Indian Journal of Chemistry Vo1.39A, Jan-March 2000, pp. 1 80- 1 88

An ab initio study of molecular charge distribution and electrostatic potentials : Role of hybridization displacement charge

Anil Kumar & P C Mishra* Department of Physics, Banaras Hindu University,

Varanasi 22 1 005, India

Received 2 October 1999; accepted 1 Decemberl999

Hybridization displacement charges (HDC), when combined with L6wdin charges, preserve SCF molecular dipole moments. One can generate near ab initio quality MEP maps using HDC combined with L6wdin charges obtained employing semiempirical methods. HDC are obtained using off-diagonal elements of the L6wdin population matrix, and correspond to charges located at different points near atoms in molecules, including lone pairs. In view of a great usefulness of HDC as evidenced by semiempirical calculations, a method of computing HDC using ab initio wave functions has been developed. It has been applied to compute charge distributions, dipole moments and molecular electrostatic potential maps of certain molecules at the SCF level using the 6-3 1 G** basis set. The molecular properties obtained using HDC and CHelpG charges are compared.

1. Introduction Charge distribution in a molecule plays an important

role from the point of view of its physical and chemical properties . Several molecular properties, e.g. dipole and multipole moments, molecular electrostatic potentials (MEP) and intermolecular interactions, e.g. hydrogen­bonding, depend strongly on molecular charge distribu­tion. Generally, charge distributions are represented by point net charges located at different atomic sites and several experimental and theoretical methods are avail­able to obtain them'-s. These methods are based on widely different models and concepts and, therefore, the point charges obtained using them are generally appreciably different . The central problem in the calculation of point charges is that there is no quantum mechanical operator as expectation values of which these charges can be com­puted'·6. Theoretical methods commonly used to com­pute point charges include the Mulliken, Lbwdin and natural population analysis (NPA) schemes, and that of fitting of charges to MEp4·6,7- 1O. One may set up the fol­lowing two general criteria for a charge distribution to be reliable or acceptable: (i) It should reproduce SCF molecular dipole moments. Here, inclusion of the con­dition that some higher electrical moments than dipole moment e.g. quadrupole moment, be also reproduced by a point charge distribution would be desirable but con-

*. E-mail : pcmishra@banaras.ernet.in

sidering the accuracy available with the existing meth­odologies in this context, it would probably be too strin­gent a condition, and so is not considered necessary here; and (ii) it should yield MEP values which, from the sta­tistical point of view, correlate linearly strongly with those obtained using other reliable types of point charges or the ab initio MEP distribution. The charges obtained by fitting to MEP e.g. CHelpG" would be expected to satisfy both these criteria. It is usually so for unsymmetric molecules but not for those molecules which have very small or vanishing dipole moments. For example, for homonuclear diatomics, the point CHelpG charges at the two atoms come out to be zero due to which the MEP values would also be zero everywhere around the mol­ecules which contradicts SCF MEP results. Another problem with MEP-derived charges is that in many sys­tems having electron-rich bonded atoms, lowest MEP values are usually obtained near the bond centres (e.g. the OF bond in HOF and the NN bond in pyridazine) and not near the individual atoms which also contradicts SCF MEP patterns 1 2 . Thus, the MEP-derived point charges satisfy the above criterion (ii) except in some situations like those mentioned above. It must be em­phasized that point charges cannot reproduce all MEP features obtained by continuous charge distributions, e.g. MEP minima. However, if point charges are reliable, this can be achieved by distributing them continuously ac­cording to the forms of squares of atomic orbital wave

KUMAR et al.: STUDY OF MOLECULAR CHARGE DISTRIBUTION AND ELECTROSTATIC POTENTIAL 1 8 1

functionsi 3 . The population analyses schemes mentioned above are commonly employed to obtain point charges located on the atomic sites but the charges obtained us­ing them are not reliable as they usually do not satisfy the above mentioned two criteria.

