Fourier transform Coulomb method

Fusti-Molnar L, Pulay P (2002) The Fourier transform Coulomb method Efficient and accurate calculation of the Coulomb operator in a Gaussian basis. J Chem Phys 117 7827... 

Fourier Transform Coulomb Method Efficient and Accurate Localization of the Filtered Core Functions and Implementation of the Coulomb Energy Forces. 

Still another method to speed up evaluation of J is the Fourier-transform Coulomb (FTC) method, which replaces the evaluation of the contributions of ERls that involve three and fonr Ganssian basis functions with a numerical evaluation using a plane-wave basis set. A plane-wave function has the form where k, I, and m are con-... 

The solutions to this approximation are obtained numerically. Fast Fourier transform methods and a reformulation of the HNC (and other integral equation approximations) in terms of the screened Coulomb potential by Allnatt [64] are especially useful in the numerical solution. Figure A2.3.12 compares the osmotic coefficient of a 1-1 RPM electrolyte at 25°C with each of the available Monte Carlo calculations of Card and Valleau [M]. 

The P M method maps the system onto a mesh, such that the necessary Fourier transformations can be accompUshed by fast Fourier routines. At the same time the simple Coulomb Green function 47r/k is adjusted to make the result of the mesh calculation most closely resemble the continuum solution. 

Ewald summation presented above calls for the calculation of AP terms for each of the periodic boxes, a computationally demanding requirement for large biomolecular systems. Recently, Darden et al. proposed an N log N method, called particle mesh Ewald (PME), which incorporates a spherical cutoff R. This method uses lookup tables to calculate the direa space sum and its derivatives. The reciprocal sum is implemented by means of multidimensional piecewise interpolation methods, which permit the calculation of this sum and its first derivative at predefined grids with fast Fourier transform methods. The overhead for this calculation in comparison to Coulomb interactions ranges from 16 to 84% of computer time, depending on the reciprocal sum grid size and the order of polynomial used in calculating this sum. 

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