Ab initio investigation of the nature of bonding in LiX dimers with first row substituents

Journal of Molecular Structure (Theo&em), 189 (1988) 149-160 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

149

AB INITIO INVESTIGATION OF THE NATURE OF BONDING IN LiX DIMERS WITH FIRST ROW SUBSTITUENTS

A.B. SANNIGRAHI

and TAPAS KAR

Department of Chemistry, Indian Institute of Technology, Khuragpur-721302

(India)

(Received 21 September 1987)

ABSTRACT Local&d molecular orbitals (LMO ) , atomic charges, bond overlap populations, bond orders and valencies of LiX (X=H, BeH, BHx, CH3, NH2, OH and F) and their dimers have been calculated using 4-31G, 6-31G* and a mixed (4-31G/6-31G*/6-31G**) basis set. The quantities related to charge distribution have been calculated using Mulliken and Liiwdin schemes of population analysis. Three-centre LiALi bonding is found in (LiH)2, (LiBeH),, (LiBH,)* and (LiCH3)2. A completely charge-separated electrostatic model appears to be more satisfactory for the description of bonding in the remaining dimers. The LMO picture of bonding is supported by changes in bond orders and valencies occurring upon dimerisation. The Lawdin scheme of population analysis appears to be inadequate for the description of charge distribution and related properties in predominantly ionic molecules.

INTRODUCTION

The dimers, (LiX),, of lithium compounds with first-row substituents (X= H, BeH, BH2, CH3, NH2, OH and F) have been the subject of numerous ab initio theoretical investigations [l-24]. While most of these studies were mainly concerned with the energetics and electronic structure of the dimers vis-a-vis that of the monomers, some attempts [8,18,20,21,24] have been made to understand the origin of their exceptional stability and the nature of their bonding. A number of ab initio calculations [25-341 dealing only with the monomers have also been reported. Exceptionally high dimerisation energies of LiX molecules are usually attributed [ 1,8,18,20,28,35] to very strong electrostatic interactions between the monomer dipoles supplemented in part by three-centre LiALi bonding. The presence of such bonding has, however, not been directly verified by means of ab initio localised molecular orbital (LMO ) calculations. In the present investigation the nature of bonding of LiX and ( LiX)2 molecules with first-row substituents has been studied on the basis of their LMO’s, atomic charges, overlap populations, bond orders and valencies. The latter two quantities and atomic charges have been calculated using the definitions based on Mulliken [ 361 and Lijwdin [ 371 SCF density matrices.

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150 METHOD OF CALCULATION

The occupied canonical MO’s are transformed into a set of LMO’s using Boys’ criterion [38] whereby the sum of the squares of the distances of the orbital centroids from the origin of some arbitrarily defined coordinate system in a molecule, is maximised. According to the Mulliken population analysis (MPA ), the atomic charge (q2 ) , bond overlap population (OP,,), bond order (BAB) and valency (VA) of a closed-shell molecule are defined [36] respectively as follows qi

=z* -; (PS),, a

OP,, =

B AB

=i% a

VA=

$;

Pabsba

b

(ps),b (psha

(2) (3)

C BAB

B#A

Here, ZA is the atomic number of atom A, P = 2CC (C is the coefficient matrix corresponding to the occupied MO’s) and S is the overlap matrix. The overlap population is zero in the Lijwdin population analysis (LPA). Now the expression for qi and B _&B are obtained [37] by replacing the PS matrix by the S” ‘PS1” matrix in eqns. (1) and (3) respectively, and VA is defined as in eqn. (4) where the modified expression is used for BAB. Three basis sets, namely 4-31G, 6-31G* and a mixed one, have been used. For LiH, LiBeH and their dimers the mixed basis set contains 4-31G functions on Li and Be and 6-31G** functions on H, while for the rest it consists of 43lG functions on Li and H and 6-31G* functions on B, C, N, 0 and F. The choice of such an unconventional basis set stems from the consideration [ 321 that in LiH and LiBeH, H is negatively charged and, Li and Be are positively charged whereas in the other LiX molecules Li’ and H are positively charged and the heavy atoms are negatively charged. Thus, the mixed basis set contains d functions only on those atoms which are more electronegative than H. The results of this basis set when compared with those obtained from the 6-31G* calculations will enable us to assess the role of Li d orbitals in bonding. All calculations were performed at the 4-31G fully optimised geometries of the dimers and five monomers, LiX (X#BeH, BH,) [ 14,16,30]. The 4-31G geometries of LiBeH and LiBHz not being at our disposal, STO-3G geometries [ 71 have been used for them. This seems to be rather inconsistent, however, our experience [ 391 indicates that quantities related to charge distribution are insensitive to the variation of geometry within a small range. For the dimer of

