Electrostatic Hartree energy

In the absence of external potentials, the electrostatic potential energy of nuclei and electrons can be represented by the Coulombic interactions among the electrons and nuclei. There are three groups of electrostatic interactions interactions between nuclei, interactions between electrons and nuclei, and interactions between electrons. Following the Born-Oppenheimer approximation, we neglect nuclei interactions in our DG-based model. Using Coulomb s law, the repulsive interaction between electrons can be expressed as the Hartree term ... 

A many-body perturbation theory (MBPT) approach has been combined with the polarizable continuum model (PCM) of the electrostatic solvation. The first approximation called by authors the perturbation theory at energy level (PTE) consists of the solution of the PCM problem at the Hartree-Fock level to find the solvent reaction potential and the wavefunction for the calculation of the MBPT correction to the energy. In the second approximation, called the perturbation theory at the density matrix level only (PTD), the calculation of the reaction potential and electrostatic free energy is based on the MBPT corrected wavefunction for the isolated molecule. At the next approximation (perturbation theory at the energy and density matrix level, PTED), both the energy and the wave function are solvent reaction field and MBPT corrected. The self-consistent reaction field model has been also applied within the complete active space self-consistent field (CAS SCF) theory and the eomplete aetive space second-order perturbation theory. ... 

We can remark that this expression for the kinetic energy does not depend on the density p(x) but directly on the wavefunctions. The second term. Eh, is the Hartree energy, i.e. the Coulomb electrostatic interaction between two charge distributions... 

Levy, M., S. C. Clement, and Y. Tal. 1981. Correlation Energies from Hartree-Fock Electrostatic Potentials at Nuclei and Generation of Electrostatic Potentials from Asymptotic and Zero-Order Information. In Chemical Applications of Atomic and Molecular Electrostatic Potentials, P. Politzer, and D. G. Truhlar, Eds. Plenum Press, New York. 

For quantitative considerations it is convenient to use atomic units (a.u.), in which h = eo = me = 1 (me is the electronic mass) by definition. They are based on the electrostatic system of units so Coulomb s law for the potential of a point charge is = q/r. Conversion factors to SI units are given in Appendix B here we note that 1 a.u. of length is 0.529 A, and 1 a.u. of energy, also called a hartree, is 27.211 eV. Practically all publications on jellium use atomic units, since they avoid cluttering equations with constants, and simplify calculations. This more than compensates for the labor of changing back and forth between two systems of units. 

The values of the ESP at the nuclear positions, as obtained from the electron and Hartree-Fock structure amplitudes for the mentioned crystals (using a K-model and corrected on self-potential) are given in table 2. An analysis shows that the experimental values of the ESP are near to the ab initio calculated values. However, both set of values in crystals differ from their analogs for the free atoms [5]. It was shown earlier (Schwarz M.E. Chem. Phys. Lett. 1970, 6, 631) that this difference in the electrostatic potentials in the nuclear positions correlates well with the binding energy of Is-electrons. So an ED-data in principle contains an information on the bonding in crystals, which is usually obtaining by photoelectron spectroscopy. 

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