Molecular modelling electrostatic bonding potential

FIGURE 1 6 Molecular models of methane (CH4) (a) Framework (tube) models show the bonds connecting the atoms but not the atoms themselves (b) Ball and stick (ball and spoke) models show the atoms as balls and the bonds as rods (c) Space filling models portray overall molecular size the radius of each sphere approximates the van der Waals radius of the atom (d) An electrostatic potential map of methane... 

Cyclopentenones. from 1.4-diketones. 886-887 Cyclopropane, angle strain in, 115 bent bonds in. 115 from alkenes. 227-229 molecular model of, 111. 115 strain energy of, 114 torsional strain in, 115 Cystathionine, cysteine from. 1177 Cysteine, biosynthesis of, 1177 disulfide bridges from, 1029 structure and properties of, 1018 Cytosine, electrostatic potential map of, 1104... 

Methanethiol, bond angles in, 20 dipole moment of, 39 electrostatic potential map of. 167 molecular model of, 20 pKa of, 604 structure of, 20... 

Trichloroacetic acid, pKa of. 759 Trifluoroacetic acid, pKa of, 756 Trifluoromethylbenzene, electrostatic potential map of, 565 Triglyceride, see Triacylglycerol, 1061 Trimethylamine, bond angles in, 919 bond lengths in, 919 electrostatic potential map of, 921 molecular model of, 919 Trimethylammonium chloride, IR spectrum of, 953 Trimethylsilyl ether, cleavage of, 627-628... 

Most commonly used is certainly the molecular electrostatic potential. It can be derived from any kind of charge distribution. Usually, the MEP is first calculated on a grid and subsequently transformed to the sphere or Gaussian representation. Quite important is the electron density distribution, which closely models the steric occupancy by a molecule. Other approaches utilize artificial fields for physicochemical properties commonly associated with binding, like a field for the hydrophobicity [193] or H-bonding potential [133,194]. 

Exploration of the potential applications of molecular mechanics to compounds of s-, p- and f-block elements is only just beginning. The difficulties arising from the electrostatic bonding in the s- and f-block elements have been tackled in a number of different ways, in most cases with reasonable success. In general, p-block elements are modeled relatively readily however, the problems of sterically active lone pairs have yet to be tackled. 

There have been many attempts to calculate AH independent of the equilibrium constant. The difficulty of a complete theoretical treatment of the H bond unfortunately requires approximations. The uncertainties thus introduced deprive the calculations of predictive value. Briefly, the usual approximations are based on some sort of electrostatic model, with computation of electrostatic, dispersion, and repulsive contributions by the methods of classical physics. Of course, the calculations require knowledge or estimation of such quantities as molecular arrangement, charge distribution, potential function, etc. Only a few systems have been treated. Reference 1327, for HF dimers 25, for carboxylic acids and 1561b, for ice furnish illustrative examples. Many other references are listed in Section 8.3, where a more complete discussion of the theoretical treatments is given. 

Kollman PA. The role of the electrostatic potential in modeling hydrogen bonding and other non-covalent interactions. In Politzer P, Truhlar DG, eds. Chemical Applications of Atomic and Molecular Electrostatic Potentials. New York Plenum, 1981 243-255. 

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 ... 

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