Coulomb electrostatic term, molecular

Note that a distinction is made between electrostatic and polarization energies. Thus the electrostatic term, Ue e, here refers to an interaction between monomer charge distributions as if they were infinitely separated (i.e., t/°le). A perturbative method is used to obtain polarization as a separate entity. The electrostatic and polarization contributions are expressed in terms of multipole expansions of the classical coulomb and induction energies. Electrostatic interactions are computed using a distributed multipole expansion up to and including octupoles at atom centers and bond midpoints. The polarization term is calculated from analytic dipole polarizability tensors for each localized molecular orbital (LMO) in the valence shell centered at the LMO charge centroid. These terms are derived from quantum calculations on the... 

Most early work was given in terms of the dissociation constant, mainly because of the analogy with acid-base equilibria where acid behaviour was considered in terms of the dissociation of the weak acid, HA(aq), into ions, H30 (aq) and A (aq). However, this analogy must not be taken too far. In the weak acid situation, dissociation of a molecular species, HA(aq), occurs, but in the ion pair situation dissociation is from a species which is not a molecule rather it is a species which is held together by simple coulombic electrostatic interactions. It is vital that this distinction is made clear. 

Many molecular modelling techraques that use force-field models require the derivatives of the energy (i e the force) to be calculated with respect to the coordinates. It is preferable that analytical expressions for these derivatives are available because they are more accurate and faster than numerical derivatives. A molecular mechanics energy is usually expressed in terms of a combination of internal coordinates of the system (bonds, angles, torsions, etc.) and interatomic distances (for the non-bonded interactions). The atomic positions in molecular mechanics are invariably expressed in terms of Cartesian coordinates (unlike quantum mechanics, where internal coordinates are often used). The calculation of derivatives with respect to the atomic coordinates usually requires the chain rule to be applied. For example, for an energy function that depends upon the separation between two atoms (such as the Lennard-Jones potential. Coulomb electrostatic interaction or bond-stretching term) we can write ... 

Thus, when evaluating the effective electrostatic term between a pair of atoms across the docking interface, a constant value of 1.5 A is added to the distance separating both nuclei. This modified Coulombic term is evaluated for every pair of atom-centered charges (a 10 A cutoff is used through this work) across the molecular interface. 

In this chapter we meet three increasingly sophisticated models of molecular shape. The first considers molecular shape to be a consequence merely of the electrostatic (coulombic) interaction between pairs of electrons. The other two models are theories that describe the distribution of electrons and molecular shape in terms of the occupation of orbitals. 

A localized molecular orbital representation is the closest approach that can be achieved, for a given determinantal wavefunction, to an electrostatic model of a molecule 44>. With truly exclusive orbitals, electron domains interact with each other through purely classical Coulombic forces and the wavefunction reduces, for all values of the electronic coordinates, to a single term, a simple Hartree product. 

Other flexible molecular models of nitromethane were developed by Politzer et al. [131,132]. In these, parameters for classical force fields that describe intramolecular and intermolecular motion are adjusted at intervals during a condensed phase molecular dynamics simulation until experimental properties are reproduced. In their first study, these authors used quantum-mechanically calculated force constants for an isolated nitromethane molecule for the intramolecular interaction terms. Coulombic interactions were treated using partial charges centered on the nuclei of the atoms, and determined from fitting to the quantum mechanical electrostatic potential surrounding the molecule. After an equilibration trajectory in which the final temperature had been scaled to the desired value (300 K), a cluster of nine molecules was selected for a density function calculation from which... 

Analogical molecular structure is possessed by other simple compounds such as potassium iodide, ammonium chloride, sodium hydroxide, barium nitrate, ammonium acetate and so on. In all these compounds there is a transfer of one or several electrons from one element to the other, positive and negative ions being thus formed, that are hold together in a crystal by electrostatic attraction. A bond of this kind is no genuine chemical bond in tbe correct meaning of the term, but is just,a result of Coulomb forces of attraction between opposite charges. 

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