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Electronic correlation is a fundamental topic in many-electron systems. To characterize this correlation, one may introduce the concept of exchange-correlation hole. In this work, we first briefly revisit its definition and relation to electron and geminal densities, followed by their intimate relations to copula functions in probability theory and statistics. We then propose a copula-based approach to estimate the exchange-correlation hole from the electron density. It is anticipated that the proposed scheme will become a promising ingredient towards the future development of strongly correlated electronic structure calculations. [ABSTRACT FROM AUTHOR]

Density functional theory (DFT) is nowadays the leading theoretical framework for quantum description of materials from first principles. Being an exact theory on one hand and computationally efficient on the other hand, DFT allows to address large and complex many‐electron systems and accurately predict their properties. The predictive power of DFT critically depends though on an accurate approximation to the generally unknown exchange‐correlation (xc) energy functional. Approximations can be constructed from first principles by satisfying known properties of the exact functional. In this work I review two such exact properties: the asymptotic behavior of the xc energy density per particle and the asymptotic behavior of the Kohn‐Sham potential, in finite many‐electron systems. The derivation of the asymptotic forms for both quantities is reviewed, employing the concepts of the adiabatic connection and of the xc hole with relation to the first quantity and the exact electron factorization approach for the second one. Furthermore, it is shown that the correct asymptotic behavior of one of the aforementioned quantities does not guarantee a correct behavior of the other. These quantities are related via the xc hole response function, which is defined, examined and its exact exchange part is analytically derived. The extent to which existing xc approximations satisfy the named exact properties is reviewed and the relationship between correct asymptotics and freedom from one‐electron self‐interaction in DFT is discussed. Finally, a strategy for development of advanced approximations for exchange and correlation with a correct asymptotic behavior is suggested. [ABSTRACT FROM AUTHOR]

Abstract: The pair density (PD) functional theory is regarded as not only an extension of the density functional theory but also one of the reduced density matrix theories. The main feature of the PD functional theory is that the PD, as a basic variable, essentially contains more information on the electron–electron interaction than the electron density. In order to develop the PD functional theory, there exist two kinds of problems to solve. In this paper, we review our recent approaches about how to tackle with these problems, and show the latest results of the atomic structure calculations for Ne. [Copyright &y& Elsevier]

We adapt the classical Ornstein-Zernike equation for the direct correlation function of classical theory of liquids in order to obtain a model for the exchange-correlation hole based on the electronic direct correlation function. Because we explicitly account for the identical-particle nature of electrons, our result recovers the normalization of the exchange-correlation hole. In addition, the modified direct correlation function is shorted-ranged compared to the classical formula. Functionals based on hole models require six-dimensional integration of a singular integrand to evaluate the exchange-correlation energy, and we present several strategies for efficiently evaluating the exchange-correlation integral in a numerically stable way. [ABSTRACT FROM AUTHOR]

The early difficulties in accounting for long-range van der Waals interactions in the framework of density functional theory (DFT) have been overcome to a certain extent in recent works by several groups, and those interactions can be computed numerically. In this paper a derivation of the analytical form of the attractive van der Waals interaction between two neutral atoms with polarizabilities α1 and α2 at large distance R, namely E int=− C 6 α1 α2/ R 6 is performed within the context of DFT. Use is made of the properties of the Coulomb correlation hole, and it is shown that nonlocal Coulomb correlations are responsible for long-range dispersion interactions. [ABSTRACT FROM AUTHOR]