Elucidation of Organic Compounds, 2nd ed.; Springer-Verlag: Berlin, 1989. (6) Fiirst, A,; Pretsch, E.; Robien, W. Anal. Chim.Acta 1990, 233, 213-22, and references therein. (7) Pretsch, E.; Fiirst, A.; Robien, W. Anal. Chim.Acta 1991, 248, 415-28, and references therein. (8) Clerc, J. T.; Sommerauer, H. Anal. Chim. Acta 1977, 95, 33-40. (9) Cheng, H. N.; Ellingsen, S. J. J. Chem. Znf. Comput. Sci. 1983,23, 197-203. (10) Hearman, A. R. Magn. Reson. Chem. 1986, 24,995-98.
(11) Zupan, J.; Novic, M.; Bohanec, S.; Razinger, M.; Lah, L.; Tusar, M.; Kosir, I. Anal. Chim.Acta 1987,200, 333-45. (12) Fiirst, A,; Pretsch, E. Anal. Chim.Acta 1990,229, 17-25. 0003-2700/93/0365-2282804.0010
parameters with those of similar substituents or of similar substructures.13 However, the price to be paid for the fairly large range of compounds to which the model can be applied is the considerable decrease of prediction accuracy. As a result, the limited accuracy has become the main disadvantage of the methods based on additivity models when compared with other methods.'3 The research work already done in this area seems to indicate that there is an unbridgeable gap between the need for high accuracy of spectrum estimation and the wide range of application of additivity methods. This difficulty is caused by two inherent limitations of the existing methods based on additivity models. One is that all these methods perform chemical shift estimation by using static parameter tables, restricting their application scope;the other is that most of the additivity models use the increments derived mainly from monosubstituted compounds,13 this restricts the estimation accuracy because the increments [substituent-induced chemical shift difference (SCSD)values] have the nature of scattered di~tributions.1~ Therefore, it is quite obvious that a good general-purpose spectrum prediction method based on SCSD values must be able to generate dynamically the corresponding additivity models for a given target structure, and it must also be able to utilize automatically SCSD values derived from polysubstituted compounds, thus taking automatically into account substituent interaction as it is represented by the reference data collection itself. The first approach which has fulfilled the above two requirements is our optimized prediction of 13C-NMRspectra using increments (OPSI) method.ls Unlike other methods based on additivity models, the OPSI approach does not use any previously prepared parameters at all. Through the analysis of the structure under consideration, OPSI automatically generates the parent structure and all other possible substructures from the given structure. Then, an identical structure search is performed in the reference database for each of these partial structures. The additivity models are then generated from those partial structures available in the database, leading to the calculation of chemical shift values of the structure considered. The SCSD values which can be derived from di- and/or polysubstituted partial structures available in the database are automatically calculated and used in the estimation process. This method has been compared with some other methods, showing better results for polysubstituted compounds.16 In this paper we first analyze the mathematical basis and the nature of the OPSI method. Then, the strategyof utilizing different parent structures for a given target structure is described. Some examples are given to illustrate the improvement of the accuracy and the extension of the practical application range with this new strategy. (13) Pretsch, E.; Fkst, A.; Badertscher, M.; Biirgin, R. J. Chem. Znf. Comput. Sci. 1992,32, 291-5. (14) Chen, L.; Robien, W. J. Chem. Znf. Comput. Sci. 1993,33,447-52. (15) Chen, L.; Robien, W. Anal. Chim.Acta 1993,272, 301-8. (16) Chen, L.; Robien, W. Fresenius' J. Anal. Chem. 1992,344,214-6.
0 1993 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 65, NO. 17, SEPTEMBER 1, 1993
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EXPERIMENTAL SECTION The OPSI algorithmwas implementedin FORTRAN 77 under a UNIX operating system on a Silicon Graphics workstation and an IBM-RS/6OOO workstation. The databases accessed are the spectral data collections containing about 85 0o0 W N M R spectra from the University of Vienna, Sadtler Research Laboratories,and the GermanCancerResearch Center at Heidelberg. The average computing time is usually less than 50 s.
