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Fast analytical evaluation of intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density. II. The Fourier transform method
Acta Crystallographica Section A Foundations and Advances Pub Date : 2019-04-30 , DOI: 10.1107/s2053273319002535
Daniel Nguyen , Anatoliy Volkov

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 theXDPROPmodule of theXDsoftware 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 [Nguyenet 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−1for 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.

中文翻译:

使用电子密度的伪原子表示快速分析评估分子间静电相互作用能量。二. 傅立叶变换法

提出了用于分析确定评估基于赝原子的电荷分布之间的静电相互作用能所需的双中心库仑积分的傅立叶变换方法,以及使用 128 位浮点算法的基于 Fortran 的实现。XDPROP的模块XD软件进行了描述。结合 Lahey/Fujitsu LF64 Linux 编译器中包含的数学库,新的实现优于之前报道的 Löwdin α 函数技术 [Nguyen等人。(2018)。阿克塔水晶。A74, 524–536] 就确定的各个库仑积分的精度而言,无论后者使用 64 位、80 位还是 128 位精度浮点格式,但始终只是稍微慢一些。当 Löwdin α 函数或傅立叶变换方法与大原子间分离的多极矩近似相结合时(这种混合方案称为解析精确势和多极矩方法,aEP/MM),所得静电相互作用能可通过以下公式进行评估:精度≤5×10−5千焦摩尔−1当前由 H、C、N 和 O 原子组成的基准系统,尺寸范围从水-水到十二肽-十二肽二聚体。使用 2012 4.0 GHz AMD FX-8350 计算机处理器,两种推荐的 aEP/MM 实现(80 位精度 Löwdin α 函数和 128 位精度傅里叶变换方法)评估两个 225 个原子单体之间的总静电相互作用能基准十二肽分子的反应时间分别为 6.0 和 7.9 秒,而之前报道的 64 位 Löwdin α 函数方法则为 3.1 秒。
更新日期:2019-04-30
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