It may be realized that the amounts and physical lo­cations of electronic charges associated with different atoms in molecules are both important and need to be studied. A common drawback of the different popula­tion analysis schemes and MEP-driven charge models is that they treat the electron densities associated with at­oms in molecules to be totally located at the correspond­ing nuclear sites . Thus these methods yield no informa­tion as to lone pair charges which are located somewhat away from the nuclear sites. It has, however, been re­ported by many authors that if some off-atomic site point charges corresponding to lone pair charges are added to atomic site-based point charge distributions, say, as sug­gested by the consideration of atomic dipoles, perfor­mance of the charge distributions is improved. Williams and Wellerl 4 found a greatly improved MEP-derived charge model for certain azabenzenes by including some lone pairs. Chipot et.al. 1 5 found that charge models for amino acids, especially those which contain sulphur at­oms, were greatly improved by inclusion of off-atomic site point charges. In a recent calculation of accurate point charges for water and water dimer, need for inclusion of off-atomic site charges was emphasized 16. In another work relating to the development of a force field, impor­tance of lone pairs was recognized 1 7 . Calculation of lone pair charges by fitting of MEP is faced with difficulties arising due to the fact that their locations and amounts are not uniquely defined. Baderl8 has studied properties of continuous charge distributions in molecules exten­sively and shown that the distribution of -V'2p, P being the charge density, has certain features which qualita­tively validate the concept of lone pairs.

In view of the difficulties mentioned above in com­puting reliable point charges in molecules, particularly lone pairs, we introduced the concept of hybridization displacement charge (HOC) 19 . It is found that a molecu­lar charge distribution obtained by combining HOC with Lbwdin charges minimizes many of the difficulties men­tioned above I 2. 1 J. 1 9-:12 . However, in the earlier work on HOCI9.32, only semiempirical methods were employed. In view of the great usefulness of the HOC concept as evidenced by the earlier work I9-32, we have now devel­oped a scheme to compute HOC at the ab initio level. Our aim is not merely to obt� ;n a method to compute

MEP maps but to develop the HOC concept further so that it can be used to generate a wide range of reliable information about molecular electronic structure and properties as well as intermolecular interactions .

2. Computational Method

Lbwdin populations33 are given as elements of the matrix defined by

. . . ( 1 )

where P i s density matrix the elements of which are given by

. . . (2)

In Eq.( I ) S is the atomic orbital overlap matrix and in Eq.(2) Cki are the LCAO coefficients. The matrix S II2

is calculated from S as follows. Let A represent the di­agonal form of S and C represent the matrix formed by the eigenvectors obtained by diagonal ising S. Let A 1/2 represent a diagonal matrix the elements of which are the square roots of the elements of A. Then S I /2 would be obtained from34

. . . (3)

The contribution of an atom to the molecular dipole moment has two parts, one being due to the net charge located at its nuclear site and the other arising due to hybridization of its atomic orbitals4 . The components of the hybridization dipole moment /ljh of an atom along the x, y and z directions arising due to the mixing of its ns and mpi atomic orbitals where i = x,y,z and n and m represent principal quantum numbers, are given by

. . . (4a)

. . . (4b)

where D;= (ns I i I mp) (n = 1 ,2,3 etc. and m=2,3 etc.) . . . (4c)

and Q; =-2P"s.mr; . . . (4d)

In Eq.(4a), K is a parameter. By varying K, the dis­tance OJ' and the charge Qj' of Eq.( 4b) can be varied to obtain desired results. One can obtain the values of K for different atoms by maximizing the linear correla-

1 82 INDIAN J CHEM, SEC. A, JAN - MARCH 2000

tion coefficient between the MEP values obtained using CHelpG charges and HDC at the van der Waals surfaces of several molecules. The parameter K was introduced in earlier semiempirical calculations in the same con­textI 3, 1 9-32. It may be noted that any charge distribution scheme that preserves the contribution of each atom to molecular dipole moment would involve the parameter K which can be fixed by imposing additional conditions e.g. that of reproduction of main features of MEP pat­terns obtained by MEP-derived charges in different mol­ecules satisfactorily. The hybridization displacement charge (HDC) corresponding to each combination of the ns and mpi orbitals (Eqs 4a-c) of an atom is separately defined as 12. 1 3. 1 9-32

Q = I1h IR = [ (Q/ + Q/ + Q/)/3 ] 1 12 . . . (5)

where !J,h is the hybridization dipole moment associated with a given combination of the ns and mpi orbitals (Eqs 4a-c) of the atom under consideration arising due to the displacement of a charge Q to a distance R from it. The quantities !J,h and R for each of such combinations would be separately given by

I1h = (l1h / + I1h / + I1h /)Ifl and R = ( Dx

2 + D/ + D/ ) 1 /2

. . . (6)

