Ab initio SCF study of the nature of bonding in Si2H2 and Si2H4

Volume 188, number 5,6

CHEMICAL PHYSICS LETTERS

17 January, 1992

Ab initio SCF study of the nature of bonding in Si2H 2 and Si2H4 A.B. S a n n i g r a h i a n d P . K . N a n d i Department of Chemistry, Indian Institute qf Technology, Kharagpur 721 302, India

Received 2 October 1991

Ab initio SCF calculations using several basis sets have been performed on a number of structural isomers of Si2H 2 and Si2H4. and their nature of bonding has been studied on the basis of bond index, valency and localized molecular orbitals (LMOs). Excepting the transition states, the stability of the SizH2 isomers is found to increase with decreasing molecular valency and increasing inert-pair effect in Si. In the case of Si2H4also, the most stable structure is associated with the least molecular valency. Analysis of the LMOs reveals that Si exhibits rather complicated hybridization.

1. Introduction Recent advances [ 1,2] in the synthesis of compounds containing multiply b o n d e d silicon have opened up a new field of organosilicon chemistry which was previously thought not to exist. Barring Si2, Si2H 4 and Si2H 2 p r o v i d e the simplest examples of molecules containing multiply b o n d e d Si. O f these two molecules, the former has been characterized [ 3 ] as an unstable species, while the latter is believed [4,5] to be one o f the i m p o r t a n t species that may appear in the m e c h a n i s m o f chemical-vapour deposition ofSi. A large n u m b e r o f a b initio theoretical studies dealing mainly with the singlet potential energy ( P E ) surfaces of Si2U 2 and Si2H4 have been reported [ 6 - 8 ] . F o r the Si2H 2 molecule, the most extensive and accurate calculations to date have been carried out by Colegrove and Schaefer [6]. They investigated the singlet PE surfaces o f eleven different structural isomers at the S C F and CISD (configuration-interaction with single and double excitations) levels using D Z P (double-zeta + polarization) and T Z 2 P (triple-zeta + double p o l a r i z a t i o n ) basis sets and observed that the global m i n i m u m of Si,H~ corresponds to a C2v-dibridged structure. S o m a s u n d r a m et al. [8] have p e r f o r m e d very accurate calculations o f the PE surfaces o f Si2H 4. F o r this molecule, silylsilylene and the trans-bent form o f disilene are predicted to be the most stable structures at the S C F and CI levels, respectively. Thus, Elsevier Science Publishers B.V.

the ground-state electronic structures o f Si2H2 and Si2H4 are drastically different from that o f C2H2 and C2H4. This structural difference suggests that a thorough study o f their nature of b o n d i n g is worthwhile. We have, therefore, carried out ab initio SCF calculations using several basis sets on a n u m b e r o f structural isomers of Si2H 2 and Si2H 4, and studied their nature of b o n d i n g on the basis o f two- and three-center b o n d indices, valencies and localized molecular orbitals ( L M O s ) . We have included seven (four m i n i m a and three transition states in the PE surface) structural isomers for Si2H2 and three for SiEH4, and c o m p a r e d their relative stability on the basis of molecular valency and average Si valency. As a supplement to this study, we have also e x a m i n e d the variation o f molecular valency with b o n d angle taking singlet Sill2 as the test case.

2. Method of calculation Atomic charges (qA), overlap populations (OPAB), two-center b o n d indices (BA~), three-center b o n d indices (BABe), atomic valencies ( l ( a ) and molecular valencies ( l ~ ) have been calculated using the following expressions [ 9,10 ] : A

qa----ZA-- ~ D . ~ ,

(1)

c/

575

Volume 188,number 5,6 A

B

OPAB = Z Z P.,, S~,~, a

A

CHEMICALPHYSICSLETTERS

tl

(2)

bent disilene (II) and silylsilylene (III), respectively.

