J. Chem. InJ Comput. Sci. 1993,33,441-452
447
Inherent Limitations of Linear Additivity Models for the Estimation of 13C-NMR Chemical Shift Values of Polysubstituted Benzenes: Some New Findings Using the SCSD Algorithm Lingran Chent and Wolfgang Robien' Department of Organic Chemistry, University of Vienna, Wahringer Strasse 38, A-1090 Vienna, Austria Received December 23, 1992 A large number of substituent-induced chemical shift difference (SCSD) values have been automatically derived from both mono- and polysubstituted benzenes for 15 different substituents by a new algorithm based on systematic investigation of all the possible structure pairs available within a large database. The average SCSD values were found to be in good agreement with the corresponding SCSD values derived from monosubstitutedbenzenes. However, very large SCSD ranges were found for almost all functionalities under investigation. The scattered distribution of SCSD values and the approximate feature of additivity equations are two inherent factors which jointly restrict the accuracy of the additivity model method. INTRODUCTION
RESULTS AND DISCUSSION
Substituent-induced chemical shift differences (SCSD) Relationship between SCSD, and SCSD,,. The accuracy play an important role in both theroretical studiesof the nature of chemical shift estimation using additivity models depends heavily upon the deviations between SCSD values considered of substituent effects on chemicalshift values and the practical application to the simulation of NMR spectra of a known and their alternative SCSD, values really used during molecular structure. The SCSD value is simply defined as calculation. In order to improve the estimation accuracy, a the difference of the chemical shift values between two new set of incrementsderived from monosubstitutedbenzenes corresponding compounds differing by a substituent under has recently been p~blished.~ In this section, we investigate investigation. Extensive effort has been directed toward the the relationship between SCSD,, values and their correanalysis of substituted benzenes, and a large number of SCSD sponding average SCSD values (SCSDav) calculated from all values for monosubstituted benzene derivatives (SCSDmo) have the possible SCSD values derived from both mono- and been collected for a wide range of substituents2 These SCSD,, polysubstituted benzene derivatives. Table I gives the statistic values have widely been used to estimate chemical shifts of information of the obtained SCSD values for 15 different polysubstituted benzene derivative^.^,^ Some computer prosubstituents, including SCSDa, values, the highest and the lowest SCSD values, and their corresponding structure pair grams based on that SCSD,, table have also been written in allowing easy access to the reference data sets order to perform automatic estimationof 13C-NMRs p e ~ t r a . ~ ~ inforamtion ~ (see Figure 1). The SCSD,, values from ref 4 are also listed However, although it has been noted that the main problem of additivity models is the limited accuracy as compared to in the right column of Table I for ease of comparison. other methods, the real reasons of the problem have not been By inspection of Table I, we can easily find the interesting completely clarified so far.' fact that almost all the SCSDav values are surprisingly The application of our novel SCSD algorithm1 allows consistent with their