TABLE1 - CALCULATEDAVERAGEELECTRICPOLARIZABILITIES[In units of 1O-2licmSj

System Average polarizability

Model potential FSGOa Exptlb

Butane 80.2 75.32 81.82,2-DimethyI. butane 116.8 110.86 118.82,2,3,3-Tetramethylbutane 153.4 146.41 153.1.Cyclohexane 109.7 101.30 109.8·-'Methy\cyc1ohexane 128.0 119.08 128.81,1-Dimethy\cyc1ohexane 146.3 136.85 146.7

(a) Obtained from ref. 4: and (b) obtained from ref. 7.

TABLE2 - CALCULATEDMAGNETICSUSCEPTIBILITIFS

SystemMagnetic susceptibility (-1 x 10-6egs)

Model potential

MethaneEthanePropaneButanen-Pentanen-Hexanen-Heptanen-Octane.n-Nonanen-Decanen-Undecanen-HexadecanePropenel-Butene2-Butene1-Hexene1-0ctene2-Methyl-4-heptene

FSGOa Exptlb

13.65 17.423.76 26.833.71 38.643.66 50.353.61 63.163.56 74.373.51 85.483.46 96.993.41 108.1

103.36 119.5113.31 131.8163.06 187.530.84 31.540.79 41.041.02 42.660.69 66.780.59 89.581.06 88.0

13.924.234.444.654.965.175.485.695.8

106.1116.3167.531.141:341.661.882.382.6

(a) Taken from ref. 4; and (b) taken from ref. 8.

K2 is O.Sand K, is - 0.2S, ne is the number of ethy-lenic C-H bonds, «c.c- cx.c_c, cx.C_H(me) and cx.C_Heare respectively the exponents of the Gaussians forthe bonds C-c (single), C=C (double), C-H(methane) and C-H (ethylene). Values of theseGaussian exponents are taken from the work of"Topiol et al» and -;:and i values are estimated usingthe equations given above. These calculated quanti-ties are given in Tables 1 and 2 along with experi-mental results. The results obtained from all-electronFSGO wavefunctions are also listed for comparison.-Considering the simplicity of the model used ourresults seem to be in excellent agreement with avail-.able experimental' data?".

The authors would like to thank Dr Ratner forproviding the model potential wavefunctions formethane ethane and ethylene. One of the authors{S. B.) thanks the UGC, New Delhi for the grant·of a junior research fellowship.

References1. RAY, N. K. s: MEHANDRU,S. P., Nat. Acad. Sci. Lett.,

1 (1978), 63.2. TOPIOL, S., FROST, A. A., MOSKOWITZ,J. W. & RATNER,

M. A., J. chem, Phys., 66 (1977), 5130; J. Am. chem,Soc .. 99 (1977), 4276.

:3. FROST, A. A., s. chem, Phys., 47 (1967), 3707.

I

I

NOTES

4. BHARGAVA, S: & RAY, N. K., Proc. Indian A cad. Sci.,88A (1979), 367.

5. BLUSTIN,P. H. & LINNETT,J. W., J. chem, Soc. FaradayTrans. IT, 31 (1975), 57.

6. AMOS,A. T. & YOFFE,J. A., Chern. Phys. Lett., 31 (1975),57; J. chem, Phys., 63 (1975),4723; Chern. Phys. Lett.,39 (1976), 53.

7. CAMAIL,M., PROUTIERS,A. & BODOT,H., J. phys. Chem.,82 (1978), 2617.

8. HABERDITZL,W., Theory & applications. of molecular dia-magnetism, edited by L. N. Mulay & E. A. Boudreaux(John Wjley, New York), 1976. .

Inclusion of Polarization Functions in MolecularSCF Calculations

R. A. THURAISINGHAMDepartment of Chemistry, University of Colombo, Sri Lanka

Received 2 April 1979; accepted 14 May 1979

Molecular SCF calculations including polarization functionsare reported for CH4, SiH., (CH3)3N, (SiH3hN and SiH s- Formolecules containing second row atoms the effect of inclusion of dfunctions in the basis set is more than just polarization of orbitals;these partake in bonding. The planar geometry of (SiH3)3Nis predicted only when the basis set includes d functions on thesilicon atom.

