A reference‐free stockholder partitioning method based on the force on electrons

Abstract

We argue that when one divides a molecular property into atom-in-a-molecule contributions, one should perform the division based on the property density of the quantity being partitioned. This is opposition to the normal approach, where the electron density is given a privileged role in defining the properties of atoms-in-a-molecule. Because partitioning each molecular property based on its own property density is inconvenient, we design a reference-free approach that does not (directly) refer atomic property densities. Specifically, we propose a stockholder partitioning method based on relative influence of a molecule's atomic nuclei on the electrons at a given point in space. The resulting method does not depend on an "arbitrary" choice of reference atoms and it has some favorable properties, including the fact that all of the electron density at an atomic nucleus is assigned to that nucleus and the fact all the atoms in a molecule decay at a uniform asymptotic rate. Unfortunately, the resulting model is not easily applied to spatially degenerate ground states. Furthermore, the practical realizations of this strategy that we tried here gave disappointing numerical results. © 2017 Wiley Periodicals, Inc.

A Single Organic Fluorescent Probe for the Discrimination of Dual Spontaneous ROS in Living Organisms: Theoretical Approach

“…The electron excitation and fluorescent properties of the four probe molecules were analyzed through the time-dependent density functional theory (TDDFT) method, which was performed under CAM-B3LYP/def2-TZVPD. This functional and basis set combination was confirmed to be appropriate for studying the excited states of single organic molecules [58][59][60][61]. TDDFT calculation under functional M06-2X and PBE0 was also conducted to be compared with the results under CAM-B3LYP.…”

Information-Theoretic Approaches to Atoms-in-Molecules: Hirshfeld Family of Partitioning Schemes

“…Several related, but more-or-less ad hoc, partitioning approaches do not perfectly fit into this information-theoretic framework, so they are not elaborated upon in this paper. Examples of this sort of method include the ever-expanding family of DDEC methods, ,, Charge Model 5 (CM5) (developed by mapping Hirshfeld charges onto a new set of charges providing a more accurate monopole approximation of electrostatic potential), and force-based partitioning (which has the advantage of being completely reference-free).…”

Constrained iterative Hirshfeld charges: A variational approach

“…where x and x denote the floor and ceiling functions, respectively. [13][14][15][16] Together with the information-theoretic viewpoint on Hirshfeld charges, 11,[17][18][19][20][21][22][23][24][25][26][27] the HI method has stimulated an explosion of new partitioning schemes. [6][7][8][28][29][30][31][32][33][34][35][36][37] Some of these new methods are variational, like the minimum basis iterative stockholder (MBIS) 7 , additive variational Hirshfeld (AVH) 38 , Hirshfeld-Iλ 31 , and the iterative stockholder analysis (ISA) 32,33,39 methods.…”