Point-charge interaction

The Fenske-Hall method is a modification of crystal held theory. This is done by using a population analysis scheme, then replacing orbital interactions with point charge interactions. This has been designed for the description of inorganic metal-ligand systems. There are both parameterized and unparameterized forms of this method. 

The QM/MM interactions (Eqm/mm) are taken to include bonded and non-bonded interactions. For the non-bonded interactions, the subsystems interact with each other through Lennard-Jones and point charge interaction potentials. When the electronic structure is determined for the QM subsystem, the charges in the MM subsystem are included as a collection of fixed point charges in an effective Hamiltonian, which describes the QM subsystem. That is, in the calculation of the QM subsystem we determine the contributions from the QM subsystem (Eqm) and the electrostatic contributions from the interaction between the QM and MM subsystems as explained by Zhang et al. [13],... 

Let us suppose provisionally that we have a system of N point charges interacting through Coulombic forces ... 

These provisions have not been included in Allinger s QCPE programs, except for simple calculations of dipole-dipole or point charge interactions. We discuss below mainly the results obtained with monofunctional molecules. 

Aij5 Bjj and CF are constants for a given pair of atoms and qj and are atomic net charges of the atoms i and j. The first two terms correspond to the Lennard-Jones potential and the third term to the electrostatic point charge — point charge interaction. 

As we have mentioned before, the complete non-relativistic Hamiltonian for a system of point charges interacting electrostatically and moving through field-free space can be written in the form... 

In the water trimer induction nonadditivity provides a dominant contribution, which effectively overshadows all the other terms. Its mechanism is simple. For instance, in a cyclic water trimer the multipoles of A inductively alter the multipoles at B, which, in turn, inductively alter the multipoles at C, which then alter those on A, and so on, until the self-consistency is reached. Various formulations of this simple model were implemented in the simulations since the 1970s [84-87,63,64,50]. To include the many-body induction effects of point charges interacting with a set of polarizable atomic centers the following classical electrostatics equation is solved iteratively... 

Born and Jordan[188] Since each molecule consists of point charges interacting via Coulomb s law, the energy function (Hamiltonian) is always invariant with respect to space inversion. Consequently there could not exist any optically active molecules, which contradicts experience. 

After discretization, as in the case of filling the matrix, we have two choices in the calculation of the above integral. In the PC approximation the integral becomes a sum of point charge - point charge interactions,... 

Whereas Eq.(5.58) serves for the determination of local interactions between cluster models of a zeolite and interacting molecules, analytical expressions are needed for the interaction potential if one wishes to compute vibrational frequencies for purpose of comparison with experiment or if the potentials are to be used in Monte Carlo or molecular-dynamics simulation calculations. Sauer and co-workers developed such analytical potentials for the water-silica interaction system. The method makes use of the molecular electrostatic potential (MEP) maps and the functional form of EPEN/2 (Empirical Potential based on interactions of Electrons and Nuclei). EPEN/2 potential functions consist of a point-charge interaction term and... 

Figure 22. The dipole moment curves of H, O, and OH interacting with a Agn cluster. Dashed line is the corresponding dipole moment curve of a negative point charge interacting with the Agi3 cluster.

Figure 3. (a) Potential energy surface of the interaction of 1, Bt. Cl, and F with a Ag g(l 11) cluster dashed line is the imenction of a negative point charge Interacting with the cluster (b) Corresponding dipole moment curves. 

Electrostatic potential-function describing the energy of in teraction for a positive point charge interacting with the nuclei and, in qirantum mechanics, the electrons of a molecular system. 

This approximation of pure electrostatic point-charge interaction between the QM and MM regions may be invalid for the interactions of near-neighbor atoms at the QM-MM border. To take into account the non-electrostatic part of the QM-MM interaction, many authors suggest to introduce an empirical term in the form of a Lenard-Jones 12-6 potential... 

Estimates of E and E in dilute solution can be obtained using Debye-Huckel theory in its simplest form. Assume the electrolyte to be point charges interacting via coulomb forces only. Ignore the molecular structure of both solvent and ions. Since the electrophoretic effect is due to the migration of the ion cloud through the fluid, the reduction in ion mobility can be calculated using Stokes law (3.21)... 

It is instmctive to investigate the weight of the atomic point charges interaction by defining the following ratio ... 

As the point charges interaction is the most long-range one (since it decreases in 1/R, while the other terms in the multipolar expansion behave like 1 0> it is intuitive that %oe is close to 100 when the fragments are sufiftciently remote. For smaller distances, a clear dichotomy appears increases, becoming larger than... 

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