corresponding SCSD,, values. For automatic extraction and analysis of the SCSD values from fluorine substituent, for instance, the absolute differences all of the substituted benzenes available in a large data between SCSD,, and SCSD,, values are less than 0.5 ppm collection for different kinds of substituents under investifor all carbon atoms in the benzene ring. In only a few cases, gation. In this paper we report some new findings by using the differences between SCSDav and SCSD,, are larger than SCSD method and investigate the reasons for errors inherent 1 ppm. The largest difference (2.7 ppm) has been found for to linear additivity models. a thiomethyl substituent at the ipso-position. This fact seems to tell us that using SCSD,, values for EXPERIMENTAL SECTION estimation of 13C-NMRspectra of polysubstituted benzenes is suitable. If this is true, we can further deduce, from the The databases accessed consist of some 80 000 I3C-NMR viewpoint of statistics, that in those cases where SCSDav and spectra, including the libraries of the University of Vienna, SCSD,, values have larger differences, using SCSD,, instead SADTLER Research Laboratories, and the German Cancer of SCSDmovalues to estimate chemical shifts should, in most Research Center at Heidelberg. The SCSD algorithm was situations, lead to better results because more SCSD values implemented in FORTRAN 77 under the UNIX operating are located within the range with the SCSDavvalue as the system on a Silicon Graphics workstationand an IBM-R6000 center than those within the identically sized range with the workstation. The program consists of about 5000 lines of SCSD,, value as the center. sourcecode. First, all those compounds which contain exactly However, when checking Table I again, we can find another one six-membered ring system were retrieved from the fact that there are very large SCSD ranges for most of the available databases, and then a partial structure search was substituents. The SCSD value of ipso-carbon atom for iodine performed using benzene as query structure. Finally, the substituent has the largest range of over 55 ppm, from +11.6 SCSD algorithmwas applied to this hit list for each substituent ppm for structure pair 20445A-5665A to -43.6 ppm for under investigation. structure pair 9512R8812B (see Figure 1). From Table I it can be seen that SCSD ranges depend upon the number of On leave from the University of Science and Technology of China, Hefei, Anhui 230026, The People's Republic of China. SCSD values. Usually more Occurrences of SCSD values +
0095-2338/93/1633-0447$04.00/0
0 1993 American Chemical Society
448 J. Chem. If. Comput. Sci., Vol. 33, No. 3, 1993
CHENAND ROBIEN
Table I. Statistic Data of the Average, Highest, and Lowest SCSD Values and Their Corresponding Structure Pair Information for 15 Substituents Obtained by SCSD Algorithm@ differences of chemical shifts in each position positions considered
highest value
entries used 1-2
1 2 3 4 6
43.5 0.8 6.1 18.0 6.3 0.8
1096F-7257C 25988514441A 48 108-2257 1A 16771B-65 17B 1988A-2119A 25988E14441A
1 2 3 4 5 6
18.2 16.1 11.8 9.8 9.3 5.6
1097F-7256C 4675B-28569B 392OA-33978 12203B-8521 B 3920A-3397B 1154352361A
5.1 -0.9 1.1 -1.7 0.9 0.1
1 2 3 4 5 6
8.4 16.2 17.3 2.7 6.1 7.8
3336B-678A 10347C-10338C 8601B4090A 1630357401B 1100F-7255C 3445C-808B
-6.0 1.8 1.3 -1.3 1.4 3.0
5
average values 1. -F 33.7 -12.9 1.4
no. of hits
lowest values
