Fast multipole moment

The original FMM has been refined by adjusting the accuracy of the multipole expansion as a function of the distance between boxes, producing the very Fast Multipole Moment (vFMM) method. Both of these have been generalized tc continuous charge distributions, as is required for calculating the Coulomb interactioi between electrons in a quantum description. The use of FMM methods in electronic structure calculations enables the Coulomb part of the electron-electron interaction h be calculated with a computational effort which depends linearly on the number of basi functions, once the system becomes sufficiently large. 

The Fast Multipole Moment (FMM) method (Section 16.2.1) was originally developed for calculating interactions between point charges. A direct calculation Tn fr. ves i-5rnTnn ii inn over. i11 pairs, i.e. n computational effort which increases as -Tlie. itlea in F TM is to split the total interaction into near- and far-fields. The near-field... 

It is possible to treat the large molecular systems that are compact and three-dimensional with high-quality basis sets in contrast to the fast multipole moment (FMM) method. 

The original FMM has been refined by also adjusting the accuracy of the multipole expansion as a function of the distance between boxes, producing the very Fast Multipole Moment (vFMM) method. ... 

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