Coulombic interactions potential energy surfaces

A.K. Dham, F.R.W. McCourt, W.J. Meath, Exhange-Coulomb model potential energy surface for the Nz-Ar interaction. J. Chem. Phys. 103(19), 8477-8491 (1995)... 

In Chapter IX, Liang et al. present an approach, termed as the crude Bom-Oppenheimer approximation, which is based on the Born-Oppen-heimer approximation but employs the straightforward perturbation method. Within their chapter they develop this approximation to become a practical method for computing potential energy surfaces. They show that to carry out different orders of perturbation, the ability to calculate the matrix elements of the derivatives of the Coulomb interaction with respect to nuclear coordinates is essential. For this purpose, they study a diatomic molecule, and by doing that demonstrate the basic skill to compute the relevant matrix elements for the Gaussian basis sets. Finally, they apply this approach to the H2 molecule and show that the calculated equilibrium position and foree constant fit reasonable well those obtained by other approaches. 

The quantity, V(R), the sum of the electronic energy Egjg. computed in a wave function calculation and the nuclear-nuclear coulomb interaction V(R,R), constitutes a potential energy surface having 3N independent variables (the coordinates R). The independent variables are the coordinates of the nuclei but having made the Born-Oppenheimer approximation, we can think of them as the coordinates of the atoms in a molecule. 

According to these considerations three subregions are defined as depicted in Fig. 1. The inner and outer parts of the QM region are termed the QM core and QM layer zone, respectively. As discussed solutes in the QM core do not require the application of non-Coulombic potentials—composite species with complex potential energy surfaces can be treated in a straightforward way, while complex potential functions are required in the case of classical and even conventional QM/MM simulation studies. Interactions at close solute-solvent distances are treated exclusively via quantum mechanics and account for polarization, charge transfer, as well as many-body effects. The solute-solvent... 

Auerbach et al. (101) used a variant of the TST model of diffusion to characterize the motion of benzene in NaY zeolite. The computational efficiency of this method, as already discussed for the diffusion of Xe in NaY zeolite (72), means that long-time-scale motions such as intercage jumps can be investigated. Auerbach et al. used a zeolite-hydrocarbon potential energy surface that they recently developed themselves. A Si/Al ratio of 3.0 was assumed and the potential parameters were fitted to reproduce crystallographic and thermodynamic data for the benzene-NaY zeolite system. The functional form of the potential was similar to all others, including a Lennard-Jones function to describe the short-range interactions and a Coulombic repulsion term calculated by Ewald summation. 

Although the underlying approximations are too crude to obtain an accurate potential energy surface, another very important observation can be made when the London equation is compared to the energy expression for H2 the total energy is not equal to the sum of pairwise H-H interactions. Thus, E(Rab, Rac, Rbc) Z Eab + Eac + Ebg, where Eab corresponds to E+ of Eq. (3.31), and Eac and Ebc are given by similar expressions. The simple summation of pairwise H-H interactions only holds for the Coulomb integrals ... 

The multidimensional potential energy surface was written as the sum of a gas-phase (LEPS) energy surface incorporating the main features of the one-dimensional double-well potential in Example 10.1, solvent-solute interactions described by Lennard-Jones potentials with added (Coulomb) interactions corresponding to point charges, and solvent solvent interactions including intermolecular degrees of freedom. The solvent consisted of 64 water molecules. 

Equations (585), (587) and (589) are very important for understanding the behavior of two unlike molecules, particles or surfaces in a third (solvent) medium. If (AV, > 0), which means that (VAs iOC 12 > VDis) in Equation (585), then the molecules tend to disperse and a repulsion occurs between the unlike molecules. This condition can be met only if the value of A3 is intermediate between A, and A2 so that when [A, > A3 > A ] or [A2 > A3 > A,] then Equation (585) must give a positive value of AV and two particles or surfaces in a third medium will repel each other. For the other conditions, we may state that unlike particles may attract or repel each other depending on the values of A A2 and A3. The same conclusions apply for the AV2 = VAssoc 11 22 — VDis interaction potential energy difference given by Equation (587). However, when we consider Equation (589) describing the [AV3 = VV iSOC-1. 22 - VAssoc 12] case, it is clear that the most favored final state will be that of particles (1) associated with particles (1) and (2) with (2) and (3) with (3), so that there is always a preferential attraction between like molecules or particles or surfaces in a multi-component mixture, except for the cases where H-bonding and/or Coulombic interactions are operative. 

The values of the four interaction terms (surface contact, side chain inter-molecular contacts, relative solvation energy and Coulombic interaction potential) were computed for the 200 best matching geometries generated by the BoGlE module, for each of the 15 docking cases. 

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