PNOF5 calculations based on the “thermodynamic fragment energy method”: C n H2n+2 (n = 1, 10) and (FH) n (n = 1, 8) as test cases

Abstract

be comparable to accurate quantum chemistry methods in many cases [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. So far this is the only natural orbital functional (NOF) that has been obtained by top-down and bottom-up methods [19]. In the bottom-up method, the functional was generated by progressive inclusion of known necessary N-representability conditions on the 2-RDM, whereas the top-down method was used through reducing the energy expression generated from an N-particle wavefunction to a functional of the occupation numbers and natural orbitals [5]. In the case of PNOF5, this wavefunction is an antisymmetrized product of strongly orthogonal geminals (APSGs), with the expansion coefficients explicitly expressed by the occupation numbers [20,21].The idea of a function of this type dates back to the early fifties [22,23] and is inspired by the valence bond theory [24,25]; in fact, PNOF5 can also be considered as a type of GVB-PP method with fixed signs for the expansion coefficients of the corresponding determinants. Many scientists have worked actively in the field of strongly orthogonal geminals, and one of them is Professor Péter R. Surján to whom is dedicated this Festschrift. Indeed, an excellent review summarizing the evolution of the geminal theory up to 1999 can be found at his work [26]. An overview of geminal-based perturbative techniques for describing electron correlation was given recently [27].Consequently, PNOF5 is an orbital-pairing approach that takes into account most of the non-dynamical effects, but also an important part of the dynamical electron correlation corresponding to the intrapair (intrageminal) interactions. The existence of a generating wavefunction confirms that PNOF5 is strictly N-representable, i.e., the 2-RDM is derived from a function that is antisymmetric in N-particles [28]. Moreover, it demonstrates the size extensivity and size consistency of PNOF5, which is an inherent property to the generating singlet-type APSG wavefunction [29,30]. AbstractThe performance of the "thermodynamic fragment energy method" (FEM) in the context of natural orbital functional theory (NOFT) in its PNOF5 implementation is assessed. Two test cases are considered: the linear chains C n H 2n+2 (n = 1, 10) and the hydrogen-bonded (FH) n (n = 1, 8) clusters. Calculations show a fast convergence of the PNOF5-FEM method, which allows the treatment of extended system at a fractional cost of the whole calculation. We show that this type of methodologies could expand the range of systems achievable by NOFT due to the significant reduction in the computational cost.