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Rohr DR, Pernal K, Gritsenko OV, et al. A density matrix functional with occupation number driven treatment of dynamical and nondynamical correlation. J Chem Phys. 2008;129(16):164105doi: 10.1063/1.2998201.
Rohr, D. R., Pernal, K., Gritsenko, O. V., & Baerends, E. J. (2008). A density matrix functional with occupation number driven treatment of dynamical and nondynamical correlation. The Journal of chemical physics, 129(16), 164105. https://doi.org/10.1063/1.2998201
Rohr, Daniel R, et al. "A density matrix functional with occupation number driven treatment of dynamical and nondynamical correlation." The Journal of chemical physics vol. 129,16 (2008): 164105. doi: https://doi.org/10.1063/1.2998201
Rohr DR, Pernal K, Gritsenko OV, Baerends EJ. A density matrix functional with occupation number driven treatment of dynamical and nondynamical correlation. J Chem Phys. 2008 Oct 28;129(16):164105. doi: 10.1063/1.2998201. PMID: 19045245.
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J Chem Phys. 2008 Oct 28;129(16):164105. doi: 10.1063/1.2998201.

A density matrix functional with occupation number driven treatment of dynamical and nondynamical correlation.

The Journal of chemical physics

Daniel R Rohr, Katarzyna Pernal, Oleg V Gritsenko, Evert Jan Baerends

Affiliations

  1. Afdeling Theoretische Chemie, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands.

PMID: 19045245 DOI: 10.1063/1.2998201

Abstract

A recently proposed series of corrections to the earliest JK-only functionals has considerably improved the prospects of density matrix functional theory (DMFT). Still, the most advanced of these functionals (correction C3) requires a preselection of the terms in the pair density Gamma(r(1),r(2)) involving the bonding and antibonding natural orbitals (NOs) belonging to an electron pair bond. Ideally, a DMFT functional should only depend on the NOs and their occupation numbers, and we propose a functional with an occupation number driven weighing of terms in the pair density. These are formulated as "damping" for certain ranges of occupation numbers of the two-electron cumulant that arises in the expansion of the two-particle density matrix of the paradigmatic two-electron system. This automatic version of C3, which we denote AC3, provides the correct dissociation limit for electron pair bonds and it excellently reproduces the potential energy curves of the multireference configuration interaction (MRCI) method for the dissociation of the electron pair bond in the series of the ten-electron hydrides CH(4), NH(3), H(2)O, and HF. AC3 reproduces closely the experimental equilibrium distances and at R(e) it yields correlation energies of the ten-electron systems with an average error in the absolute values of only 3.3% compared to the MRCI values. We stress the importance of treatment of strong correlation cases (NO occupation numbers differing significantly from 2.0 and 0.0) by appropriate terms in the cumulant.

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