151

LiNHz and LiBHB only the more stable conformation (perpendicular and planar form respectively) has been considered. RESULTS AND DISCUSSION

Dipole moment and energetics of the monomers

Since we intend to study the nature of bonding of LiX dimers on the basis of LMO’s, atomic charges, valencies etc., none of which corresponds to an observable within the confines of quantum mechanics, the quality of the three basis sets has been assessed by calculating the dipole moments of the monomers. The calculated values of dipole moments are given in Table 1 which includes also the values [ 341 obtained using the 6-31+ G* basis set and the available experimental data. First of all, it is noted that dipole moments corresponding to 6-31G* and the mixed basis set are virtually identical. With the exception of LiH, the 6-31+ G* dipole moments are overestimated compared to the present calculated values. The experimental dipole moment [40] of LiCH3, as deduced from matrix isolation studies, is 6 D. Using a basis set of near Hartree-Fock quality and invoking large CI, Graham et al. [ 281 found a value of 5.4 D while the most elaborate calculations made to date on LiCH, [ 331, yield a value of 5.7 D. Thus, the present calculated values corresponding to the mixed or 6-31G* basis set are in very good agreement with the available experimental or accurate ab initio values. All the basis sets predict the same order of dipole moments, namely, LiF > LiH > LiCH3 > LiBH2 > LiBeH > LiNH2 > LiOH. The close agreement of the results corresponding to the mixed and 6-31G* basis sets indicates that Li d orbitals do not contribute to any TABLE 1 Calculated and experimental dipole momenta (D) of LiX molecules System

LiH LiBeH LiBHz LiCHB LiNH, LiOH LiF

Calculated”

Expt.

I

II

III

6-31+G*b

5.97 4.86 5.15 5.52 4.37 4.10 6.43

5.95 4.84 5.19 5.66 4.56 4.25 6.22

5.99 4.84 5.20 5.67 4.58 4.25 6.20

5.99 5.30 5.75 5.98 4.99 4.67 6.56

5.88’

6.00d

6.32”

“Entries under I, II and III refer to the present calculated values using 4-31G, mixed and 6-31G* basis sets respectively. bRef. 34. ‘Ref. 2. dRef. 40. ‘Ref. 1.

152

significant extent to the SCF dipole moments of LiX molecules. Because of their symmetric structure, all the dimers are predicted to have zero dipole moment. In Table 2 are given the SCF energies of the monomers for the three basis sets. Comparing the dE, and dEz values, it is found that most of the energylowering results are due to the addition of d orbitals on atoms which are more electronegative than H. The dE, values show that Li d orbitals contribute only marginally to the energy lowering. The dimerisation energies of LiX, calculated from the relation, dE=E[ (LiX),] -2E(LiX) are given in Table 3. In these calculations, corrections due to zero point energy and basis set superposition error are not taken into account. As can be seen, the dE values are quite insensitive to the basis sets: similar observations were made by several investigators [l&22,24]. TABLE 2 Calculated total energies

(E, hartree)

of the LiX molecules

System

E (4-31G)

AEIa

AEp”

LiF LiOH LiNHz LiCH, LiBH, LiBeH LiH

- 106.8241 - 82.8170 - 62.9705 - 46.9600 -33.1680 - 22.5952 - 7.9774

-0.1016 -0.0810 - 0.0674 -0.0521 - 0.0365 - 0.0018 - 0.0007

-0.0076 - 0.0045 -0.0034 -0.0031 - 0.0042 -0.0122b - 0.0034s

*AE,=E (mixed basis set)-E (6-31G*) -E (4-31G).

(4-31G) and AE,=E

(6-31G*)-E

(mixed basis set). bAE2=E

energies (kcal mol-‘)

of LiX molecules

TABLE 3 Absolute values of dimerisation System

LiH LiBeH LiBHz LiCH, LiNHP LiOH LiF

Expt. or theor. est.

