Potential functions induced-dipole terms

Potential functions induced-dipole terms, 84-85 minimization, 113-116 nonbonded interactions, 84-85 Potential of mean force, 43, 144 Potential surfaces, 1,6-11, 85, 87-88, 85 for amide hydrolysis, 176-181,178,179, 217-220, 218... 

The Direct Lattice Sum. Dispersion forces between two atoms can be described by a potential function expressed in terms containing inverse powers of the internuclear separations, s. The simplest function of this sort includes a potential energy of attraction proportional to the inverse sixth power of the separation and a repulsion that is zero at distances of separation greater than a particular value se and infinite at separations less than sc. This is the so-called hard sphere or van der Waals model. Such an approximate potential function can be improved in two respects. Investigations of the second virial coefficient have revealed that the potential energy of repulsion is best described as proportional to the inverse twelfth power of the separation and the term in sr9, which accounts for the greater part of the total attraction potential, due to the attraction of mutually induced dipoles, should have added to it the dipole-quadrupole and quadrupole-quadru-pole attractions, expressed as terms in sr8 and s-10, respectively. The complete potential function for the forces between two atoms is, therefore ... 

The X and Y are thus expressed in terms of the profiles of the up and their inverse down (r v ) transitions. The spectral moments can thus be written as a simple combination of the moments of the up and down transitions, which may be computed from the induced dipole components and the interaction potential. Furthermore, the function X satisfies the (old) detailed balance condition, Eq. 6.72, and is conveniently represented by the successful BC or K0 models. A simple choice for Y could be (co/A) r (ft)) where A is a constant to be specified and r (ci)) is another model function T which satisfies Eq. 6.72. In other words, according to Eq. 6.75, the ro to vibrational profiles K can be represented by the familiar model functions whose parameters may be defined with the help of the associated moment expressions. 

Attempts to represent the three-body interactions for water in terms of an analytic function fitted to ab initio results date back to the work of dementi and Corongiu [191] and Niesar et al. [67]. These authors used about 200 three-body energies computed at the Hartree-Fock level and fitted them to parametrize a simple polarization model in which induced dipoles were generated on each molecule by the electrostatic field of other molecules. Thus, the induction effects were distorted in order to describe the exchange effects. The three-body potentials obtained in this way and their many-body polarization extensions have been used in simulations of liquid water. We know now that the two-body potentials used in that work were insufficiently accurate for a meaningful evaluation of the role of three-body effects. 

When a weak dipole is in the presence of a polarisable functional group/molecule, then the electric field of that dipole will induce a temporary dipole in the polarisable functional group/molecule. The electrostatic influence of the weak dipole may be expressed in terms of a permanent dipole moment /r i, and that of the induced dipole in terms of an induced dipole moment The potential energy of interaction may then be defined by... 

The van der Waals interaction is one of the most significant types of electron correlations, even though it has been neglected in the development of most correlation functionals. By definition, the van der Waals interaction is a collective term that includes dipole-dipole, dipole-induced dipole, and dispersion interactions (Israelachviii 1992). The dipole-dipole interaction is the electrostatic interaction between permanent dipoles in polar systems. For the interactions between systems A and B, the corresponding potential is given classically as... 

The accuracy of the simulation results depends on a suitable choice of the parameters in the potential functions. On account of equation (23.1), an essential restraint of the calculation method is the pair-wise addition of atomic forces. Although effective pair potentials are used, three-body terms and interactions of higher order are neglected. Consequently, the major many-body contributions to the induced dipole interactions in aqueous ionic systems are not modelled accurately. A further simplification is a common application of... 

Chandrasekhar and Madhusudana have also considered the calculation of the coefficients required in V. The first contribution that these authors examined was the permanent dipole-permanent dipole forces. These were shown to vary as and provided a V dependence to Ui. It was shown however, that this term vanished when the pair potential V12 is averaged over a spherical molecular distribution function. The authors thus discard this term and provide further arguments for its neglect based on the empirical result that permanent dipoles apparently play a minor role in providing the stability of the nematic phase. The second contribution considered was the dispersion forces based on induced dipole-induced dipole interactions and induced dipole-induced quadrupole interactions. As mentioned above, the first of these gives a dependent contribution, while the second provides a contribution depending on The final contribution considered... 

The decrease of Qe with increasing 0 values on metal surfaces is due mainly to the change in the work function of the metals by the discrete dipole layers formed by the chemisorbed atoms. The author wishes to state here that he does not recommend the phrase induced heterogeneity, introduced by Boudart (385). He would rather recommend the term work-function effect or surface potential effect. 

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