Approximate one-matrix functionals for the electron–electron repulsion energy from geminal theories

Abstract

Articles you may be interested inExcitation energies from extended random phase approximation employed with approximate one-and twoelectron reduced density matrices Communication: Constrained search formulation of the ground state energy as a functional of an idempotent one-matrix J. Chem. Phys. 133, 151102 (2010); 10.1063/1.3505036Systematic construction of approximate one-matrix functionals for the electron-electron repulsion energy A simple extension of the antisymmetrized product of strongly orthogonal geminals theory produces a ''JK-only'' one-matrix functional for the electron-electron repulsion energy of a closed-shell system that is exact for two-electron singlet ground states, size-extensive, and incorporates some intergeminal correlation and thus dispersion effects. The functional is defined only for one-matrices with occupation numbers that can be arranged into sets with elements that sum up to two. Its possible generalizations are discussed.

Noncollinear spin-spiral phase for the uniform electron gas within reduced-density-matrix-functional theory

“…Furthermore we can see that the relative correlation is dominant in the region of the ferromagnetic configuration. This can be understood by noticing that the density-matrix-power functional approximates the correlation energy by a prefactor times a Fock integral ͑most present-day functionals in RDMFT approximate correlations in this way 13,15,[20][21][22][23][24][25][26][27][28] ͒. Since Fock integrals imply that equal spins are particularly correlated, one would expect a similar dependence of the relative correlation energy for other RD-MFT functionals.…”

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.…”

An improved density matrix functional by physically motivated repulsive corrections

“…In Ref. 20 an approximate functional of the two-electron J and K integrals with ͕ i ͖ has been derived from the theory of the antisymmetrized products of strongly orthogonal geminals and in Ref. 21 the NO occupations n i in an approximate functional were obtained as diagonal elements of an idempotent matrix, the elements of which represent the variational parameters to be optimized.…”