I
I
U pair 1
RESULTS AND DISCUSSION Mathematical Basis of the Opsi Method. The OPSI algorithm estimates chemical shift values of a target structure according to the following general additivity equation:
c
pair 2
r
NPI
,a' =,a' +
(aip1ti) - aip*)
J"1
(i = 1,2, ...,N,) Where ai, ai, and 6',&j) are chemical shift values of the ith carbons of the target structure, the parent structure, and the jth partial structure, respectively; NPlis the number of the partial structures used in the calculation; N , is the number of carbon atoms of the parent structure. The basic requirements of the relationship between the target structure, partial structures, and parent structures are as follows: (a) All the partial structures and parent structures must be the substructures of the target structure. (b) The parent structure must be a substructure of all the partial structures in the specific equation. (c) The sum of the number of substituents of the parent structure and the number differences of substituents of each partial and parent structure pair used in an equation must be equal to the number of substituents of the target structure. From above conditions we can conclude that, for a target structure with n substituents, the largest partial structure and the largest parent structure can separately have n - 1 and n - 2 substituents, and the smallest partial structure and the smallest parent structure have 1 and 0 substituent, respectively. It must be pointed out that there are no restrictions about the structural class of the target structure, partial structures, and parent structures. Therefore, in principle, eq 1 is a universal model for any class of organic compounds. In order to investigate the nature of the OPSI method, we first deduce eq 1through analyzing a simple example. The target structure is a three-substituted benzene (structure I) as shown in Figure 1. The use of eq 2 shown in Figure 1 means that the chemical shift values of carbon atoms at the benzene ring of structure I can be calculated from the corresponding shift differences between structures I and I1 plus the corresponding shift values of structure 111. Without question, eq 2 is accurate. However, it is apparent that this equation cannot be used in the practical estimation process of chemical shift values because the shifts of structure I are not known. According to the concept of substituent-induced chemical shift differences," we know that the SCSD values derived from structure pairs 2-4 should be approximately equal to the corresponding SCSD values derived from pair 1 (see Figure 1). Therefore, it is reasonable to replace pair 1of eq 2 by pairs 2 or 3 or 4, leading to eqs 3-5, respectively, as shown in Figure 2. These three equations all contain one approximate term and are independent of each other. They can be changed into another forms as shown in Figure 3. (17) Chen, L.; Robien, W. Chemom. Zntell. Lob. Syst., in prese..
pair 3
pair 4
Figure 1.
Structures and definition used to deduce eqs 3-5.
J
L
1
A
C Figure 2.
L
C
A
J
Three approximate equations deduced from definition 2.
Figure 3. Other
forms of eqs 3-5.
In a similar way we can deduce another three independent eqs 9-11 also containing only one approximate term aa shown in Figure 4. One common feature of eqs 6-11 is that they all use SCSD values derived from disubstituted benzenes. The equation using SCSD values derived from only monosubsti-
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 17, SEPTEMBER 1, 1993
Number of Approximate Terms of Additivity Equations. In ref 14 we pointed out that linear additivity models based on only SCSD, values (SCSD values derived from monosubstituted compounds) are approximate equations containing n - 1 approximate terms for n-substituted benzenes. In the following sections we discuss more general problems. The number of approximate terms of an additivity equation can be calculated from eq 14 where Napis the number of
1
A
1 r
A
1
M
Nap= M -
(i - l)Nsp(i) 1=1
Flgure4. Three other independentapproximateequationsof the t h r e e substituted benzene target structure (structure I) as shown in Figure
1.