IN an atom the potential field which deter-mines the orbital shape has spherical symmetry.However as soon as the atom is a part 'of a moleculethe effectivefieldon its electrons is no longer spherical.The charge cloud will be perturbed' or polarizedinto a nonspherical charge. The simplest way toexpress the polarization is by the addition of smallamounts of p functions for s orbitals and dg and d«functions for Pg and P« wavefunctions respectively.This could be done by including in the basis set of aself-consistent field(SCF) calculation, d functionson the first row atom and p functions on the hydrogen.

In the case of second row atoms which have lowlying d orbitals the effect may be different, morethan mere polarization. They could partake inbonding, in which case the coefficients of these dfunctions in the molecular orbitals can be quite high.These effects will be examined in the calculationsreported in this note.

Near Hartree-Fock (HF) calculations on CH4and SiH4 - The calculations in this section weremade to find out the contribution of polarizationfunctions(PF's) to the SCF energy and the effectthey have when the central atom changes from afirst row atom to a second row atom.

The calculations were made for the methane mole-cule using the tetrahedral geometry! with C-R =2.066a.u.t with and without polarization functions(PF's). In the calculation without PF's the basisset used was:C (10 s, 6 piS s, 3 p) and R(S s! 3 s).The gaussian exponents of hydrogen contractionwere scaled to fit a Slater type orbital (STO) of 1.2.The calculations including PF's used a basis setof C (10 s, 6 piS s, 3 p, I d)2 and H (S s, 1

tl a.u. (atomic unit) of length = 5.292 X 10-11 m

509

-,

\

INDIAN J. CHEM., VOL. 18A, DECEMBER 1979

p/3 s, 1p). The Slater exponents of the 3d functionon carbon and 2 p function on hydrogen were taken

. as 2.0.The calculation on silane was carried outu sing the

tetrahedral geometry with Si-H = 2.797a.u3•The basis set without PF's was SiC12 s, 9 p/7 s, 4p)and H (4 s/2 s). The contraction for silane wasobtained from Veillard's! (12 s, 9 p) primitive setwith the rules formulated by Dunning". The gaussianexponents of hydrogen were scaled to fit Slater typeorbital of 1.2. The basis set which includes PF'swas Si (12 s, 9 p, 1 dl Ts, 4 p, I d) and H(4 s,1 p/2 s, 1p). The Slater exponent of the 3 d orbitalson silicon and 2 p orbitals on hydrogen were 1.302and 1.5 respectively. In Table 1 the results of thesecalculations are given.

Table 1 indicates that the change in energy due toPF's in the case of methane is - 0.0195a.u.t whilethat for silane is - 0.0450a.u. The largest coefficientof the d functions in the valence MO of silane is0.07 as compared to 0.03 in the case of methane.Thus the effect of 3 d functions is much greater insilane as compared to methane indicating possibleparticipation in bonding rather than just actingas mere polarization functions.

Calculations on (CH3)3N and (SiH3)3N - Thegeometrical shape of (CH3)3 N is pyramidal, whiletrisilylamine (SiH3)3N is planar. This on the faceof it appears peculiar, since we would expect thebinding to be essentially pure p or near it whichwould lead to a pyramidal shape. The qualitativeexplanation for this planarity is the possibility of thelone pair of electrons on nitrogen flowing into thed orbitals of silicon, and back again. Such deloca-lization is favoured when the atoms are coplanar.Baybutt et af.8 have done a calculation where theyhave predicted the observed geometry oftrisilylaminewhen 3 d functions only are included in the basis.For trimethylamine the pyramidal basis geometryis predicted without inclusion of 3 d functions oncarbon. These calculations used a poor minimalbasis of 2 gaussian functions for each Gaussiantype orbital (GTO). The calculations reported herewere carried out to see whether this interesting resultholds when a better basis set of STOs is used.

Two calculations were done for each molecule.Geometry for trimethylamine was taken from ref. 9,while that for trisilylamine was taken from ref. 10.In the first calculation the heavy atoms were coplanar,while in the second calculation the nitrogen atomwas inclined at 5° to this plane.