entries used 1-2
2744 2745 2746 2746 2744 2745
7.2 -30.5 -7.8 -30.1 -7.7 -21.9
20446A-5705A 11852A-14337A 6972B-954C 25988E14441A 17920A-970B 19345E1988A
33.6 -13.0 1.6 -4.4
4763 4753 4750 477 1 4746 4757
-5.0 -14.0 -10.2 -13.4 -14.1 -12.6
12142B-2095A 241B-6127A 16692B-88 16B 594F-263 1B 3008B-7951C 594F-263 1B
5.3 0.4 1.4 -1.9
2822 2843 2841 2856 2839 2840
-20.2 -11.0 -14.2 -5.2 -5.3
-5.4 3.3 2.2 -1.0
-6.5
21438B-3520A 860152208B 10347C-10338C 23757B-6009A 860 152208B 18079A-18078A
1934 1930 1933 1932 1934 1929
-43.6 -3.9 -7.3 -4.8 -9.8 -11.3
9512B-88 12B 3718520927A 15146A-677A 15395A-10303B 698859515B 1762551601H
-31.2 8.9 1.6 -1.1
609 609 609 609 608 609
3.9 -3.5 -4.8 -2.2 -5.7
15 13F-15 12F 15314B-6031A 3435B-15443 422658413B 16653B-6009A 4226B-8413B
9.3 0.3 0.2 0.0
587 587 587 587 586 587
4.3 -3.4 -4.2 -3.4 -2.8 -2.2
25443B-6060A 7011E1544F 701 15 1544F 7367C-736OC 74OOC-736OC 241 llB-6927A
9.5 0.7 0.3 0.2
6.1 -30.9 -12.8 -32.3 -14.0 -23.9
27252B-1731B 15349B-19820B 10382B4687C 22 17758963B 2148 1B-4570B 80015571A
28.8 -12.8 1.4 -7.4
17.3 -23.5 -12.3 -27.5 -12.3
33.5 -14.4 1.o -7.7
-31.7
13158B-11750B 6434E18072A 17403517395B 764452348A 17403E17395B 214OOE18063A
23.0 -17.8 -10.2 -11.1 -3.0 -23.1
47 15E6060A 2852B-695C 7183B-577A 273B-6060A 6395B-3525B 7854B-684A
30.3 -14.3 0.6 -8.4
-4.3 -20.1 -4.1 -5.6 -3.0 -7.4
13037A-2275A 646658560A 15865A-1088F 24824B-6153A 18221B-8568A 27918A-5589A
4.0 0.7 0.3 -3.2
-4.0 1.5 -13.1
SCSDmO4
2. -C1
3. -Br
4. -I 1 2 3 4 5
6 1 2 3 4 5 6
1 2 3 4 5 6
1 2 3 4 5
6 1 2 3 4 5
6
11.6 17.5 11.4 8.4 12.6 15.7
20445A-5665A 15108A-5729B 6988B-9515B 21423A-9296C 951258812B 3443C-808B
13.3 3.8 6.9 3.9 2.8 4.3
3435B-13578A 2058351084A 422658413B 16653B-366A 8413B-2345A 20583B454K
13.6 3.6 3.6 3.0 2.8 4.0
7011E13578A 2427 1E l 8 15H 7063C-2119A 23259A-22908A 353 1E 2 1 19A 7367C-736 1C
46.0 2.2 17.9 15.6 15.3 1.4
2217758963B 16771B-18633B 800155729B 24691E1253F 837A-900B 864A-9119B
45.4 16.5 22.1 16.7 16.5 8.5
22019B-2367A 2348A-7259C 896352367A 24998524839B 13158E11750B 8963B-6798B
5
42.1 4.9 12.8 2.1 8.7
6
-5.0
3839B-800B 229552852B 3839B-800B 2142OA-9296C 3839B-800B 7 1 8 3 5 1 1538A
1 2 3 4
11.3 19.8 3.9 4.8 3.0 18.6
26546B366A 27918A-5589A 265465366A 27918A-5589A 13037A-22569A 6466550K
1 2 3 4
5
6
-33.5 7.2 1.2 -0.6 1.4 9.2 5 . -CH2-C1 9.3 0.0 0.4 0.3 0.3 0.3 6. -CH*-Br 9.6 0.5 0.5
0.1 0.5
0.7 7. - O H 28.5 5426 -13.2 5414 1.4 5424 -8.3 5404 1.5 5429 -12.7 5410 8. -0-CH3 31.3 4650 -12.7 4622 4629 1.o -7.7 4642 4621 1.o -15.4 4649 9. -O-CHZCH~ 30.6 769 -13.0 768 1.1 768 -7.6 767 1.o 768 -14.6 768 10. S H 2.9 445 -0.2 44 1 0.5 445 -2.5 445 0.4 44 1 1.7 445
-4.5
ESTIMATION OF "C-NMR CHEMICAL SHlR VALUESOF BENZENE
J . Chem. If. Comput. Sci., Vol. 33, No.3, 1993 449
Table I (Continued) ~~
~~
differences of chemical shifts in each position positions considered
highest value
entries used 1-2
1 2 3 4 5 6
18.4 7.6 4.4 9.4 6.7 7.6
16143B450K 1252F-5300C 16143B450K 16968B4714B 20914E2068A 1252F-53OOC
1 2 3 4 5 6
22.6 1.9 4.1 3.0 2.9 1.9
25280A-22569A 12245E22560A 25309A-2119A 12075E22559A 12245E364A 9735A-1389H
1 2 3 4 5 6
-1.3 6.9 2.3 2.1 2.3 6.9
4426C-5325C 3404C-1815H 1991A-5293C 4427C-5325C 1991A-5293C 3404C-1815H
1 2 3 4 5 6
16.2 19.8 12.0 12.4 8.7 19.8
9785E13827A 8403E7794B 8325E7078B 19348E1675H 241095801 1B 8403E7794B
1 2 3 4 5 6
33.3 30.9 18.6 15.5 15.2 17.9
8924B-6135B 26557B-364K 19129B9522B 8454B4495C 15338A-15908A 21481E11363B
(I
.
