A size extensive energy functional derived from a double configuration interaction approach: The role of N representability conditions

Abstract

Starting from a configuration interaction (CI) approach including only doubly excited configurations, the corresponding energy functional is modified by introduction of a topological factor in the normalization condition of the CI coefficients in such a way that it gets inherently size extensive. Constraints imposed by N representability conditions on the modified functional are discussed and lead to a specific choice of the topological factor. The basic variable in the modified energy functional is the second-order reduced density matrix parametrized in terms of CI-like coefficients. Test calculations for a variety of small molecules show that the numerical results obtained with the new functional are in very good agreement with those obtained from coupled cluster singles doubles calculations.

Performance of one-body reduced density-matrix functionals for the homogeneous electron gas

“…20,21 On the other hand, the Müller functional yields the correct dissociation limit but, in all cases, overestimates substantially the correlation energy. 20,21 In the last decade, several other functionals of the 1-RDM have been introduced [8][9][10][11][12][13][14][15][16][17] and applied to atomic and molecular systems. Recently, Gritsenko et al 13 proposed improved 1-RDM functionals based on a hierarchy of repulsive corrections to the Müller functional.…”

“…[1][2][3][4] Nevertheless, only relatively recently have approximate total-energy functionals of the 1-RDM been used in practical applications. [5][6][7][8][9][10][11][12][13][14][15][16][17] All these approximate functionals give a satisfactory account of electronic correlations in small atoms and molecules at the equilibrium distance. The latest generation of functionals performs equally well at the molecular dissociation limit.…”

Parametric two-electron reduced-density-matrix method with application to diradical rectangular H4

“…A weaker set of conditions are implied by the 2-positivity conditions:, the Cauchy-Schwarz inequalities [18,19,33]:…”

“…The parametric 2-RDM method can be used to obtain 2 D directly without the N -particle wavefunction [18,19,33,[43][44][45][46][47][48]. We parameterize the 2-RDM as a functional of itself.…”

“…They parameterized the 2-RDM as a functional of the parameters of the configuration interaction doubles (CID) wave function with the goal of developing a more general parametrization beyond a specific wave-function ansatz. More recently, Kollmar [33] and one of the authors (Mazziotti) [18,19] extended the work of Weinhold and Wilson to obtain 2-RDM parameterizations that are size extensive generalizations of the CID parametrization.…”