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Depending on its specific approximations and atom Parametrization, every semiempirical MO method can give a molecular geometry more or less close to the ..... linear correlation between the nonhydrogen atom distance matrices. When we ...
RevueRoumaine de Chimie, 1997, 42 (4), 319-324


MARTAMRACEC,"MIRCEA MRACEC"andLUDOVIC KURLTNCZID oRoumanianAcademyTimigoaraBranch,InorganicChemistryLaboratory, Blvd. M ihai V iteanJJ24, I 900-Timi $oara,Roumania tRoumanianAcademy,ChemistryInstituteof TimiqoaraBlvd. Mihai Viteazul24, 1900-Timigoara, Roumania

ReceivedMarch 16, 1995

Several statistical criteria were tested on the series of l,3-heterobenzenesC5H5E (E = N, P, As, Sb, Bi) fur order to estimate the capability of different semiempirical MO methods to give the best molecular geometry with respect to the experimental one. Global statistical index root-mean-squaredeviation, s, is a weaker criterion than fit standarderor, FSE. This (FSE) resulted from the linear correlation between the eleoents of tbe experimental and calculated distance matrices. According to FSE, the best ground state geometry is obtained with MNDO for benzene and with MINDO/3 for phosphabenzene.The best endocyclic geometry of pyridine is given by AM1, but the best geometry including hydrogen atoms too is obtained from MNDO. The geometries of arsa- and stibabenzeneare well optimised by PM3 method (within the level of experimental accruacy). Also, the unknown geometry of bismabenzene$eemsto be well calculated by PM3 method'

INTRODUCTION One of the basic information for chemists is molecular geometry. This can be determined experimentally or cald,rlatedby quantum chemical methods. It is generally recognisedthat ab initio methods are preferable. However, in many casessemiernpirical MO rnethods are as effective as ab initio ones with a lower CPU time cost. Depending on its specific approximations and atom Parametrization,every semiempirical MO method can give a molecular geometry more or less close to the exPerimental geomehy. The aim of this note is to find out one or more statistical criteria to appreciate the power of different semiempirical MO methods to provide the best molecular geometry with respectto the experifor which the experimental geometry (except bismabenmental one. The series of 1,3-heterobenzenes, MO methods are contained in HyperChem2.A,2 semiempirical tested zene) is known, was chosen-The MOPAC 6.0,3and PcMol 3.ll packages.4Hyperchem package,running under Windows, is able to perform ExtendedHuc-kel,s CNDO,6INDO,6 MINDO/3,? MNDO,8 and AMle calculations.MOPAC 6.0 pac-kageperforms MINDO/3, MNDO, AMI and PM3.lo PcMol packagecarriesout MNDO, AMI and PM3 calculations. Each package is more effective in specific fields'

CALCULATIONS For all MO methods contained in MOPAC or PcMol packagesthe following input strategy was adopted. In the standard benzene geometry @ond lengths and angles with their standardvalues), substitution of a C by an E atom was performed, and symmetry constraints corresponding to Cr" point group were imposed. All input geometries were fully optimised using BFCS algorirhm. Herbert's or Peter's tests were satisfied with gradient norms below 0.5 kcaUA mole. For CNDO and INDO methods, the geomery initially optimis6d with MM+ force field was submitted to full optimisation using Polak-Ribiere conjugate gradient algorithm with the default gradient norm of 0.01kcaVA mole.

Maria Mracec et al.


RESULTS AND DISCUSSION The geometry data resulted from all the above-mentionedMO methods are similar to litera$re published data so, only bismabenzenedata are presentedin Table I together with all experimental geometriesused in correlations. Benzene.The experimentalll values of C-C and C-H bond lengths are 1.396 and 1.0834, respectively. There are small differences in the optirnised bond distancesresulted from different semi' empirical MO methods,but the anglesare all 120". The Pyridine geometry was intensively studied especially by microwave spectroscopy.12*16 substitutionof a C atom with a N atom has important effects on bond anglesand lengths.The decreaseof C6NC2and the increase of NC'C, bond angles (see Fig. I for the numbering of atoms) are well reproducedby AMl and MNDO, but the most close valuesto the experimentalonesare given by AMI method. Table I Experimental bond lelgths (in A) and angles for pyridine, phospha-, arsa-, and stibabenzeneand PM3 ones for bismabenzene


crct crco C,H, C,H,

c.H^ c6EC2 EC2Ca c2cac4 c3c4c5 EC2H7 c2c3HE cac4He Ref



1.338 1.394 1.392 1.087 l.083 1.082 I 16.9 123.8 118.5 118.4 I16.0 120.1 12c.8 14