. . . (7)

the direction of displacement R from the atom under consideration is given in spherical polar coordi­nates by the following angles

. . . (8)

. . . (9)

The distances D , D , D depend on the exponents of x y z the Slater type atomic orbitals which are considered to be the same for the s and p orbitals associated with a given principal quantum number3) . The values of these exponents are available in the literature3) . Each of the distances Dx' Dy and Dz in Eq.(4c) is given for Slater type orbitals (STO's) by

. . . ( 1 0) .y3 .y(2n(s) ! ) .y(2m(p) ! ) d"+1

where a= n(s)+m(p)+ 1 , b= n(s)+ I 12, c= m(p)+ I 12, d= Ss + S . Here n(s) and m(p) are the principal quantum num­p

bers of the s and p atomic orbitals and Ss and Sp are the Slater exponents of the same respectively. It is to be noted that for given n(s) and m(p) values, Dj (i= x,y,z) depend only on the Slater exponents of the orbitals. In the present calculations, the Slater exponents for the inner shells (n= I ) of the atoms were taken to be the same as those given in the literature35, while those for the higher shells (n=2,3) were adjusted so as to maximize the linear cor­relation coefficient between the molecular dipole mo­ments obtained using SCF wave functions and those cal­culated using the combinations of HDC with Lbwdin charges for the molecules studied here. This adjustment of S of the valence shell was made after getting the SCF density matrix . We calculated the HDC displacements using STO's and not actual Gaussian expansions of the same incorporated in the Gaussian 94 program (Win­dows version)36 which was employed to generate the necessary data for the calculations. The calculations were carried out at the ab initio SCF level using the STO-6G and 6-3 1 G** basis sets36 but the results obtained with the latter basis set only are presented here. It may be mentioned that Slater exponents were parametrically adjusted in the earl ierl 9-32 semiempirical calculations also but there they were obtained by maximizing the linear correlation coefficient ' etween the MEP minima ob­tained by ab initio and semi empirical calculations while they were adjusted here on a different basis as mentioned above.

3. Results and Discussion

3. 1 Dipole moments The adjusted values of the parameter K and valence

shell Slater exponents (S) along with the standard val­ues of S taken from the literature35 for the atoms that occur in the molecules studied here, appropriate to the STO-6G and 6-3 1 G** basis sets, are given in Table I . It may be noted that the values of the parameter K given in Table I were found to be satisfactory for both the basis sets. The calculated dipole moments for nine molecules, inc1ud.ing two homonuc1ear diatomics, using HDC and CHelpG charge distributions, along with the correspond­ing values computed using SCF wave functions are pre­sented in Table 2. It is seen that the dipole moments cal­culated using HDC differ from those obtained using SCF calculations, on the average by about I I %, the differ­ence in some cases being larger. Further, we find that the relative values of dipole moments of molecules e.g. those of �CO, HFCO and F2CO (Table 2), are obtained

KUMAR et al.: STUDY OF MOLECULAR CHARGE DISTRIBUTION AND ELECTROSTATIC POTENTIAL 1 83

Table 1 - Parameters K and S for the atoms occurring in the molecules studied here for STO-6G and 6-3 1 G** basis sets (n = principal quantum number).

Atom K S values for STO-6G and 6-3 1 G** basis sets"

STO-6G 6-3 IG**

S(n= I ) S(n=2) S(n=2) S(n=3) H 0.3h 1 .24 NA 1 .24 7.0 Li 1 .0 2.69 0.72(0.80) 0.72 1 .35 C 0.3 5 .67 2.72( 1 .72) 2.72 8.0 N 0.3 6.67 2.25( 1 .95) 2.25 7.0 N(NH2) 1 .0 6.67 2.25( 1 .95). 2.25 7.0 0 0.3 7.66 2.95(2.25) 2.95 1 1 .0 F. 0.3 8.65 3.45(2.55) 1 5 .0 1 5 .0

NA: Not applicable for hydrogen. "The original S values from ref. [35] are given in parantheses. The other S values for n=2 and 3 are the adjusted ones. The same S values taken fromsRef. [35] were used for n=1 with both the basis sets. hFor the 6-3 1 G** basis set only. K is not required for H with the STO-6G** basis set.

using HOC satisfactorily. The linear correlation coeffi­cient between the SCF and HOC dipole moments, ex­cluding the two homonuclear diatomics in view of the fact that the calculation of their dipole moments is trivial, was found to be 0.99. Thus, statistically speaking, HOC can be used to obtain molecular dipole moments satis­factorily.