B

B A B = E 2 Dah DI,. , 61 D A

B

(3)

(

B , B , = E E E D,,, D/,, D,,, ,

(4)

I[4= F_. B~,B,

(5)

B~A

(6) A

where ZA is the atomic number of atom A. The SCF density matrix D is defined by the relation D = S " t ' S ~-'' ,

(7)

where S is the AO overlap matrix and P = 2 C C ( C is the coefficient matrix of the doubly occupied MOs and C is its transpose). For the sake of comparison, two values, 0.0 and 0.5, have been used for n in eq. (7). These correspond to Mulliken population analysis ( M PA) and L6wdin population analysis (LPA) respectively. The LMOs are obtained from the canonical MOs of a molecule using Boys' method [ 11 ]. The populations of the valence AOs and the corresponding LMOs have been calculated using only the MPA scheme. The single-point calculations for bonding analysis of the Si2H2 isomers have been carried out at the SCF/TZ2P geometry [6] using 6-31G, 6-31G**, Si(13sgp/6s5p) and H(Ss/5s) [12] and Si(13s9pl d / 6 s 5 p l d ) and H ( 8 s l p / 5 s l p ) basis sets. These are referred to as A, B, C and D, respectively. In basis set D, C~d= 0.45 and ap = 1.1 [ 13 ]. For the Si2H4 isomers, the single-point calculations have been carried out at their 6-31G** optimized geometry [7] using basis sets A, B and E (this is basis set D without the hydrogen p orbitals). The geometrical parameters of the structural isomers of Si2H2 and Si2H4 considered herein are given in fig. 1. Here, the structures I-VII correspond to trans (I), planar dibridged (II), CI TS (III), bridged-I (IV), bridged-2 (V), disilavinylidene (VI) and the most stable C2v-dibridged (VII), respectively. For the Si2H4 molecule structures, I - I I I correspond to planar disilene (I), trans576

17 January 1992

3. Results and discussion Calculated values of two- and three-center bond indices and valencies of various structural isomers of SizH: and SigH4 are listed in table 1. In order to reduce the size of the table, atomic charges and overlap populations are not included. We shall, however, use these quantities for the discussion of bonding as and when necessary. Let us first confine our attention to the Si2H, isomers. As usual [ 14-16], the LPA bond indices and valencies are always considerably overestimated compared to the corresponding MPA values. The reason for this trend is well known. From the bond indices and valencies, it appears that structure I contains a SiSi triple bond; its bond index is less than 3.0 due to the slightly ionic character of the Sill bonds. The presence ofa SiSi triple bond is also consistent with the bond length. Basis sets A. B and C predict negative SiSi overlap population in structure II. The MPA Bs~s~values corresponding to basis sets B and C are also abnormally low. Thus, the bonding in structure II is accounted for satisfactorily only by basis set D which predicts a SiSi single bond and two three-center SiHSi bonds (note that the corresponding bond index is positive and appreciably high [ 10] ). It is due to the presence of the latter that Bsls. > 1.0 and Bs,n ~0.5 (note that in normal Sill bonds, the bond index is slightly less than 1.0). The bond indices and valencies in structure IIl indicate that it can be described by one normal Sill bond, one three-center SiHSi bond and one SiSi bond having a character intermediate between that of a single and a double bond. The relatively short Si-Si bond length also suggests multiple bonding. In structure IV, the SilH2 bond is considerably long indicating a very weak interaction which is supported by very small values of bond index and overlap population (~0.02). This isomer exhibits feeble threecentre bonding involving He and the silicons. The SiSi bond index and Si valencies indicate the presence of a SiSi double bond. The pattern of bonding in structure V does not differ much from that in structure IV. The former contains a three-center SiHSi bond, one SiSi double bond and one normal

Volume 188, number 5,6

CHEMICAL PHYSICS LETTERS

17 January. 1992

Hz .%%'/.-.~J 9 H ~,, .Si 2"083(S i /

.Y

Si

4--~Si

--H-~(c~

~H

.~%~'H2~1.619

s2.o9?_

S'l

2"085

59 1-t.69

s~22.189 s;1 112-6

v(cs~

IV(C~)~ 14,

I[i (%)~

u (O2h)4¢

.~4"%.s~s

,%0, ,

i%' 2.1o8 sh

VI(C2v)

