Comparison of multipole moment expansions by direct summation or finite-field SCF methods with full electrostatic interaction energies: Application to CO and N2

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.

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Fast analytical evaluation of intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density. I. The Löwdin α-function method

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273318008690 ◽

2018 ◽

Vol 74 (5) ◽

pp. 524-536 ◽

Cited By ~ 2

Author(s):

Daniel Nguyen ◽

Zbigniew Kisiel ◽

Anatoliy Volkov

Keyword(s):

Electrostatic Interaction ◽

Multipole Moment ◽

Chem Phys ◽

Processing Unit ◽

Interaction Energies ◽

Electron Densities ◽

Molecular Systems ◽

Analytical Technique ◽

Central Processing ◽

The University

The previously reported [Volkovet al.(2004).Chem. Phys. Lett.391, 170–175] exact potential and multipole moment (EP/MM) method for evaluation of intermolecular electrostatic interaction energies using the nuclei-centered pseudoatom representation of electron densities is significantly improved in terms of both speed and accuracy by replacing the numerical quadrature integration of the exact potential with a fully analytical technique. The resulting approach, incorporated in theXDPROPmodule of the software packageXD, has been tested on several molecular systems ranging in size from water–water to dodecapeptide–dodecapeptide dimers using electron densities constructedviathe University at Buffalo Aspherical Atom Databank. The improved hybrid method provides electrostatic interaction energies within the uncertainty of ≤0.2 kJ mol−1for all benchmark systems. The running time for a dimer of a sizable, 225-atom dodecapeptide is under 4 s on a 2012 central processing unit (2.8 GHz AMD Opteron 6348) and under 3 s on a relatively modern processor (2.8 GHz Intel Xeon E3-1505M v5).

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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 ◽

10.1107/s2053273319002535 ◽

2019 ◽

Vol 75 (3) ◽

pp. 448-464 ◽

Cited By ~ 1

Author(s):

Daniel Nguyen ◽

Anatoliy Volkov

Keyword(s):

Fourier Transform ◽

Electrostatic Interaction ◽

Multipole Moment ◽

Floating Point ◽

Interaction Energies ◽

Transform Method ◽

Fourier Transform Method ◽

The Fourier Transform ◽

Coulomb Integrals ◽

Löwdin Α Function

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.

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Electrostatic interaction energies with overlap effects from a localized approach

Chemical Physics Letters ◽

10.1016/j.cplett.2007.07.065 ◽

2007 ◽

Vol 445 (4-6) ◽

pp. 315-320 ◽

Cited By ~ 10

Author(s):

Fazle Rob ◽

Rafał Podeszwa ◽

Krzysztof Szalewicz

Keyword(s):

Electrostatic Interaction ◽

Interaction Energies

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Electrostatic interaction energies of independent aspherical atoms in molecules

Chemical Physics Letters ◽

10.1016/0009-2614(91)85002-e ◽

1991 ◽

Vol 180 (6) ◽

pp. 509-516 ◽

Cited By ~ 9

Author(s):

S.G. Wang ◽

W.H.E. Schwarz ◽

H.L. Lin

Keyword(s):

Electrostatic Interaction ◽

Atoms In Molecules ◽

Interaction Energies

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ELECTROSTATIC INTERACTION ENERGIES FROM DIPOLE MOMENTS IN NITRILES, AMMONIA AND AMINES. CORRELATIONS WITH HYDROGEN BOND BASICITY

Journal of Physical Organic Chemistry ◽

10.1002/(sici)1099-1395(199703)10:3<167::aid-poc881>3.0.co;2-f ◽

1997 ◽

Vol 10 (3) ◽

pp. 167-174 ◽

Cited By ~ 1

Author(s):

Marine H�rail ◽

Eug�ne Megnassan ◽

Alain Prouti�re

Keyword(s):

Hydrogen Bond ◽

Electrostatic Interaction ◽

Dipole Moments ◽

Interaction Energies ◽

Hydrogen Bond Basicity

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Matrix Elements for Many-Electron Atoms: Electrostatic Interaction Energies for One-Open-Shell Configurations

Canadian Journal of Physics ◽

10.1139/p74-033 ◽

1974 ◽

Vol 52 (3) ◽

pp. 238-240

Author(s):

J. Karwowski ◽

S. Fraga

Keyword(s):

Electrostatic Interaction ◽

Open Shell ◽

Numerical Results ◽

Interaction Energies ◽

Matrix Elements ◽

The Matrix ◽

Racah Parameters

The matrix elements of the electrostatic interaction have been determined and tabulated, in terms of Slater–Condon integrals or Racah parameters, for the states arising from pN, dN, fN, and gN configurations; in particular, the results for gN configurations have never been determined before. The effect of the interaction between states of the same symmetry and multiplicity, arising from a given configuration, is exemplified with numerical results for Pr, 4f36s2.