3.2 ME? values The calculated lowest negative MEP values on the

van der Waals surfaces of the molecules near the differ­ent atoms obtained using SCF wave functions, HOC and CHelpG charges are presented in Table 3 . For three molecules, i .e. CO, N2 and F2, the lowest surface MEP values obtained using SCF/STO-6G wave functions are also presented in the same table for the sake of compari­son. We make the following observations: (i) In LiH, a negative MEP region is located near the hydrogen atom. The negative MEP values near the hydrogen atom in this case obtained using the HOC and CHelpG charges are quite close;(ii) In CO, the magnitude of negative MEP near the carbon atom is larger than that near the oxygen atom according to both the CHelpG charges and HOC. The magnitudes of MEP minima obtained near the at­oms of CO using the SCF/STO-6G wave function quali­tatively support the results obtained by the CHelpG charges and HOC. A similar result for CO has also been reported earlier'7 ; (ii i)The negative MEP magnitudes near fluorine in HFCO and F2CO are much smaller than those near the oxygen atoms of the corresponding carbonyl

Table 2- Molecular dipole moments calculated using SCF wave functions and, HDC and CHelpG charges obtained using

the 6-3 1 G** basis set.

SI. No. Molecule l1""r I1h�c Whc1pg I . LiH 5 .96 5.97 5.88 2. CO 0.26 0.25 0.37 3. NH3 1 .84 2.24 1 .88 4. Hp 2. 1 5 2. 1 8 2. 1 9 5 . H2CO 2.66 2.32 2.66 6. N2 0.0 0.0 0.0 7. F2 0.0 0.0 0.0 8. HFCO 2.40 1 .94 2.42 9. F2CO 1 .34 1 .05 1 .33

Table 3- Lowest negative molecular electrostatic potentials (MEP) (kcal/mol) on the van der Waals surfaces near the various atomic

sites of different molecules obtained using HDC and CHelpG charges.

SI. Molecule Atom · MEP No. yc.:hclpg yhdc

I . LiH H - 1 1 9.8 - 1 20. 1 2. CO C -30. 1 - 1 9.7(-42.6)"

0 -22.4 - 1 5 .7(-29.6)" 3 . NH) N -58.8 -73.7 4. Hp 0 -56.7 -60.0 5 . H2CO 0 -46. 1 -48.4 6. N2 N 0.0 -24.6(-3 1 .4 )" 7. F2 F 0.0 -5.9(-4.5)" 8. HFCO 0 -48.4 -40.4

F -24.8 - 1 7 .0 9. F2CO 0 -38.0 -37.4

F -5 . 1 -5 .8

"Minimum MEP value obtained using SCF/STO-6G wave functions.

1 84 INDIAN J CHEM, SEC. A, JAN - MARCH 2000

1 4 0

1 2 0

100 0 E 80 "-0 U .:£

60 u "0 .c >

40

20 cP 0

00 20

0

40

0

0

0

60 80 100 I VCh.'po I ( k col /mol )

120 140

Fig. 1 - Variation of MEP magnitudes (kcal/mol) obtained using HOC charges (Vhdc) with those obtained using ChelpG charges(VChc'pg) . The least squares fitted straight line is also shown.

groups. The negative MEP magnitude near the fluorine atom in F2 is also much smaller than that near the nitro­gen atom in N2 as shown by both the HOC and SCF results. It is known that MEP near an atom is a measure of its hydrogen bond forming ability l9-32 . Thus despite its well known high electronegativity, fluorine in mol­ecules seems to be a poor hydrogen bond acceptor; (iv) The MEP values near the atoms of the homonuclear diatomics N2 and F2 are zero according to the CHelpG charges. However, the lowest surface MEP values ob­tained using HOC calculations and the minimum MEP values obtained from SCF calculations near the atoms of these molecules are non-zero and fairly large in mag­nitude. Thus CHelpG charges are found to yield wrong MEP features for such molecules as mentioned earlier; and (v) The linear correlation coefficient between the MEP values obtained using the CHelpG charges and HOC, excluding N2 and F2 , was found to be 0.98. The MEP magnitudes obtained using HOC and CHelpG charges are plotted in Fig. I where the corresponding least squares fitted straight line is also shown. On the whole, the above discussion shows that in many cases HOC would be a more reliable charge distribution than CHelpG. Further, this discussion also shows that the two criteria suggested in the introduction for a charge distri­bution to be reliable or acceptable are satisfied by HOC while in some cases they are not satisfied by CHelpG

,..... N .... .......

