A new approach for the two‐electron cumulant in natural orbital functional theory

Abstract

ABSTRACT:The cumulant expansion gives rise to a useful decomposition of the two-matrix D in which the pair correlated matrix (cumulant) is disconnected from the antisymmetric product of the one-matrix ⌫. A new explicit antisymmetric approach for the two-particle cumulant matrix in terms of two symmetric matrices, ⌬ and ⌳, as functionals of the occupation numbers is proposed for singlet ground states of closedshell systems. It produces a natural orbital functional that reduces to the exact expression for the total energy in two-electron systems. The functional form of matrix ⌳ is readily generalized to any system with an even number of electrons. The diagonal elements of ⌬ equal the square of the occupation numbers, and the N-representability positivity necessary conditions of the two-matrix impose several bounds on the offdiagonal elements of matrix ⌬. The well-known mean value theorem and the partial sum rule obtained for the off-diagonal elements of ⌬ provide a prescription for deriving a practical functional. In particular, when the mean values { J * i } of the Coulomb interactions { J ij } for a given orbital i taking over all orbitals j i are assumed to be equal {K ii /2}, a functional close to self-interaction-corrected GU functional is obtained, but the two-matrix fermionic antisymmetric holds. An additional term for the matrix elements of ⌳ between HF occupied orbitals is proposed to ensure a correct description of the occupation numbers for the lowest occupied levels. The functional is tested in fully variational finite basis set calculations of 57 molecules. It gives reasonable molecular energies at the equilibrium geometries. The calculated values of dipole moments are in good agreement with the available experimental data.

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.…”

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

“…Over the past decade, a series of functionals has been proposed by one of us (MP) [50][51][52] using a reconstruction of the two-particle reduced-density matrix (2-RDM) in terms of the one-particle RDM (1-RDM) by ensuring some necessary Nrepresentability positivity conditions on the 2-RDM. [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.…”

“…[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.…”

Perspective on natural orbital functional theory

“…[19] Appropriate forms of matrices D and P lead to different implementations of the NOF known in the literature as PNOFi (i 5 1-5). [18,[20][21][22][23] The PNOF series has been recently reviewed in Ref. [7] The performance of these functionals is comparable to those of best quantum chemistry methods in many cases.…”