Triplet instability in semiempirical RPA calculations of conjugated systems containing heteroatoms

Abstract

It is well known [l-51 that the Hartree-Fock (HF) ground state of many closed-shell molecules appears to be triplet unstable in the random-phase approximation (RPA). Recently, we have studied [6] in detail the effect of semiempirical parameters on the RPA triplet instability of conjugated hydrocarbons using a pw-type model Hamiltonian. The molecular orbitals of conjugated hydrocarbons being rather insensitive to the choice of semiempirical parameters, the triplet instability in these systems mainly stems from the possible variation of the A and B matrices with respect to such parameters. However, in conjugated systems containing heteroatoms, the molecular orbitals themselves depend to some extent on the choice of parameters as a result of which the parametric dependence of the A and B matrices will be somewhat different from that in conjugated hydrocarbons. This indicates that the nature ofthe triplet instability in conjugated systems with and without heteroatoms may not be identical. It is the purpose of this paper to verify this point taking formaldehyde, borazine, and s-triazine as test molecules. We have omitted more complicated molecules because of the involvement of too many semiempirical parameters.Exactly the same method of calculation as employed by Guha Niyogi et al.[5] has been followed here.The Roothaan-Mulliken model [7,8] is used to describe the a-bonding in borazine. The C-0, C-N.and B~-N bond lengths are taken to be 1.21, 1.34, and 1.44 A, respectively. For the one-center electron repulsion integrals, the necessary input parameters are taken from Hinze and Jaffe [9]. The two-center repulsion integrals are evaluated using the approximations due to Mataga and Nishimoto ( M N ) [ eV. and the results for the limiting value o f @ = 0 were obtained by extrapolation.In Figure 1 the p-dependence of the oxygen 2 a AO coefficients in the bonding and antibonding MOS of formaldehyde is shown. In all three cases, i.e., M I , Ohno, and MN approximations, with the decrease of 1/31, the bonding and antibonding M O~ become more and more localized on the oxygen and carbon atoms, respectively. For the M I approximation, as p -0, the ground state of formaldehyde passes on very smoothly to a separated-atom-type H F state. This is almost the situation with the Ohno approximation. In this case, however, the variation of the AO coefficients is somewhat more sensitive t o p than that in the M I approximation at small values of this parameter. The situation with the MN approximation is appreciably different from the other two cases. The variation is rather slow in this case, as a result of which the molecule maintains its symmetry throughout the variation of and no separated-atom-type H F state is obtained at the limiting value of fl = 0. These results can be qualitatively understood from a consideration of the perturbation theory.