International Workshop on 'New challenges in Reduced Density Matrix Functional Theory: Symmetries, time-evolution and entanglement'
NOF-MP2: A global method for the electron correlationMario Piris
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the energy functional has important consequences: the theorems obtained for the exact functional of the 1-RDM  are no longer valid.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  will be analyzed.
The 1-RDM functional is called Natural Orbital Functional (NOF)  when it is based upon the spectral expansion of the 1-RDM. Appropriate forms of the two-particle cumulant have led to different implementations , being the most recent an interacting-pair model called PNOF7 . 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) , 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.
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