Calculated 4-31G

Mixed

6-31G*

45.0 20.9 36.4 42.6 73.4 74.1 76.1

45.0 20.7 36.3 42.3 71.4 73.2 73.0

46.1 21.5 37.1 42.5 71.0 72.6 71.3

“Ref. 22. bRef. 24. “Ref. 20. dRef. 43.

46.2”

44.3s 62.5” 62.4 f 12d 61.4f8d

153

Localised molecular orbitals

In order to save space, the lengthy tables of LMO’s are omitted and only the salient features of bonding deduced from these LMO’s are discussed here. Almost identical results were obtained for LMO’s, atomic charges etc. using 431G and the mixed basis set. We shall, therefore, henceforth compare the results for two standard basis sets (4-31G and 6-31G*). The LMO’s corresponding to the inner shells are perfectly localised and not important from the viewpoint of bonding. The monomers, LiH, LiBeH, LiBHz and LiCH3 do not contain any valence lone pair orbitals (LPO ) and their LMO description is in conformity with the classical valence theory. In LiH, LiBeH, LiBH2 and LiCH,, the LiA (A= H, Be, B and C) bonds are polar covalent and Li is the positive end of the dipole. However, in LiBeH, Be is the positive end of both LiBe and BeH dipoles. The LMO description of LiNH2, LiOH and LiF differs from that of the rest due to the presence of valence LPO’s. Now the LiA (A = N, 0 and F ) bonds are so ionic (the ionicity increases roughly from 80% to 90% while going from LiNH, to LiF) that the pertinent LMO may be identified as an LPO centred on A. If such an identification is made, then the LMO’s of LiNH*, LiOH and LiF can be described by two NH bonds and two LPO’s on N, one OH bond and three LPO’s on 0 and four LPO’s on F respectively. The present LMO description of LiNH2 tallies with that of Hinchliffe [ 271. While discussing the nature of the NLi bond in LiNH2, Wurthwein et al. [ 311 have remarked that due to N+Li back donation, this bond has considerable n character. This, however, does not tally with the results of the present calculations (or those of Hinchliffe [ 271) , or the observation made by Armstrong et al. [ 211 that the planarity of LiNHz can be accounted for without including the Li 2p, orbitals in the basis set. Thus, we are led to conclude that the remark made by Wurthwein et al. is not tenable and the phenomenon of N-+Li back donation may be an artifact of the 3-21G basis set employed by them. In this context we would like to mention that STO-3G and CND0/2 calculations [ 411 also predict multiple LiN bonding in LiNH2 and LiF. The LMO’s of (LiX)2 (X = H, BeH, BH, and CH3) consist of symmetric three-centre two-electron LiALi (A = H, Be, B and C ) bonds and an appropriate number of AH bonds. The 4-31G (Mulliken) populations of Li are 0.31, 0.45,0.31 and0.21 in (LiH)2, (LiBeH),, (LiBH2)z and (LiCH3)z respectively. Slightly higher Li populations are predicted by the 6-31G* calculations due to the inclusion of Li d orbitals in the basis set. Neither the 4-31G nor the mixed basis set predicts any three-centre bonding in (LiNH2)2, (LiOH), and (LiF)2. When d orbitals on Li are included as has been done in the 6-31G* basis set, very feeble three-centre bonding (Li population is about 0.04) is predicted in (LiOH), and ( LiF)2 but not in (LiNH2)2. An LMO with such a low population

154

on Li should be better regarded as LPO centred on A. Thus, according to the present LMO studies, the fully charge-separated electrostatic model appears to be more appropriate for the description of bonding in LiX (X = NH2, OH and F) molecules and their dimers. Overlap populations, bond orders, atomic charges and valencies

