CFMM continuous fast multipole

Cartesian coordinates system for locating points in space based on three coordinates, which are usually given the symbols x, y, z or i, j, k CBS (complete basis set) an ah initio method CC (coupled cluster) a correlated ah initio method CFF (consistent force field) a class of molecular mechanics force fields CFMM (continuous fast multipole method) a method for fast DFT calculations on large molecules... 

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). 

One of the major selling points of Q-Chem is its use of a continuous fast multipole method (CFMM) for linear scaling DFT calculations. Our tests comparing Gaussian FMM and Q-Chem CFMM indicated some calculations where Gaussian used less CPU time by as much as 6% and other cases where Q-Chem ran faster by as much as 43%. Q-Chem also required more memory to run. Both direct and semidirect integral evaluation routines are available in Q-Chem. 

Calculation of the Coulomb matrix element J s in (15.79) involves not point charges (as in the FMM method) but continuous distributions of charge defined by the basis functions. Therefore, quantum chemists modified the FMM method to deal with interactions involving continuous charge distributions. One such modification for rapid evaluation of the Coulomb matrix elements for large molecules is the continuous fast multipole method (CFMM) [C. A. White et al., Chem. Phys. Lett., 253,268 (1996)]. Another is the Gaussian very fast multipole method (GvFMM) [M. C. Strain, G. E. Scuseria, and M. J. Frisch, Science, 271, 51 (1996)]. 

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