Molecular mechanics Coulombic interactions

Many problems in force field investigations arise from the calculation of Coulomb interactions with fixed charges, thereby neglecting possible mutual polarization. With that obvious drawback in mind, Ulrich Sternberg developed the COSMOS (Computer Simulation of Molecular Structures) force field [30], which extends a classical molecular mechanics force field by serai-empirical charge calculation based on bond polarization theory [31, 32]. This approach has the advantage that the atomic charges depend on the three-dimensional structure of the molecule. Parts of the functional form of COSMOS were taken from the PIMM force field of Lindner et al., which combines self-consistent field theory for r-orbitals ( nr-SCF) with molecular mechanics [33, 34]. 

For allowed transitions on D and A the Coulombic interaction is predominant, even at short distances. For forbidden transitions on D and A (e.g. in the case of transfer between triplet states (3D + 3A —> 1D + 3A ), in which the transitions Ti —> S0 in D and So —> Ti in A are forbidden), the Coulombic interaction is negligible and the exchange mechanism is found, but is operative only at short distances (< 10 A) because it requires overlap of the molecular orbitals. In contrast, the Coulombic mechanism can still be effective at large distances (up to 80-100 A). 

The classical potential energy term is just a sum of the Coulomb interaction terms (Equation 2.1) that depend on the various inter-particle distances. The potential energy term in the quantum mechanical operator is exactly the same as in classical mechanics. The operator Hop has now been obtained in terms of second derivatives with respect to Cartesian coordinates and inter-particle distances. If one desires to use other coordinates (e.g., spherical polar coordinates, elliptical coordinates, etc.), a transformation presents no difficulties in principle. The solution of a differential equation, known as the Schrodinger equation, gives the energy levels Emoi of the molecular system... 

The molecular mechanics energy of a molecule is described in terms of a sum of contributions arising from distortions from ideal bond distances ( stretch contributions ), bond angles ( bend contributions ) and torsion angles ( torsion contributions ), together with contributions due to non-bonded (van der Waals and Coulombic) interactions. It is commonly referred to as a strain energy , meaning that it reflects the strain inherent to a real molecule relative to some idealized form. 

Force Field. The set of rules underlying Molecular Mechanics Models. Comprises terms which account for distortions from ideal bond distances and angles and for Non-Bonded van der Waals and Coulombic Interactions. 

Continuum models are the most efficient way to include condensed-phase effects into quantum-mechanical calculations, and this is typically accomplished by using the self-consistent reaction field (SCRF) approach for the electrostatic component. Therefore it is very common to replace the quantal problem by a classical one in which the electronic energy plus the coulombic interactions of the nuclei, taken together, are modeled by a classical force field—this approach usually called molecular mechanics (MM) (Cramer and Truhlar, 1996). 

Table 3.2 Coulombic, van der Waals, and total interaction energy and data from molecular mechanics study. All the energies are in units of kcal/mol. (From ref. [46])...

Table 3.2 shows the additive total interaction energy, the Coulombic, and the van der Waals interaction energy values from the molecular mechanics study for each polymer fragment. 

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... 

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