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Oxidation states represent the ionic distribution of charge in a molecule and are significant in tracking redox reactions and understanding chemical bonding. While effective algorithms already exist based on formal Lewis structures as well as using localized orbitals, they exhibit differences in challenging cases where effects such as redox noninnocence are at play. Given a density functional theory (DFT) calculation with chosen total charge and spin multiplicity, this work reports a new approach to obtaining fragment-localized orbitals that is termed oxidation state localized orbitals (OSLO), together with an algorithm for assigning the oxidation state using the OSLOs and an associated fragment orbital localization index (FOLI). Evaluating the FOLI requires fragment populations, and for this purpose a new version of the intrinsic atomic orbital (IAO) scheme is introduced in which the IAOs are evaluated using a reference minimal basis formed from on-the-fly superposition of atomic density (IAO-AutoSAD) calculations in the target basis set and at the target level of theory. The OSLO algorithm is applied to a range of challenging cases including high valent metal oxide complexes, redox noninnocent NO and dithiolate transition metal complexes, a range of carbene-containing TM complexes, and other examples including the potentially inverted ligand field in [Cu(CF3)4]-. Across this range of cases, OSLO produces generally satisfactory results. Furthermore, in borderline cases, the OSLOs and associated FOLI values provide direct evidence of the emergence of covalent interactions between fragments that nicely complements existing approaches.

Given the piecewise approach to modeling intermolecular interactions for force fields, they can be difficult to parameterize since they are fit to data like total energies that only indirectly connect to their separable functional forms. Furthermore, by neglecting certain types of molecular interactions such as charge penetration and charge transfer, most classical force fields must rely on, but do not always demonstrate, how cancellation of errors occurs among the remaining molecular interactions accounted for such as exchange repulsion, electrostatics, and polarization. In this work we present the first generation of the (many-body) MB-UCB force field that explicitly accounts for the decomposed molecular interactions commensurate with a variational energy decomposition analysis, including charge transfer, with force field design choices that reduce the computational expense of the MB-UCB potential while remaining accurate. We optimize parameters using only single water molecule and water cluster data up through pentamers, with no fitting to condensed phase data, and we demonstrate that high accuracy is maintained when the force field is subsequently validated against conformational energies of larger water cluster data sets, radial distribution functions of the liquid phase, and the temperature dependence of thermodynamic and transport water properties. We conclude that MB-UCB is comparable in performance to MB-Pol, but is less expensive and more transferable by eliminating the need to represent short-ranged interactions through large parameter fits to high order polynomials.