Pair density functional theory by means of the correlated wave function

We present a density functional scheme for calculating the pair density (PD) by means of the correlated wave function. This scheme is free from both of problems related to PD functional theory, i.e., (a) the need to constrain the variational principle to $N$-representable PDs and (b) the development of a kinetic energy functional. By using the correlated wave function, the searching region for the ground-state PD is substantially extended as compared with our previous theory[Physica B \textbf{372} (2007), in press]. The variational principle results in the simultaneous equations that yield the best PD beyond the previous theory, not to mention the Hartree-Fock approximation

A Proposal of the Approximate Kinetic Energy Functional of the Pair Density Functional Theory

We propose the approximate kinetic energy (KE) functional of the pair density (PD) functional theory on the basis of the coupling-constant expression that is recently derived [Phys. Rev. A 85, 062508 (2012)]. The proposed KE functional, which is called the “correlated Gaussian model”, consists of the modified version of the Thomas-Fermi (TF) model and correlation energy functional of the local density approximation. We check the validity of the correlated Gaussian model by means of numerical calculations for the Ne atom. It is shown that the correlated Gaussian model gives better results of not only the KE, Hartree energy, exchange–correlation (xc) energy, potential energy but also the xc-hole than the previously proposed correlated TF model [J. Phys.: Conf. Ser. 454, 012056 (2013)].ArticleJPS Conference Proceedings. 3:017009 (2014)journal articl

Extension of the search region of pair densities by means of the scaling of the electron coordinates

26th International Conference on Low Temperature Physics (LT26) IOP PublishingWe present a scheme for correcting the pair density (PD) to get it close to the ground state one. The search region of PDs is efficiently extended by adding the uniformlyscaled PDs to its elements. The key point is that the search region of PDs is kept within the set of N-representable PDs. The validity of this scheme is confirmed by numerical calculations of neutral neon atom. It is shown that the root-mean-square error of the electron-electron interaction and external potential energies, which can be a benchmark for the error of the PD, is reduced to about two-third without additional heavy calculations.ArticleJournal of Physics: Conference Series. 400:032019 (2012)journal articl

Checking the validity of the correlated Thomas-Fermi functional in the pair density functional theory

24th IUPAP Conference on Computational Physics (IUPAP-CCP 2012)To check the validity of the recently proposed kinetic energy (KE) functional of the pair density (PD) functional theory, we perform the numerical calculation for the neutral Ne atom. This is the first computational trial for the PD functional theory which includes the KE functional that is approximately derived on the basis of the rigorous expression with the coupling-constant integration. In this work we adopt the correlated Thomas-Fermi functional as the approximate KE functional. Although it is shown that non-negligible errors exist in the resulting PD, the present results will be useful as reference data in cases of developing further the approximate KE functional.ArticleJournal of Physics: Conference Series. 454:012056 (2013)journal articl

Approximate forms of the pair-density-functional kinetic energy on the basis of a rigorous expression with coupling-constant integration

We propose approximate kinetic energy (KE) functionals of the pair-density (PD)-functional theory on the basis of the rigorous expression with the coupling-constant integration (RECCI) that has been recently derived [Phys. Rev. A 85, 062508 (2012)]. These approximate functionals consist of the noninteracting KE and correlation energy terms. It is found that the Thomas-Fermi-Weizsacker functional is shown to be better as the noninteracting KE term than the Thomas-Fermi and Gaussian model functionals. It is also shown that the correlation energy term is also indispensable for the reduction of the KE error, i.e., reductions of both inappropriateness of the approximate functional and error of the resultant PD. Concerning the correlation energy term, we further propose an approximate functional in addition to using the existing familiar functionals. This functional satisfies the scaling property of the KE functional, and yields a reasonable PD in a sense that the KE, electron-electron interaction, and potentials energies tend to be improved with satisfying the virial theorem. The present results not only suggest the usefulness of the RECCI but also provide the guideline for the further improvement of the RECCI-based KE functional.ArticlePHYSICAL REVIEW A. 90(6):062511 (2014)journal articl

N-representability of the Jastrow wave function pair density of the lowest-order

Conditions for the N-representability of the pair density (PD) are needed for the development of the PD functional theory. We derive sufficient conditions for the N-representability of the PD that is calculated from the Jastrow wave function within the lowest order. These conditions are used as the constraints on the correlation function of the Jastrow wave function. A concrete procedure to search the suitable correlation function is also presented.ArticleSCIENTIFIC REPORTS. 7:7590 (2017)journal articl

Computational pair density functional theory: A proposal for the kinetic energy functional

We present a computational pair density (PD) functional theory using multiple Slater determinants in constructing the PD. Compared to the effective initial scheme [M. Higuchi and K. Higuchi, Phys. Rev. B 78, 125101 (2008)], the search region for the ground-state PD is substantially extended within the set of N-representable PDs. The merit of the present scheme is to guarantee the resultant PD to be N-representable and to describe correlation effects beyond the effective initial scheme, which enables us to tackle with the development of the approximate form of the kinetic energy functional. We derive two restrictive conditions on the kinetic energy functional. With the aid of these restrictive conditions, we also propose several types of approximate functionals of the kinetic energy. To check the abilities and limitations of the present scheme including such approximate functionals, actual calculations are performed for the neutral neon atom. The results show that the present scheme provides the N-representable and correlated PDs, though it would have some limitations. What we need to do first for improvement of the computational PD functional theory is that the development of the approximate functional of the kinetic energy is further advanced along the present scheme.ArticlePHYSICAL REVIEW B. 82(15):155135 (2010)journal articl