VI� .-.......

� """' '-''' ,...... -N -..1 .- 1O .. .. .. .. N ..- N "-......., "-"' '-' '''''''

! 0

H2 )�(

VI N

) ! { I • • • 0

( a ) I,J H

( b ) co

.. .. . .. .-. - - �

....... )1 11 •• 0 - •

0,

� ,..... .- M . .- .-....... ...,.

� 0 L i,

Fig. 2- Relative locations of atoms and HOC in (a) LiH and (b) CO. In (a), the atom Li is numbered as I and H is numbered as 2. The locations of six HOC arising due to the mixing ( I s,2p), (2s,2p), ( l s,3p), (2s,3p) (3s,2p) and (3s,3p) of orbitals of Li are labelled from ( I , I ) to ( 1 ,6) respectively. The two HOC val­ues arising due to the mixing ( I s,3p) and (2s,3p) of orbitals of H are labelled as (2, I ) and (2,2) respectively. In (b) the oxygen atom is numbered as I and carbon atom is numbered as 2. The locations of six HOC arising due to the mixing ( I s, 2p), (2s,2p), ( I s,3p), (2s,3p), (3s,2p) and (3s,3p) of orbitals of oxygen are labelled from ( I , I ) to ( 1 ,6) respectively while the correspond­ing quantities for carbon are labelled from (2, I ) to (2,6).

charges. It may be mentioned that we considered CHelpG charges as a representative of MEP-derived class of charges, and so whatever is true for CHelpG charges would also be, by and large, true for the other types of MEP -deri ved charges 1 1 ,38-40

.

3.3 HDC magnitudes and displacements The magnitudes of HOC arising due to the mixing of

atomic orbitals of the constituent atoms and their dis­placements from the corresponding atoms are presented in Table 4. We make the following observations from the results presented in Table 4.

In all the cases, the magnitudes of HOC resulting due to the mixing (ns,mp) of the atomic orbitals when n= l and m=2,3 are appreciably smaller than those caused by the mixing of orbitals when n, m=2 and/or 3 . The HOC magnitudes associated with hydrogen atoms are also appreciable.

KUMAR e/ aL.: STUDY OF MOLECULAR CHARGE DISTRIBUTION AND ELECTROSTATIC POTENTIAL 1 85

Table 4 - Amounts of hybridization displacement charges (HOC) (in the unit of the magnitude of electronic charge) associated with different atoms in some representative molecules and their distances from the corresponding atoms due to

mixing of the different electronic shell wave functions calculated using the 6-3 1 G** basis set at the SCF level.

SI. No. Molecule Atom and Amount of Distance of HOC location and mixing of shells' HOC or point HOC (A) displacement direction

charge from the atom I . LiH Li ( I s,2p) -0.099 0. 1 2 Away from bond

(2s,2p) -0.250 1 .84 Towards H (beyond H) ( I s,3p) -0.043 0. 1 6 Away from bond (2s,3p) -0. 1 37 1 .43 Towards H (3s,2p) -0.258 1 .43 Towards H (3s,3p) -0. 1 42 1 .37 Towards H

NS 0.958 0.00 H ( I s,3p) -0. 0 1 6 0.2 1 Towards Li

(2s,3p) -0.072 0.03 Towards Li NS 0.060 0.00

2. CO 0 ( I s,2p) -0.0004 0.G7 Towards C (2s,2p) -0.462 0. 1 4 Away from bond ( I s,3p) -0.0 1 8 0. 1 2 Towards C (2s,3p) -0.647 0.04 Away from bond (3s,2p) -0.764 0.04 Away from bond (3s,3p) -0.577 0.05 Away from bond

NS 2.399 0.00 C ( I s,2p) -0.004 0. 1 2 Away from bond

(2s,2p) -0.5 1 9 0. 1 5 Away from bond ( I s,3p) -0.045 0. 1 6 -Towards 0 (2s,3p) -0.728 0.06 Away from bond (3s,2p) - 1 04 1 2 0.06 Away from bond (3s,3p) - 1 .0 1 2 0.G7 Away from bond

