One - determinantal pure state versus ensemble Kohn-Sham solutions in the case of strong electron correlation: CH 2 and C 2

Abstract

The possibility that the Kohn-Sham (KS) solution for a noninteracting auxiliary electron system is not the conventional one-determinantal pure state but a few-determinantal ensemble has been investigated. The KS solutions (the exchange-correlation potential v xc and the orbitals) have not been approximated by local-density or density-gradient approximations but have been constructed from an accurate ab initio electron density. The lowest singlet states of the CH2 and C2 molecules have been selected for this investigation since for these cases the ground-state wave function Ψ is nondegenerate but has an essentially multideterminantal character (electron correlation is strong). For C2 the dependence of the type of KS solution on the bond distance R(C–C) has been studied at the QZ level. For the shortest distance considered, R(C–C)=1.8 a.u., a pure-state KS solution has been obtained. For the equilibrium distance R e(C–C)=2.348 a.u. and at larger distances ensemble solutions have been obtained with widely varying weights of the individual determinants, depending on the bond distance. For CH2 the dependence of the type of KS solution on the basis has been studied: calculation in the triple zeta (TZ) basis for the KS orbitals yields an ensemble solution, while the pure-state KS solution has been obtained in the quadruple zeta (QZ) basis. The form of the KS orbitals has been compared with that of the natural orbitals (NOs). It has been shown for the model example of the stretched H2 molecule as well as for CH2 and C2, that the KS orbitals of the pure state may be rather different from the corresponding NOs, while the occupied KS orbitals of the ensemble solution can be considered as plausible approximations to the corresponding NOs.