Multipole technique

W. Pascher, Analysis of Waveguide Bends and Circuits by the Method of Lines and the Generalized Multipole Technique, Assoc. Prof, thesis, (FemUniversitat Hagen, Germany, 1998). 

C. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House, Boston London, 1990)... 

A. C. Ludwig, The generalized multipole technique, Comput. Phys. Commim. 68, 306 (1991)... 

N.B. Piller, O.J.F. Martin, Extension of the generalized multipole technique to three-dimensional anisotropic scatterers. Opt. Lett. 23, 579 (1998)... 

By combining the separation into Coulomb and exchange terms with the multipole technique of Section 9.14, it is possible to arrive at an operation count that scales linearly with the size of the system, allowing us to cany out direct Hartree-Fock calculations for very large systems. However,... 

The fifth and final chapter, on Parallel Force Field Evaluation, takes account of the fact that the bulk of CPU time spent in MD simulations is required for evaluation of the force field. In the first paper, BOARD and his coworkers present a comparison of the performance of various parallel implementations of Ewald and multipole summations together with recommendations for their application. The second paper, by Phillips et AL., addresses the special problems associated with the design of parallel MD programs. Conflicting issues that shape the design of such codes are identified and the use of features such as multiple threads and message-driven execution is described. The final paper, by Okunbor Murty, compares three force decomposition techniques (the checkerboard partitioning method. 

Molecular dipole moments are often used as descriptors in QPSR models. They are calculated reliably by most quantum mechanical techniques, not least because they are part of the parameterization data for semi-empirical MO techniques. Higher multipole moments are especially easily available from semi-empirical calculations using the natural atomic orbital-point charge (NAO-PC) technique [40], but can also be calculated rehably using ab-initio or DFT methods. They have been used for some QSPR models. 

One recent development in DFT is the advent of linear scaling algorithms. These algorithms replace the Coulomb terms for distant regions of the molecule with multipole expansions. This results in a method with a time complexity of N for sufficiently large molecules. The most common linear scaling techniques are the fast multipole method (FMM) and the continuous fast multipole method (CFMM). 

A. M. Mathiowetz, A. Jain, N. Karasawa, W. A. Goddard III. Protein simulations using techniques suitable for very large systems the cell multipole method for nonbond interactions and the Newton-Euler inverse mass operator method for internal coordinate dynamics. CN 8921. Proteins 20 221, 1994. 

Murray, J. S., M. E. Grice, P. Politzer, and J. R. Rabinowitz. 1990. Evaluation of a Finite Multipole Expansion Technique for the Computation of Electrostatic Potentials of Dibenzo-p-dioxins and Related Systems. J. Comp. Chem. 11, 112. 

Inacker, O., Kuhn, H., Bucher, H., Meyer, H. and Tews, K. H. (1970). Monolayer assembling technique used to determine the multipole nature of the phosphorescence of a dye molecule. Chem. Phys. Lett. 7, 213-8. 

There have been many attempts to formulate a procedure to avoid it and both a posteriori and a priori schemes are available. The counterpoise approach (CP) (Boys and Bemardi, 1970) and related methods are the most conunon a posteriori procedures. Although this technique represents the most frequently employed a posteriori procedure to estimate this error, several authors have emphasised that the method introduced by Boys and Bemardi does not allow a clear and precise determination of the BSSE. The addition of the partner s functions introduces the "secondary superposition error" a spurious electrostatic contribution due to the modification of the multipole moments and polarizabilities of the monomers. This is particularly important in the case of anisotropic potentials where these errors can contribute to alter the shape of the PES and the resulting physical picture (Xantheas, 1996 and Simon et al., 1996). 

Spectroscopic techniques have been applied most successfully to the study of individual atoms and molecules in the traditional spectroscopies. The same techniques can also be applied to investigate intermolecular interactions. Obviously, if the individual molecules of the gas are infrared inactive, induced spectra may be studied most readily, without interference from allowed spectra. While conventional spectroscopy generally emphasizes the measurement of frequency and energy levels, collision-induced spectroscopy aims mainly for the measurement of intensity and line shape to provide information on intermolecular interactions (multipole moments, range of exchange forces), intermolecular dynamics (time correlation functions), and optical bulk properties. 

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