DoNOF: an open-source implementation of natural-orbital-functional-based methods for quantum chemistry

Abstract

The natural orbital functional theory (NOFT) has emerged as an alternative formalism to both density functional (DF) and wavefunction methods. In NOFT, the electronic structure is described in terms of the natural orbitals (NOs) and their occupation numbers (ONs). The approximate NOFs have proven to be more accurate than those of the density for systems with a significant multiconfigurational character, on one side, and scale better with the number of basis functions than correlated wavefunction methods, on the other side. A challenging task in NOFT is to efficiently perform orbital optimization. In this article we present DoNOF, our open source implementation based on diagonalizations that allows to obtain the resulting orbitals automatically orthogonal. The one-particle reduced-density matrix (1RDM) of the ensemble of pure-spin states provides the proper description of spin multiplets. The capabilities of the code are tested on the water molecule, namely, geometry optimization, natural and canonical representations of molecular orbitals, ionization potential, and electric moments. In DoNOF, the electron-pair-based NOFs developed in our group PNOF5, PNOF7 and PNOF7s are implemented. These JKL-only NOFs take into account most non-dynamic effects plus intrapair-dynamic electron correlation, but lack a significant part of interpair-dynamic correlation. Correlation corrections are estimated by the single-reference NOF-MP2 method that simultaneously calculates static and dynamic electron correlations taking as a reference the Slater determinant formed with the NOs of a previous PNOF calculation. The NOF-MP2 method is used to analyze the potential energy surface (PES) and the binding energy for the symmetric dissociation of the water molecule, and compare it with accurate wavefunction-based methods.

17 pages, 4 figures, 9 tables

References in corpus (15)

• Perspective on density functional theory
• Structure of Fermionic Density Matrices: Complete N-representability Conditions
• Global Method for Electron Correlation
• The dynamic electron-correlation energy in the NOF-MP2 method from the orbital-invariant perturbation theory
• Natural orbital functional for multiplets
• Phase Dilemma in Natural Orbital Functional Theory from the N-representability Perspective
• An efficient method for strongly correlated electrons in two-dimensions
• An efficient method for strongly correlated electrons in one dimension
• Molecular electric moments calculated by using natural orbital functional theory
• Analytic gradients for spin multiplets in natural orbital functional theory
• Analytic gradients for natural orbital functional theory
• Performance of the NOF-MP2 method in hydrogen abstraction reactions
• Natural orbital functional for spin-polarized periodic systems
• Avoiding the 4-index transformation in one-body reduced density matrix functional calculations for separable functionals
• Analytic second-order energy derivatives in natural orbital functional theory

Cited by in corpus (17)

• Global Natural Orbital Functional: Towards the Complete Description of the Electron Correlation
• Refining and relating fundamentals of functional theory
• Benchmarking GNOF against FCI in challenging systems in one, two and three dimensions
• An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability
• Towards a Resolution of the Static Correlation Problem in Density Functional Theory from Semidefinite Programming
• Deriving density-matrix functionals for excited states
• Electron correlation in the Iron(II) Porphyrin by NOF approximations
• Exploiting the hessian for a better convergence of the SCF RDMFT procedure
• Outstanding Improvement in Removing the Delocalization Error by Global Natural Orbital Functional
• Softmax parameterization of the occupation numbers for natural orbital functionals based on electron pairing approaches
• Connections between Richardson-Gaudin States, Perfect-Pairing, and Pair Coupled-Cluster Theory
• Time-Reversal Symmetry in RDMFT and pCCD with Complex-Valued Orbitals
• Impact of Parametrizations of the One-Body Reduced Density Matrix on the Energy Landscape
• A toolbox of spin-adapted generalized Pauli constraints
• Refining ensemble $N$-representability of one-body density matrices from partial information
• Resolution of the identity approximation applied to PNOF correlation calculations
• Spin adaptation of the cumulant expansions of reduced density matrices