Zhixin Qian

Quantum-mechanical interpretation of time-dependent density-functional theory

Abstract In this paper we derive the differential virial theorem for both time-dependent (TD) Schrodinger theory and Kohn-Sham (KS) density-functional theory. As such we obtain an exact integral expression for the TD electron-interaction potential of KS theory that is independent of the choice of action. The expression, valid for general TD phenomena other than the ionization or scattering process, is afforded the physical interpretation at each instant of time as being the work done to move an electron in a conservative field. The field is a sum of four component fields representative of Pauli and Coulomb correlations, correlation-kinetic effects, and as discovered here, correlations due to the difference in current densities of the KS and Schrodinger systems. The interpretation further reduces to that for the corresponding electron-interaction potential of stationary-state KS theory for time-independent external potentials.

Time‐dependent differential virial theorems

In this article we derive for an arbitrary, real, local (multiplicative), time-dependent (TD) external potential, the differential form of the virial theorem for the pure state in TD Schrodinger theory. We contrast this pure-state theorem with the many-body theory equation of motion for both equilibrium and nonequilibrium phenomena. We also derive the corresponding pure-state theorem for a model system of noninteracting fermions with equivalent TD density. These theorems are valid for both adiabatic and sudden switching on of the external potential. The theorems furthermore lead to a line-integral expression for the local effective potential of the noninteracting system that may be provided the physical interpretation, at each instant of time, as being the work done to move an electron in the force of a conservative field.

Atomic shell structure in Hartree theory

In this paper we show that atomic shell structure is exhibited throughout the periodic table, and accurate core–valence separations thereby obtained, via the radial probability density determined from the uncorrelated wave functions of Hartree theory. Further, essentially equivalent results are obtained via Hartree-theory-level quantal density functional theory in an approximation in which the correlation contributions to the kinetic energy are also neglected. Thus, accurate atomic shell structure can be obtained solely via electrostatic fields determined from charge distributions that are derived from wave functions which neither obey the Pauli exclusion principle nor incorporate Coulomb correlations.

PHYSICAL ORIGIN OF THE DISCONTINUITY OF THE KOHN-SHAM THEORY EFFECTIVE POTENTIAL

Abstract We derive a formal line-integral expression for the discontinuity that occurs in the electron-interaction potential of the Kohn-Sham (KS) theory as the electron number passes through an integer. The discontinuity may thus be interpreted as the work done to move an electron in the force of a conservative field. This result is derived via the rigorous description of the KS theory in terms of density matrices, and as such we provide an explanation for the physical origin of the discontinuity from a distinctly different perspective. The derivation further shows that the different electron correlations represented in the KS potentials, viz. those due to the Pauli exclusion principle, Coulomb repulsion, and correlation-kinetic effects, all contribute to the discontinuity, and the contribution of each to the conservative field is given explicitly. The same physics shows that the KS representation of Hartree-Fock and Hartree theories as well as other approximations must also exhibit the discontinuity, and we demonstrate this for the work formalism Hartree-Fock approximation.