\

H~ 2-189

2-129 Si--Si

,'~ H 115-3

H VII ( C2v )

I (O2h)

H H 4 ~ .,-112-7,2'/~--" Si2 z~,

oC

2-131

Si

~H H

II (C2h)

III(Cs)

Fig. 1. Equilibrium geometrical parameters (bond lengths in A and bond angles in deg) of various structural isomers of Si2H2 (l-gll) and Si2H4 (I-III). In the structures II and III of SizH4, a = 5.8°,#= 125.5° and 7= 54.2° (X is a point on the line of intersection formed by the planes HsSi3Hs and Si3Si2H~so that zk X-Si3Si2-H~=0 ° ). The structures with an asterisk indicate transition states (TS) in the PE surface. Sill bond. The b o n d i n g in structure VI can be easily explained in terms of two n o r m a l Sill bonds a n d one SiSi double bond. Structure VII represents the global m i n i m u m in the PE surface of Si2H2. It contains two equivalent three-center SiHSi bonds a n d one SiSi single bond. Basis set A fails to describe the nature of b o n d i n g in this structure; it predicts negative SiSi overlap population and an a b n o r m a l l y small value for the corresponding MPA b o n d index. The b o n d i n g in the Si2H4 isomers is rather

straightforward. Both the planar and the trans-bent forms of disilene exhibit a similar pattern of bonding. They are described by four normal Sill bonds and one SiSi double bond. The similarity is due to the fact that the rocking angle (c~) in the trans-bent form has been assumed to be 6 ° which is too small to distinguish between the planar and the trans-bent form on the basis of b o n d index and valency. The silylsilylene isomer contains four normal Sill bonds and one SiSi single bond. 577

Volume 188, number 5,6

CHEMICAL PHYSICS LETTERS

17 January 1992

Table 1 Calculated a) bond indices (BAB and BABC) and valencies ( I'A ) of various structural isomers ofSi2H, and SizH4 Molecule

Isomer

Calculated quantity b~

Basis set ~) A

B

M

SigH:

