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

Abstract

Specific features of application of the Hartree−Fock method with the orthogonality restrictions proposed earlier (V. N. Glushkov, Chem. Phys. Lett. 287, 189 (1998)) to calculations of energies of highly excited electronic states of the same symmetry are studied. Different schemes are discussed that allow one to avoid the variational collapse in constructing determinant wave functions for excited states. The accuracy of the method is demonstrated for the example of calculation of more than 30 excited states of He and Li atoms.

State-Targeted Energy Projection: A Simple and Robust Approach to Orbital Relaxation of Non-Aufbau Self-Consistent Field Solutions

“…The MOM procedure attempts to avoid variational collapse by selecting the occupied MOs at each SCF iteration based on their overlap with a set of reference orbitals, an approach that is formally simple, conceptually appealing, and introduces only a small additional overhead on top of the usual cost per SCF iteration. This approach is considerably simpler than alternatives based on constrained variation − or modified variational principles, − and that simplicity facilitates the use of ground-state machinery to compute energy gradients and properties. The non-Aufbau SCF solutions obtained using MOM are generally not orthogonal to the ground-state determinant, a fact that has consequences for properties such as oscillator strengths, although often the optimized excited-state determinants are nearly orthogonal to the SCF ground state .…”

Highly Excited States from a Time Independent Density Functional Method

“…Such calculations for highly excited states have been carried out only recently [41]. Comparison of the calculated energies of excitation from the 1s 2 3s state with the high precision results [39] shows that the proposed implementation for ESs yields excellent agreement with the precision excitation energies (compare columns 5 and 6 of Table 6). Our calculation of the x-COEP ground state (1s 2 2s) energy yields E =´7.431724 hartrees.…”

“…[43] were restricted to only singly excited states. Therefore we compare doubly excited energies with our HF calculations [39] and accurate theoretical calculations (named in Tables 2-4 as E exact ) based on a configuration interaction approach with the explicitly correlated Hylleraas basis set functions [40]. A comparison of excited state energies presented in x-COEP-bgs and x-COEP-Vgs columns of Table 1 with the fully optimized results (x-COEP column) shows that basis set optimization plays a crucial role for a correct description of excited states with respect to optimization of potential parameters.…”

“…[39] and high precision data obtained by the configuration interaction method in the basis set of Hylleraas functions that explicitly depend on interelectron separations [40,41]. Calculations were carried out using 42s-gaussians.…”

Density Functional Theory of Highly Excited States of Coulomb Systems

“…Table 1 presents the total energies for the ground state and the excited states with configuration 1s 2 ms, m = 2, ..., 7 for the Li atom. The KLI values can be directly compared with the exchange-only results of the spin-dependent localized Hartree-Fock (SLHF) [63], xCOEP [64], and Hartree-Fock (HF) [65] methods. x-COEP refers to exchange-only constrained optimized effective potential (xCOEP) methodology [64].…”