Distributed multipole analysis

The distributed multipole analysis (DMA) embodies a wavefimction partitioning method pioneered by Stone and coworkers [31, 108, 109], similar to a number of procedures developed by others [35, 101, 110]. DMA relies on the expansion of the charge density as a function of a product of basis wavefunctions 

We point out to the reader that DMA provides an expansion— rather than a fit—of the charge density. As such, the individual MTP coefficients derived from DMA will not depend on the order of the expansion. Despite its overwhelming use in the field, the method suffers from being tied to a single conformation Koch et al. showed that MTP can be highly conformation dependent [57] and may thus show a lack of transferability across the distribution 

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Stone A J 1981 Distributed multipole analysis or how to describe a molecular charge distribution Chem. Phys. Lett. 83 233... 

Stone A J and Alderton M 1985 Distributed multipole analysis—methods and applications Mol. Phys. 56 1047... 

Stone A J 1981. Distributed Multipole Analysis, or How to Describe a Molecular Charge Distribution. Chemical Physics Letters 83 233-239. 

Stone A J and M Alderton 1985. Distributed Multipole Analysis Methods and Applications. Molecular Physics 56 1047-1064. 

The scaling factor Sj can take any value between 0 and 1 and is applied to site j. The superscripts p and m indicate permanent and mutual induction, respectively. Equation (9-19) can be solved iteratively using similar procedures to those used to solve Eq. (9-3). The formal permanent moments can be calculated by subtracting induced moments from moments from ab initio calculations. For any conformation of a given compound the atomic multipoles can be determined from Distributed Multipole Analysis (DMA) [51]. 

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... 

Since the single-center multipole expansion of the interaction energy is divergent, one could use a kind of multicenter expansion. One can hope that the multipole expansion will provide better results if multipole moments and polarizabilities localized at various points of a molecule are used instead of global multipole moments and polarizabilities. This idea forms the basis of the so-called distributed multipole analysis of the electrostatic, induction, and dispersion interactions between molecules187 195. 

Stone AJ (1981) Distributed multipole analysis, or how to describe amolecular charge distribution. 

Stone AJ, Alderton M (1985) Distributed multipole analysis methods and applications. Mol Phys... 

At this stage, when the nature of the basis is known, we return to the question, how the MME needed to evaluate (i > I FPerm. cj) and (i > I Fp0i. cj) is done in practice. We use a method that takes advantage of basic properties of Gaussian functions, which is also very similar to the distributed multipole analysis of Stone [123,124,125], For an arbitrary pair of basis functions we use the orbital expansion... 

The Distributed Multipole Analysis (DMA) developed by Stone uses the fact that the electrostatic potential arising from the charge overlap between two basis functions can... 

A.J. Stone and M. Alderton, Distributed multipole analysis. Methods and applications. Mol. Phys., 56 (1985) 1047-1064. 

D.L. Cooper and N.C.J. Stutchbury, Distributed multipole analysis for charge partitioning by zero-flux surfaces tbe structure of HF complexes, Cbem. Pbys. Lett., 120 (1985) 167-172. 

The method that is used in most of the work described in this chapter is the distributed multipole analysis (DMA) of Stone,which is implemented in the CADPAC ab initio suite. DMA is based on the density matrix p,y of the ab initio wavefunction of the molecule, expressed in terms of the Gaussian primitives q that comprise the atomic orbital basis set ... 

D. L. Cooper and N. C. J. Stutchbury, Ghent. Phys. Lett., 120, 167 (1985). Distributed Multipole Analysis from Charge Partitioning by Zero-Flux Surfaces The Structure of HF Complexes. 

S. L. Price and A. J. Stone, Chem. Phys. Lett., 98, 419 (1983). A Distributed Multipole Analysis of the Charge Densities of the Azabenzene Molecules. 

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. 

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