NS 3.789 0.00

3 . H2O 0 ( I s,2p) -0.0 1 4 0.07 Inside HOH angle (2s,2p) -0.600 0. 1 4 Outside HOH angle ( Is,3p) -0.0 1 7 0. 1 2 Inside HOH angle (2s,3p) -0.623 0.04 Outside HOH angle (3s,2p) -0.521 0.04 Outside HOH angle (3s,3p) -0.538 0.05 Outside HOH angle

NS 1 .870 0.00 H ( I s,3p) -0. 1 64 0.2 1 Towards 0

(2s,3p) -0.4 1 5 0.03 Towards 0 NS 0.80 1 0.00

4. H2CO C ( I s,2p) -0.0\ 8 0. 1 2 Inside HCH angle (2s,2p) -0.057 0. 1 5 Inside HCH angle ( I s,3p) -0.022 0. 1 6 Towards 0 (2s,3[1) -0.326 0.06 Inside HCH angle (3s,2p) -0.482 0.06 Inside HCH angle (3s,3p) -0.348 0.07 Inside HCH angle

NS 1 .325 0.00 0 ( l s,2p) -0.0 I I 0.07 Towards C

(2s,2p) -0.527 0. 1 4 Away from CO bond ( l s,3[1) -0.02 1 0. 1 2 Towards C (2s,3p) -0.639 0.04 Away from CO bond (33,21') -0.653 0.04 Away from CO bond (3s,3p) -0.6 1 1 0.05 Away from CO bond

NS 2.22 1 0.00 H ( I s,3p) -0. 1 1 1 0.2 1 Towards C

(2s,3p) -0.332 0.03 Towards C Contd . . . NS 0.528 0.00

1 86 INDIAN J CHEM, SEC. A, JAN - MARCH 2000

Table 4 - Amounts of hybridization displacement charges (HOC) (in the unit of the magnitude of electronic charge) associated with different atoms in some representative molecules and their distances from the corre-sponding atoms due to mixing of the different electronic shell wave functions calculated using the 6-3 1 G**

basis set at the SCF level. Contd . . .

S I . No. Molecule Atom and Amount of Distance of HOC location and mixing of shells· HOC or point HOC (A) displacement direction

charge from the atom

5 . N2 N ( I s,2/1) -0.005 0.07 Away from NN bond

(2s,2/1) -0.468 0. 1 8 Away from NN bond

( l s,3/1) -0.029 0. 1 3 Towards the other N

(2s,3/1) -0.7 1 9 0.07 Away from NN bond

(3s,2p) - 1 .097 0.07 Away from NN bond

(3s,3" ) -0.76 1 0.08 Away from NN bond

NS 3 .080 0.00

6. F2 F ( l s,2p) -0.020 0.09 Towards the other F

(2s,2p) -0.49 1 0.03 Away from FF bond

( 1 5,31') -0.020 0. 1 0 Towards the other F

(2s,3/1) -0.562 0.03 Away from FF bond (3s,2/1) -0. 384 0.03 Away from FF bond

(3s,3p) -0.382 0.04 Away from FF bond

NS .60 0.00

7. F2CO C ( I s,2p) -0.032 0. 1 2 Inside FCF angle

(2s,2/1) -0.222 0. 1 5 Towards 0 ( l s,3p) -0.006 0. 1 6 Inside FCF angle

(2s,3p) -0.005 0.06 Towards 0 (3s,2p) -0.065 0.06 Towards 0 (3s,3p) -0.04 1 0.07 Towards 0 NS 0.79 1 0.00

0 ( l s,2p) -0.0 1 1 0.07 Towards C

(2s,2p) -0.585 0. 1 4 Away from CO bond

( 1 5,3p) -0.02 1 0. 1 2 Towards C

(2s,3,,) -0.65 1 0.04 Away from CO bond (3s,2p) -0.633 0.04 Away from CO bond

(3s,3p) -0.594 0.05 Away from CO bond.