M

L

D

M

L

M

L

I

Bsin Bs,s~ l/u 1~s~

0.925 2.227 0.969 3.191

0.968 2.717 1.012 3.721

0.942 2.250 0.980 3.228

0.966 2.632 1.016 3.643

0.913 2.291 0.942 3.229

0.972 2.724 1.031 3.745

0.936 2.305 0.960 3.262

0.980 2.648 1.042 3.683

11

Bsin

0.443 1.530 -0.240 0.967 2.415

0.473 2.197 -0.081 0.999 3.144

0.467 0.501 -0.028 0.968 1.436

0.534 1.017 0.080 1.094 2.086

0.475 0.514 -0.050 1.025 1.464

0.588 0.993 -0.027 1.233 2.168

0.456 1.335 0.202 0.972 2.248

0.594 1.662 0.235 1.232 2.849

0.414 0.427 0.882 1.261 0.101 1.747 0.842 2.570 0.955

0.498 0.515 0.928 1.860 0.221 2.435 1.019 3.303 1.011

0.464 0.463 0.911 1.340 0.156 1.865 0.927 2.714 0.972

0.515 0.529 0.935 1.818 0.254 2.414 1.050 3.282 1.021

0.483 0.484 0.881 1.323 0.149 1.872 0.968 2.687 0.950

0.582 0.560 0.933 1.835 0.204 2.505 1.163 3.328 1.043

0.511 0.495 0.911 1.381 0.176 1.943 1.000 2.787 0.956

0.594 0.576 0.947 1.786 0.23(/ 2.472 1.188 3.3O9 1.056

0.176 0.722 0.954 1.742 0.092 1.955 0.898 3.418 0.991

0.237 0.769 0.943 2.313 0.166 2.615 1.010 4.025 1.011

0.184 0.757 0.950 1.854 0.113 2.076 0.941 3.561 0.987

0.246 0.777 0.946 2.281 0.185 2.592 1.029 4.004 1.015

0.195 0.745 0.882 1.892 0.098 2.095 0.933 3.518 0.884

0.284 0.771 0.918 2.334 0.157 2.690 1.078 4.023 1.013

0.198 0.740 0.910 1.991 0.115 2.220 (I.929 3.642 0.933

0.29/) 0.779 /).936 2.297 0.172 2.657 1.087 4.011 1.025

0.333 0.521 0.944 1.659 0.127 2.038 0.853 3.124 0.988

0.421 0.588 0.938 2.322 0.226 2.814 1.013 3.848 1.011

0.368 0.565 0.944 1.808 0.176 2.221 0.932 3.317 0.987

0.438 0.600 0.942 2.308 0.256 2.817 1.041 3.850 1.016

0.371 0.539 0.881 1.832 0.146 2.222 0.906 3.250 0.895

0.485 0.596 0.916 2.335 0.214 2.895 1.105 3.847 1.015

0.386 0.547 0.916 1.947 0.178 2.371 0.924 3.410 0.945

0.497 0.609 0.935 2.310 0.240 2.882 1.124 3.854 1.028

0.935 1.760 0.965 3.630 1.813

0.971 2.153 1.009 4.094 2.218

0.949 1.824 0.973 3.722 1.864

0.972 2.112 1.016 4.056 2.184

0.909 1.852 0.931 3.670 1.886

0.955 2.189 1.022 4.099 2.281

0.920 1.897 0.934 3.738 1.924

0.963 2.148 1.03/) 4.074 2.242

0.446 0.525 --0.126 0.892 1.417

0.504 1.493 --0.001 1.016 2.501

0.459 1.170 0.169 0.920 2.088

0.519 1.708 0.252 1.052 2.747

0.481 1.099 0.165 0.969 2.062

0.567 1.639 0.189 1.168 2.773

0.503 1.204 0.188 0.999 2.210

0.583 1.640 0.220 1.193 2.806

Bsisi Bs,ns, In I~, I11

BSi,H~ Bs~.,

BSi~H. Bs,si~ Bs,,,:si~ l's~,

1'H2 Is,~

I"H4 IV

Bsi,.., Bs~n, Bsi3n4 Bshs. Bsi~n2su l's~,

l'n2 Is,~ Vn4 V

Bs, m

BSi~H: Bsi3tl4 Bsilsi, Bs~,n,.s,3 Isi,

I'H2 Is.

VH4 VI

Bs,n

Bsi,si2 I"n l's~, ~s,_, VII

578

L

C

Bsiu Bsisi Bs,nsi VH Is,

Volume 188, number 5,6

17 January 1992

CHEMICAL PHYSICS LETTERS

Table [ Continued Molecule

Isomer

Calculated quantity b~

Basis sel c) A

Si~H~

B

I)

M

L

M

L

M

L

I

Bsin Bsisi l"n l'si

0.928 1.897 0.960 3.780

0.969 2.072 1.009 4.052

0.952 1.906 0.973 3.830

0.97 I 2.037 1.015 4.031

0.943 1.894 0.946 3.781

0.969 2.022 1.027 4.02 I

II

Bsin Bs,s. Vn I~,

0.928 1.891 0.960 3.775

0.969 2.069 1.009 4.049

0.952 1.901 0.973 3.824

0.971 2.033 1.015 4.028

0.942 1.889 0.946 3.776

0.969 2.019 1.027 4.018

III

Bsum Bs~sn4 Bsisn5 Bsisi IN, IS~2 IS,~ Vn4 l"n,

0.874 0.911 0.914 0.880 0.895 1.800 3.632 0.934 0.942

0.965 0.965 0.969 1.128 1.000 2.155 4.053 1.003 1.004

0.917 0.938 0.939 0.934 0.933 1.882 3.761 0.949 0.955

0.978 0.971 0.973 1.114 1.014 2.156 4.057 1.012 1.012

0.919 0.923 0.918 0.955 0.917 1.889 3.713 0.913 0.913

1.005 0.961 I).959 1.120 1.048 2.207 4.0311 1.02 I 1.017

~'~M and L stand, respectively,for MPA and LPA values. t,) See fig. I for the numbering of atoms. '~ For Si2H4,the values under D refer to basis set E.