Atomic charges, overlap populations, bond orders and valencies of the monomers are given in Table 4. Let us first confine our attention to atomic charges. It is well known [ 29,34,39,42] that both Mulliken and Lowdin atomic charges are highly sensitive to basis sets. In this respect the natural population analysis (NPA) of Reed et al. [32], although it has a marked tendency [ 331 to overestimate charge separation in ionic molecues, is more satisfactory. For the 63lG* basis set, the natural positive charge on Li in the monomers are 0.73 (LiH),0.19 (LiBeH),0.57 (LiBH2),0.80 (LiCHB),0.90 (LiNH2),0.94 (LiOH) and 0.93 (LiF). The corresponding 4-31G charges are slightly lower. Thus, both Mulliken and Lijwdin atomic charges, especially the latter ones, are considerably underestimated. Further, not only the magnitude but also the sign of charge on Li and Be in LiBeH and that on Li and B in LiBHz is highly basis set dependent according to both MPA and LPA. That MPA is not satisfactory for ionic molecules is well known [ 29,301: what emerges from this study is that LPA is still worse. The Lijwdin bond orders, especially for LiA bonds and 6-31G* basis set, are overwhelmingly overestimated compared to the corresponding Mulliken values. The discrepancy between the two sets of values is less pronounced in the case of essentially covalent bonds like LiBe, BeH, LiB, BH and CH. The Mulliken bond orders bear a linear relationship (the plot is not shown here) with the overlap population. The LiA overlap population varies in the order LiBe > LiB > LiH > LiC > LiN > LiO > LiF. Interestingly, the calculated dimerisation energies (Table 3 ) of these molecules also follow the same order. The qualitative trend in the electronegativities of A is reflected from the OP values. However, as pointed out by Streitwieser et al. [ 261, the calculated OP values of the LiA bonds are rather high and thus they cannot be used as a reliable criterion to assess the bond polarity. The variation of valencies in the series, follows a trend opposite to that of atomic charges. Wherever atomic charges are underestimated, the valencies are overestimated. In general, the Liiwdin valencies are abnormally high and do not reflect at all the ionic character of the molecules. The overlap populations, bond orders, atomic charges and valencies of the dimers are given in Table 5. Negative overlap populations for the LiLi interaction are found in ( LiNH2)2, ( LiOH )2 and (LiF&+ This tallies with the observation of Armstrong et al. [21] made in connection with (LiNH2)2,

Bond

LiH LiBe BeH

LiB BH

LiC CH

LiN NH

LiO OH

LiF

System

LiH LiBeH

LiBH,

LiCHB

LiNHz

LiOH

LiF

Overlap populations

TABLE 4

0.42 0.39

0.36 0.37

0.33 0.32

0.25 0.28

0.19

0.39 0.38

0.33 0.37

0.29 0.31

0.22 0.27

0.16

0.54

0.62 0.81

0.75 0.88

0.81 0.94

0.98 0.95

0.82

1.00 0.92

1.04 0.94

0.91 0.95

1.03 0.97

0.58

0.69 0.78

0.83 0.86

0.86 0.94

1.00 0.97

0.97 1.00 0.98

0.40 0.42 0.41

0.38 0.42 0.37 0.98 1.02 0.96

MPA 0.93 1.00 0.89

MPA

4-31G

6-31G*

4-31G LPA

6-31G*

B AB

OP

1.21

1.40 0.89

1.22 0.90

0.98 0.93

1.04 0.96

1.00 1.04 0.98

LPA Li Li Be H Li B H Li c H Li N H Li 0 H Li

Atom

+0.26 -0.08 + 0.39 -0.31 +0.21 +0.05 -0.13 + 0.46 -0.76 +0.10 +0.58 - 1.10 +0.26 +0.66 - 1.03 +0.37 +0.72

MPA

4-31G

qi

+0.15 -0.11 +0.24 -0.18 +0.11 -0.05 - 0.03 +0.33 - 0.60 +0.09 +0.39 -0.77 +0.19 +0.48 -0.75 +0.27 +0.58

LPA +0.18 -0.13 +0.25 -0.12 +0.17 -0.01 - 0.08 +0.42 -0.79 +0.12 +0.53 -1.15 +0.31 +0.62 - 1.04 +0.41 +0.69

MPA

6-31G*

(OP),bond orders (BAB ) , atomic charges (9%) and valencies ( VA) of LiX molecules

-0.06 +o.os -0.03 +0.11 -0.15 +0.02 + 0.27 -0.64 +0.12 f0.21 -0.67 +0.23 +0.23 -0.54 +0.31 + 0.35

