Dear colleagues,
In my research, I've
encountered a question about real-valued versus complex-valued molecular
orbitals. Normally, most software programs that perform DFT, Hartree-Fock,
coupled cluster, or configuration interaction type quantum chemistry
computations on molecules use real-valued
molecular orbitals.
My first question is
whether there exists any theorem that shows this will converge to the ground
state (i.e., that using complex valued orbitals would not reach a lower energy
state) when the Hamiltonian does not contain any spin-orbit coupling or applied
magnetic field? In other words, when the multi-electronic Hamiltonian is
comprised of the normal terms: electron kinetic energy, nuclear-electron
potential energy, nuclear-nuclear potential energy, electron-electron Coulomb
& exchange-correlation energies.
My second question
is regarding periodic DFT calculations for which many software programs use
complex-valued molecular orbitals. Are their any kinds of chemical bonds that
exist for complex-valued molecular orbitals that do not exist for real-valued
molecular orbitals? Are their any new bonding symmetries made possible for the
complex-valued orbitals that cannot exist for the real-valued orbitals? For
real-valued molecular orbitals, the primary covalent bond-orbital symmetries are
sigma, pi, delta, and phi. Do complex-valued orbitals enable any additional
bond-orbital symmetries?
I sincerely appreciate any
insights into this topic you can
provide.
Tom