A natural orbital functional for multiconfigurational states

Abstract

An explicit formulation of the Piris cumulant λΔ,Π matrix is described herein, and used to reconstruct the two-particle reduced density matrix (2-RDM). Then, we have derived a natural orbital functional, the Piris Natural Orbital Functional 5, PNOF5, constrained to fulfill the D, Q, and G positivity necessary conditions of the N-representable 2-RDM. This functional yields a remarkable accurate description of systems bearing substantial (near)degeneracy of one-particle states. The theory is applied to the homolitic dissociation of selected diatomic molecules and to the rotation barrier of ethylene, both paradigmatic cases of near-degeneracy effects. It is found that the method describes correctly the dissociation limit yielding an integer number of electrons on the dissociated atoms. PNOF5 predicts a barrier of 65.6 kcal/mol for the ethylene torsion in an outstanding agreement with Complete Active Space Second-order Perturbation Theory (CASPT2). The obtained occupation numbers and pseudo one-particle energies at the ethylene transition state account for fully degenerate π orbitals. The calculated equilibrium distances, dipole moments, and binding energies of the considered molecules are presented. The values obtained are accurate comparing those obtained by the complete active space self-consistent field method and the experimental data.

Conditions for Describing Triplet States in Reduced Density Matrix Functional Theory

“…We also perform RDMFT minimizations for larger systems with an even number of particles with the approximate constraint (19), where we assume that the triplet is formed from the two outermost electrons and the inner orbitals have occupations pinned to one and with the constraint (22), where we allow the inner occupations to be less than one. We compare the occupation numbers from these RDMFT minimizations, with and without enforcing the constraints, with occupation numbers from "exact" MCSCF calculations to check whether the constraints help to get a density matrix closer to the exact one.…”

“…This guarantees that the core electrons do not contribute to the total spin. We loosened the constraint for the inner occupations by enforcing only the constraint (22). The results are given in the second line for each system.…”

“…Several other functionals were introduced [7] aiming to correct its overcorrelation: the functional of Goedecker and Umrigar [9] the BBCn (n = 1,2,3) [11,12,15], the approximation of Marques and Lathiotakis [16] and the Power functional [17][18][19]30]. In a different fashion, PNOFn approximations, n = 1,· · · 6 [13,[20][21][22], and the theory of the antisymmetrized product of strongly orthogonal geminals (APSG) [14,[23][24][25] were developed focusing on improving the reconstruction of the 2RDM.…”

“…RDMFT [1,7] got significant attention in the last 20 years as an alternative to DFT. Several approximations have been introduced [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] with promising results in cases like molecular dissociation [10][11][12][13][14]27] or the gaps of periodic systems [17,18,28,29], where the results of basic DFT functionals are not satisfactory. Among these approximations, a central position is held by the Müller functional * iris.theophilou@mpsd.mpg.de [8,10] which was found to overcorrelate substantially.…”

Chemical and ionization potentials: Relation via the Pauli potential and NOF theory

“…[50] In this work, we employ PNOF5, [49,53] which has proved to give a remarkable accurate description of systems with neardegenerate one-particle states and of homolytic dissociation processes. [54][55][56] The one-electron picture provided by PNOF5 is really very appealing since its orbitals agree closely with the orbitals provided by the valence bond method and with those obtained by a standard molecular orbital calculation.…”