Distributed multipole, description molecular charge distribution

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 ... 

All transferable force fields discussed in Sect. 4.1 employ point charges to account for the molecular charge distribution, although a more accurate description of the electrostatics with higher multipole moments may be used. Hasse, Vrabec, and coworkers [102,109] proposed a set of simple united-atom force fields for more than 70 compounds of different classes that describe the intermolecular interactions using two LJ 12-6 sites plus a point dipole (15) or a point quadrupole (16). The potential... 

We have thus closed a loop the least square fitting was adopted to improve simple descriptions of the molecular charge distribution, and subsequently refined to reach levels of complexity in the models very similar to those employed in the segmented multipole expansions of the charge distribution. The presence of a loop does not means that there has not been progress in the description of the MEP on the contrary, the PD/LSF approaches represent one of the most promising ways of getting less expensive MEP descriptions of acceptable quality. 

The Distributed Multipole description of a molecular charge distribution is not unique it depends on the coice of sites and on the precise definition of the region boundaries. (The conventional single-site multipole description is not unique either, since it depends on the choice of origin. ) There are many ways of determining these distributed multipole moments many authors have used distributed charges alone, but it is now widely accepted that an accurate and efficient description requires multipoles up to at least quadrupole. 

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. 

---