Biomedical subjects

Xiao-Yin Pan

Publications and source records attributed to Xiao-Yin Pan.

4 recordsLinked to original sources

PubMed2006

Fundamental importance of the Coulomb hole sum rule to the understanding of the Colle-Salvetti wave function functional.

In this paper we consider the general form of the correlated-determinantal wave function functional of Colle and Salvetti (CS) for the He atom. The specific form employed by CS is the basis for the widely used CS correlation energy formula and the Lee-Yang-Parr correlation energy density functional of Kohn-Sham density functional theory. We show the following: (i) The key assumption of CS for the determination of this wave function functional, viz., that the resulting single-particle density matrix and the Hartree-Fock theory Dirac density matrix are the same, is equivalent to the satisfaction of the Coulomb hole sum rule for each electron position. The specific wave function functional derived by CS does not satisfy this sum rule for any electron position. (ii) Application of the theorem on the one-to-one correspondence between the Coulomb hole sum rule for each electron position and the constraint of normalization for approximate wave functions then proves that the wave function derived by CS violates charge conservation. (iii) Finally, employing the general form of the CS wave function functional, the exact satisfaction of the Coulomb hole sum rule at each electron position then leads to a wave function that is normalized. The structure of the resulting approximate Coulomb holes is reasonably accurate, reproducing both the short- and the long-range behavior of the hole for this atom. Thus, the satisfaction of the Coulomb hole sum rule by an approximate wave function is a necessary condition for constructing wave functions in which electron-electron repulsion is represented reasonably accurately.

Models, Theoretical↗

PubMed2004

Determination of a wave function functional.

We propose expanding the space of variations in traditional variational calculations for the energy by considering the wave function psi to be a functional of a set of functions chi:psi=psi[chi], rather than a function. A constrained search in a subspace over all functions chi such that the functional psi[chi] satisfies a sum rule or leads to a physical observable is then performed. An upper bound to the energy is subsequently obtained by variational minimization. The rigorous construction of such a constrained-search-variational wave function functional is demonstrated.

Quantum Theory↗

PubMed2004

Quantal density functional theory of the hydrogen molecule.

In this paper we perform a quantal density functional theory (Q-DFT) study of the hydrogen molecule in its ground state. In common with traditional Kohn-Sham density functional theory, Q-DFT transforms the interacting system as described by Schrodinger theory, to one of noninteracting fermions--the S system--such that the equivalent density, total energy, and ionization potential are obtained. The Q-DFT description of the S system is in terms of "classical" fields and their quantal sources that are quantum-mechanical expectations of Hermitian operators taken with respect to the interacting and S system wave functions. The sources, and hence the fields, are separately representative of all the many-body effects the S system must account for, viz. electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and correlation-kinetic effects. The local electron-interaction potential energy of each model fermion is the work done to move it in the force of a conservative effective field that is the sum of the individual fields. The Hartree, Pauli, Coulomb, and correlation-kinetic energy components of the total energy are also expressed in virial form in terms of the corresponding fields. The highest occupied eigenvalue of the S system is the negative of the ionization potential energy. The Q-DFT analysis of the hydrogen molecule is performed employing the highly accurate correlated wave function of Kolos and Roothaan.

Journal Article↗

PubMed2003

Quantal density functional theory of degenerate states.

The treatment of degenerate states within Kohn-Sham density functional theory is a problem of long-standing and current interest. We propose a solution to this mapping from the interacting degenerate system to that of the noninteracting fermion model whereby the equivalent density and energy are obtained via the unifying physical framework of quantal density functional theory. We describe the quantal theory of both ground and excited degenerate states, and for the cases of both pure state and ensemble v-representable densities. The quantal description further provides a rigorous physical interpretation of the corresponding Kohn-Sham energy functionals of the density, ensemble density, bidensity and ensemble bidensity, and of their respective functional derivatives. We conclude with examples of the mappings within the quantal theory.

Journal Article↗