Multipole analysis

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... 

Distributed multipole models for Nj and HF. (Figure adapted from Stone A j and M Alderton 19S5. ibuted Multipole Analysis Methods and Applications. Molecular Physics 56 3 047-1064.)... 

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

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... 

Multipole analysis with high-resolution X-ray data for [Ni(thmbtacn)]2+ was carried out to determine the electron configuration in the C3 symmetry-adapted orbitals of the Ni ion, confirming a higher occupancy of the crystal field-stabilized t2g orbitals relative to the destabilized eg orbitals. This is interpreted in terms of a predominantly ionic metal-ligand interaction.1424... 

Avilov, A.S., Eepeshov, G.G., Pietseh, U., Tsirelson, V.G. Multipole Analysis of the Electron Density and Eleetrostatie Potential in Germanium by High-resolution Eleetron Diffraetion. J.Phys.Chem.Solids. (2001), 62, 2135. 

The summation in Eq. (8.53) is slowly converging if a molecular charge distribution is represented by a single set of moments. However, the expression can be written as the summation over the distributed moments, centered at the nuclei j, which is precisely the information available from the multipole analysis ... 

Olovsson and coworkers have pointed out that the superposition of the electron density of adjacent molecules in the experimental deformation density may lead to modification of the contours in the lone-pair region of the water molecules (Fernandes et al. 1990, McIntyre et al. 1990). To avoid this complication, it is preferable to partition the crystal density through the multipole analysis, after which comparisons can be based on individual molecule or fragment densities. 

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... 

II. Critical Study of Multipole Analysis of the Electron Density. 267... 

Once the multipole analysis of the X-ray data is done, it provides an analytical description of the electron density that can be used to calculate electrostatic properties (static model density, topology of the density, dipole moments, electrostatic potential, net charges, d orbital populations, etc.). It also allows the calculation of accurate structure factors phases which enables the calculation of experimental dynamic deformation density maps [16] ... 

Does the multipole analysis of the structure factors permit a real deconvolution between thermal motions parameters and deformation density parameters ... 

II. CRITICAL STUDY OF MULTIPOLE ANALYSIS OF THE ELECTRON DENSITY... 

As an important result of this joint use of resonant scattering and advanced multipole analysis we note that partial structure X hm(r) Y (co) can be split into... 

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. 

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