Charge delocalization error in Piris natural orbital functionals

Abstract

Piris Natural Orbital Functionals (PNOF) have been recognized as a low-scaling alternative to study strong correlated systems. In this work, we address the performance of the fifth functional (PNOF5) and the seventh functional (PNOF7) to deal with another common problem, the charge delocalization error. The effects of this problem can be observed in charged systems of repeated well-separated fragments, where the energy should be the sum of the charged and neutral fragments, regardless of how the charge is distributed. In practice, an energetic overstabilization of fractional charged fragments leads to a preference for having the charge delocalized throughout the system. To establish the performance of PNOF functionals regarding charge delocalization error, charged chains of helium atoms and the W4-17-MR set molecules were used as base fragments and their energy, charge distribution and correlation regime were studied. It was found that PNOF5 prefers localized charge distributions, while PNOF7 improves the treatment of interpair static correlation and tends to the correct energetic limit for several cases, although a preference for delocalized charge distributions may arise in highly strong correlation regimes. Overall, it is concluded that PNOF functionals can simultaneously deal with static correlation and charge delocalization errors, resulting in a promising choice to study charge-related problems.

Electron Correlation in the Iron(II) Porphyrin by Natural Orbital Functional Approximations

“…The solutions of PNOFs can be characterized according to the recently proposed M-diagnostic adapted to the NOF multiplet calculations, namely, M = [ 1 − n L S O N O ] + n L W O N O where LSONO stands for the least strongly occupied NO, that is, the orbital with ON farthest from 1 below N II /2, so it belongs to Ω II b subspace, and LWONO for the least weakly occupied NO, that is, the orbital with ON farthest from 0 above N Ω , so it belongs to Ω a subspace. Recall that M values close to zero indicate the predominance of dynamic correlation, while values beyond 0.1 indicate the predominance of static correlation.…”

“…61 Finally, if the intersubspace static term (E sta inter ) is also disregarded, then GNOF reduces to PNOF5. 52 The solutions of PNOFs can be characterized according to the recently proposed M-diagnostic 87 adapted to the NOF multiplet calculations, 47 namely,…”

“…Recent developments − show that NOF theory has become an active field of research. Nowadays, an open-source implementation of NOF-based methods is available (github.com/DoNOF) to the scientific community.…”

Refining and relating fundamentals of functional theory

“…The main goal of this work is to elaborate on the vrepresentability problem and its relation to other fundamental features and concepts in 1RDMFT. Accordingly, we complement all the recent theoretical investigations of 1RDMFT and hope that our insights could guide the intense development of novel functionals and their implementations [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] . To achieve this, we first discuss by concise means the so-called scope of a functional theory and explain how it identifies a functional variable in a natural way.…”

Excited States by Coupling Piris Natural Orbital Functionals with the Extended Random-Phase Approximation

“…The equations of PNOF coupled to ERPA0, ERPA1, and ERPA2 have been implemented in the DoNOF and in PyNOF software . It is important to notice that several techniques have been developed to avoid explicit storage of A and B matrices, as well as the full diagonalization of large matrices. , In particular, the algorithm of Stratmann, Scuseria, and Frisch, that take advantage of the fact that the excitation energies appear in pairs, may be applicable to ERPA0 and ERPA1, although with some modifications, as the vectors X + Y and X – Y are not orthonormal as in TD-SCF, but instead the orthonormality is hold by the vectors X – Y and ΔN ( X + Y ).…”