1.?33 1.413 1.384 t.172 t.122 1.t22 t0l.l r24.4 r23.7 r22.7 I 17.8 I14.8 118.6 18

As 1.847 1.388 1.396 1.110

97.0 125.3 123.9 124.5 tt7.4 I18.8" I17.8 21


2.050 1.400 1.392 1 . 11 0

92.8 123.8 125.0 127.8 I l8.l lt?.l 116.1 23

Bi 2.127 |.375 1.396 1.099 1.100 I .100 89.6 125.0 126.0 128.3 120.6 11 8 . 9 11 5 . 9 b

Estimated from eqs. ofTable 2

2.090* 0.050

* 0.6 126.1 t 2 7 . 9+ 1 . 2

1 1 6 .+ 1 0.6

" ref. 19 b this notePM3 values Phosphabenzene is a planar aromatic ring as resulted from microwave spectroscopylT and microwave speckoscopy combined with electron From a NMR study of phosphabenzene partially oriented in a liquid crystalline solvent a new better estimation of C*H bond distance was possible.le The uniform decrease from P to Co of C-C bond lengths is correctly reproduced only by MINDO/3. The best overall fit with the experimental values is obtained also with MINDO/3 method. The trend in bond angle variation is reproduced both by AMI and PM3, the better values being obtained with PM3. The CCH bond angles are also better reproduced by PM3 method.

Fig. I . - Labeling of the atoms of the aromatic l,3-heterocycles E = C(H), N, P, As, Sb and Bi.


Aromatic 1,3-heterocvcles.III

Arsabenzeneis also a planar ring. Microwave spectroscopy,20 electron diff&actionl3'2lor microwave combined with electron diffraction studies22give the geometry from Table l. Values for C-H bond lengths were corrected by a NMR study of arsabenzenepartially oriented in a nematic solvent.le The experimental structural values axewell optimised with PM3 method. Stibabenzenegeomety was studied by microwave spectroscopy23and NMR partially oriented in crystalline solvent.24This ring is also planar and his geometry is well reproducedby PM3 method. Bismabenzeneexperimental geometry is not known. In order to get more information about the structural properties of bismabenzene,in the previous notesl linear correlations between the experimental EC2 (E = N, F, As, Sb) bond lengths or C.EC, bond angles of }.3-heterobenzenes and different structural properties of the free heteroatom, E, were carried out. From these linear correlations a Bi-C bond length around 2-10 A and a CBiC bond angle around 90" resulted. In Table 2 other four linear correlations between the experimental values of C.NC, bond angles and the experimental values of CrCrCo, C3C4C5,C3C4Hebond angles or EC, bond lengths are presented.When benzene is taken in correlation the values of statistic paf,ametersare much lower, probably due to the different benzenesymmetry (D6h) with respect to X3-heterobenzenesymmetry (Cr"). The quality of correlations is only satisfactory. However, we present in the last column of Table I the values of CrCrCa, CaC4C5,C3C4Hebond angles and Bi-C bond length calculated from the equations of Table 2 for a C6BiC2bond angle of 89.6 This value (89.6) resulted from PM3 optimisation is very close to the values resulted from linear correlations (- 90"). As can be seen from Table I the values obtained from PM3 for bismabenzeneseem to be very reasonable.Also they are in accord with the trend shown by the ring deformation in the seriesof heterobenzenens. Table 2 Statistic parametersof linear correlations y = a + bx between C'EC, bond angles (x) and other experimental data of l"r-beterobenzenes(y)

c2c3c4 c3c4c5 cac4He ECt

0.975 0.935 0.939 0.981


F stat

0.6 t.2 0.6 0.050

76.8 28.6 30.8 103.8



-0.2726 150.6 -0-3633 160.4 100.1 0.1196 4 . 6 1 5 5 -0.0282

In the limits of experimental errors, all tested MO methods give a good ring geometry, in accord with the experimental values. However, the most of the MO methods do not give the correct variation trend of internal coordinates, observed in heterobenzeneexperimental geometry. In order to choose a MO method capable to give both the best concordanceswith the experimental geometry and the variation trend of the ring geometry, we used a global statistical index, s, root-mean-squaredeviation,25calculatedaccordingto the equation:



N is the number of distance matrix elementstaken in the sum. Becausethe distance matrix is symmetrical and its diagonal elements are equal to zero, N is equal to n(n - l)/2; n representsthe number of atoms in ttre }"3-heterobenzene molecule. DDMij is the ij element of difference distance matrix obtained from equation(2): DDMij=lDMl,,-DM2ijl