As can be seen from the AE values (basis sets B and D) given in table 2, the stability of the various structural isomers of Si2H2 increases in the sequence I < I I * < I I I * < I V * < V < V I < V I I . For Si2H4, the stability increases in the order I < II < I I I . In table 2, the stability of these isomers is compared on the basis of molecular valency. It is observed that, barring the transition states, the stability of the Si2H2 isomers increases with decreasing VM (LPA values). A similar trend is followed by the MPA values also, but only for basis set D. The average Si valencies (not tabulated) follow a parallel trend. In the most stable structure, silicon tends to be divalent due to the inert-pair effect. Although not shown here, the stability of Si2H~ isomers generally increases with increasing average positive charge on Si. In the Si2H4 molecule also, the stability of its isomers increases with decreasing VM and average Si valency. The above finding, that the stability of a series of conformers decreases with their increasing VM, is at variance with the observations of Jug and co-work-

ers [ 17, 18 ]. Siddarth and G o p i n a t h a n [ 19 ] postulated that [M reaches a m a x i m u m at or near the equilibrium bond angle of a molecule. Although numerous exceptions to this postulate were found [9,15 ], we have verified it again taking singlet SiHz as the test case. Using STO-3G and 6-31G** basis sets, we calculated VM of Sill2 for various bond angles (keeping r ( S i H ) fixed at 1.512 ~, [ 2 0 ] ) , and observed that the VM versus 0 curves show a minim u m instead of a m a x i m u m . In the case of the STO3G basis set, the m i n i m u m occurs almost at the experimental bond angle (92.1 ° ). However, the higher basis set predicts a very shallow m i n i m u m in the range 0 = 1 10-120 °. Therefore, we can conclude that the previously observed trend in the variation of VM with the stability of conformers and with bond angle breaks down when the inert-pair effect is operative. One of the limitations of the study of b o n d i n g on the basis of bond indices and valencies is that these quantities do not provide direct information on the nature and n u m b e r of bonds needed to describe the 579

Volume 188, number 5,6

17January1992

CHEMICAL PHYSICS LETTERS

Table 2 Calculated relative energies (zXE, kcal mol-t ) and molecular valencies ( ~M ) ofSizH 2 and Si2H4 isomers Molecule

Si2H:

Si2H4

Isomer

AE "~

l/r, b)

basis set c~

basis set "~

B

D

A

B

C

D

1

24.1

25.0

11

-

20.8

Ill

17.7

18.2

IV

13.8

14.7

V

13.1

13.8

VI

3.8

5.0

VII

0.0

0.0

1.7

2.2

I1

1.7

2.2

III

0.0

0.0

4.208 4.659 2.404 3.180 3.239 3.883 3.783 4.320 3.728 4.362 3.765 4.136 3.008 3.799 5.775 6.062 5.769 6.058 4.717 5.131

4.171 4.776 2.490 3.402 3.239 4.019 3.715 4.402 3.637 4.431 3.709 4.212 3.030 3.941

!

4.159 4.734 3.382 4.143 3.057 3.884 3.631 4.330 3.501 4.343 3.687 4.165 2.309 3.517 5.701 6.070 5.695 6.066 4.573 5.109

4.22 l 4.724 3.220 4.081 3.343 4.013 3.862 4.390 3.826 4.444 3.764 4.189 3.209 3.999 5.673 6.075 5.667 6.072 4.629 5.170

,,7 The SCF energies of isomer VII for basis sets B and D are -578.89131 and -578.93177 hartree, respectively. The corresponding values for isomer III of Si2H4 are - 580.08550 and - 580.11943 hartree (basis set E), respectively. u~ Thc two successive values stand for MPA and LPA, respectively. c~ For SizH4 isomers, basis set E is used instead of basis set D.

