Barua, A K

Chatterjee, S

English

IACS Institutional Repository

ON THE REPRESENTATION OF THE DISTORTIONS IN U ORBITALS IN THE BONDING MOLECULAR ORBITAL OF A HOMONUCLEAR DIATOMIC MOLECULES. CHATTERJEE aKD A. K. BARUAI n d i a n  A s s o c i a t i o n  f o r  t h e  O i t l t i v a t t o n  o f  S c i e n c e , Ca l c u t t a -32 .(Eeceived M arch  10, 1965)ABSTRACT. 'I'hc energy of the lowowt stute oi' law been (‘aleulatod bynuing Inui-NordsitJt'k type orbitals. The; n 'siilts sliow that this typ(‘ of orbitals ar(' flexible enough to  give a  very satisfVietory reprosentatuui of the distortions in Is orbitals in the bonding orbital o f a homonuclear diatomie molecule.I  N T K 0  D U C T I 0  NThe success of the ab initio calculation of the molecular ciKM’gics depends largely on the choice of molecular wave funtdions. Till now, mostly linear combinations of Slater type orbitals (S.T.O.’s) have been used for constructing molecular orbitals. However, a serious drawback of the>se orbitals is the inability to represent ade­quately and economically tlie distortion in the attjinic charge (‘loud when it be­comes a part of the molecular system, TJiis aspect of tlie problem has recently been dise.ussed in some detail by Geller, Frost and Lykos (1962) and Miller and Lykos (1962). They have shoAvn that the main effect in the electron cloud of an atom when it forms a part of a molc(;ul(  ^is the ‘charge shift which means the move­ment of the centre of electron density from around tlu  ^ attractive nucleus in an atom to a region between the nuclei in a diatomic system. A second ordei effect is the deformation of the charges cloud associated with a jiarticular nucleus as it is stretched along the internuclear axis.I t  has been pointed out by Harris (1960) and Barua and Chattorjee (1964) that attempts to represent the deformations in molecular orbitals by using S.T.O.’s of added complexities may not h(^  worth while. For diatomic molecules, wav^ functions in the ellipsoidal coordinat(iS with the m uM  at the foci, though quite simple in form, are expected to represent the distortion of the atomi(> oibitals to a large degree. The success of this approach has been proved by the recent cal­culation of the repulsive energy of the H-He system by using Inui-Nordsieck type orbitals (Barua and Chatter]ee, 1964).The Inui-Nordsieck type orbitals have been used by Sakamoto and Ishigoro (1'956) for the calculation of the repulsive energy of the He-He system which was27227228 S. Chatterjee and A. K . Baruanot quite successful. The reason for this has been shown by Huzinaga (1957) to be the failure of the same set of parameter for both the bonding and anti-bonding orbitals to represent properly the distortions of the atomic orbitals. For a hetero- nuclear system like H-He, tht  ^ sets of parameters for the atomic orbitals of the two atoms are independently variables and the limitation found in the case of is not present.For tht  ^ calculation of the lowest state of molecule only the bonding orbital is to be used. I t  is interesting to see how far the Inui-Nordsieck type orbitals can represent the distortions in the is  orbitals of the bonding molecular orbital. With this end in view, in this paper we have made sample calculations of the energy of the state of I t  is also expected that the use of different sets ofparameters for thc^  1 s orbitals will mak(^ it possible to rej)resent the distortions in the antibonding state propt^rly.C A I. C U L A T I O N  O F  E  N E  K (J Y I N  V E U K A L SFor the state of inolocule, the molecular orbital may be representedas,'I^^Xa+ Xb — (I)Xa and