Showing papers by "Ernest R. Davidson published in 2010"

Koopmans’s theorem in the restricted open-shell Hartree–Fock method. II. The second canonical set for orbitals and orbital energies

Abstract: A treatment of the validity of Koopmans’s theorem (KT) in the restricted open-shell Hartree–Fock (ROHF) method can be separated into two essentially different cases. The first of them involves the one-electron processes X→Xj± in which the spin state of an ion Xj± having a hole or an extra electron in the closed, open or virtual orbital ϕj is correctly described by a one-determinant wave function. This case was analyzed using different methods by Plakhutin et al. [J. Chem. Phys. 125, 204110 (2006)] and by Plakhutin and Davidson [J. Phys. Chem. A 113, 12386 (2009)]. In the present work we analyze more complex processes where the state of an ion cannot be described by a single determinant. An example of such processes is the removal of an alpha electron from the closed shell of a high-spin half-filled open-shell system X. For this case we give a slightly generalized formulation of KT in both the “frozen” orbital approximation (i.e., within the canonical ROHF method) and the limited configuration interaction ...

Spin-state splittings, highest-occupied-molecular-orbital and lowest-unoccupied-molecular-orbital energies, and chemical hardness

Abstract: It is known that the exact density functional must give ground-state energies that are piecewise linear as a function of electron number. In this work we prove that this is also true for the lowest-energy excited states of different spin or spatial symmetry. This has three important consequences for chemical applications: the ground state of a molecule must correspond to the state with the maximum highest-occupied-molecular-orbital energy, minimum lowest-unoccupied-molecular-orbital energy, and maximum chemical hardness. The beryllium, carbon, and vanadium atoms, as well as the CH(2) and C(3)H(3) molecules are considered as illustrative examples. Our result also directly and rigorously connects the ionization potential and electron affinity to the stability of spin states.