Advances in electric field and atomic surface derived properties from experimental electron densities

Abstract

The present study is devoted to a general use of the Gauss law. This is applied to the atomic surfaces derived from the topological analysis of the electron density. The method proposed here is entirely numerical, robust and does not necessitate any specific parametrization of the atomic surfaces. We focus on two fundamental properties: the atomic charges and the electrostatic forces acting on atoms in molecules. Application is made on experimental electron densities modelized by the Hansen-Coppens model from which the electric field is derived for a heterogenic set of compounds: water molecule, NO(3) anion, bis-triazine molecule and MgO cluster. Charges and electrostatic forces are estimated by the atomic surface flux of the electric field and the Maxwell stress tensor, respectively. The charges obtained from the present method are in good agreement with those issued from the conventional volume integration. Both Feynman and Ehrenfest forces as well as the electrostatic potential at the nuclei (EPN) are here estimated from the experimental electron densities. The values found for the molecular compounds are presented and discussed in the scope of the mechanics of atomic interactions.

Charge density and electrostatic potential analyses in paracetamol

“…As we have reported earlier (Bouhmaida & Ghermani, 2008), the atomic electrostatic force reflects the anisotropy of the electron density in different bonding directions and therefore is related to the hybridization state and also to the local symmetry of the atomic site.…”

“…For molecules at equilibrium, the Feynman force on each nucleus is zero. However, that is not the case when experimental electron density is used (Bouhmaida & Ghermani, 2008, and references therein). In our calculations we use the divergence theorem to estimate the total electrostatic forces acting on atoms of the molecule…”

“…The sum of the Feynman force acting on the nucleus [here E(R) is the electric field at the nucleus] and the second term which is the force acting on the electrons within the basin of the atom, that is, the Ehrenfest force (Bader, 1998;Bader et al, 2007;Herná ndez-Trujillo et al, 2007;Bouhmaida & Ghermani, 2008). For molecules at equilibrium, the Feynman force on each nucleus is zero.…”

“…Moreover, the BADERWIN program provides the volume of each atom in a separate file which is very useful for further integration or to define the atomic surface. From the Gauss divergence theorem, AIM charges Q can also be estimated by the flux of the electric field E (Popelier, 2001;Bouhmaida & Ghermani, 2008) generated by the total charge distribution, including the positive charge of the nucleus, through the atomic basin surface S having vectors n as normals…”

“…For many years we have been involved in the developments of electrostatic property methodologies and calculations. In our recent research, a software to calculate the forces acting on atoms in the molecules has been developed (Bouhmaida & Ghermani, 2008). We have previously characterized the electrostatic potential through its first derivative, i.e.…”