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) are widely used throughout the chemical sciences to concisely summarize key information about charge transfer between atoms in materials. The vast majority of NAC definitions proposed to date are unsuitable for describing the wide range of material types encountered across the chemical sciences. In this article, we show the DDEC6 method reproduces important chemical, theoretical, and experimental properties across an extremely broad range of material types including small and large molecules, organometallics, nanoclusters, porous solids, nonporous solids, and solid surfaces. Some important comparisons we make are: (a) correlations between various NAC models and spectroscopically measured core-electron binding energy shifts for Ti-, Fe-, and Mo-containing solids, (b) comparisons between DDEC6 and experimentally extracted NACs for formamide and natrolite, (c) comparisons of accuracy of different NAC methods for reproducing the electrostatic potential surrounding a material across one and multiple system conformations, (d) comparisons between calculated and chemically expected electron transfer trends for atoms in numerous dense solids, solid surfaces, and molecules, (e) an assessment of NAC transferability between three crystal phases of the diisopropylammonium bromide organic ferroelectric, and (f) comparisons between DDEC6 and polarized neutron diffraction atomic spin moments for the Mn 12 -acetate single-molecule magnet. We find the DDEC6 NACs are ideally suited for constructing flexible force-fields and give reasonable agreement with force-fields commonly used to simulate biomolecules and water. We find the DDEC6 method is more accurate than the DDEC3 method for analyzing a broad range of materials. This broad applicability to periodic and non-periodic materials irrespective of the basis set type makes the DDEC6 method suited for use as a default atomic population analysis method in quantum chemistry programs. † Electronic supplementary information (ESI) available: Tables listing spectroscopically measured core electron energies and Bader, CM5, DDEC3, DDEC6, HD NACs for Ti-and Mo-containing solids; plot comparing DDEC6 to DDEC3 NACs for 14 systems comprised almost entirely of surface atoms; DDEC6 and DDEC3 NACs for Mo 2 C(110) surface with K adatom and NaF (001) surface; DDEC6 and DDEC3 NACs, atomic dipoles, and atomic quadrupoles for SrTiO 3 (100) surface and bulk crystal; DDEC6, DDEC3, Bader, and IH NACs for NaF and SrTiO 3 bulk crystals; xyz les (which can be read using any text editor or the free Jmol visualization program downloadable from jmol.sourceforge.net) containing geometries, NACs, atomic dipoles and quadrupoles, tted tail decay exponents, and ASMs. See

The DDEC6 method is one of the most accurate and broadly applicable atomic population analysis methods. It works for a broad range of periodic and non-periodic materials with no magnetism, collinear magnetism, and non-collinear magnetism irrespective of the basis set type. First, we show DDEC6 charge partitioning to assign net atomic charges corresponds to solving a series of 14 Lagrangians in order. Then, we provide flow diagrams for overall DDEC6 analysis, spin partitioning, and bond order calculations. We wrote an OpenMP parallelized Fortran code to provide efficient computations. We show that by storing large arrays as shared variables in cache line friendly order, memory requirements are independent of the number of parallel computing cores and false sharing is minimized. We show that both total memory required and the computational time scale linearly with increasing numbers of atoms in the unit cell. Using the presently chosen uniform grids, computational times of $9 to 94 seconds per atom were required to perform DDEC6 analysis on a single computing core in an Intel Xeon E5 multiprocessor unit. Parallelization efficiencies were usually >50% for computations performed on 2 to 16 cores of a cache coherent node. As examples we study a B-DNA decamer, nickel metal, supercells of hexagonal ice crystals, six X@C 60 endohedral fullerene complexes, a water dimer, a Mn 12 -acetate single molecule magnet exhibiting collinear magnetism, a Fe 4 O 12 N 4 C 40 H 52 single molecule magnet exhibiting non-collinear magnetism, and several spin states of an ozone molecule. Efficient parallel computation was achieved for systems containing as few as one and as many as >8000 atoms in a unit cell. We varied many calculation factors (e.g., grid spacing, code design, thread arrangement, etc.) and report their effects on calculation speed and precision. We make recommendations for excellent performance. † Electronic supplementary information (ESI) available: ESI documentation includes a pdf le containing: the 14 charge partitioning Lagrangians (S1); spin partitioning Lagrangian and ow diagram (S2); equations for bond order analysis (S3); algorithm for total electron density grid correction (S4); table and description listing big arrays and in which modules they are allocated and deallocated (S5); table and description of computational parameters (S6); description of how to use the enclosed reshaping sub routines (S7); and description of how to use the enclosed spin functions (S8). Additionally ESI includes a zip format archive containing: the system geometries; Jmol readable xyz les containing DDEC6 NACs, atomic multipoles, electron cloud parameters, ASMs, SBOs, and r-cubed moments; DDEC6 bond orders and overlap populations; a Fortran module containing reshaping subroutines; and a Fortran module containing spin functions. See