Rogelio Cuevas-Saavedra

Exact expressions for the Kohn–Sham exchange-correlation potential in terms of wave-function-based quantities

ABSTRACT Several workers have deduced various exact expressions for the Kohn–Sham exchange-correlation potential in terms of quantities computable from the interacting and noninteracting wave functions of the system. We show that all these expressions can be obtained by one general method in which the interacting N-electron wave function is expanded in products of one- and (N − 1)-electron functions. Different expressions correspond to different choices of the latter functions. Our analysis unifies and clarifies the previously proposed exact treatments of the exchange-correlation potential, and suggests new ways of expressing this quantity.

Kohn–Sham exchange-correlation potentials from second-order reduced density matrices

We describe a practical algorithm for constructing the Kohn-Sham exchange-correlation potential corresponding to a given second-order reduced density matrix. Unlike conventional Kohn-Sham inversion methods in which such potentials are extracted from ground-state electron densities, the proposed technique delivers unambiguous results in finite basis sets. The approach can also be used to separate approximately the exchange and correlation potentials for a many-electron system for which the reduced density matrix is known. The algorithm is implemented for configuration-interaction wave functions and its performance is illustrated with numerical examples.

EXCHANGE-CORRELATION FUNCTIONALS FROM THE IDENTICAL-PARTICLE ORNSTEIN-ZERNIKE EQUATION: BASIC FORMULATION AND NUMERICAL ALGORITHMS

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.

Generalized average local ionization energy and its representations in terms of Dyson and energy orbitals

Ryabinkin and Staroverov [J. Chem. Phys. 141, 084107 (2014)] extended the concept of average local ionization energy (ALIE) to correlated wavefunctions by defining the generalized ALIE as Ī(r)=-∑jλj|fj(r)|(2)/ρ(r), where λj are the eigenvalues of the generalized Fock operator and fj(r) are the corresponding eigenfunctions (energy orbitals). Here we show that one can equivalently express the generalized ALIE as Ī(r)=∑kIk|dk(r)|(2)/ρ(r), where Ik are single-electron removal energies and dk(r) are the corresponding Dyson orbitals. The two expressions for Ī(r) emphasize different physical interpretations of this quantity; their equivalence enables one to calculate the ALIE at any level of ab initio theory without generating the computationally expensive Dyson orbitals.

Kinetic Energy Density Functionals from Models for the One-Electron Reduced Density Matrix

Orbital-free kinetic energy functionals can be constructed by writing the one-electron reduced density matrix as an approximate functional of the ground-state electron density. In order to utilize this strategy, one needs to impose appropriate N-representability constraints upon the model 1-electron reduced density matrix. We present several constraints of this sort here, the most powerful of which is based upon the March-Santamaria identity for the local kinetic energy.

Two-point weighted density approximations for the kinetic energy density functional

We construct a model for the one-electron reduced density matrix that is symmetric and which satisfies the diagonal of the idempotency constraint and then use this model to evaluate the kinetic energy. This strategy for designing density functionals directly addresses the N-representability problem for kinetic energy density functionals. Results for atoms and molecules are encouraging, especially considering the simplicity of the model. However, like all of the other kinetic energy functionals in the literature, quantitative accuracy is not achieved.

A Gradient Corrected Two-Point Weighted Density Approximation for Exchange Energies

A successful symmetric, two-point, nonlocal weighted density approximation for the exchange energy of atoms and molecules can be constructed using a power mean with constant power p when symmetrizing the exchange-correlation hole [Phys. Rev. A 85, 042519 (2012)]. In this work, we consider how this parameter depends on the system’s charge. Exchange energies for all ions with charge from \(-1\) to \(+12\) of the first eighteen atoms of the periodic table are computed and optimized. Appropriate gradient corrections to the current model, based on rational functions, are designed based on the optimal p values we observed for the ionic systems. All of the advantageous features (non-locality, uniform electron gas limit and no self-interaction error) of the original model are preserved.