Electrostatic energy interaction calculation

The electrostatic energy is calculated using the distributed multipolar expansion introduced by Stone [39,40], with the expansion carried out through octopoles. The expansion centers are taken to be the atom centers and the bond midpoints. So, for water, there are five expansion points (three at the atom centers and two at the O-H bond midpoints), while in benzene there are 24 expansion points. The induction or polarization term is represented by the interaction of the induced dipole on one fragment with the static multipolar field on another fragment, expressed in terms of the distributed localized molecular orbital (LMO) dipole polarizabilities. That is, the number of polarizability points is equal to the number of bonds and lone pairs in the molecule. One can opt to include inner shells as well, but this is usually not useful. The induced dipoles are iterated to self-consistency, so some many body effects are included. 

Electrostatic energy. The calculation of the total electrostatic energy, starting from the effective energies, requires some qualification. It is not a simple sum of effective energies es(X) and 8m(X), for the simple reason that the interaction energy is counted twice. Thus, for each subsystem a "polarization work" has to be withdrawn in... 

All of our atomistic simulations were performed using standard Grand Canonical Monte Carlo (GCMC) and Equilibrium Molecular Dynamics (EMD) simulation methods. The RASPA [15] code was employed. Electrostatic energies were calculated using Ewald summation [16, 17] with a relative error of 10 . A 12 A van der Waals cutoff was used for the short-range interactions. Periodic boundary conditions were employed. 

In periodic boimdary conditions, one possible way to avoid truncation of electrostatic interaction is to apply the so-called Particle Mesh Ewald (PME) method, which follows the Ewald summation method of calculating the electrostatic energy for a number of charges [27]. It was first devised by Ewald in 1921 to study the energetics of ionic crystals [28]. PME has been widely used for highly polar or charged systems. York and Darden applied the PME method already in 1994 to simulate a crystal of the bovine pancreatic trypsin inhibitor (BPTI) by molecular dynamics [29]. 

Here 0p and 0 correspond to the terms in r" and respectively in Equation (1.8) as already pointed out, these contributions are always present, whereas the electrostatic energies 0, and may or may not be present according to the nature of the adsorbent and the adsorptive. In principle. Equation (1.16) could be used to calculate the numerical value of the interaction potential as a function of the distance z of any given molecule from the surface of a chosen solid. In practice, however, the scope has to be limited to systems composed of a simple type of gas molecule and... 

The intermolecular distance was calculated here relative to the center of mass (C. M.) of the water molecule. For this particular choice of the origin the quadruple term is rather small and the total electrostatic energy of interaction is reproduced fairly well by the first term of the expansion, the ion-dipole term alone. The difference between zIEcou and zIEcou of course is not exclusively... 

CoMFA is based on interactions between a molecule and a probe traditionally, the probe has the properties consistent with a van der Waals sp3 carbon and a charge of +1.0. The interactions calculated between the probe and the molecules of interest are steric (van der Waals 6-12) and electrostatic (Coulombic with a 1/r dielectric) energies (4). The CoMFA process starts by constructing a 3D grid... 

Another class of 3D descriptors is molecular interaction field (MIF) descriptors, with its well-known example of Comparative Molecular Field Analysis (204,205) (CoMFA). In CoMFA, the steric and electrostatic fields are calculated for each molecule by interaction with a probe atom at a series of grid points surrounding the aligned molecules in 3D space. These interaction energy fields are correlated with the property of interest. The 3D nature of the CoMFA technique provides a convenient tool for visualization of the significant features of the resulting models. 

Waller et al. (237) performed a CoMFA study to analyze the metabolic rates of CYP2E1 in rodents as intrinsic clearance of a 12 chlorinated volatile organic compounds (VOCs). After superimposition, the steric and electrostatic field interaction energies, the HINT (/jydropathic interactions) energy (238), and molecular orbital field were calculated in addition to clogP. The best model... 

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