Multipole expansion method

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. 

Apart from the ASC-PCM method developed by the Pisa group, there are several other methods based on the polarizable continuum model the MPE (multipole expansion method) by the Nancy group [19,20] and by Mikkelsen and co-workers [21,22], the GBA (generalized Bom approximation) by the Minneapolis group - Cramer and Truhlar [23-26] and others. 

Apart from the ASC-PCM method developed by the Pisa group, there are several other PCM-based methods the MPE (multipole expansion method) of the Nancy group... 

Atomic multipoles are estimated by fitting the atomic multipole expansion to the detailed features of the ground-state wave function obtained from ab initio quantum mechanical calculations. Rein (1975) reviewed the problem of estimating atomic multipoles and presented examples of use of the atomic multipole expansion method to the problem of molecular recognition in biology. More recently, Liang and Lipscomb (1986) considered the problem of transferabilities of atomic multipoles in atomic multipole expansions. 

Whitehead C, Breneman C, Sukumar N, Ryan M. Transferable atom equivalent multicentered multipole expansion method. J Comput Chem 2003 24 512-29. 

For any method of structure reconstruction by ab-initio methods additional assumptions must be made. The multipole expansion method of Harrison, Stuhr-MANN, and SvERGUN ([86], Sect. 5.3 [101], Chap. 6) assumes homogeneous internal density. The shape of the scattering curve is fitted by varying the envelope of the particle. 

The porous sphere approach by Vanni (2000) adopts essentially the same concept for the internal aggregates structure. Yet, this approach yields smaller hydrodynamic diameters than the multipole expansion method because the local porosity at the convex huU, i.e. the decisive parameter of the model, is systematically underestimated when the aggregate is considered spherical. 

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