Abstract
Theoretical discussions are given on issues in relativistic molecular
orbital theory to which the quantum electrodynamics (QED) Hamiltonian
is applied. First, several QED Hamiltonians previously proposed are
sifted by the orbital rotation invariance, the charge conjugation and
time reversal invariance, and the nonrelativistic limit. The
discussion on orbital rotation invariance shows that orbitals giving a
stationary point of total energy should be adopted for QED
Hamiltonians that are not orbital rotation invariant. A new total
energy expression is then proposed, in which a counter term
corresponding to the energy of the polarized vacuum is subtracted from
the total energy. This expression prevents the possibility of total
energy divergence due to electron correlations, stemming from the fact
that the QED Hamiltonian does not conserve the number of
particles. Finally, based on the Hamiltonian and energy expression,
the Dirac–Hartree–Fock (DHF) and electron
correlation methods are reintroduced. The QED-based DHF equation is
shown to give information on positrons from negative-energy orbitals
while having the same form as the conventional DHF equation. Three
electron correlation methods are derived: the QED-based configuration
interactions and single- and multireference perturbation
methods. Numerical calculations show that the total energy of the QED
Hamiltonian indeed diverged and that the counter term is effective in
avoiding the divergence. The relativistic molecular orbital theory
presented in this article also provides a methodology for dealing with
systems containing positrons based on the QED Hamiltonian.