electronic structure o f a molecule (especially molecules with highly polar b o n d s ) . F o r example, a BAB value o f 1.90 may c o r r e s p o n d to a slightly polar double b o n d or a highly polar triple bond. We have, therefore, carried out L M O studies in o r d e r to obtain a d d i t i o n a l i n f o r m a t i o n about the nature o f b o n d i n g in the Si2H 2 and S i 2 H 4 isomers. In table 3, the valence L M O p o p u l a t i o n s ( M P A ) of the Si2H 2 isomers are s u m m a r i z e d only for basis set D. The corresponding data for the Si2H4 molecule are o m i t t e d since they do not p r o v i d e any additional i n f o r m a t i o n other than what has been obtained previously. As can be seen from the population in table 3, the L M O s are well localized in almost all cases. Structure I contains two S i l l and three SiSi bonds. There are one SiSi a n d two SiHSi b o n d s and two LPOs (lone-pair o r b i t a l s ) on Si in structure II. Structure I I I is described by one SiSi, one S i l l and one SiHSi b o n d s and two Si LPOs. Both structures 580

IV and V contain two SiSi, one S i l l and one SiHSi b o n d s and one Si LPO. As already mentioned, the SiHSi b o n d in IV is very weak; it can be regarded as the Si3H2 b o n d slightly delocalized over Si~. There are two SiSi and two S i l l b o n d s and one Si LPO in structure VI. Structure VII contains one SiSi and two SiHSi bonds and one LPO on each Si. Thus, the n u m b e r o f b o n d s as deduced from b o n d indices and valencies and from L M O s is almost identical in the majority of the cases. Let us now examine the nature o f the LMOs especially with regard to the h y b r i d i z a t i o n of Si (the AO populations are not t a b u l a t e d ) . The Si k P O s in various structures o f Si2H2 are not pure s orbitals; there is a significant contribution from the p , orbital (the molecules are taken in the xy plane with the SiSi b o n d coinciding with the x axis) whose population varies from 0.3 to 0.6. However, in structure III, the LPO o n Si 3 consists o f s, p~ and p- orbitals with pop-

Volume 188, number 5,6

17 January 1992

CHEMICAL PHYSICS LETTERS

Table 3 Calculated valence LMO populations (MPA) a) of Si2H2 (basis set D) Isomer

LMO type u)

!

Si-H bond (2) Si-Si bond (3)

I1

Si-Si bond Si-H-Si bond (2) Si LPO (2)

III

Atomic populations Si

H

0.917 1.005

1.088 -0.005 Si

Si

H

-0.006 1.005

0.000 - 0.005

H

Si

H

0.995 0.431 2.019

0.005 1.177 -0.007

0.995 0.431 -0.006

0.005 -0.039 -0.007

Si~ 1.176 0.023 0.392 1.987 0.146

H2 -0.062 -0.010 1.234 0.028 0.024

Si3 0.924 0.840 0.383 -0.022 1.829

H4

Si-Si bond Si-H bond Si-H-Si bond Si~ LPO Si3 LPO Si-Si bond (2) Si-H bond Si-H-Si bond Si~ LPO

Si~ 0.848 0.004 0.153 1.992

H2 -0.030 - 0.008 1.218 0.010

Si3 1.193 0.937 0.648 - 0.006

H4

IV

Si-Si bond (2) Si-H bond Si-H-Si bond Si~ LPO

Si~ 0.740 0.006 0.334 2.003

H2 -0.035 - 0.006 1.229 0.002

Si3 1.298 0.937 0.460 -0.009

H4

V

VI

Si-Si bond (2) Si-H bond (2) Si2 LPO

H -0.016 1.139 0.003

Si~ 1.060 0.877 0.005

Si2 0.972 -0.006 1.987

H -0.016 -0.010 0.003

Si Si-Si bond Si-H-Si bond Si LPO (2)

H -0.061 1.255 0.026

Si

VII

H -0.061 -0.028 0,026

1.061 0.386 1.962

1.061 0.386 -0.013

-0.038 1.147 - 0.009 0.007 0.001 - 0.008 1.067 -0.019 0.004 - 0.003 1.062 -0.022 0.004

"~ See fig. 1 for the numbering of atoms. b) The numbers in parentheses indicate the number of equivalent LMOs.

