Electron point charge

Force and Field Intensity due to Single Electron Point Charge... 

We have finally calculated the matrix elements of the electronic point-charge potentials together with those of the corresponding nuclei in terms of the AO basis functions also used to construct the Bloch orbitals of the polymers. These matrix elements were then added to the one-electron part of the Fock matrix. 

One of the most useful approximations of nuclear shielding is that for the diamagnetic term by Flygare et With the origin at the nucleus N, a can be written as a free atom contribution plus the contribution of the electronic point charges centered at the other nuclei N ... 

Instead of using point charges one may also approximate the mteraction Hamiltonian in temis of solute electrons and nuclei interacting with solvent point dipoles... 

Hecaiise the repulsion interaction energy of two point charges is inversely proportional to the distance separating the two charges, Dewar and co-workers, for example, represent the (ssiss) two-ceri-ter two-electron integral by ... 

The electrostatic potential at a point r, 0(r), is defined as the work done to bring unit positive charge from infinity to the point. The electrostatic interaction energy between a point charge q located at r and the molecule equals The electrostatic potential has contributions from both the nuclei and from the electrons, unlike the electron density, which only reflects the electronic distribution. The electrostatic potential due to the M nuclei is ... 

A number of types of calculations can be performed. These include optimization of geometry, transition structure optimization, frequency calculation, and IRC calculation. It is also possible to compute electronic excited states using the TDDFT method. Solvation effects can be included using the COSMO method. Electric fields and point charges may be included in the calculation. Relativistic density functional calculations can be run using the ZORA method or the Pauli Hamiltonian. The program authors recommend using the ZORA method. 

For a molecule with a continuous electron charge distribution and nuclear point charges, the expression becomes ... 

Electron distribution governs the electrostatic potential of molecules. The electrostatic potential describes the interaction of energy of the molecular system with a positive point charge. Electrostatic potential is useful for finding sites of reaction in a molecule positively charged species tend to attack where the electrostatic potential is strongly negative (electrophilic attack). 

The electron density distributions are approximated by a series of point charges. There are four possible types of contributions, i.e. 

The exact expression for the dipole moment does n( consider atoms as point charges, but rather as nuclei (eat with a positive charge equal to the atomic number) ar electrons (each with unit negative charge). Atoms wii lone pairs may contribute to the dipole moment, even the atom is neutral, as long as the lone pair electrons a not symmetrically placed around the nucleus. 

Molecules do not consist of rigid arrays of point charges, and on application of an external electrostatic field the electrons and protons will rearrange themselves until the interaction energy is a minimum. In classical electrostatics, where we deal with macroscopic samples, the phenomenon is referred to as the induced polarization. I dealt with this in Chapter 15, when we discussed the Onsager model of solvation. The nuclei and the electrons will tend to move in opposite directions when a field is applied, and so the electric dipole moment will change. Again, in classical electrostatics we study the induced dipole moment per unit volume. 

Terms up to order 1/c are normally sufficient for explaining experimental data. There is one exception, however, namely the interaction of the nuclear quadrupole moment with the electric field gradient, which is of order 1/c. Although nuclei often are modelled as point charges in quantum chemistry, they do in fact have a finite size. The internal structure of the nucleus leads to a quadrupole moment for nuclei with spin larger than 1/2 (the dipole and octopole moments vanish by symmetry). As discussed in section 10.1.1, this leads to an interaction term which is the product of the quadrupole moment with the field gradient (F = VF) created by the electron distribution. 

Those electrons must not only avoid each other but also the negatively charged anionic environment. In its simplest form, the crystal field is viewed as composed of an array of negative point charges. This simplification is not essential but perfectly adequate for our introduction. We comment upon it later. 

We are concerned with what happens to the (spectral) d electrons of a transition-metal ion surrounded by a group of ligands which, in the crystal-field model, may be represented by point negative charges. The results depend upon the number and spatial arrangements of these charges. For the moment, and because of the very common occurrence of octahedral coordination, we focus exclusively upon an octahedral array of point charges. 

Each lobe of the d 2 yi orbital interacts predominantly with one point charge. The repulsive effects relate to the electron density within any given orbital so we might describe the interaction in units of lobe repulsion and say that, for the dp. yi orbital, this amounts to 4 = 16 repulsion units (4 squared because electron density oc jF). 

The dy. p and dp yi orbitals each interact with four point charges in precisely the same way as does the dyi yi orbital. Again the repulsion relates to electron density, so the total interaction of the combination is (4/ /2) + (4/ /2) = 16 of our repulsion units. In other words, the d.2 and dp y2 orbitals are degenerate in octahedral symmetry. 

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