+0.09

LPA 0.93 1.00 1.89 0.89 0.98 2.88 0.94 0.84 3.64 0.94 0.76 2.50 0.89 0.63 1.44 0.83 0.54

MPA

4-31G

VA

1.06 1.98 1.00 1.12 2.96 1.02 1.05 3.77 1.01 1.10 2.92 0.98 1.02 1.92 0.95 0.82

0.98

LPA

0.97 0.99 1.98 0.97 1.01 2.94 0.96 0.88 3.68 0.93 0.84 2.54 0.86 0.70 1.47 0.79 0.58

MPA

6-31G*

1.00 1.07 2.01 1.01 1.14 2.97 1.02 1.17 3.77 1.00 1.32 3.03 0.96 1.43 2.29 0.92 1.21

LPA

LiH LiLi HH LiBe BeH LiLi BeBe LiB BH LiLi BB LiC CH CH’ LiLi cc LiN NH LiLi NN LiO OH LiLi 00 LiF LiLi FF

WW,

0.50 0.58 0.00 0.51 0.98 0.70 0.01 0.55 0.92 0.46 0.01 0.58 0.90 0.86 0.33 0.10 0.76 0.88 0.29 0.01 0.80 0.86 0.24 0.00 0.73 0.19 0.02

0.47 0.29 0.00 0.50 0.97 0.48 0.00 0.49 0.94 0.21 0.00 0.42 0.93 0.91 0.10 0.00 0.40 0.84 0.01 0.09 0.32 0.77 0.03 0.00 0.29 0.03 0.00

0.20 0.13 -0.01 0.22 0.41 0.20 0.00 0.22 0.37 0.09 -0.01 0.19 0.38 0.35 0.06 -0.01 0.17 0.31 -1.10 -0.01 0.13 0.27 -0.44 -0.01 0.11 -0.14 -0.01

0.18 0.09 -0.01 0.21 0.37 0.18 0.00 0.20 0.36 0.07 -0.01 0.16 0.36 0.35 0.04 -0.01 0.15 0.31 -0.78 -0.01 0.12 0.26 -0.39 -0.01 0.09 -0.27 -0.01 0.49 0.43 0.01 0.50 0.96 0.68 0.01 0.53 0.93 0.36 0.02 0.49 0.93 0.90 0.21 0.02 0.58 0.92 0.14 0.01 0.53 0.90 0.12 0.03 0.45 0.11 0.03

MPA

MPA 0.42 0.20 0.00 0.50 0.88 0.41 0.00 0.44 0.93 0.16 0.01 0.37 0.93 0.92 0.07 0.00 0.38 0.87 0.01 0.00 0.30 0.86 0.03 0.00 0.27 0.02 0.00

LPA

6-31G*

4-31G

6-31G*

+0.39 -0.39 +0.10 +0.22 -0.32 +0.34 -0.10 -0.12 +0.52 - 0.87 +0.11 +0.12 +0.57 - 1.15 +0.29 +0.67 - 1.06 +0.38 +0.71 -0.71

Li Be H Li B H Li C H H’ Li N H Li 0 H Li F

MPA

4-31G

qi

Li H

Atom

+0.51 -0.51

+0.40 - 0.70 +0.29

+0.28 -0.70 +0.21

+ 0.24 -0.58 +0.12 +0.11

+0.06 -0.03 -0.01

-0.14 + 0.28 -0.14

+0.11 -0.11

LPA

and valencies ( VA)of LiX dimers

4-31G

(41)

BAB

LPA

, atomic charges

OP

(OP),bond orders (B,)

