Electron and spin transfer theory based on the time-dependent variational principle

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Time-dependent variational principle (TDVP) under inequality constraints with general physical quantity expectation values has been investigated to apply for the time-development of many-electron wavefunctions in the electron- and spin-transfer processes in molecules. The Hilbert subspace in which the inequality constraints are satisfied is defined as phase-I. The subspace in which the equality constraints are active is defined as phase-II. The total action for the TDVP is defined with the direct sum of actions in subspaces. Weierstrass-Erdmann's corner condition is also considered.The spin-unrestricted Hartree-Fock (UHF) wavefunctions are often adopted as initial states of spin- and electron-transfer processes. The unpaired orbitals in the UHF wavefunctions take an important role in the transfer processes. We have investigated a handy way to find radical orbitals buried in UHF wavefunctions and the variational meaning of Koopmans' theorem. For doublet radicals, the highest occupied molecular orbital (HOMO) of α-orbitals usually corresponds to the radical orbital which is occupied by an unpaired electron. Occasionally, however, the α-HOMO fails to identify the radical orbital while the lowest unoccupied MO (LUMO) of β-orbitals indicates the radical orbital correctly. In this work, we have examined the applicability of the handy way to identify the radical orbital with the α -HOMO or the β -LUMO of UHF wavefunctions. Koopmans' theorem not only provides a numerical method to calculate approximate ionization potential energies but also has another variational meaning. We have shown that an extension of the variational meaning of the theorem to many-electron ionization processes leads naturally to the SCF equation for hole orbitals.