Distributed multipole, description

Unfortunately this is still too severe a requirement in many cases. It is often possible for molecules to approach to distances at which such spheres would overlap, without encountering the repulsive part of the potential and even when they do not overlap, they may approach so closely that convergence becomes very slow. For this reason, it has become common to adopt a distributed multipole description, in which each molecule is divided into a number of regions, each described by its own multipole moments. There are many ways of determining these distributed multipole moments [6-11] many authors have used distributed charges alone, but it is now widely... 

Stone s DMA method has been applied in several other papers. Our review cannot be exhaustive but we would like to quote two additional papers using this approach because they give additional information on the basic problems of the electrostatic approach. Price, Harrison and Guest [89] examined the DMA description of the MEP of a large molecule, with formula C63H113N11O12, obtained from a 3-21G SCF wavefunction. The description of the electrostatic potential obtained in such a way is comparable to that obtained with potential derived atomic charges (PD-AC) to which we shall refer later on in more detail. The superiority of a distribute multipole description, in describing the anisotropic contributions to the MEP on the van der Waals surface is shown clearly. 

A useful alternative approach is to isolate the components of the perturbation expansion, namely the repulsion, electrostatic interaction, induction, and dispersion terms, and to calculate each of them independently by the most appropriate technique. Thus the electrostatic interaction can be calculated accurately from distributed multipole descriptions of the individual molecules, while the induction and dispersion contributions may be derived from molecular polarizabilities. This approach has the advantage that the properties of the monomers have to be calculated only once, after which the interactions may be evaluated easily and efficiently at as many dimer geometries as required. The repulsion is not so amenable, but it can be fitted by suitable analytic functions much more satisfactorily than the complete potential. The result is a model of the intermolecular potential that is capable of describing properties to a high level of accuracy. 

Thus it is unwise to attempt to obtain distributed multipole models solely by reference to experimental data, especially as experimental data for the multipole moments are usually very unreliable for all but the first one or two non-vanishing moments. There is no difficulty in obtaining the information needed for the distributed multipole description from ab initio calculations the distributed multipole analysis takes a fraction of the time... 

Ferenczy GG, Winn PJ, Reynolds CA, Richter G (1997) Effective distributed multipoles for the quantitative description of electrostatics and polarisation in intermolecular interactions. Abs Papers Am Chem Soc 214 38-COMP... 

Chipot C, Angyan JG, Ferenczy GG, Scheraga HA (1993) Transferable net atomic charges from a distributed multipole analysis for the description of electrostatic properties — a case-study of saturated-hydrocarbons. J Phys Chem 97(25) 6628—6636... 

The distributed multipole model incorporates a nearly exact description of the molecular charge distribution into the evaluation of the electrostatic energy. Is the increase in accuracy gained by representing the effects of lone pair and 7i-electron density worth the extra complexity in the potential model Even if there is a significant enhancement, is it worth using such an elaborate model when only crude models, such as the isotropic atom-atom 6-exp potential, are available for the other contributions ... 

The distributed multipole analysis method of Stone and co-workers is similar in concept but is based on nonredundant spherical harmonic representation of the multipoles (recall that whereas there are six second moments, only five are independent). He initially places numerous site multipoles at centers of orbital overlap. The individual monopoles are spread out along the molecular axis, and are thought to represent the distribution of charge the site dipoles are also spread out along the bond axis. This very detailed description is simplified into a three-site model, which includes a site in the F—H bond. However, the multipole expansion does not converge well, especially for the bond center site. 

It has recently become clear that classical electrostatics is much more useful in the description of intermolecular interactions than was previously thought. The key is the use of distributed multipoles, which provide a compact and accurate picture of the charge distribution but do not suffer from the convergence problems associated with the conventional one-centre multipole expansion. The article describes how the electrostatic interaction can be formulated efficiently and simply, by using the best features of both the Cartesian tensor and the spherical tensor formalisms, without the need for inconvenient transformations between molecular and space-fixed coordinate systems, and how related phenomena such as induction and dispersion interactions can be incorporated within the same framework. The formalism also provides a very simple route for the evaluation of electric fields and field gradients. The article shows how the forces and torques needed for molecular dynamics calculations can be evaluated efficiently. The formulae needed for these applications are tabulated. 

There is always an element of arbitrariness in the multipole description of a charge distribution. Even when the conventional single-site description is used, the position of the origin can be chosen freely. However the values of all multipole moments of higher rank than the first nonvanishing moment depend on the choice of origin. If... 

We have seen that we cannot describe the electrostatic interaction between molecules at short range adequately in terms of multipole moments for each molecule as a whole, and that a distributed-multipole treatment is needed. Similar refinements are required for a proper description of the distortion of the charge distribution in response to the fields due to neighbouring molecules. 

Equivalent description [32] of multipolar term could be also obtained in spherical harmonic formulation from Distributed Multipole Analysis (DMA) [2,33]. 

Crystal structure prediction The field of organic crystal structure prediction remains one of the best testing grounds for intermolecular potentials. Acciuades need not be as high as that needed for spectroscopic calculations, but the effects of molecular flexibility and many-body non-additivity need to be accounted for. See Price (2008, 2009) for recent reviews of this subject. For a description of dispersion-corrected DFT methods specially parametrized for organic crystals see Neumann and Perrin (2005). For a comprehensive examination of the role of detailed distributed multipole models in this field see Day et al. (2005). 

The original FMM has been refined by adjusting the accuracy of the multipole expansion as a function of the distance between boxes, producing the very Fast Multipole Moment (vFMM) method. Both of these have been generalized tc continuous charge distributions, as is required for calculating the Coulomb interactioi between electrons in a quantum description. The use of FMM methods in electronic structure calculations enables the Coulomb part of the electron-electron interaction h be calculated with a computational effort which depends linearly on the number of basi functions, once the system becomes sufficiently large. 

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