average values
no. of hits
11. S - C H 3 9.8 1179 -1.2 1200 0.5 1199 -2.5 1171 0.6 1198 -0.8 1200 12. -CH=CH* 8.4 1206 -2.2 1206 -0.3 1207 -1.5 1206 -0.3 1206 -2.2 1206 13. a H -5.8 346 3.4 346 -0.2 346 0.3 346 -0.1 346 4.0 346 14. -COOH 1.7 2392 1.4 2392 0.1 2389 3.9 2394 -0.3 2392 1.4 2389 15. -NO* 19.4 4635 -4.5 4674 1.2 4670 5.5 4676 0.5 4664 -4.4 4677
lowest values
entries used 1-2
-16.8 -7.7 -5.0 -6.8 -3.0 -7.4
1253F-2280A 1545F-13 12H 1270F-1088F 7389C-7 360C 7423C-736OC 15755A-19987B
7.1 -1.9 0.2 -3.6
3.4 -6.0 -3.1 4.5 -3.0 4.8
9733A-91B 12433B-6058A 25298A-8573A 9744A4068A 2357A-6068A 25310A-6009A
6.4 -2.3 -0.1 -0.8
-8.3 -0.3 -3.5 -3.1 -2.8 1.6
4429C-13 12H 54K-8560A 4426C-1088F 27755B1360C 34O4C-18 15H 17769E9445B
-6.2 3.6 -0.4 -0.3
-6.9 -7.0 -8.3 -5.4 -15.5 -9.8
19349B4495C 19071B-9785B 4480B4503C 494K-1319H 15349E1225B 4560E21674B
2.1 1.6
-1.3 -17.7 -21.2 -16.0 -20.8 -18.1
1075H-1074H 8566B4630B 17625E15148A 265575 364K 11852A-15329A 66 16E14826A
SCSDmO4
-0.1 5.2
19.9 -4.9 0.9 6.1
The data in the right column are cited from ref 4. The numbering of the carbon atoms in the benzene ring is shown on structure B in Figure 3.
Table 11. Chemical Shift Deviations Resulting Mainlya from Substituent Interactions chemical shift values of carbons holding the halogen atom compound
calculated"
experimental"
deviation
o-fluoroanisole m-fluoroanisole p-fluoroanisole o-chloroanisole m-chloroanisole p-chloroanisole o-bromoanisole m-bromoanisole p- bromoanisole o-iodoanisole m-iodoanisole p-iodoanisole
148.67 a 163.27 c 155.27 a 119.97 a 135.37 a 126.57 a 108.32 a 123.50d 114.92 a 80.12 a 95.30 d 86.84 c
152.90 a 160.10 b 157.40 a 121.20a 134.90 a 125.50 a 111.70a 122.80 d 112.58 a 86.00 a 94.30 d 82.85 c
4.2 3.2 -2.1 -1.2 0.5 1.1 -3.4 0.7 2.3 -5.9 1.o 4.0
The letter indicates the solvent: a = chloroform-dl; b = DMSO; c DMSO-&; d = CDC13.
enlarge the corresponding SCSD range. These facts demonstrate that using SCSD,, values to predict chemical shifts for polysubstituted benzene derivatives is a very dangerous procedure. In view of the above mentioned findings, it would be helpful to establish a criterion for checking when SCSDmo values can be properly used in spectrum simulation. Unfortunately, it has W n pointed out5 that such a criterion does not exist. Thus, we would like to know how many spectrum estimation
problems can be solved by using SCSD,,values. This problem will be discussed in detail in the following paragraphs. Distribution of SCSD Values. Parts of the individual distribution diagrams of SCSD values for 15 different substituents are given in Figure 2. The visual inspection of the various distribution diagrams shows that in most cases SCSD values have the distributions of approximate Gaussian-curve shape. The peak maximum is usually located at or near the corresponding SCSD,, or SCSDmo values. The scattered distributions of SCSD values are mainly caused by various substituent interactions. Suppose all of the spectra used in calculation were measured under identical experimental conditions and there would be no interaction between the substituents within the benzene ring; then the SCSD values corresponding to the same carbon atoms at the benzene ring should be exactly identical for one substituent under investigation, independent of the calculation of the SCSD values from mono- or polysubstituted benzenes. However, there exist various interactionsbetween substituents located at the ring system. It is not appropriate to discuss these effects in detail here; this topic has been reviewed elsewhere.2 Some illustrative examples shown in Table I1 can help us better understand the interactions of substituents. For disubstituted benzenes, the deviations between calculated and experimental chemical shift values directly reflect the extent of interaction between two substituents at the benzene ring.
