Fast analytical evaluation of intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density. III. Application to crystal structures via the Ewald and direct summation methods

Abstract

The previously reported exact potential and multipole moment (EP/MM) method for fast and accurate evaluation of the intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density [Volkov, Koritsanszky & Coppens (2004). Chem. Phys. Lett. 391, 170–175; Nguyen, Kisiel & Volkov (2018). Acta Cryst. A74, 524–536; Nguyen & Volkov (2019). Acta Cryst. A75, 448–464] is extended to the calculation of electrostatic interaction energies in molecular crystals using two newly developed implementations: (i) the Ewald summation (ES), which includes interactions up to the hexadecapolar level and the EP correction to account for short-range electron-density penetration effects, and (ii) the enhanced EP/MM-based direct summation (DS), which at sufficiently large intermolecular separations replaces the atomic multipole moment approximation to the electrostatic energy with that based on the molecular multipole moments. As in the previous study [Nguyen, Kisiel & Volkov (2018). Acta Cryst. A74, 524–536], the EP electron repulsion integral is evaluated analytically using the Löwdin α-function approach. The resulting techniques, incorporated in the XDPROP module of the software package XD2016, have been tested on several small-molecule crystal systems (benzene, L-dopa, paracetamol, amino acids etc.) and the crystal structure of a 181-atom decapeptide molecule (Z = 4) using electron densities constructed via the University at Buffalo Aspherical Pseudoatom Databank [Volkov, Li, Koritsanszky & Coppens (2004). J. Phys. Chem. A, 108, 4283–4300]. Using a 2015 2.8 GHz Intel Xeon E3-1505M v5 computer processor, a 64-bit implementation of the Löwdin α-function and one of the higher optimization levels in the GNU Fortran compiler, the ES method evaluates the electrostatic interaction energy with a numerical precision of at least 10−5 kJ mol−1 in under 6 s for any of the tested small-molecule crystal structures, and in 48.5 s for the decapeptide structure. The DS approach is competitive in terms of precision and speed with the ES technique only for crystal structures of small molecules that do not carry a large molecular dipole moment. The electron-density penetration effects, correctly accounted for by the two described methods, contribute 28–64% to the total electrostatic interaction energy in the examined systems, and thus cannot be neglected.

On the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model. II. Evaluation of the properties in an infinite crystal

“…The R aMM parameter governs the distance at which the EP/ MM method switches the evaluation of the ESP, EF and EFG from the exact formulae (exact potential) to the atomic multipole moment (aMM) approximation Nguyen et al, 2018;Nguyen & Volkov, 2019). We note that a thorough numerical analysis for the choice of the R aMM parameter when calculating the intermolecular electrostatic interaction energies performed in Paper III suggested an optimal precision/performance value of 5 Å for the first-and second-row atoms.…”

“…The boundary at which the exact and approximate values are expected to converge is defined by the userspecified parameter R aMM . For the intermolecular electrostatic interaction energies, the parameter R aMM was estimated to be 4-5 Å for the first-and second-row atoms Nguyen et al, 2018;Nguyen & Volkov, 2019;Nguyen et al, 2020), while for the ESP, EF and EFG the preliminary work suggested a value of 6 Å for organic systems . A more detailed and thorough analysis for the choice of R aMM in the ES/EP/MM calculations is presented in Section 5.1 below.…”

“…Since the classical Ewald summation approach is based on point multipoles, it is unable to account for the short-range electron-density penetration effects that arise from the overlap of neighbouring charge distributions. The previously reported EP/MM method Nguyen et al, 2018;Nguyen & Volkov, 2019;Nguyen et al, 2020) corrects for that deficiency by evaluating the short-range contributions to a given property (for example, energy, ESP, EF or EFG) using both the exact potential (EP) approach and the atomic multipole moment approximation (aMM). For the ESP, EF and EFG, the exact potential is evaluated using equations given in Paper I, while the aMM-based approximations employ equations ( 12), ( 15) and (17) listed above.…”

“…Recently, we combined the EP/MM method with the Ewald summation (ES) technique for the evaluation of the intermolecular electrostatic interaction energies in molecular crystals [Nguyen et al (2020), referred to as Paper III in the following]. An efficient combination of the Ewald-type summation via the pseudoatom-based atomic multipole moments (aMM) up to the hexadecapolar level in direct (real) and reciprocal (Fourier) spaces, augmented by the exact potential (EP) correction for interactions between pseudoatoms located below a certain distance threshold R aMM (for first-and second-row atoms, the optimal precision/performance distance was found to be 5 Å ), resulted in a fast and numerically stable algorithm that reproduced the intermolecular electrostatic interaction energies in an infinite crystal within 10 À5 kJ mol À1 .…”

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The previously reported exact potential and multipole moment (EP/MM) method for fast and precise evaluation of the intermolecular electrostatic interaction energies in molecular crystals using the pseudoatom representation of the electron density [Nguyen, Macchi & Volkov (2020), Acta Cryst. A76, 630-651] has been extended to the calculation of the electrostatic potential (ESP), electric field (EF) and electric field gradient (EFG) in an infinite crystal.

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