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


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the energy functional has important consequences: the theorems obtained for the exact functional of the 1-RDM [1] are no longer valid.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.


[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).