CHENAND ROBIEN 5665/A
20145/A
4.0
6
9.2
1
2
5665/A
2
I
1
1
20445/A
200
#1
SCREEN-DUMP:
***
SSI
I
I
I
I
150
100
50
0
***
AB
16/10/1992
16:27:56
8812/B
9512/8
2
1
I
I
9512/0
200
SCREEN-DUPIP:
1
150
42
***
SSI
***
I
I
/I
50
100
AB
0 16/10/1992
16:28:42
+
Figure 1. Two structure pairs which give the largest SCSD range of over 55 ppm, from 11.6 ppm for structure pair 20445A-5665A to 4 3 . 6 ppm for structure pair 95 12B-88 12B for the ipso-carbon in the benzene ring. The maximal common substructural fragment (MCSS)is marked by bold lines.
FromTable 11, it can beseen that, for all threefluoroanisoles, the interactions between fluorine and the methoxy group are quite different, depending upon the substitution pattern; the other halogen-anisolesshow a similar behavior. On the other hand, for the same substitution pattern, different halogen anisoles also show different interactions between halogen atom and methoxy group. Besides, the differences of experimental conditionsused in the measurement of spectra also contribute the scattering of SCSD values to some minor extent. From distribution diagrams we can roughly estimate that about 50% of all SCSD values are within the range of SCSD,,
f 1 ppm. This fact seems to indicate that SCSD,, values can be properly applied to some 50% simulation problems for substituted benzenes. But the real situation is more cornplicatd. In order toclarify t u point we should first investigate the inherent problem of additivity models.
Limitation of Linear Additivity Models. As has been most recently P i n t 4 out by Pretsch et 81.: the Principal drawback of the additivity models is their limited accuracy as compared to other approaches. In this section the inherent problem of this method will be discussed.
ESTIMATION OF ''C-NMR
-
I 2 DISPLAY: C
CHEMICAL
SHIn VALUES OF BENZENE
J. Chem. In& Comput. Sci., Vol. 33, No.3, 1993 451
2745 HITS LEFT- 23 RIGHT- -53 Ppm
.... tt
at.
........ ............. tt.
.I/
ttl
t
.I.tltt.*.t
**
-20
0
-40
Figure 2. Distribution diagrams of SCSD values. (Note: For fluorine substituent the distribution diagrams for carbons 1, 2, 3, and 4 are given; for chlorine, bromine, and iodine substituents only, one distribution diagram corresponding to the ipso-carbon atom at benzene ring is
shown.)
X
X
Y
A
B
C
First, we consider disubstituted benzenes. In order to estimate the chemical shift value of carbon 1 of structure A shown in Figure 3, we can deduce a mathematically accurate equation. The mathematical description of the SCSD definition is given as follows: Figure 3. Four structures used in deducing eqs 1-6.
Substituents. where, A6h,kijis the SCSD value of carbon h of structure i and its corresponding carbon k of structure j, ahi and akj represent the chemical shift values of carbons h and k of structures i and j, respectively. Thus, we can easily write the following expressions:
A6134c,0=
- a4,
(4)
D
X, Y:
From definitions 2 and 3, we obtain
Equation 5 is accurate because no hypothesis was introduced during the above deduction process. However, when we try to use this equation, the problem immediatelyoccurs. Because of the lack of a value (which is just what we want to calculate), the A6'q6~,,Value is in fact unknown. Considering that both A 6 ' v 6 ~and , ~ A 6 1 . 4 ~are , ~ SCSD values of the ipsocarbon atom for the substituent Y,we may use the latter to
452 J. Chem. In$ Comput. Sci., Vol. 33, No. 3, 1993
estimate AS1s6~,e; thus we get
a’,
+
+
= S3, A61’4c,D (6) It can be easily seen that eq 6 is exactly the same as the additivity model presented in ref 4 for solving the problem except that 128.5 ppm has been selected as the value of S 3 ~ in the literature. Therefore, from the above deduction process we know that the additivity model for carbon 1 of structure A is in fact an approximate equation which contains one approximate term (= A 6 1 , 4 ~ , ~This ) . conclusion is also tenable for any other carbon in the benzene ring of disubstituted benzenes. Now it is clear that, for disubstituted benzenes, the deviation of calculated shift values directly depends upon the difference between the SCSD value derived from disubstituted benzene and its alternative SCSD,, value really used in the calculation. For the above example, for instance, the deviation of calculated shift value via eq 6 is solely determined by A 6 1 . 