  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.