approximate terms within the equation under investigation; of substituenta of the target structure and the parent structure, respectively; N,p(i)is the number of partial and parent structure pairs in each of which the difference of the number of substituents between partial and parent structures is equal to i in the equation under consideration. Now, let us analyze some typical cases: (a) Equations using parent structures with no substituents: Some equations of this kind consist of one partial structure containing N8ubta - 1 substituenta and one partial structure containing one substituent. These equations have the lowest Napvalue: Neubt" and NsubPe are the number
pair 5
(12)
1 A
\
J
A
1
"=-+@-@
+
1
9-0
Nap= (Nsubta-o-1) - [((Naubb.1) - I)* + (1 - 1)*1] = 1 (15)
+
C
C
r
r
1 (13)
Flgure 5. Deduction of the equation based on only SCSD, values for three-substituted benzene target structure (structure I) as shown in Figure 1. tuted benzenes can be deduced from any one of these equations. Starting from eq 10, first, we rewrite this equation into eq 12 as shown in Figure 5. Then, replacing pair 5 of eq 12 with pair 4 (see Figure l),we get eq 13, which is what we desire to get. Unlike the other equations deduced previously, eq 13 contains two approximate terms. Now let us summarize some common characteristics of the above-deduced eqs 6-11 and 13. The first term of the righthand side of these equations representa the chemical shift values of the corresponding parent structures; each of the rest of the terms of the right-hand sides represents the SCSD values derived from a pair consisting of a partial structure and a parent structure. The left-hand side of these equations represent the chemical shift values of the target structure. Therefore, we can easily generalize these equations into the algebraic form as given in eq 1. From any other target structures we can also deduce this general equation in the same way. From above discussion, we known that, for a given target structure, there is usually more than one independent additivity equation for the prediction of ita spectrum. However, the quality of different equations may be quite different because they may contain different numbers of approximate terms.
The deduction process of eqs 6-11 confirms this result. The equations based on only monosubstituted partial structures have the largest N a p value: Nap= Nsubta - 1 This conclusion is in agreement with that for the substituted benzene derivatives in ref 14. It is also confirmed by the deduction process of eq 13. (b) Equations using parent structures with at least one substituent: It can be easily seen from eq 14 that, for a given target structure, the N a p value decreases with the increase of the NsubPa value. Therefore, the worst equations based on those parent structures with at least one substituent are better thanthe worst equationsbased on only SCSD, values because the former has fewer approximate terms than the latter. In the extreme case, Naubp@gets ita largest value (Nsubp. = &bt" - 2) and then Naphas the minimal value Nap= 1 This result is as good as eq 15. From above discussion we know that any additivity equation contains at least one approximate term. The linear additivity models using only SCSD,, values as reported in the chemical literature are the equations having the largest number of approximate terms. A great advantage of the OPSI method is ita inherent ability to generate different equations for a target structure with the one containing the smallest number of approximate terms as the first choice. However, we should keep in mind that all the linear additivity equations are based on the assumption that the SCSD values derived from different structure pairs for the same substituent under consideration are very similar. Ref 14 has demonstrated that SCSD values derived from substituted benzene derivatives for 15 substituents have considerably large ranges, showing the feature of scattered
ANALYTICAL CHEMISTRY, VOL. 65, NO. 17, SEPTEMBER 1, 1993 F
F
.OH
OH
F
2285
F pair 6
F
F
1
F UNIW-119
UNIW-104
pair 7
1
I
F
1
F
1
H
O
W
O
H
HO
pair 8
1
F
UNIW-3427
UNIW-112
Figure 7. Reference structures used to estimate chemical shift values of target structure UNIW-119. pair 9
Flgure 6. Equations for hexafiuorobenzene.
