Molecular mechanics dipole terms

Electrostatic terms other than the simple charge interactions above are commonly included in molecular mechanics calculations. particularly dipole-dipole interactions. More recently, second-order electrostatic interactions like those describing polarizability have been added to some force fields. 

The key differences between the PCM and the Onsager s model are that the PCM makes use of molecular-shaped cavities (instead of spherical cavities) and that in the PCM the solvent-solute interaction is not simply reduced to the dipole term. In addition, the PCM is a quantum mechanical approach, i.e. the solute is described by means of its electronic wavefunction. Similarly to classical approaches, the basis of the PCM approach to the local field relies on the assumption that the effective field experienced by the molecule in the cavity can be seen as the sum of a reaction field term and a cavity field term. The reaction field is connected to the response (polarization) of the dielectric to the solute charge distribution, whereas the cavity field depends on the polarization of the dielectric induced by the applied field once the cavity has been created. In the PCM, cavity field effects are accounted for by introducing the concept of effective molecular response properties, which directly describe the response of the molecular solutes to the Maxwell field in the liquid, both static E and dynamic E, [8,47,48] (see also the contribution by Cammi and Mennucci). 

In molecular quantum mechanics, we often find ourselves manipulating expressions so that one of a pair of interacting operators is expressed in laboratory-fixed coordinates while the other is expressed in molecule-fixed. A typical example is the Stark effect, where the molecular electric dipole moment is naturally described in the molecular framework, but the direction of an applied electric field is specified in space-fixed coordinates. We have seen already that if the molecule-fixed axes are obtained by rotation of the space-fixed axes through the Euler angles (, 6, /) = >, the spherical tensor operator in the laboratory-fixed system Tkp(A) can be expressed in terms of the molecule-fixed components by the standard transformation... 

Although few applications of these very recently implemented models have yet appeared, some calculations for free energies of transfer into aqueous solution are available.Polarization of the solute has been analyzed by reference to the molecular dipole moment,including comparison to a hybrid quantum mechanics/molecular mechanics approach,and the effect of aqueous solvation on conformational equilibria and simple nucleophilic reactions has been examined.] jo consideration of CDS solvation terms in conjunction with these models has appeared. 

In molecular mechanics calculations, the electrostatic energy terms have been represented by various mathematical formulations. The earliest approach was to assign bond dipoles to bonds between different kinds of atoms and to calculate the electrostatic energies from dipole-dipole interactions, according to Jeans (Eq. [10]). (See ref. 40 for a explanation of the angles % and a,.)... 

The effect can be described by classical mechanics in terms of forced vibrations of harmonic oscillators. Here since the molecular polarizability t. changes slightly as Ihe bond distorts, nonlinear effects give rise to dipole oscillations at frequencies other than the imposed frequency. Raman himself seems to have been led to this discovery, at least In part, by his theoretical studies of Ihe vibrations of musical instruments such as the violin. 

The molecular mechanics approach to conformational analysis has the virtue of analyzing conformational factors in terms of molecular properties that are easy to describe in physical terms. Contributions from bond-length distortions, bond-angle strain, van der Waals repulsions, and dipole-dipole interactions can be calculated. The use of carefully chosen potential functions can give highly precise information as to the relative energies of various conformations. The accuracy and reliability of the calculation depend on the potential functions and parameters that describe the various interactions. 

---