DMtii and DM2,, are the ij elementsof DMI and DM2 distancemahices.For a correctcomparison,the atom numbering-in the two matrices Ml and M2 must be the same. "s" was calculatedwith a small


Maria Mracec et al.

program written in FORTRAN language. A certain discrepancy resulted between the order of fitness predicted by this index and the variation trend of the experimental ring geometry. Therefore, we searchedanother criterion to order MO semiempirical methods. More reasons determined us to choose the linear conelation, y(calc) = a * bx.(exp). For the evaluation of linear regression we dispose of at least five important statistic indexes: f, fit standard error (FSE), Fishertest, "a" and "b" values. Three seriesof linear correlationsare tested.In the first series(Al) the experlmental values of bond lengths and angles are correlated wlth thelr correspondlng calculated values. The number of observationsfor every correlation is 13. ln the secondseries(A2) the elementsof the experlmental and calculated d.lstancematrlces are correlated. Obviously, the number of values taken in correlation is n(n - l)/2; n representing the number of atoms in the heterobenzenemolecule. In order to avoid redundant data, and considering that for a better optimisation we used symmetr;r constraints, in the third series(A3) we carried out the same type of correlatlon as A2, but uslng a reduced number of observatlons, hnposed by symmetry. This number is l0 for benzene,and 3l for the rest ofheterobenzenes" The values of statistic parametersobtained from these linear correlations show a certain variability for different MO methods, however, 12 does not statistically differ from I and Fisher test has such huge values comparatively to the table reference values, that these two statistic indices are not of much help for the ordering of MO methods. Moreover, the values of "a" and "b" are significantly close to zero and 1, respectively, being also of no importance in the ordering of MO methods. The only criterion left is FSE (Table 3). The sequencegiven by this index is shown below, for the three series Al, A2, and A3. The order given by A3 series is the same with that given by A2 series. Some differences aPpearin pyridine case. Comparatively, the order resulted from s index is also given. For benzenethe order is:



A2), A.3)




The orderfor pyridine is: A1)








The order for phosphabenzeneis: Al)


A2), A3)



MIN DO/3>PM3>CNDO>MNDO>INDO>AM I . The symbol '5" standsfor a better fit given by a method in comparison with its right neighbour

Aromatic 1,3

Some inversions in Al and A2, A3 series for pyridine and phosphabenzeneoccur. They could be due to the greater weight of long bond lengths in FSE values for both A2 and A.3 series.We verified this supposition for pyridine. By elimination distanceelementsimplying H atoms the obtained order for A2 and A'3 seriawas AMI>MNDO. Table 3 Statistic parametersfor pyridine, phospha-, arsa- and stibabenzeneresulted from A l, A2, and 43 series of linear correlations Method\FSE

A1 A2 A3 S

AI A2 A3 s AI A2 A3 s AI A2 A3 s AI A2 A3 s A1 A2 A3





0.0063 0.0067 0.0085 0.0009 0.0066 0.0075 0.0095 0.00r9 0.0015 0.0004 0.0005 4.4027 0.0040 0.0061 0.0077 0.0045 0^0170 0.0156 0.0196 0.0025 0.0166 0.0187 0.0235 0.0029

r.1227 0.0192 0.0213 0.0039 0.3638 0.0089 0.0101 0.0039 0.5046 0.0089 0.0096 0.0043 I .l179 0.il03 0.0835 0.0147 0.8059 0.021 I 0.0221 0.0046 0.9193 0.0196 0.0204 0.0036

LM49 0.4271 0.0282 4.0072 2.4377 0.0601 0.0612 0.0122 1.9529 0.0478 4.0d.97 0.0093 l.6545 0.4246 0.0255 0.0034 2.4397 0.0627 0.0642 0.0093 2.3387 0.0630 0.0646 0.0089



0.5758 0.0138 0.0140 0.0418

0.8472 0.0176 0.0195 0.0042

Al = correlafion between values from Table 2 (experimental and calculated geometries; l3 observations) ,{2 = correlation between elements of experimental and calculated distance matrix (55 observations) A3 = correlation of A2 type taking into account symmetry constaints (31 observations)

To explain the poorer results given by root-mean-squaredeviation, s, let us analyse the meaning of s and FSE indexes"From eq. (1), we observethat s representsan averageerror of all deviations of calculated values with respect to the experimental ones. This averaging effect prevents s index to reflect the correct variation trend of geometry data. In comparison to s, FSE has a different signification. It representsan average error with respect to the regression line. In its turn the regression line includes the normal sequcnceof all geometry data. Hence, FSE index has better chancesthan s, to correctly order the geomebies calculated by different semiempirical Mo methods.