distributions. As expected, similar behavior of SCSD values has also been observed from other compounds for a variety of substituents by means of the SCSD method.17 Therefore, in order to achieve good estimation, besides using the equation with fewer approximate terms, it is also important to choose better SCSD values for approximate terms in the equation used. Selection of Better SCSD Values for Approximate Terms. Suppose we want to estimate the spectrum of hexafluorobenzene. According to definition 16 we can easily obtain three equations (17-19) with only one approximate term by replacing pair 6 with pairs 7-9, respectively, as shown in Figure 6. It can be easily seen that structure pair 7 is the most similar to structure pair 6 among three alternate pairs, therefore, the SCSD values derived from pair 7 should be the best approximation for the corresponding SCSD values from pair 6. In contrast, the SCSD values derived from pair 9 should be the worst alternates of the corresponding SCSD values of pair 6. The standard deviations of the estimated chemical shift values by using eqs 17-19 are 1.4,3.6, and 4.7 ppm, respectively, supporting the above analysis. Furthermore, when remembering the way in which eqs 6-8 (Figure 3) were deduced from eqs 3-5 (Figure 2), we can easily understand that eq 17 uses the largest parent structure (1,2,3,4-tetrafluorobenzene) for the target structure hexafluorobenzene, while eq 19 uses the smallest parent structure (benzene). Thus, we reach an important conclusion: The equation using the larger parent structure can automatically assign better SCSD values for its approximate terms than those using smaller parent structures do. Therefore, for the equations with the same number of approximate terms, those which use larger parent structures are better. Using larger parent structures has also other advantages which will be described later in this paper. The original OPSI-algorithm has been improved in order to utilize automatically all the possible parent structures. Implementation of the Strategy of Using Different Parent Structures in the OPSI Program. After the substituents with no rings have been perceived, a table containing the information on all the possible parent structures is generated from the target structure. During the estimation process, these parent structures are handled with
the largest one first. After a set of chemical shift values of the carbon atoms of the target structure have been succeasfully estimated, the program gives the user a choice of terminating the current calculation or dealing with further possible parent structures in order to get new sets of chemical shift estimates. During the implementation of above strategy, two decisive points must be taken into account: (a) to avoid a second identical structure search in the database caused from the fact of utilization of different parent structures, because a parent structure of an equation may become the partial structure of another equation; (b) to avoid generating duplicate estimating ways16 (i.e., additivity equations) from the same parent structure. Fortunately, the equations generated from different parent structures are independent of each other. Another point which should be mentioned here is that any substituent connected to the ring atom with a multiple bond is treated as a part of all the possible parent structures. Thus, for the substituted 9,10-anthraquinones,for instance, the 9,lOanthraquinone will be selected as the smallest parent structure; other larger parent structures will automatically contain this basic unit. The new ability of utilizing different parent structures has improved the OPSI algorithm in several aspects. Besides the better accuracy of the estimated chemical shift values as has been described previously, other main points are discussed in the following paragraph. Extensionof the Range of Practical Applications. The original OPSI program generates additivity equations based on only the parent structure with no substituents for a given structure. Thus, if such a parent structure is not available in the database, the estimation fails even though all the other larger substructures of the target structures exist in the database. For example, because the unsubstituted parent structure of steroidal compounds is not available in the current database, the original OPSI method cannot be applied to this class of structures. With the new ability of systematic consideration of different parent structures, the OPSI method is now able to utilize more efficientlythe information available in the database accessed, and thus the range of the practical application has been significantly extended. For structure UNIW-119 as shown in Figure 7, for instance, very good chemical shift values have been estimated for all of its 24 carbon atoms by using structure UNIW-104 as the parent structure (see Figure 7 and Table I).
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 17, SEPTEMBER 1. 1993
Table I. Estimated Chemical Shift Values (ppm) for the Target Structure UNIW-119from Figure 7 As Given by the Program estimating way la no.
