Coulomb potentials, molecular modelling

Coulomb gauge, phase transitions 287 Coulomb interaction, diffusion 585 Coulomb potentials, molecular modelling 73 coupling constants... 

The first simulation studies of full double layers with molecular models of ions and solvent were performed by Philpott and coworkers [51,54,158] for the NaCl solution, using the fast multipole method for the calculation of Coulomb interactions. The authors studied the screening of a negative surface charge by free ions in several highly concentrated NaCl solutions. A combination of (9-3) LJ potential and image charges was used to describe the metal surface. 

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... 

Since in current molecular modeling tasks the Gaussian orbitals or their linear combinations are used, one can guess that they provide the explicit form of the core states. Inserting the Gaussians in the expressions for the Coulomb and exchange superoperators yields numerous approximate forms of the pseudopotentials, which can be exemplified by the formulae employed in the ab initio model potential (AIMP) [36] ... 

The electrostatic contribution is modelled using a Coulombic potential. The electrostatic energy is a function of the charge on the non-bonded atoms, their interatomic distance, and a molecular dielectric expression that accounts for the attenuation of electrostatic interaction by the environment (e.g. solvent or the molecule itself). Partial atomic charges can be calculated for small molecules using an ab initio or semiempirical quantum mechanics program. 

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 ... 

Hassan, S.A., Mehler, E.L., Zhang, D., Weinstein, H. Molecular dynamics simulations of peptides and proteins with a continuum electrostatic model based on screened Coulomb potentials. Proteins 2003, 51(1), 109-25. 

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