“Hydrogen atoms denoted by prime are out of the CLiCLi plane

(LiF),

(LiOH)2

(LiNH2)*

(LiCH,),B

(LiiHz)z

(LiBeH),

Bond

System

Overlap population

TABLE 5

+0.69 - 0.69

+0.65 -1.08 +0.43

+0.55 -1.21 +0.33

+0.46 -0.89 +0.15 +0.14

+0.24 -0.10 -0.07

+0.03 +O.ll -0.14

+0.25 -0.25

MPA

6-31G*

+0.17 -0.17

+0.04 -0.38 +0.34

-0.02 -0.50 +0.26

+0.06 -0.53 +0.15 +0.16

-0.03 -0.05 +0.04

-0.14 +0.18 -0.04

+0.02 -0.02

LPA

0.57 0.55

0.64 1.41 0.82

0.79 2.48 0.87

0.87 3.52 0.94 0.94

1.11 2.76 0.95

1.41 1.87 0.89

1.04 0.85

MPA

4-31G

vA

1.01 0.93

1.21 1.99 0.93

1.39 3.02 0.97

1.40 3.75 1.00 1.00

1.56 2.94 1.02

1.70 1.97 0.99

1.42 0.99

LPA

0.62 0.59

0.68 1.41 0.78

0.83 2.49 0.84

0.98 3.59 0.93 0.93

1.23 2.86 0.96

1.48 1.98 0.97

1.23 0.94

MPA

6-31G*

1.65 1.47

1.88 2.48 0.90

1.93 3.28 0.95

1.76 3.82 0.99 0.99

1.73 2.97 1.01

1.74 2.00 1.01

1.59 1.01

LPA

157

(Li,NH ), and (L&N) 2:because of this strong LiLi antibonding interaction no three-centre bonding in the dimers ( LiX)z (X = NH2, OH and F) was found. The AA interactions are generally slightly antibonding and the bonding LiLi interactions in the dimers of LiH, LiBeH, LiBH, and LiCHB are in conformity with the three-centre bonding present in these molecules. It may be noted that the Lijwdin bond orders for the LiLi interactions are overestimated than the corresponding Mulliken values by a wide margin. How the various quantities related to charge distribution change upon dimerisation is summarised in Table 6. First it is noted that the overlap populations and bond orders of LiX bonds decrease upon dimerisation. The changes in LiA overlap population are virtually identical for the two basis sets. The absolute values of this change decrease in the order B x Be x H > C > N > 0 > F. For dimers with three-centre bonding the changes in bond order upon dimerisation are almost independent of the basis set and the method of population analysis. For the essentially ionic dimers the pertinent changes depend both on basis set and population analysis scheme. The changes in bond order roughly follow the same trend as that in OP. According to MPA, the Li atoms become more positive upon dimerisation in all cases. The essentially ionic character of the LiN, LiO and LiF bonds is reflected by the negligibly small change in the atomic charge of Li and A. Schleyer and Pople [ 221 observed that the natural atomic charge on Li in LiH changes only by 0.01(6-311+ + G**) upon dimerisation. However, for the smaller basis sets they found somewhat larger changes. According to Baskin et al. [3] the Mulliken positive charge on Li in LiF increases by only 0.007 upon dimerisation. For the 3-21G basis set, the natural positive charge [24] on Li in CHBLi increases by about 0.05. The present MPA results tally with these observations. Thus, although the absolute values of atomic charges are not reliable,the changes of these quantities upon dimerisation are in agreement with the NPA results. The Lijwdin scheme predicts an opposite trend for the changes in atomic charges both on Li and A. Unlike changes in overlap populations, bond orders and atomic charges, the changes in valencies @VA) are sensitive to basis sets and the method of population analysis. In general, the Mulliken valency of the electropositive centre increases and that of electronegative centre decreases upon dimerisation. In the case of predominantly ionic dimers, an opposite trend in dV,i is predicted by the 6-31G* basis set. However, the magnitude of this change is negligibly small. The Liiwdin scheme overestimates not only the absolute valencies but also the changes in valency. For both basis sets d VLi is abnormally high which is due to the overestimation of the nonbonded interaction. The substantial increase in valency is in contradiction to the fact that the dimerisation energy in the present series of molecules stems mainly from the electrostatic interaction.

LiBe

(LiBeH)Z

LiF

-0.01

OH

(LiF),

-0.10

LiO

(LiOH),

-0.07

0.00

-0.14

-0.02

LiN NH

CH CH’

-0.17 -0.01

-0.02

BH

LiC

-0.19

LiB

-0.21 0.00

-0.20

-0.08

-0.12 -0.01

-0.01

-0.16

0.00 - 0.02

-0.17

-0.20 - 0.02

0.00

-0.20

-0.20

-0.50 - 0.04

- 0.54

-0.27

-0.32 -0.01

-0.01

-0.37

-0.02

-0.47

-0.46 -0.02

-0.29

-0.37 -0.01

-0.02

- 0.43

-0.48

-0.03

-0.60

- 0.46 -0.02

F

H Li

Li 0

N H

Li

- 0.05

-0.02 -0.37

-0.03 -0.07

Li C H H’