efP shifts
dev
1 35.70 2 30.60 3 71.60 4 39.60 5 42.00 6 35.10 7 68.00 8 39.90 9 26.70 10 35.10 11 22.80 12 28.50 13 72.50 14 46.80 15 12.80 16 42.00 17 23.50 18 28.00 19 47.40 20 35.70 21 17.60 22 31.30 23 31.20 24 174.50
SD a
0.20 0.50 -0.30 -0.30 0.30 0.40 -0.30 0.30
-0.10 0.10 0.40 0.50 -0.30 0.00 0.20 0.60 0.30 -1.40 -0.20 0.20 0.10 0.00 0.00 2.80 0.72
calc .shifts
increments base val UNIW104 UNIW3427 UNIWll2 35.60 30.40 71.80 36.50 42.50 27.50 26.70 36.10 40.60 34.80 23.20 21.10 40.50 43.00 11-80 56.70 24.40 28.40 56.50 35.60 18.10 31.20 31.10 174.50
35.90 31.10 71.30 39.30 42.30 35.50 67.70 40.20 26.60 35.20 23.20 29.00 72.20 46.80 13.00 42.60 23.80 26.60 47.20 35.90 17.70 31.30 31.20 177.30
0.20 0.60 -0.40 3.20 -0.40 7.90 41.10 3.80 -7.30 0.70 -0.20 0.00 -0.60 0.00 0.10 -5.80 -0.40 0.10 -0.20 0.20 0.20 0.00 0.00 0.10
0.10 0.10 -0.10 -0.40 0.20 0.10 -0.10 0.30 -6.70 -0.30 0.20 7.90 32.30 3.80 1.10 -8.30 -0.20 -1.90 -9.10 0.10 -0.60 0.10 0.10 2.70
Entries used: UNIW-104, UNIW-3427, and UNIW-112.
11
UWED-2609
+
+
UWED-2607
UWED-2605
-0 UNIW-527
Table 11. Measured and Estimated Chemical Shift Values (ppm) for the Target Structure UWED-2609As Shown in Figure 8 estimated results
no.
mead chem shifts
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
72.30 83.10 79.50 3.40 42.20 16.90 30.00 47.10 32.30 27.50 27.50 27.50 30.00 42.20 16.90
SD
set 1
set 2
shifts
dev
shifts
dev
72.10 83.10 79.60 3.50 42.30
-0.2 0.0 0.1 0.1 0.1
77.90
5.6
30.10 47.90 32.30 27.40 27.40 27.40 30.10 42.30
0.1 0.8 0.0 -0.1 -0.1 -0.1 0.1 0.1
41.20 16.80 30.10 47.60
-1.0 -0.1 0.1 0.5
30.90 47.00
0.9 4.8
0.3
3.1
symmetric to carbon atom 6, it should have the same shift value as carbon 6 does. Thus, the chemical shift values of all 15 carbon atoms of the target structure have in fact been estimated. Above results are summarized in Table 11. From Table I1 it can be seen that the standard deviation of the 13 estimated chemical shift values of the first set is very small (0.3 ppm). A somewhat larger standard deviation (3.1 ppm) is found for the second set with seven chemical shift values, which is mainly caused by the relatively large deviations of estimated chemical shift values of carbon atoms 1and 14;stereochemical factors are responsible for this result. This reveals a main shortcoming of the current OPSI algorithm: It does not take into account stereochemical effects at the moment because most of the structures in the database accessed are represented by their topological graphs. This is a fundamental problem for almost all database-oriented approaches. However, the OPSI method has the potential advantage in dealing with stereochemical problems because it estimates chemical shift values starting usually from the largest substructures of the target structure; therefore stereochemical information can be easily accessed by improved substructure matching algorithm.
UNIW-631
Flgure 8. Reference structuresused to estimate chemical shift values
of target structure UWED-2609.
