Effective local potentials for excited states

Abstract

The constrained variational Hartree-Fock method for excited states of the same symmetry as the ground state [Chem. Phys. Lett. 287, 189 (1998)] is combined with the effective local potential (ELP) method [J. Chem. Phys. 125, 081104 (2006)] to generate Kohn-Sham-type exact-exchange potentials for singly excited states of many-electron systems. Illustrative examples include the three lowest (2)S states of the Li and Na atoms and the three lowest (3)S states of He and Be. For the systems studied, excited-state ELPs differ from the corresponding ground-state potentials in two respects: They are less negative and have small additional "bumps" in the outer electron region. The technique is general and can be used to approximate excited-state exchange-correlation potentials for other orbital-dependent functionals.

Orthogonality of determinant functions in the Hartree-Fock method for highly excited electronic states

“…Derivation of the HF equations for orbitals of an ES in the formalism of the asymptotic projection (AP) methodology has been considered in detail in our earlier [27,32]. Below we will restrict ourselves to the initial problem and will focus our attention on the matrix representation of equations for an arbitrary ES.…”

Deflation techniques in quantum chemistry: Excited states from ground states

“…It must be noticed that our HF method for excited states is different from other SCF extensions to excited states . Traditional SCF extensions to excited states, as the method described above, require some knowledge of the ground state, but they are derived in a different way.…”

“…This is essential for these approaches as they attempt to find an approximation to the excited state in the form of a single Slater determinant relating the spin orbitals of the excited state determinant to the spin orbitals of the ground state determinant by means of Brillouin's theorem and/or orthogonality constraints. [29,31–36] This can be seen analyzing the constrained variational HF method for excited states, which is based on the orthogonality between the ground and excited states. Choosing the ground state as one determinant allows formulating the orthogonality constraint between the highest occupied spin orbitals of the ground state Slater determinant and the spin orbitals forming the excited state determinant, without the need to consider the complete ground state determinant …”

“…In the past, many attempts have been made in order to extend ground state tools to the study of excited states, particularly, generalizations of the RR principle suitable to tackle excited states problems . As a result, many excited states extensions of ground state methods have been obtained, which are different from its ground state counter parts despite being closely related . In other words, the methods used to study excited states are generally different from the methods designed for ground states.…”

Communication: Kohn-Sham theory for excited states of Coulomb systems

“…3-5), although several time-independent approaches have also been given to treat excited states within DFT. [6][7][8][9][10][11][12][13][14][15][16][17][18] The subspace theory of Theophilou 6 and its generalization by Gross, Oliveira, and Kohn 7 are complicated by the requirement that a whole ensemble of states has to be considered. Individual excitedstates can be targeted using time-independent approaches based on the adiabatic connection 19 or the constrained search.…”