Fast analytical evaluation of intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density. II. The Fourier transform method. Issue 3 (30th April 2019) - Nguyen, Daniel; Volkov, Anatoliy
Abstract : Numerical implementations of the presented Fourier transform method and the previously reported Löwdin α‐function approach for analytical determination of the two‐center Coulomb integrals that appear in calculations of the electrostatic interaction energies between pseudoatom‐based charge distributions are carefully examined in terms of precision and speed. The refined Fortran‐based computer code allows a fast evaluation of electrostatic interaction energies with a precision of 5 × 10 −5 kJ mol −1 or better using either of the two techniques. Abstract : The Fourier transform method for analytical determination of the two‐center Coulomb integrals needed for evaluation of the electrostatic interaction energies between pseudoatom‐based charge distributions is presented, and its Fortran‐based implementation using the 128‐bit floating‐point arithmetic in the XDPROP module of the XD software is described. In combination with mathematical libraries included in the Lahey/Fujitsu LF64 Linux compiler, the new implementation outperforms the previously reported Löwdin α‐function technique [Nguyen et al. (2018). Acta Cryst. A74, 524–536] in terms of precision of the determined individual Coulomb integrals regardless of whether the latter uses the 64‐, 80‐ or 128‐bit precision floating‐point format, all the while being only marginally slower. When the Löwdin α‐function or Fourier transform method is combined with a multipole moment approximation for large interatomic separations (such a hybrid scheme is called the analytical exact potential and multipole moment method, aEP/MM) the resulting electrostatic interaction energies are evaluated with a precision of ≤5 × 10 −5 kJ mol −1 for the current set of benchmark systems composed of H, C, N and O atoms and ranging in size from water–water to dodecapeptide–dodecapeptide dimers. Using a 2012 4.0 GHz AMD FX‐8350 computer processor, the two recommended aEP/MM implementations, the 80‐bit precision Löwdin α‐function and 128‐bit precision Fourier transform methods, evaluate the total electrostatic interaction energy between two 225‐atom monomers of the benchmark dodecapeptide molecule in 6.0 and 7.9 s, respectively, versus 3.1 s for the previously reported 64‐bit Löwdin α‐function approach.