As can be seen from previously deduced equations, for a given target structure, the chemical shift values of only those carbon atoms which correspond to the carbon atoms of the parent structure can be calculated. As the old version of the OPSI algorithm can only use the unsubstituted parent structure, it was impossible to estimate chemical shift values for those carbon atoms located within the substituents. This limitation has now been automatically removed by the new strategy of using different parent structures as shown in above example. In some cases, however, different parent structures must be used in order to estimate chemical shift values of all the carbon atoms of the substituents. Consider the target structure UWED-2609 as shown in Figure 8; the first set of chemical shift values were obtained from an equation with structure UWED-2605 as the parent structure and UWED2607 as the partial structure (see Figure 8 and Table 11).The missing chemical shift value of carbon atom 6 was calculated from another equation using structure UNIW-531 as the new parent structure and UWED-2607 and UNIW-527 as two partial structures (see Figure 8). As carbon atom 15 is
CONCLUSION From the deduction process of eq 1, it can be understood that the number of the independent linear additivity equations for a given structure are, in principle, infinite because for a specific structure pair (e.g., pair 6 of eq 16 in Figure 6) there exists the infinite number of its alternative structure pairs, which cannot only consist of the substructures of the target structure under investigation (e.g., pairs 7-9 in Figure 6), but also other structures not belonging to the substructures of the given structure (e.g., 3-chlorofluorobenzene/chlorobenzene pair). Of course, the equations derived from such "unusual" structure pairs are beyond the scope of the general eq 1.Unlike all other computer programs which were designed only to use already established additivity models, the OPSI program is both the automatic generator and the user of linear additivity models. It can systematically generate all the possible linear additivity equations which obey the general eq 1for a given target structure. The new strategy of using different parent structures with the largest one first for a given structure enables the OPSI method not only to use those equations with fewer approximate terms but also to assign automatically better SCSD values to the approximate terms; therefore, a
ANALYTICAL CHEMISTRY, VOL. 65, NO. 17, SEPTEMBER 1, 1993
better accuracy of estimation for polysubstituted compounds can be achieved. Furthermore, the range of practical application of the method has also been significantly extended at the same time. The linear additivity models based on only SCSD,, values as described in the literature contain n - 1approximate terms for a target structure with n substituents; these models are only the worst special cases of the OPSI method. However, it should be pointed out that, for an equation with more than one approximate term, the accuracy of the result is affected by both the absolute values and the signs of deviations contributed from each approximate term. That is the reason why, in some cases, a principly worse equation may produce better results than another one does for the same target structure. In the current version of the OPSI algorithm there is the limitation that the structure under investigation must contain at least one ring system and two substituents. However, according to the simple mathematical principle, eq 1can be used to determine the value of any one of the variables [bit, or 8, or Si&)] if the values of all other variables are known. For example, the chemical shift values of benzene can be estimated from the shift values of hexafluorobenzene, pentafluorobenzene, and fluorobenzene by using the rearranged eq 19 given in Figure 6. It should be pointed out that now our target structure is benzene instead of hexafluorobenzene. Monosubstituted ring systems can be handled in a similar way. But these strategies are not implemented in our OPSI algorithm at the moment. Furthermore, the general eq 1is also applicable to noncyclic compounds. For example, the chemical shift values of 3,4dimethylhexane (UNIW-7034 in Figure 9) can be estimated from those of 3-methylpentane (UNIW-7015; parent structure), 2,3-dimethylpentane (UNIW-7021;partial structure), and 3-methylhexane (UNIW-7020;partial structure) with a standard deviation of 1.2 ppm. It can be easily seen that eq 20 in Figure 9 is consistent with the general eq 1. Obviously, there exist no great difficulties in the expansion of the OPSI algorithm to cover noncyclic molecules; the main parts which must be modified are those of perceiving substituents and selecting parent structures. It should be noted that this
r
l?.B
36.8 11.4 14,s
Calculated shift values
1
40.6 10.0
18.7
UNlW-7015
2287
18.7
]
UNW-7021
UNW-7020 15.8 25.8
139.5 11.8
ii.8
UNIW-7034
Experimental shift values
Flguro Q. An example used to illustrate the possibility of applying the OPSI method to estimate lSGNMRchemical shift values of noncyciic compounds. This example is not the part of the current OPSI version; the calculation was performed manually.
method to deal with noncyclic compounds is quite different from the well-known Grant/Paul's additivity model.' According to the above discussion,there should be no doubt that the general eq 1 is suitable for any class of organic molecules and the OPSI algorithm is a universal method for the prediction of 13C-NMR spectra.
ACKNOWLEDGMENT L.C. thanks the Austrian Academic Exchange Service for a research fellowship. The authors are grateful to the staff of the University Computing Center for helpful discussion during the program development. This project was supported by the European Academic Supercomputing Initiative (EASI). RECEIVED for review February 10, 1993. Accepted May 4, 1993.