Xb being the atomic orbitals of the two nuclei of Hg * and are given asA'a =  .f  ... (2)a and being the parameters of the atomic orbitals andi  {ra+r(>)lit -|V (ra-r„)IR )where R  is the distance between two nuclei, r« and rj, are the distances of the elec­tron from the nuclei a and b respectively.The Hamiltonian of the system, in atomic units is given by... (3)/ / = 7 "- „ -  -  +  -EBThe energy of the system may be written asIff ^(4)(5)We define the following integralsJ Xadr =I XaXbdr -.nR^nR^EF... (6)f  X u(~V‘)Xa<lr ^  fXb(-V^)X6dT -  nB d  /  Xai-V^)XbdT = Sxbi ' -- JtRIOn the Representation of the Distortions, etc. 229i _  drfattR^ Kdr[ XaXb^ drJ r«XaXb^ dr fhnR^MnR^ N(7)The expressions for the integrals in Eq. (6) have been given in the Appendix. In  terms of (7) the energy may he written as.E(a, fi\ R) XRYR^withX  -  2[-(/f+X+J»/-|-iV)/(A’ l-/’)H  I Y  ^2{G+J)l(fiJ+F)(»)(»a)( « h )For a particular value of R. the values of are to be varied till the minimumvalue of the energy is obtained. First, the parameters were varied at an interval of 0.125 by using the tables of Miller et al. (1958). The exact values of a, /J which gave the minimum value of E  were obtained by the method of Sakamoto and Ishiguro (1956).TABLE TEnergy of the stab* of for R — 2auWave functionOne parameter® One parameter® Two parameter® Three parameter® PresentV a lu e s  o f  th e  p a r a m e te r s- 1I  --1.293a -1.3625 p r= .9100Energy —Eau  0.55377 0.58651 0.59980 0.60183 0.60228Bates et. al. (1953) (aotual)0.60262« Miller and Lykos (1962)2^30 S. Chatterjee and A . K . BaruaR E S U L T S  A N D  D T S V U S S I O NTh(‘ results of our (calculation at i? — 2 a a are shown in Table I together with the result of a few other accurate (calculations including ,the exact values obtained by Bates rt al, (1954). It may be scon that our values obtained with only a two-parameter wavefunction is in bettor agreement with the exact values of Bates ff al. (1954) than even the values obtained with three parameter hybrid orbitals used by Miller and l^ykos (1962). The present sample calculations show that the Inui-Nordsieck orbitals are flexible enough to represent adequately the distortions in the Is  orbitals in the bonding orbital of a homohucloar diatomic? molecuk'. In fact, they represent thc^  atomic charge chjuds in a molecule better than th(‘ cornplicatc'd combinations of different 8.T.O.’s. Further studies of the repn^simtation of the distortion of atomic orbitals in molecular orbitals on tlu^  basis of Inui-N()rdsie(?k type orbitals are in progress.The authors are grateful to Professor B. N. Srivastava for his interest and encouragement.R E F E R E N V E SRates, D. Rm Ledsham, K., and StowHi'l, A. L., ]9r»3, Phil. Trr/r?.s. Roy. Soc. (London), A 246, 21 f).Rarua, A. K., and (UiaKorjee, >S., 1964, Mol. P h y s . ,  7, 443.Oeller, M., Frost, A. A., and Lykos, V. D., 1902, J. Chem. Phya., 86, 2693.Harris, F. E., 1960, J. Chem. Phys., 82, 3.Huzinagn, S., 1957, Prog. Theor. Phys., 17, 169.Miller, R. V., and Lykos, ? . (L, 1962, J. Chem.. Pkys.. 87, 993.Miller, J., Gorhauser, J. M., and Mat sen, F. A., 195S, Quantum Chemistry Integrals and Tables (Austin: University of Texas Press).8akam)to, M., and Tshiguro, E., 1956, Prog. Theor. Phys., 15, 37,

On the Representation of the Distortion in ls Orbitals in The Bonding Molecular Orbital of a Homonuclear Diatomic Molecule

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On the Representation of the Distortion in ls Orbitals in The Bonding Molecular Orbital of a Homonuclear Diatomic Molecule

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