The atomic softness matrix

Abstract

The conventional approach to the electronegativity equalization principle suffers from a serious conceptual drawback that stems from discontinuities in the first derivative of the electronic energy with respect to the total charge of a molecule. A formalism that avoids the resulting ill-defined atomic hardness matrices employs a simple definition of the atomic softness matrix σ. The matrix σ, which is a generalization of the Hückel atom–atom polarizability matrix, can be easily and rigorously computed to arbitrary accuracy with any of the contemporary electronic structure methods. Properties of the atomic softness matrix are reviewed and illustrated with several numerical examples involving the first-row hydrides and a linear polyyne.

ACKS2: Atom-condensed Kohn-Sham DFT approximated to second order

“…[121][122][123] It was even suggested by Cioslowski that one could use the atom-condensed Kohn-Sham response kernel to construct an alternative EEM-like model with improved linear response properties. 99 We conclude that the derivation of the (spherical atom) EEM is only accurate for certain parts of the energy functional, i.e. the Hartree term, the interaction with the external potential and those parts of E txc [ρ] for which good semi-local approximations are available.…”

“…atom-condensed softness matrix. 99 We will refer to this matrix as the KS response matrix. This matrix is negative semidefinite and one can also show that:…”

Direct computation of parameters for accurate polarizable force fields

“…(25) without including additional hardness parameters. 59,60 Because such parameters are only valid for systems of non-interacting fermions, the derived parameters must be rescaled empirically to obtain a quantitatively accurate ERFF. 59…”

“…57 To overcome such issues, several authors use physical arguments to fix some parameters a priori and to calibrate only the remainder of the ERFF parameters. 51,56 There are also a few attempts to eliminate these issues entirely with a direct approximation of all ERFF parameters as expectation values of density response basis functions, e.g., using a Jellium model 42,58 or by partitioning the non-interacting response in Hartree-Fock theory 59,60 (used in the NEMO method 61,62 ). Next to the relatively direct calibration of ERFF parameters with ab initio linear response data, it is also common to fit all parameters in the whole PFF to more diverse experimental and/or ab initio reference data.…”

QuBiLS‐MIDAS: A parallel free‐software for molecular descriptors computation based on multilinear algebraic maps

“…several combinations according to the different values of the vectors , , , and are obtained for the two‐linear, three‐linear, and four‐linear algebraic maps. In this way, the algebraic forms shown in the Table are used, and as component of the molecular vectors the following “standard” atom‐ and fragment‐based properties (weights): (1) atomic mass (M), (2) the van der Waals volume (V), (3) the atomic polarizability (P), (4) atomic electronegativity in Pauling scale (E), (5) atomic Ghose‐Crippen LogP (A), (6) atomic charge (C) (Gasteiger–Marsili), (7) atomic polar surface area, (8) atomic refractivity (R), (9) atomic hardness (H), and (10) atomic softness (S).…”