CONCLUSIONS In order to compare the value of different semiempirical MO methods in prediction of molecular geometqr,from the tested indices we suggestFSE index as a suitable criterion, but even this must be used carefirlly. For instance,when we are interestedonly in a good skeleton geometry, the best test is a linear correlation between the nonhydrogen atom distance matrices. When we are interested in a global geomefy fit for high symmetry molecules, in order to eliminate the redundant elements, a good complementary test is a linear correlation of A3 type. For the global geomebryfit of molecules with low


Maria Mracec et al

symmetry, a good test is a linear correlation of A2 type, i.e., a correlation between all elementsbelonging to the lower half of calculated and experimental distancematrices. Ground stategeometries of arsa-, stiba-, and bismabenzeneare well optimised by PM3 method. ACKNOWLEDGEMENIS: We greatly appreciate the support provided by OTKA Budapest, Contract no. T.4316, that offered us the possibility to work with the HyperChem package on a PC 4T-486 4MB RAM. Also we are grateful to ProfessorG. Tasi (Univ. Szeged)for PcMol 3.1I demo version.

REF'ERENCES I M. Mracec, M. Mracec, M. Medeleanu M. Ihos and Z. Simon, Anal- Univ. Timisoara, Ser. Chim., lgg2, 1,9; M. Mracec, M. Mracec, M. Medeleanu,M. Ihos, O. Costisorand Z. Simon,Anal. Univ. Timisoara, Ser.Chim.,1992, I,23. 2 HyperChem 2.0, Autodesk Inc.,1992. 3 J. J. P. Stewart, QCPE Bull", 1986, 6,43; MOPAC 6.0, QCPE program 455; the shareware MOPAC 6.0 (K. E. Gilbert, l99l) recompiled for 40 heavy and 40 light atoms (adaptedto 16 MB RAM) by F. Mateoc and L. Kurunczi, 1992. Accuracy tested using the MOPAC 4.0 manual. 4 G. Tasi, I. P6link6, J. Haldsz and G. Naray-Szab6, "semiempirical Quantum Chemical Calculations on Microcomputers"; CheMicro Limited: Budapest, 1992. s ft. flsffiaann, J. Chem. Phys.,1963, 39, 1397. 6 J. A. Pople and D. L. Beveridge: "Approximate Molecular Orbital Theory", McGraw-Hill, New York, 1970. 7 R. C. Bingham, M. J. S. Dewar and H. Lo, J. Am. Chem. Soc.,1975,97, 1285. t M. J. S. Dewar and W. Thiel, ./. Am. C hem- Soc., 1977, 99, 4899. e M. J. S. Dewar, E. G. Zoebish,E. F. Healy and J. J. P. Stewart,L Arn. Chem. ioc.,1985,107,3902. roJ. J. P. Stewart,J. Comput. Chem., 1989, /0,209,221. rr A. Langsethand B. P. Stoicheff, Can. J. Phys.,1956,.t4, 350. 12B. Bak, L. Hansenand J. R.-Andersen,J. Chem.Phys.,1954,22,2013. 13G. O. Sorensen,L. Mahler and N. R.-Andersen,J.Mol. Struct.,1974,20,ll9. raF. Mata, M. J. Quintanaand G. O. Sorensen,J. Mol. Struct.,1977,42, l. 15S. D. Sharmaand S. Doraiswamy, Chem.Phys.Lett., 1976,41,192. 16M. J. S. Dewar, Y. Yamaguahi, S. Doraiswarny,S. D. Sharmaand S. H. Snik, Chem.Phys.,1979,41 ,21. 17R. L. Kuczkowski and A. J. Ashe, J. Mal. Speetrosc., 1972,42, 457. rET. C. Wong and L. S. Bafiell, -/. Chem.Phys,,1974, 61,2840. re T. C. Wong and A. J. Ashe, J. Mol. Struct.,t978,48,219. D R. Latimer, R. L. Idpczkowski,A. J. dshe and A. L. Meirzer, J. Mol. Spectrosc.,1975,57,428. 2r T. C. Wong, A. J. Ashe and L.S. Bartell, J. Mol. ltruct.,1975,25,65. 22T. C. Woog and A. Ashe, J. Mol. Struct.,1978,44,169. 23C. Fong., R. L. Kuczkowski and J. Ashe,./. Mol. Spectrosc., t978, 70, 197. 24T. C. Wong, M. G. Ferguson and A. J. Ashe, J. Mol. Struct., 1979, 52, 2ll. 25E. A. Padlanand D. R. Davies, Proc. Natl. Acad. Sci.,1975, 72,819.