Core Ionization Energies, Mean Dipole Moment Derivatives, and Simple Potential Models for B, N, O, F, P, Cl, and Br Atoms in Molecules

Abstract

Simple potential models relating experimental 1s electron ionization energies for B, N (sp and sp3 hybrids), O, and F atoms; 1s and 2p ionization energies for P atoms; and 2s and 2p ionization energies for Cl atoms as a function of their atomic mean dipole moment derivatives determined from experimental gas phase infrared fundamental band intensities are reported. Potential models using theoretical Koopmans' energies and generalized atomic polar tensor (GAPT) charges are found to form even more precise models than those using experimental data. This is expected because the potential models depend only on the electronic structures of molecules before ionization takes place and do not take into account relaxation effects. If the experimental ionization energies are adjusted by their relaxation energies, models similar to those obtained using Koopmans' energies are determined. The models permit a simple understanding of substituent effects on core ionization energies in terms of atomic charges in molecules. Most of the potential model slopes investigated are shown to be approximately proportional to the inverse atomic radii of the atom being ionized. Core-valence electron repulsion values inferred from the potential models obtained from experimental data are somewhat smaller than those calculated using Slater orbitals of isolated atoms. The potential model intercepts for 1s and 2p electrons are shown to be proportional to the square of the nuclear charge, consistent with their interpretation as core electron ionization energies of neutral atoms. 1s He, Ne, and Ar and 2p Ar, Kr, and Xe core ionization energies obey the linear relationships obtained for the model intercepts. The results suggest that mean dipole moment derivatives obtained from infrared intensities can be interpreted as atomic charges.

Review of Experimental GAPT and Infrared Atomic Charges in Molecules

“…[81][82][83][84] Siegbahn et al's simple potential model 85 corrected for relaxation energy of the 1s core ionization energy of the carbon atom is given by (12) where E C,1s is the carbon 1s core ionization energy, q A and q C are atomic charges, R AC is the internuclear distance between the A and C atoms and E relax is the relaxation energy for the ionization process. The first two terms in this equation can be derived from purely electrostatic considerations 85 or from quantum mechanical argument.…”

The linear relationship between Koopmans' and hydrogen bond energies for some simple carbonyl molecules

“…This is more conveniently explained using the GAPT charges. Siegbahn and co-workers 11 have shown that Koopmans' energy can be calculated using a simple potential model represented by the equation: 17,18 Evidently, the formation energy of the hydrogen bond and GAPT oxygen charges are not highly correlated because the electrostatic potential at the oxygen atom contributed by the neighboring atoms is also important in the hydrogen bonding process. In other words an approaching donor molecule is influenced not only by the charge of the acceptor oxygen atom but also by the charges on the other atoms in the molecule.…”

“…Furthermore the GAPT charges have been shown to be related to atomic electrostatic potentials by Siegbahn's simple potential model. 17,18 These relationships suggest the use of Koopmans' energies for core electrons as QSAR descriptors in activity problems for which the H-bonding phenomenon is important.…”

Characteristic Substituent-Shift Models for Carbon 1s Ionization Energies and Mean Dipole-Moment Derivatives

“…[1][2][3] Theoretical models based on Koopmans' energies and mean dipole-moment derivatives calculated by quantum chemical procedures have also been reported for all of the above atoms and for the 1s, 2s, 2p, 3s, 3p, and 3d electrons of the bromine atom. 3 Siegbahn introduced the simple potential model for core electron ionization energies using atomic point charges. The fact that mean dipole-moment derivatives work so well in these models leads to the proposal that these derivatives can be identified with atomic charges.…”

“…Furthermore, they have been shown to be related [1][2][3] by a simple potential model, first proposed by Siegbahn,4 in which the ionization energies are a function of atomic charges and internuclear distances. In terms of mean dipole-moment derivatives, p j R and p j , of the nucleus being ionized, R, and other nuclei in the molecule, where E R,core represents the ionization energy of a core electron of the Rth nucleus.…”