4 ~- ,A~8 1 , 6 ~ , ~ , provided the reference shift data are free from a variety of experimental conditions. Therefore, taking f 1 ppm as the threshold values of the largest acceptable deviations in shift simulation, we can reasonably conclude that SCSD,, values can be properly applied to some 50%simulation problems for disubstituted benzenes. For polysubstituted benzenes, however, the situation is more complicated. It can be proved in a similar manner that for an n-substituted benzene (n 2 3), there are n - 1 approximate terms in the corresponding additivity equation. Thus, the total deviation between the calculated shift value and the experimental one is equal to the sum of deviation contributions of n- 1 approximate terms. In the worst case, all the individual deviations have the same sign. Therefore, even in those cases where all the individual absolute deviation values are less than 1 ppm, the total absolute deviation value may be greater than 1 ppm. On the other hand, in some cases, although all the individual absolute deviation values are larger than 1 ppm, the total absolute deviation value may be less than 1 ppm because of the counteractions of the individual deviations with different signs. For most of the polysubstituted benzenes, the situation is between the above two extreme cases. Therefore, it is difficult to estimate the application scope of SCSD,, values for polysubstituted benzenes. However, using several approximate terms in an additivity equation without any correction for substituent interaction is by no means a reliable method. CONCLUSION
A large number of SCSD values derived from both monoand polysubstituted benzenes were obtained for 15 different
CHENAND ROBIEN
substituents by means of the SCSDapproach. For most carbon atoms, their SCSD values have a distribution similar to a Gaussian-curve shape. The SCSD,, values show good consistencies with the corresponding SCSD,, values. For most substituents, there exist considerably large ranges of SCSD values. Linear additivity models are approximate equations containing n - 1 approximate terms for n-substituted benzenes. This fact, together with the scattered distribution of SCSD values, determines that the method based on the linear additivity equations described in the chemical literature has the inherent disadvantage of limited accuracy. Better results can be achieved by using a new approach which has the ability to utilize automatically SCSD values derived from polysubstituted benzenes.8-10 ACKNOWLEDGMENT
L.C. thanks the Austrian Academic Exchange Service for the research fellowship. This project was supported by the European Academic Supercomputing Initiative (EASI). REFERENCES AND NOTES (1) Chen, L.;Robien, W. SophisticatedAlgorithm for Automatic Extraction and Analysis of Substituent-InducedChemical Shift Differences of I ‘CNMR Spectra. J . Chem. InJ Comput. Sci., preceding paper in this issue. (2) Ewing, D. F. I3CSubstituent Effects in MonosubstitutedBenzenes. Org. Magn. Reson. 1979, 12,499-524. (3) Pretsch, E.; Clerc, J. T.; Seibl, J.; Simon, W. Tables of Spectral Data for Structure Elucidation of Organic Compounds, 2nd ed.;
Springer-Verlag: 1989. (4) Pretsch, E.; Fiirst, A.; Robien, W. Parameter Set for the Prediction of the IT-NMR Chemical Shifts of sp2-and sp-HybridizedCarbon Atoms in Organic Compounds. Anal. Chim. Acra 1991, 248, 415428. (5) Fiirst, A.; Pretsch, E. A Computer Program for the Prediction of “CNMR Chemical Shifts of Organic Compounds. Anal. Chim. Acra 1990, 229, 17-25. (6) Hearmon, R. A,; Liu, H.-M.; Laverick, S.;Tayler, P. Microcomputer Prediction and Assessment of Substituted Benzene IT NMR Chemical Shifts. Magn. Reson. Chem. 1992, 30, 240-248. (7) Pretsch, E.; Forst, A,; Badertscher, M.; Biirgin, R.; Munk, M. E. C13SHIFT:A Computer Program for the Prediction of IT NMR Spectra Based on an Open Set of Additivity Rules. J . Chem. InJ Comput. Sci. 1992, 32, 291-295. (8) Chen, L.; Robien, W. Optimized Prediction of I3C-NMR Spectra Using Increments. Anal. Chim. Acta 1993, 272, 301-308. (9) Chen, L.; Robien, W. Optimized Prediction of IT-NMR Spectra Using
Increments. Comparison with Other Methods. Fresenius Z . Anal. Chem. 1992, 344, 214-216. (10) Chen, L.; Robien, W. Submitted for publication.
