Electrostatic interactions molecular charge distribution

Intcrmolecular bonds arc the weak interactions that hold liquids and solids together. Atoms and molecules repel each other when they are too close, attract when they are further apart, and are stable at the equilibrium bond length in between. Intcrmolecular attractions make the pressures of van der Waals gases lower than the pressures of ideal gases at low densities. To a first approximation, intcrmolecular attractions can be explained as electrostatic interactions between charge distributions, due to internal charge asymmetries in molecules, to the freedom of molecules to rotate, or to molecular polarizabilities. 

Several issues remain to be addressed. The effect of the mutual penetration of the electron distributions should be analyzed, while the use of theoretical densities on isolated molecules does not take into account the induced polarization of the molecular charge distribution in a crystal. In the calculations by Coombes et al. (1996), the effect of electron correlation on the isolated molecule density is approximately accounted for by a scaling of the electrostatic contributions by a factor of 0.9. Some of these effects are in opposite directions and may roughly cancel. As pointed out by Price and coworkers, lattice energy calculations based on the average static structure ignore the dynamical aspects of the molecular crystal. However, the necessity to include electrostatic interactions in lattice energy calculations of molecular crystals is evident and has been established unequivocally. 

Polarization Potential. Afimction describing the energy of electronic relaxation of a molecular charge distribution following interaction with a point positive charge. The polarization potential may be added to the Electrostatic Potential to provide a more accurate account of the interaction of a point-positive charge and a molecule. 

The model of a dipole in a spherical cavity can only provide qualitative insights into the behaviour of real molecules moreover, it cannot explain the effect of electrostatic interactions in the case of apolar molecules. More accurate predictions require a more detailed representation of the molecular charge distribution and of the cavity shape this is enabled by the theoretical and computational tools nowadays available. In the following, the application of these tools to anisotropic liquids will be presented. First, the theoretical background will be briefly recalled, stressing those issues which are peculiar to anisotropic fluids. Since most of the developments for liquid crystals have been worked out in the classical context, explicit reference to classical methods will be made however, translation into the quantum mechanical framework can easily be performed. Then, the main results obtained for nematics will be summarized, with some illustrative... 

The symbol V is often associated with the electrical potential in the literature, but U is employed here so as not to conflict with the volume descriptor. Another aspect of chemical reactivity involves the molecular electrostatic potential (MEP). The MEP is the interaction energy between a unit point charge and the molecular charge distribution produced by the electrons and nuclei. The electrostatic potential, U r), at a point, r, is defined by Eq. [13]. 

The electrostatic energy is the first-order term in long-range perturbation theory and is usually the interaction that persists over the longest range. The Coulombic interaction between the undistorted molecular charge distributions... 

The electrostatic interaction, which is defined as the classical Coulombic interaction between the undistorted charge distributions of the isolated molecules, is the easiest to derive from wavefunctions. When there is no overlap of the charge distributions of the molecules, all that is required is a representation of the molecular charge density. The traditional, and simplest, representation of the molecular charge distribution is in terms of the total multipole moments. The first nonvanishing multipole moment could often be derived from experi-... 

The distance between the two molecules D and A is large enough so that the relevant intermolecular coupling is electrostatic. Moreover, the intermolecular distance is assumed large relative to the spatial extent of the individual molecular charge distributions. Under these circumstances the dominant electrostatic interaction is dipole-dipole coupling... 

The molecules were kept rigid at the experimental X-ray structure, except that the C H and N-H bond lengths were standardized to 1.08 A and 1.01 A, respectively. The electrostatic model used was the DMA of a 6-31G SCF wave function, with all multipoles multiplied by a factor of 0.9 to model crudely the effect of electron correlation on the molecular charge distribution. An initial repulsion-dispersion model was constructed from earlier studies. Combining rules were assumed, so that the repulsion-dispersion interaction between an atom i of type i and atom k of type k in another molecule, separated by Rik is given by... 

In conclusion, it is clear that considerable information about a molecule s inherit stability, and its ability to interact with other chemical species, can be deduced from the electrostatic potential and some other well defined properties that reflect the molecular charge distribution. It should be emphasized that this approach only requires the wavefunction of the isolated molecule to be calculated, and it is therefore considerably more economical than the conventional supermolecule approach for calculation of intermolecular interaction energies. In particular, we believe that this methodology can be very useful for studying interactions in biological systems, since these often involve large molecules with several interaction sites. 

The exact behavior of electrostatic interactions in a simulation is generally determined by four factors molecular charge distributions, solute atomic radii, mobile ionic species, and solvent. Molecular charge distributions are... 

All transferable force fields discussed in Sect. 4.1 employ point charges to account for the molecular charge distribution, although a more accurate description of the electrostatics with higher multipole moments may be used. Hasse, Vrabec, and coworkers [102,109] proposed a set of simple united-atom force fields for more than 70 compounds of different classes that describe the intermolecular interactions using two LJ 12-6 sites plus a point dipole (15) or a point quadrupole (16). The potential... 

Fig. 13.9. For sufficiently large intermolecular separations, the interaction of the lowest non-vanishing multipoles dominates. Whether this is an attraction or repulsion can be recognized by representing the molecular charge distributions by non-pointlike multipoles (clusters of point charges). If such multipoles point to each other by point charges of the opposite (same) sign, then the electrostatic interaction of the molecules is attraction (repulsion), (a) A few examples of simple molecules and the atomic partial charges (b) even the interaction of the two benzene molecules obeys this rule in the face-to-face configuration they repel, while they attract each other in the perpendicular configuration.

In their work and in many other force fields, a potential is used to describe the interactions between charge distributions based on Coulomb s law, where the partial charges on the atom centres, qt and qj, are derived from analysis of the electrostatic potential around the molecule calculated using molecular quantum mechanics. Such charges are sometimes called potential derived charges ... 

A further complication of the interpretation of contour maps results from the requirement of electroneutrality of a molecule. Electrostatic coefficient contours may be found close to ligand atoms that have polar interactions with specific receptor atoms. However, electrostatic contours, of the opposite sign, may also surround ligand atoms not involved in any polar interaction. The charge distribution pattern is felt by CoMFA from both extremes of the molecular dipole. As a result, both elearon-rich and electron-poor regions will be included in the model. Statistically, this is a simple case of correlation between descriptors (collinearity). 

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