Coulomb electrostatic term, molecular modeling

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... 

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 ... 

Nowadays, molecular modeling packages are applied to calculate relevant conformations of a molecule via an energy function (i.e., force fields [1]) that is adjusted to experimentally derived reference geometries (mostly X-ray structures). Van der Waals and Coulomb terms define steric and electrostatic features and each mismatch to reference values is penalized. 

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. 

Inductive effect — is an effect of the transmission of charge through a chain of atoms by electrostatic induction on rates of reaction, etc. A theoretical distinction may be made between the field effect, and the inductive effect as models for the Coulomb interaction between a given site within a -> molecular entity and a remote unipole or - dipole within the same entity. The experimental distinction between the two effects has proved difficult, except for molecules of peculiar geometry, which may exhibit reversed field effects . Typically, the inductive effect and the field effect are influenced in the same direction by structural changes in the molecule and the distinction between them is not clear. Therefore, the field effect is often included in the term inductive effect . Thus, the separation of a values (see -> electronic effect) into inductive and resonance components does... 

Electrostatics. The most difficult aspect of molecular mechanics is electrostatics (35-38). In most force fields, the electronic distribution surrounding each atom is treated as a monopole with a simple coulombic term for the interaction. The effect of the surrounding medium is generally treated with a continuum model by use of a dielectric constant. More... 

The remainder of this section discusses several important classes of calculations in which the PB model has been, or will be, used to compute short-range electrostatic interactions. In understanding these examples, it is helpful to keep in mind the following unifying principle. Within the PB model, the electrostatic energy of a molecule or system of molecules in solution is the sum of two contributions the electrostatic interaction energy of the solute atoms, computed using Coulomb s law and the dielectric constant of the solute interior, and the electrostatic interaction between the atoms and the solvent. The first term is simple to compute and depends only on the conformation of the system under study. The second term is the one that is difficult to compute. It depends on both molecular conformation and the nature of the solvent. All the examples in this section may be viewed as varied applications of this principle. 

Depending on the force field used in a molecular dynamics or a Monte Carlo simulation, sensitivity coefficients with apparently similar forms may have very different values. For example, the electrostatic energy of a biomolecule in solution may be modeled by using Coulomb s law with effective atomic partial charges that implicitly approximate the effects of electronic polarization of the atoms of the biomolecule by their surroundings. On the other hand, explicit polarization terms can also be used in a force field to calculate the electrostatic energy of a system. 

An additional extension of the Drude model includes terms to improve the treatment of the orientation of molecular polarizabilities. Traditionally, in non-polarizable models electrostatic interactions, as well as LJ terms, between atoms bonded to each other or separated by two covalent bonds, 1,2 and 1,3 pairs, respectively, are ignored. Similarly, in the Drude model the interactions between core charges as well as those between the Drude oscillators and core charges are excluded for 1-2 and 1-3 pairs. However, the ability to preserve Coulomb interactions between Drude oscillators (i.e., dipole-dipole interactions) for the 1,2 and 1,3 atom pairs is important for accurate reproduction of the molecular polarizability tensor. At the same time, the use of point charges for these interactions is problematic as their spatial separation is small enough that the Coulombic approximation fails. To overcome this, the electrostatic shielding treatment proposed by Thole [30] is applied, in which the Coulomb interactions between charges / and j are modulated by a factor, S,y, as follows ... 

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