ulations 1.04, 0.28 and 0.53, respectively. T h e Si hybrids i n v o l v e d in t h r e e - c e n t e r b o n d i n g are o f variable c o m p o s i t i o n . In s t r u c t u r e II, the h y b r i d consists o r s ( 0 . 0 7 ) , Px ( 0 . 1 9 ) a n d p,. ( 0 . 1 3 ) orbitals w h e r e the figures in p a r e n t h e s e s i n d i c a t e A O p o p u l a t i o n s . In s t r u c t u r e III, Px ( 0 . 0 6 ) a n d py ( 0 . 2 8 ) o f Si~ a n d s ( 0 . 0 3 ) , Px ( 0 . 0 5 ) a n d py ( 0 . 2 5 ) o f Si3 are i n v o l v e d in b o n d i n g . T h e P v ( 0 . 1 3 ) o f Sil a n d s ( 0 . 1 3 ) a n d Pv ( 0 . 4 7 ) o f Si3 are engaged in b o n d i n g in IV. In V, the hybrids on b o t h Si a t o m s c o m p r i s e s (0.02, 0.05 ), p., (0.06, 0 . 0 2 ) a n d py (0.22, 0 . 3 5 ) orbitals. T h e t h r e e - c e n t e r b o n d s in s t r u c t u r e V I I m a k e use o f Si

h y b r i d s c o n s i s t i n g o f s ( 0 . 0 2 ) , p~ ( 0 . 0 6 ) , Pv (0.1 1 ) a n d p: ( 0 . 1 5 ) orbitals. T h e m u l t i p l e SiSi b o n d s are always o f the ~ type f o r m e d by h y b r i d s with v a r y i n g p r o p o r t i o n o f s a n d p orbitals. T h e c o n t r i b u t i o n o f the p,: orbitals in these h y b r i d s is negligible in structures IV, V and VI. S t r u c t u r e s II, I I I and V I I c o n t a i n a SiSi single b o n d w h i c h is o f p u r e Pz-P~ n-type in II. In structure III, the p e r t i n e n t h y b r i d s consist o f s, Px a n d py orbitals, while in s t r u c t u r e V I I the h y b r i d s are a p p r o x i m a t e l y o f s p 2 type (s ( 0 . 3 ) , Px ( 0 . 3 ) , p~ ( 0 . 4 ) ) . T h e h y b r i d s on Si i n v o l v e d in each o f the two 581

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equivalent Si-Si bonds in the disilene isomers (I and It) of Si2H4 are o f s p 3 type (s (0.2), p, (0.2) and p: (0.4)). In silylsilylene ( l I I ) , the SiSi single bond is formed by the overlap of hybrids on both Si atoms which comprise s (0.20, 0.40) and p: (0.69, 0.69) orbitals. The hybrid LPO on Si2 in Ill consists of s (1.37), p, (0.35) and p: (0.33) orbitals.

4. Concluding remarks The results of the present investigation indicate that the nature of bonding in the SizH2 isomers is quite complicated, especially with regard to the type of hybridization exhibited by Si. Despite the fact that there is no ideal environment in Si for hybridization due to the large difference in the spatial extension of its valence 3s and 3p orbitals [21 ], hybridization does occur in silicon compounds, but in an unbalanced manner unless equivalent hybridization is forced by symmetry. The description [6] that in the most stable structure of Si2H2, the bonding occurs through mutually perpendicular p orbitals, and the LPO on Si comprises mainly 3s orbital, is only an oversimplified picture. The populations of the p orbitals vary from 0.3 to 0.6 in the LPOs of various structures. A hybridized LPO reduces the lone-pair/ bond-pair repulsion and, thus, provides a better description of bonding. According to 6-31G** calculations, Si in Si2H4 (disilene) is approximately sp 2 (S1.18 p 2 4 8 ) hybridized. In SiH2, also s p 3 (S 019 pOS8) hybrids are involved in bonding. These hybrids are equivalent but not in the same sense as that in C H 4. In S i l l 4, four equivalent sp 2 hybrids are bonded to the hydrogenic ls orbitals. One of the reasons [21 ] for anomalous hybridization in Si is its positively charged environment (the MPA values ofqsi in Sill2, Sill4, Si2H4 and S i a H 2 a r e +0.376, +0.666, +0.216 and + 0.212, respectively, according to our 6-31G** calculations). The Si d orbitals do not play any significant role in bonding. They do not contribute practically to the LPOs and three-center bonds. The d orbitals participate to some extent only in Sill bonding. Another important finding of the present study is that some of the trends [22-24] followed by VM are not followed when the role of the inert-pair 582

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effect is prominent (as in SieH2 and Sill2).

