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the energy functional has important consequences: the theorems obtained for the exact functional of the 1-RDM [1] are no longer valid.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 this presentation, 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 whole static (non-dynamic) correlation and the intrapair dynamic correlation. The interpair electron correlation is recovered by the NOF-MP2 method [5]. In the second part of the presentation, a new NOF [6] that allows describing an electronic system with any value of the spin, that is, a new reconstruction of the 2-RDM for spin multiplets will be presented.
Calculation of ionization potentials of the first-row transition-metal atoms is presented as test case. The values obtained agree with those reported at the CCSD(T) and experimental data [6]. In addition, the correlation energies obtained by using PNOF7 for the two-dimensional square lattice Hubbard model of up to 144 electrons with different spin multiplicities are also presented. Our results are comparable to those of exact diagonalizations, density matrix renormalization group (DMRG) and auxiliary-field quantum Monte Carlo (AFQMC) calculations. Accurate results are obtained when particle-hole symmetry is broken away from half-filling. Finally, dissociation processes are studied in two-dimensional hydrogen networks in order to consider the missing interactions of the Hubbard model.
References:
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- M. Piris, Phys. Rev. A 100 (2019). arXiv: 1908.05501 [physics.chem-ph]