Electronic States of C2-Molecule, II: Effect of 2s-Shells

Abstract

Adiabatic potentials corresponding to 62 electronic states, arising 'from various configurations of the C2-molecule which consists 'of two carbon atoms with two 2p-electrons each, are calculated taking into account the effect of 2s-shells. The complete adiabatic Hamiltonian of eight electrons, but not a so-called interaction operator, is used, and direct, exchange, higher permutation, and overlapping integrals are all taken into account. The Same effective charge lC is assumed for 2s, 2ptl, and two 2p77: orbitals, and the minimum electronic energy is obtained by varying lC for each nuclear distance. It is found that !ls-shells repel 2ptl electrons and attract 2p77:-electrons. Thus (s2t12, S2t12)1~O+ state, which was found to be .attractive and deepest when the effect of 2s-shells was neglected in the previous. paper, becomes very higher and repulsive. The results of the present calculation are that the deepest state is, (s2t177:, .,2t1 77:)1.4/1 and that (s2t177:, 2t1'ii3.)1::E1I+ and (s2t111:, s211:$o)1ll .. are next and third respectively. Introdnction In the first part(l) (which will be referred to in what follows as I) of this paper we discussed the interaction between 2p-electrons of two carbon atoms in their ground states. The purpose was not only to separate the contribution of p-electrons to the binding energy of the C2-molecule from other effect but also to study the general character of the interaction between p-electrons in the complex molecule with double bonds due to p-electrons. It was found that the deepest attractive state was (2pq 2, 2p( 2)11]: in contradiction to Pauling's theory(!) which does not allow atoms with fully occupied orbitals to bind. The reasons for this result were that the binding energy is mainly supplied by the Coulomb energy and the effect of exchange and permutation energy is small owing to the large value of effective charge involved in the 2p-orbitals, and that the Coulomb energy is the larger the more q-orbitals involved in the wave function. The same phenomenon was observed in the result of calculation by Bartlett(S) on the single pp-bond. This shows that Pauling's theory can not literally be applied to any simple model for complex molecules. This was an important result of the study in the first part as well as Bartlett's result that the triplet state is deepest in the single pp-bond in contradiction to Pauling's fundamental idea.(2) We shall consider the effect of 2s-shells in the present paper in order to see the general character of interactions of a closed s-shell with Pq- and jJ1r-electrons as well as the quantitative contribution of these interactions to the binding energy