Net atomic charges (NACs) are widely used in all chemical sciences to concisely summarize key information about the partitioning of electrons among atoms in materials. The objective of this article is to develop an atomic population analysis method that is suitable to be used as a default method in quantum chemistry programs irrespective of the kind of basis sets employed. To address this challenge, we introduce a new atoms-in-materials method with the following nine properties: (1) exactly one electron distribution is assigned to each atom, (2) core electrons are assigned to the correct host atom, (3) NACs are formally independent of the basis set type because they are functionals of the total electron distribution, (4) the assigned atomic electron distributions give an efficiently converging polyatomic multipole expansion, (5) the assigned NACs usually follow Pauling scale electronegativity trends, (6) NACs for a particular element have good transferability among different conformations that are equivalently bonded, (7) the assigned NACs are chemically consistent with the assigned atomic spin moments, (8) the method has predictably rapid and robust convergence to a unique solution, and (9) the computational cost of charge partitioning scales linearly with increasing system size. We study numerous materials as examples: (a) a series of endohedral C 60 complexes, (b) high-pressure compressed sodium chloride crystals with unusual stoichiometries, (c) metal-organic frameworks, (d) large and small molecules, (e) organometallic complexes, (f) various solids, and (g) solid surfaces. Due to non-nuclear attractors, Bader's quantum chemical topology could not assign NACs for some of these materials. We show for the first time that the Iterative Hirshfeld and DDEC3 methods do not always converge to a unique solution independent of the initial guess, and this sometimes causes those methods to assign dramatically different NACs on symmetry-equivalent atoms. By using a fixed number of charge partitioning steps with well-defined reference ion charges, the DDEC6 method avoids this problem by always converging to a unique solution. These characteristics make the DDEC6 method ideally suited for use as a default charge assignment method in quantum chemistry programs. † Electronic supplementary information (ESI) available: Summary of alternative charge partitioning algorithms considered; summary of integration routines; iterative algorithm for computing the Convex functional NACs; ow diagrams for the DDEC6 method; and .xyz les (which can be read using any text editor or the free Jmol visualization program downloadable from http://jmol.sourceforge.net) containing geometries, net atomic charges, atomic dipoles and quadrupoles, tted tail decay exponents, and ASMs. See

Net atomic charges (NACs) can be used both to understand the chemical states of atoms in a material as well as to represent the electrostatic potential, V, of the material outside its electron distribution. However, many existing definitions of NACs have limitations that prevent them from adequately fulfilling this dual purpose. Some charge methods are not applicable to periodic materials or are inaccurate for systems containing buried atoms, while others work for both periodic and nonperiodic materials containing buried atoms but give NACS that do not accurately reproduce V. We present a new approach, density derived electrostatic and chemical (DDEC) charges, that overcomes these limitations by simultaneously optimizing the NACs to be chemically meaningful and to reproduce V outside the electron distribution. This atoms-in-molecule method partitions the total electron density among atoms and uses a distributed multipole expansion to formally reproduce V exactly outside the electron distribution. We compare different methods for computing NACs for a broad range of materials that are periodic in zero, one, two, and three dimensions. The DDEC method consistently performs well for systems with and without buried atoms, including molecules, nonporous solids, solid surfaces, and porous solids like metal organic frameworks.

We develop a nonempirical atoms-in-molecules (AIM) method for computing net atomic charges that simultaneously reproduce chemical states of atoms in a material and the electrostatic potential V(r) outside its electron distribution. This method gives accurate results for a variety of periodic and nonperiodic materials including molecular systems, solid surfaces, porous solids, and nonporous solids. This method, called DDEC/c3, improves upon our previously published DDEC/c2 method (Manz, T. A.; Sholl, D. S. J. Chem. Theory Comput. 2010, 6, 2455-2468) by accurately treating nonporous solids with short bond lengths. Starting with the theory all AIM charge partitioning functionals with spherically symmetric atomic weights must satisfy, the form of the DDEC/c3 functional is derived from first principles. The method is designed to converge robustly by avoiding conditions that lead to nearly flat optimization landscapes. In addition to net atomic charges, the method can also compute atomic multipoles and atomic spin moments. Calculations performed on a variety of systems demonstrate the method's accuracy, computational efficiency, and good agreement with available experimental data. Comparisons to a variety of other charge assignment methods (Bader, natural population analysis, electrostatic potential fitting, Hirshfeld, iterative Hirshfeld, and iterative stockholder atoms) show that the DDEC/c3 net atomic charges are well-suited for constructing flexible force-fields for atomistic simulations.