Acknowledgement PKN is thankful to the CSIR, New Delhi for the award of a Junior Research Fellowship. We would also like to thank Mr. Lingaraj Behera for his help in computation. The time and service made available by the Computer Center, l i t Kharagpur were essential to this study, and are gratefully acknowledged.

References [ 1 ] M. Michalczyk, R. West and J. Michl, Organometallics 4 ( 1985 ) 826, and references therein. [2] H. Sakurai, Organosilicon and bioorganosilicon chemistry (Wiley, New York, 1985 ). [ 3 ] R. West, M.J. Fink and J. Michl, Science 214 ( 1981 ) 1343. [4] M.E. Coltin, R.J. Kee and J.A. Miller, J. Electrochem. Soc. 131 (1984) 425. [ 5]J. Steinwandel and J. Hoeschele, Chem. Phys. Letters 116 (1985) 25. [6] B.T. Colegrove and H.F. Schaefer 111, J. Phys. Chem. 94 (1990) 5593, and references therein. [7] K. Krogh-Jesperson, J. Phys. Chem. 86 (1982) 1493. [8] K. Somasundram, R.D. Amos and N.C. Handy, Theoret. Chim. Acta 70 (1986) 393, and references therein. [9] T. Kar, L. Behera and A.B. Sannigrahi, J. Mol. Struct. T H E O C H E M 209 (1990) 45. [ 10 ] A.B. Sannigrahi and T. Kar, Chem. Phys. Letters 173 ( 1990 ) 569. [ 11 ] S.F. Boys, in: Q u a n t u m theory' of atoms, molecules and the solid state, ed. P.-O. L/3wdin (Academic Press, New York. 1966) p. 253. [12]R. Poirier, R. Kari and I.G. Csizmadia, Handbook of Gaussian basis sets (Elsevier, Amsterdam, 1985 ) pp. 161, 381. [ 13] W.J. Hehre, L. Radom, P. yon R. Schleyer and J.A. Pople, Ab initio molecular orbital theory (Wiley, New York, 1986 ) p. 82. [ 14] T. Kar and A.B. Sannigrahi, J. Mol. Struct. T H E O C H E M 165 ( 1 9 8 8 ) 4 7 . [ 15 ] T. Kar, A.B. Sannigrahi and L. Behera, Chem. Phys. Letters 163 (1989) 157. [16] L. Behera, T. Kar and A.B. Sannigrahi, J. Mol. Struct. T H E O C H E M 209 (1990) 111. [ 17 ] K. Jug and S. Buss, J. Comput. Chem. 6 ( 1985 ) 507. [ 1 8 ] K . Jug and M.S. Gopinatban, Theoret. Claim. Acta 68 (1985) 343. [ 19] P. Siddarth and M.S. Gopinathan, J. Am. Chem. Soc. 110 (1988) 96.

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[20] P.M. Agrawal, D.L. Thompson and L.M. Raft, J. Chem. Phys. 88 ( 1988 ) 5948. [21 ] W. Kutzelnigg, Angew. Chem. Int. Ed. Engl. 23 (1984) 272. [22] K. Jug, in: Molecular organization and engineering, Vol. 3, ed. J. Maruani (Reidel, Dordrecht, 1988) p. 149.

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[23] K. Jug and M.S. Gopinathan , in: Theoretical models of chemical bonding, Part 2, ed. Z.B. Makzic (Springer, Berlin, 1990) p. 77. [ 24] A.B. Sannigrahi, Advan. Quantum Chem., in prcss.

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