Distributed dipole model

As emphasized, the Born—Kirkwood—Onsager (BKO) approach includes only the solute s monopole and dipole interaction with the continuum. That is, the full classical multipolar expansion of the total solute charge distribution is truncated at the dipole term. This simplification of the electronic distribution fails most visibly for neutral molecules whose dipole moments vanish as a result of symmetry. A distributed monopole or distributed dipole model is more... 

A molecular multipole expansion is poorly converged at distances of chemical interest, for instance, at distances between atoms of molecules in a dimer or crystal. To obtain electrostatic interaction energy between heteronuclear diatomic molecules at close distance it is always better to model observed molecular point dipoles by a distributed dipole model that places net charges on the atoms. In general, a distributed multipole model of a molecule consists of a set of sites with each site having its own multipoles. Obviously distributed multipole models are not uniquely defined. For instance, at which site in a polyatomic ion is the ionic charge (monopole) located Do you spread it around evenly among the sites ... 

Z. Gamba and H. Bonadeo, / Chem. Phys., 75, 5059 (1981). Lattice Dynamical Calculations on Azabenzene Crystals The Distributed Dipole Model. 

The exact computation of P W) in this simple one-dipole model is already a very arduous task that, to my knowledge, has not yet been exactly solved. We can, however, consider a limiting case and try to elucidate the properties of the work (heat) distribution. Here we consider the limit of large ramping speed r, where the dipole executes just one transition from the down to the up orientation. A few of these paths are depicted in Fig. 13b. This is also called a first-order Markov process because it only includes transitions that occur in just one direction (from down to up). In this reduced and oversimplified description, a path is fully specified by the value of the field H at which the dipole reverses orientation. The work along one of these paths is given by... 

Early numerical estimates of ternary moments [402] were based on the empirical exp-4 induced dipole model typical of collision-induced absorption in the fundamental band, which we will consider in Chapter 6, and hard-sphere interaction potentials. While the main conclusions are at least qualitatively supported by more detailed calculations, significant quantitative differences are observed that are related to three improvements that have been possible in recent work [296] improved interaction potentials the quantum corrections of the distribution functions and new, accurate induced dipole functions. The force effect is by no means always positive, nor is it always stronger than the cancellation effect. 

The MFA [1] introduces the perturbation due to the solvent effect in an averaged way. Specifically, the quantity that is introduced into the solute molecular Hamiltonian is the averaged value of the potential generated by the solvent in the volume occupied by the solute. In the past, this approximation has mainly been used with very simplified descriptions of the solvent, such as those provided by the dielectric continuum [2] or Langevin dipole models [3], A more detailed description of the solvent has been used by Ten-no et al. [4], who describe the solvent through atom-atom radial distribution functions obtained via an extended version of the interaction site method. Less attention has been paid, however, to the use of the MFA in conjunction with simulation calculations of liquids, although its theoretical bases are well known [5]. In this respect, we would refer to the papers of Sese and co-workers [6], where the solvent radial distribution functions obtained from MD [7] calculations and its perturbation are introduced a posteriori into the molecular Hamiltonian. 

The contribution to the predicted electrostatic potential of the anisotropic atomic multipoles (Q , / > 0), which represent the lone pair and n-electron density, rapidly become less important as the distance between the molecules increases. This not only results from the inverse power of R increasing with I, but also from the cancellation between the contributions from different multipoles and different atoms. For example, there is generally an atomic dipole component along a bond that opposes the polarity implied by the atomic charges, as shown in the results of distributed multipole analyses (DMAs) of the azabenzenes. ° Thus, the accuracy gained by using a distributed multipole model is very dependent on the relative separation and orientation of the molecules, as well as the actual distribution of charge in the molecule. 

The expressions of Vint which are now in use belong to two categories expressions based on a discrete distribution of the solvent, and expressions based on continuous distributions. The first approach leads to quite different methods. We quote here as examples the combined quantum me-chanics/molecular mechanics approach (QM/MM) which introduces in the quantum formulation computer simulation procedures for the solvent (see Gao, 1995, for a recent review), and the Langevin dipole model developed by Warshel (Warshel, 1991), which fits the gap between discrete and continuum approaches. We shall come back to the abundant literature on this subject later. 

A rather novel scheme for modeling molecular polarizabilities as distributed dipole polarizabilities has recently been reported [141]. In this approach, the overall quadrupole induced in a molecule by an external field, as calculated with ab initio methods, is decomposed into induced dipoles distributed to atomic sites. In turn, this yields the dipole polarizability values at those sites. In effect, this relates the overall dipole quadrupole polarizability to a distribution of dipole polarizabihties. 

We should clarify here that the above cited studies are largely exploratory and the role of each parameter in reaction specificity is currently unclear. They show, however, the need for a fundamental understanding of molecular and electronic surface interactions that determine electrocatalytic as well as catalytic specificity. Thus, adsorption isotherms, surface states, molecular configurations, electronic distributions, dipole formation, and bond hybridization should be explored for well-characterized catalysts and model reactions in the presence and in the absence of an electric field. 

Dinur and Hagler propose a novel method to determine atomic point charges and point dipoles from derivatives of the molecular dipole moment and second moments. The method is limited to planar molecules and has been applied to hydrogen fluoride, water, formaldehyde, formamide, ethylene, benzene, and pyridine. As was also noted by Williams, they found that atomic dipoles do not necessarily point along the bond directions. Price proposed a distributed multipole model for several aromatic hydrocarbons using carbon sites only. 

Luo237 has attempted to establish a power law for scaling the static y-hyperpolarizabilites of the fullerenes as a function of the number of carbon atoms. C6o does not fit into the relationship, a result attributed to its exceptional electron localization. An intermolecular potential model of with distributed dipole interactions has been used by Gamba238 to obtain the polarizability and multipole moments. Measurements of the third order response of fullerenes in CS2 have been reported by Huang et al.239 and correlated with chemical structure. 

The Drude oscillator model has a number of advantages over other polarizable models facilitating its implementation in multiple simulation packages including CHARMM [150], NAMD [165], ChemSell QM/MM [192] and the OpenMM suite of utilities for GPU [193]. Representing a dipole as two point charges provides an intuitive physical picture in terms of displacement of the electronic distribution the model is able to represent delocalization without need of additional non-atomic sites since the dipole is not point-like as, e.g., in the induced dipole model. For example, the use of auxiliary particles allows for the inclusion of mechanical polarizabilities [194]... 

In order to understand ionic distributions in the EDL a realistic description of hydration or, more generally, solvation phenomena is necessary, which in protic liquids implies an adequate description of the hydrogen-bond network. Theory and computer simulation of bulk liquids showed that the most efficient way to include these properties into the models is via distributed charge models in which the intramolecular charge distribution is represented by several point charges. The point charges are adjusted to reproduce experimental dipole and/or quadrupole moments of the molecule, the bulk structure... 

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