-0.40

-0.43 -0.01 -0.03

H

B

+0.01 -0.01 +0.01

-0.03

+0.03 +0.01

- 0.05

+0.01 -0.01

+0.02

+0.06 -0.11

-0.15 +0.01

-0.01 +0.13

H Li

-0.07 +0.07

+0.05 +0.02

-0.08

+0.07 +0.02

+0.03 -0.11

+0.02 +0.02

- 0.09

+ 0.02 + 0.02

-0.05

+0.04 -0.01

-0.04 +0.04 -0.03

+0.13 -0.13 +0.1a -0.17

LPA

MPA

4-31G

Aqi

Li Be

Li H

-0.02

-0.49 -0.04

0.00

- 0.53

- 0.50

-0.44

-0.03

-0.51

-0.50 -0.01

-0.50

LPA

Atom

-0.44 -0.01

-0.02

- 0.52 0.00

-0.49

-0.50 -0.01

-0.51

MPA

MPA

LPA

6-31G*

4-31G

4-31G

6-31G*

ABAB

AOP

(LiNH2)2

(LiCH&

(LiBH&

LiH

(LiH),

BeH

Bond

System

Changes (A) in OP, BAB, @Aand VA upon dimerisation

TABLE6

0.00

0.00

-0.04 +0.01

+0.02 + 0.03

+0.02 - 0.06

+ 0.02

+0.03

+0.04 -0.10

-0.09 +0.01

+0.07

-0.02

+0.16 -0.14

+ 0.07 -0.07

MPA

6-31G*

-0.18 +0.18

+0.16 +0.03

+ 0.03 -0.19

-0.23 +0.17

+0.03 +0.04

+0.11

+0.02 -0.21

+0.10

-0.14

-0.08 +0.09 -0.01

+ 0.07

-0.07

LPA

+0.01

+0.03

-0.03 -0.01

+0.01

-0.02 -0.02

0.00 +0.03

0.00

+0.03 -0.12

-0.12 +0.01

0.00 +0.13

-0.02

- 0.08 +0.41

+0.11

MPA

4-31G

AVA

+0.09

-0.02 +0.19

+0.07

-0.01 +0.19

+0.29 +0.10

-0.01 -0.01

+0.35 -0.02

0.00

+0.44 -0.02

-0.01 -0.01

+0.10

+0.01

+0.44

LPA

+0.04 +0.01

-0.01

-0.02 -0.06

-0.02

0.00 -0.01 -0.05

0.00

-0.09

0.00 +0.10

+0.22 - 0.08

0.00 0.00

-0.03 +0.43

+0.26

MPA

6-31G*

+0.44 +0.26

+0.19 -0.02

-0.01 + 0.45

+0.61 +0.25

-0.01

-0.01

+0.59 +0.05

0.00 -0.01

0.00 +0.59

+0.67 -0.01

+0.59 +0.01

LPA

159 CONCLUSIONS

The present LMO studies show that multi-centre electron-deficient bonding is not a general characteristic of the LiX dimers with first-row substituents. Three-centre LiALi bonds are present in the dimers of LiH, LiBeH, LiBHz and LiCH3. The fully charge-separated electrostatic model appears to be more adequate for the description of bonding in LiNH2, LiOH and LiF and their dimers. The hypothesis that four-electron, three-centre bonding is present in ( LiF)2 [ 1,181 is not substantiated by our LMO calculations. Inclusion of Li d orbitals in the basis set does not have any pronounced effect on the dipole moments, energetics and dimerisation energies of the monomers. The bonding in the dimers is also somewhat insensitive to these orbitals. The MPA, although it underestimates charge separation, provides a more consistent picture of bonding in LiX dimers. The LPA on the other hand underestimates charge separation to a greater extent and appreciably overestimates the covalent interaction. ACKNOWLEDGEMENTS

We are grateful to Professor S. Mitra and Dr. R. Das of T.I.F.R., Bombay, India for their invaluable help in computation. The time and service made available by the computer centre, T.I.F.R., were essential to this study, and are gratefully acknowledged. T.K. thanks C.S.I.R., New Delhi for the award of senior fellowship and financial support.

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