TABLE 1 - NEAR HF CALCULATIONSON CH. AND SiH,[Values in atomic unit (a.u.) of energy]

CH. SiB.

Total energywithout PF's -40.1896 -291.1941

Total energywith PF's -40.2091 -291.2391

HF limit -40.23" -291.275b

a, see ref. 6; b, see ref. 7; 1a.u. of energy=2625 kJ mol-1

t1 a.u. of energy = 2625 k Jrnol"!

510

,(

TABLE2 - TOTAL ENERGIESFOR AMINES(IN a.u.)

Devia tion from planarity

-172.7377-922.4693*(-922.1126)t

-172.7412-922.4679*(-922.1133)t

*, +d; t. -d

In the (CH3)3N calculations a minimal STObasis was used. These STOs were expanded in.terms of GTOs using the data of Huzinaga-'. TheIs STOs were expanded in terms of 5GTOs. TheSlater exponents in bothc alculations are the sameand are shown below.lse = 5.67, 2sc = 1.72, 2pc = 1.72, IsN = 6.672SN = 1.95, 2PN = 1.95, ISH = 1.24

In the (SiH3)3 N calculation, the basis employed?tas a minimal basis STO, where these were expandedIII terms of GTOs using the data of Stewart'>. The-Is STOs were expanded in terms of 5GTOs; while-the rest were expanded in terms of 3 GTOs. TheSlater exponents used were as follows:lssi = 13.5745, 2sSi 4.51, 2pSi = 4.9725,3sSi =1.6344, 2PSi = 1.4284, ISN=6.67, 2sN = 1.95, 2PN =1.95, ISH = 1.2585.

For trisilylamine, in addition to the minimal basis-calculation, another calculation was done for the 2-g~?metries where 3d STOs were augmented on thesilicon atom. The 3d STOs were expanded in termsof 1 GTO with Slater exponent being equal to 1.302.The results of these calculations are given in Table 2.

The (~H\l)3~ calculations agree with experimentalres~lts, mdlcat~ng a bent geometry at nitrogen atom,while the expenmentally planar (SiH3)sN is predictedonly by the calculation which includes d functions.The results obtained confirm the findings of Baybuttet a18•

The difference in the total energies between 0°and 5° geometries is +0.0007a.u. (- d) and -0.0014a.u.( +d) for trisilylamine. The silicon d orbitalparticipation i~ quite high, electron density being0.30 and 0.31 WIthnon-planar and planar geometries.In the absence of d functions on silicon, the highestMO in trisilylamine is essentially a bonding MO,between the 2p orbital of nitrogen and the 1s orbitalon hydrogens. Examination of this MO after in-clusion of dfunctions shows coefficients of d functionsof the same magnitude as that of the hydrogen Isfunctions, showing an appreciable participation ofd functions in the bonding. These evidences showthe importance of including 3d functions in thebasis f or the silicon atom and lend support to thequalitative interpretation of bonding postulatedbetween the d functions on the silicon and the pfunctions on nitrogen.

The stability of the SiHs radical - The existence ofSiH5 radical in preference to the decompositionproducts, SiH4 + H, is examined. Experimentalresults from flow measurements, photochemical'experiments'? invoke a SiHs radical for interpretation.

r:NOTES

TABLE 3 - TOTAL ENERGIES FOR THE SiH. + H~SiH6 SYSTEMIN a.u.

SiH.SiR. + H/::,.E

Without PFs-291.6449-291.6798+0.0339

With PFs-291.7014-291.7296+0.0282

A CNDO/2 study carried out on this system's also-predicted that the SiH5 radical was stable by 3.6eVrelative to SiH4 + H. Of all the configurationsconsidered, the lowest energy was found for the C3Vgeometry.

The SCF calculation reported here was carriedout primarily to study the importance of d functionson silicon, especially for SiH4 where the coordinationnumber of silicon is five. In addition the stabilityof SiH5 relative to SiH4 + H is also examined.

The geometry of SiH4 was taken from ref. 13.Two calculations were carried out. In the firstcalculation a contracted basis (12s, 9p/7s, 4p)was used for silicon. For hydrogen, 2 STOs ofexponents 1.2 and 0.6 were used, which were expandedusing Dunning's contraction'