Electrostatic Perturbations

The form of this equation makes explicit the fact that intermolecular forces do depend upon their vibrational states as well as on their electronic states. Due to the antisymmetrization of the global electronic wave function, Vaia2(R R12) contains Coulomb exchange terms and a direct term formed by the Coulomb multipole interactions and the infinite order perturbation electrostatic effects embodied in the reaction field potential [21, 22],... 

If the long-range mteraction between a pair of molecules is treated by quantum mechanical perturbation theory, then the electrostatic interactions considered in section Al.5.2.3 arise in first order, whereas induction and dispersion effects appear in second order. The multipole expansion of the induction energy in its fill generality [7, 28] is quite complex. Here we consider only explicit expressions for individual temis in the... 

It is often the case that the solvent acts as a bulk medium, which affects the solute mainly by its dielectric properties. Therefore, as in the case of electrostatic shielding presented above, explicitly defined solvent molecules do not have to be present. In fact, the bulk can be considered as perturbing the molecule in the gas phase , leading to so-called continuum solvent models [14, 15]. To represent the electrostatic contribution to the free energy of solvation, the generalized Bom (GB) method is widely used. Wilhin the GB equation, AG equals the difference between and the vacuum Coulomb energy (Eq. (38)) ... 

Caution C omparing the shifted constant dielectric to a constant dielectric function without a cutoff shows that the sh ifted dielectric, iin like a switch in g fun ction, perturbs the en tire electrostatic energy curve, not only the region near the cnioff. 

Choose the region (single or multiple molecules) of interest for an ab initio calculation from the total molecular system. HyperChem performs the ab initio calculation for the selected region using the perturbation of an electrostatic potential arising from the net charges on the atoms of the un selected part. (For further details of this electrostatic potential perturbation implemented in HyperChem, please see the second part of this book. Theory and Methods). 

Since we normally deal with electrostatic field perturbations that are small, we can profitably expand the electric moments as a Taylor series in the external field ... 

Wigner, E. P., Phys. Rev. 94, 77, "Application of the Rayleigh-Schrodinger perturbation theory to the hydrogen atom." The whole electrostatic potential is considered as a perturbation. 

The perturbation energy is here just the electrostatic energy calculated for the electron distribution given by perturbation theory which led Schrodinger to... 

An area of development is the inclusion of code necessary for free energy perturbation calculations for internal, van der Waals and electrostatic energy terms ( ). Another area of development is the option to use lookup tables for both nonbond energies and for constraint energy terms such as a solvent boundary energy term (16). Other features and options are routinely added as needed to aid in the execution of current projects underway within the NIH. 

A perturbative approach to Eq. (12) has recently been developed by Gomez-Monivas et al. [37]. For a dielectric film on top of a flat metallic surface, these authors find that the electrostatic force is a convolution of the instrumental resolution with an effective profile... 

The electricity-producing system of electric fishes is built as follows. A large number of flat cells (about 0.1 mm thick) are stacked like the flat unit cells connected in series in a battery. Each cell has two membranes facing each other. The membrane potentials of the two membranes compensate for each other. In a state of rest, no electrostatic potential difference can be noticed between the two sides of any cell or, consequently, between the ends of the stack. The ends of nerve cells come up to one of the membranes of each cell. When a nervous impulse is applied from outside, this membrane is excited, its membrane potential changes, and its permeability for ions also changes. Thus, the electrical symmetry of the cell is perturbed and a potential difference of about 0.1 V develops between the two sides. Since nervous impulses are applied simultaneously to one of the membranes in each cell, these small potential differences add up, and an appreciable voltage arises between the ends of the stack. 

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