Continuous fast multipole method

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. 

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... 

White, C. A., Johnson, B. G., Gill, P. M. W, Head-Gordon, M., 1994, The Continuous Fast Multipole Method , Chem. Phys. Lett., 230, 8. 

White CA, Johnson BG, Gill PMW, Head-Gordon M (1996) Linear scaling density functional calculations via the continuous fast multipole method. Chem Phys Lett 253 268-278 Lee TS, Lewis JP, Yang W (1998) Linear-scaling quantum mechanical calculations of biological molecules the divide-and-conquer approach. Comput Mater Sci 12 259-277 Van Alsenoy C, Yu CH, Peelers A, Martin JML, Schafer L (1998) Ab initio geometry determinations of proteins. 1. Crambin. J Phys Chem A 102 2246-2251... 

White CA, Johnson BG, Gill PMW, Flead-Gordon M. The continuous fast multipole method. Chem Phys Lett 1994 230 8-16. 

White C A, Johnson B G, Gill P M W and Head-Gordon M 1994 The fast multipole method Chem. Phys. Lett. 230 8-16 White C A, Johnson B G, Gill P M Wand Head-Gordon M 1996 Linear sealing density funotional oalculations via the continuous fast multipole method Chem. Phys. Lett. 253 268-78... 

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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