A variationally stable compact Hartree–Fock-style wavefunction for a non-degenerate first excited state

Abstract

A compact approximate wavefunction for a non-degenerate first excited state constructed as a Slater determinant from which the ground state Hartree–Fock (HF) wavefunction has been projected out explicitly is introduced, together with all expressions required for its calculation through gradient-based energy optimization schemes. The explicit projection makes this wavefunction suitable for the description of a non-degenerate first excited state which is of the same symmetry as the HF ground state without any danger of a variational collapse to the lower energy ground state. The equations allowing the calculation of a spin-unrestricted version of the proposed wavefunction have been implemented in code. The results of excited state calculations on HeH+, H2, C2, N2, H2O and H2O2 show that this excited state wavefunction which, effectively, is comprised of just two Slater determinants, only one of which is optimized variationally, is capable of producing results which compare favourably to those coming from standard approaches such as single-excitation configuration interaction (CIS), time-dependent HF (TDHF), symmetry-adapted-cluster CI (SAC-CI) and equations-of-motion coupled-cluster with singles and doubles (EOM-CCSD).