NS 2.284 0.00

F ( I s,2p) -0.0 1 7 0.09 Towards C

(2s,2,,) -0.457 0.03 Away from CF bond

( l s,3/1) -0.0 1 7 0. 1 0 Towards C

(2s,3,,) -0.496 0.03 Away from CF bond

(3s,2,,) -0.384 0.03 Away from CF bond

(3s,3,,) -0.379 0.04 Away from CF bond

NS 1 .647 0.00

• NS stands for the nuclear site of the atom under consideration

KUMAR et al.: STUDY OF MOLECULAR CHARGE DISTRIBUTION AND ELECTROSTATIC POTENTIAL 1 87

The directions of displacements of HOC resulting due to the mixing ( l s,2p) and ( l s,3p) of orbitals of non-hy­drogen atoms are usually but not always opposite to those of HOC caused by the mixing (ns,mp) (n,m=2,3) of or­bitals. The displacements of HOC associated with hy­drogen atoms caused by the mixing ( l s,3p) and (2s,3p) of their orbitals are always towards the atoms bonded to them.

The bond length of LiH was found by optimization at the RHF/6-3 1 G** level to be about 1 .63 A. The dis­placement of HOC caused by the (2s,2p) mixing of or­bitals of Li from the Li atom was found to be 1 .84 A. (Table 4). Thus the HOC caused by the (2s,2p) mixing of orbitals of Li is displaced towards the hydrogen atom so much away from it that it goes beyond the H atom. The magnitude of this HOC related to the mixing (2s,2p) of orbitals of Li is, however, not very large. But it is clear that it would give rise to a negative MEP region near the H atom (Table 3) and would make it a hydrogen bond accepting site, as found earlier4 1 .42 . The other HOC magnitudes and displacements (towards H) caused by the mixing (ns,mp) (n,m=2,3) of orbitals of Li where n,m :t- 2 are only moderate and such HOC are located on the LiH bond. The sum of the HOC values of Li and the charge located at the nuclear site of Li, and similarly the sum of the corresponding charges associated with H in LiH show that there is only a small amount of charge transfer (-0.03) from the Li atom to the H atom in LiH. It is to be realized that the amount of charge transfer between atoms in a given molecule cannot be obtained simply by considering the charges located at the nuclear sites obtained by an approximate scheme e.g. Mulliken population analysis. Instead, one should examine the various off-diagonal elements of the density matrix also before deriving a conclusion in this regard . This is what is done in the present HOC-based scheme of charge analysis. The present results show that it is the polariza­tion or hybridization effect on Li which causes a large displacement of the charge of Li to near the hydrogen atom which broadly looks like charge transfer but it is really not a charge transfer. Thus the present study shows an urgent need to study charge distributions in charge transfer complexes considering the magnitudes and lo­cations of HOC. The relative locations of the atoms and HOC in LiH are shown id Fig. 2(a).

The sums of HOC values caused by the mixing (ns,mp) (n,m=2,3) of orbitals of carbon atoms in HCHO, HFCO and F2CO are appreciably smaller than that in CO. It would be expected to g ive a large negative MEP

value near the carbon atom as is actually found (Table 3) here using HOC and earlier from SCF calculations37 . The relative locations of the atoms and HOC in CO are shown in Fig. 2(b) .

If we compare N2 with F2, we find that in the former case, the sum of the HOC magnitudes is much larger than that in the latter, and in both the cases, the displace­ments of HOC caused by the mixing (ns,mp) (n,m=2,3) of orbitals are directed away from the bond region. It would give rise to negative MEP values near the corre­sponding atoms in both the molecules. Further, consid­ering the HOC valucs, one would expect much larger negative MEP values near the atoms in N2 than those near the atoms in F2. This is what is found from MEP calculations using SCF wave functions (Table 3).

4. Conclusions We arrive at the following conclusions from this

study : (i) HOC can be computed within the framework of

ab initio methodology using the procedure adopted here; (i i) A combination of HOC with L6wdin charges

yields molecular dipole moments and MEP features re­liably, and in some cases, e.g. for homonuclear diatomics, this charge distribution performs even better than MEP­derived charges;

(iii) The magnitudes of HOC caused by the mixing (ns,mp) (n= 1 ,m=2,3) of atomic orbitals and their dis­placements are much smaller than those arising due to the mixing (ns,mp) (n,m=2,3) .of orbitals. Further, the directions of HOC displacements when n= I and n=2 or 3 are also usually quite different, being opposite to each other in many cases; and

(iv) HOC provide valuable information regarding molecular electronic structure, properties and bonding. The results for LiH suggest the need to study the phe­nomenon of charge transfer further in detai l .

Acknowledgement The authors are thankful to the C S I R (New Oelhi)

and the U G C (New Oelhi) for financial support.

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