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International Workshop on 'New challenges in Reduced Density Matrix Functional Theory: Symmetries, time-evolution and entanglement'

September 26, 2017 to September 29, 2017
Location : CECAM-HQ-EPFL, Lausanne, Switzerland
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NOF-MP2: A global method for the electron correlation

Mario Piris
University of the Basque Country, Spain

Abstract

The energy of an electron system can be determined exactly from the knowledge of the one- and two-particle reduced density matrices (1- and 2-RDMs). In practical applications, we employ this exact energy functional but using an approximate 2-RDM that is built from the 1-RDM. Approximating the energy functional has important consequences: the theorems obtained for the exact functional of the 1-RDM [1] are no longer valid. As a consequence, the functional N-representability problem arises, that is, we have to comply the requirement that reconstructed 2-RDM must satisfy N-representability conditions to ensure a physical value of the approximate ground-state energy. In the first part of this talk, the role of the N-representability in approximate one- particle functional theories [2] will be analyzed.

The 1-RDM functional is called Natural Orbital Functional (NOF) [3] when it is based upon the spectral expansion of the 1-RDM. Appropriate forms of the two-particle cumulant have led to different implementations [4], being the most recent an interacting-pair model called PNOF7 [5]. The latter is able to treat properly the static (non-dynamic) correlation and recover an important part of dynamic correlation. However, accurate solutions require a balanced treatment of both types of correlation. In the second part of the talk, a new method capable of achieving dynamic and static correlation even in those difficult cases in which both types of correlation are equally present will be presented. The starting-point is a determinant wavefunction formed with PNOF7 natural orbitals. Two new energy functionals are defined for both dynamic (Edyn) and static (Esta) correlation. Edyn is derived from a modified second-order Møller-Plesset perturbation theory (MP2) [5], while Esta is obtained from the static component of the PNOF7. Double counting is avoided by introducing the amount of static and dynamic correlation in each orbital as a function of its occupation. The total energy is represented by the sum Ehf + Edyn + Esta. The resulting working formulas allow for correlation to be achieved in one shot. Some challenging examples will be presented as well.



References

[1] T. L. Gilbert, Phys. Rev. B 12 2111 (1975); M. Levy, Proc. Natl. Acad. Sci. USA 76 6062 (1979); S. M. Valone, J. Chem. Phys. 73 1344 (1980).
[2] M.Piris, in Many-body approaches at different scales: a tribute to N. H. March on the occasion of his 90th birthday, Chap. 22, pp. 231-247. New York: Springer (2017).
[3] M. Piris, Adv. Chem. Phys. 134 387 (2007).
[4] M. Piris and J. M. Ugalde, Int. J. Quantum Chem.114 1169 (2014).
[5] M. Piris, Phys. Rev. Lett. 119 063002 (2017).