Point-multipole model

In GBEMP model, point multipoles are included inside Gay-Berne particles for providing a reasonable approximation to the charge density of corresponding all-atom model, and they are usually placed at the mass centers of the Gay-Berne particles and/or specific locations inside the Gay-Berne particles. In some cases, non-interaction EMP sites, which do not involve non-bonded interactions, are used to connect two different Gay-Berne particles. Thus, the interaction energy between two electric multipole sites (/ and j) can be computed as... 

A common feature of many mesogenic molecules is the presence of polar substituents and aromatic cores [3]. The electrostatic interactions between such groups can be incorporated into a molecular potential with the addition of dipolar and quadrupolar terms, respectively. Rather than represent these permanent electrostatic interactions by using a model in which a charge distribution is scattered over the surface of the molecule, it is very common to use one (or more) point multipoles [2,29]. Thus for an electrostatic Gay-Berne model, the pair potential is given by the sum... 

Sharma, R.R., Das, T.P., and Orbach, R. 1966. Zero-field splitting of S-state ions. I. Point-multipole model. Physical Review 149 257-269. 

The asymmetry found in the electron density of these soft ions can be modelled by adding one or more point multipoles to the point charge used to... 

In this work the use of molecular electrostatic potential (MEP) maps for similarity studies is reviewed in light of the latest results. First, methods of obtaining MEP maps is overviewed. The methodology, reliability and the efficiency of calculations based on semi-empirical as well as ab initio methods are discussed in detail. Point-charge models and multipole expansion methods which provide MEP maps of satisfactory quality are evaluated critically. Later on, similarity indices of various kinds are analyzed, compared and examples of their use are shown. Finally, the last section lists and summarizes software packages capable of calculating MEP map based similarity indices. 

Under the assumption of the existence of ideal ionic crystals, built up from point charges and point multipoles, the NQR spectrum is completely determined by the crystal field of the electric multipoles. The experimental results of NQR can be explained within the frame of this model. Refinements of the model, such as the dependence of multipole polarizabilities upon the crystal field or the influence of overlapping of the electron clouds, are not yet understood quantitatively. 

The point multipole expansion of the Coulombic matrix element governing the first-order electric dipole moment in Eq. (3) gives the selection rules of the ligand polarization model through Eq. (4),... 

The variation of this approach merges with the PD point multipole models discussed in the next section. It is well known that an atom in a molecule can possibly have a dipole, quadrupole, etc. An atomic dipole, quadrupole, etc. can be simulated by a distributed multipole. For example, an atomic dipole ascribed to a lone pair can be simulated by placing a lone pair charge site near the atom, at the appropriate direction and distance. An atomic quadrupole can be simulated by placing several monopolic sites near the atom. 

All successful water models make use of a distribution of point charges rather than of point multipoles. The main reason is that the directional properties of intermolecular hydrogen bonds can be obtained efficiently with oifly 3 or 4 point charges. Furthermore, Goldman and Backx [39] have shown that model molecules with such distributions of point charges are more effective as solvents (for instance in their ability to dissociate ion pairs) than molecules with equivalent point dipoles and quadrupoles. 

It is natural to contemplate the next extensions to less-simple models. Of course, a fluid of spherical particles carrying point multipoles presents no... 

There have been some debates among people using the COSMO approach [33, 34] there are no formal reasons asking for a constant factor equal for all tesserae anyway, the examination of simple models for which there are analytical solutions (point multipoles within a regular cavity) suggests a constant value of the type (e — l)/(e + 1 ) with k ranging from 0 to 2. In the present implementation we have selected k = 0 and then f = e — l)/e. 

The description of the mDC method in the present work is supplemented with mathematical details that we Have used to introduce multipolar densities efficiently into the model. In particular, we describe the mathematics needed to construct atomic multipole expansions from atomic orbitals (AOs) and interact the expansions with point-multipole and Gaussian-multipole functions. With that goal, we present the key elements required to use the spherical tensor gradient operator (STGO) and the real-valued solid harmonics perform multipole translations for use in the Fast Multipole Method (FMM) electrostatically interact point-multipole expansions interact Gaussian-multipoles in a manner suitable for real-space Particle Mesh Ewald (PME) corrections and we list the relevant real-valued spherical harmonic Gaunt coefficients for the expansion of AO product densities into atom-centered multipoles. 

The point multipoles can give the accurate description of the electrostatic interactions between Gay-Berne particles separated with a certain distance (independent of the particle sizes). As the two particles are getting too close to each other, the point multipoles are not able to accurately describe the overlap of their charge density, causing the so-called penetration error [59]. An effective solution to avoid the penetration error would be to seek a proper damping function [60]. In current GBEMP model, we employed the damping function defined as... 

Golubkov, P. A., and Ren, P. [2006). Generalized coarse-grained model based on point multipole and Gay-Beme potentials,/. Chem. Phys., 125, pp. 064103... 

Isotropic hyperfine interaction in EPR. Calculation of zero-field splitting of S-state ions. Point-multipole model. 

In the Buckingham-Fowler model, each monomer electric charge distribution is described by a set of point multipoles (charges, dipoles and quadru-poles) located on the atoms and, sometimes, additionally at bond midpoints. The values of the point multipoles are determined by the so-called distributed multipole analysis (DMA) of an ab initio wavefunction. This multicentric representation of the charge distribution shows superior convergence behaviour to the one-centre molecular multipoles when calculating the electrostatic potential around a molecule. 

A Gaussian-based electrostatic model (GEM) has been explored as an alternative to distributed point multipole electrostatic representation. GEM computes the molecular interaction energies using an approach similar to SIBFA... 

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