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New Ligands and New Insights for Vitamin D Receptor from Charge Density

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273314090330 ◽

2014 ◽

Vol 70 (a1) ◽

pp. C966-C966

Author(s):

Maura Malińska ◽

Andrzej Kutner ◽

Krzysztof Woźniak

Keyword(s):

Vitamin D ◽

Hydrogen Bonds ◽

Charge Density ◽

Interaction Energy ◽

Vitamin D Receptor ◽

Electrostatic Interaction ◽

Interaction Energies ◽

Average Strength ◽

Vitamin D Analogs ◽

Wide Range

Vitamin D protective effects result from its role as a nuclear transcription factor that regulates cell growth, differentiation, and a wide range of cellular mechanisms crucial to the development and progression of cancer.[1] Many academic investigators and pharmaceutical companies try to develop calcitriol analogs that exhibit equal or even increased anti-proliferative activity while exhibiting a reduced tendency to cause hypercalcemia. Analysis of 24 Vitamin D analogs bearing similar molecular structures with a complex of a Vitamin D Receptor (VDR) enabled the design of new agonists (TB1, TB2, TB3 and TB4). Undertaken approach was to minimize the electrostatic interaction energies available after the reconstruction of charge density with the aid of the pseudoatom databank (UBDB[2]). Comprehensive studies revealed 29 residues crucial for agonist binding. Trp286, which is specific to VDR among the representatives of the Nuclear Receptor Family, plays the crucial role of positioning the ligand forming dispersive interactions, mostly C-H...π, with an average strength of -4 kcal mol-1. The ligand binding pocket is primarily composed of hydrophobic residues, however there are 6 hydrogen bonds characteristic for all the ligands. They electrostatic interaction energies strongly contribute to the total interaction energy, with an average strength of -8, -19, -11 and -12 kcal mol-1 for hydrogen bonds to Ser237, Arg274, Ser278 and Tyr143. The aliphatic chain of the Vitamin D analogs adopt an extended conformation and the 25-hydroxyl group is hydrogen bonded to His305 and His397 with electrostatic interaction energies of -13 and -11 kcal mol-1. The geometries of complexes of the proposed ligand with VDR were obtained by the docking procedure implemented in Autodock4.3[3]. New agonsits form all mentioned before interactions with VDR. The final results of electrostatic interaction energy for TB1 and TB2 are -153 and -120 kcal mol-1, and this results are the smallest among all studied Vitamin D analogs.

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A rush to explore protein–ligand electrostatic interaction energy with Charger

Acta Crystallographica Section D Structural Biology ◽

10.1107/s2059798321008433 ◽

2021 ◽

Vol 77 (10) ◽

pp. 1292-1304 ◽

Cited By ~ 1

Author(s):

Vedran Vuković ◽

Theo Leduc ◽

Zoe Jelić-Matošević ◽

Claude Didierjean ◽

Frédérique Favier ◽

...

Keyword(s):

Ligand Binding ◽

Interaction Energy ◽

Electrostatic Interaction ◽

Glutathione Transferase ◽

Multipole Moment ◽

Point Of View ◽

Electrostatic Energy ◽

Electron Densities ◽

Acta Cryst ◽

Ligand Interaction

The mutual penetration of electron densities between two interacting molecules complicates the computation of an accurate electrostatic interaction energy based on a pseudo-atom representation of electron densities. The numerical exact potential and multipole moment (nEP/MM) method is time-consuming since it performs a 3D integration to obtain the electrostatic energy at short interaction distances. Nguyen et al. [(2018), Acta Cryst. A74, 524–536] recently reported a fully analytical computation of the electrostatic interaction energy (aEP/MM). This method performs much faster than nEP/MM (up to two orders of magnitude) and remains highly accurate. A new program library, Charger, contains an implementation of the aEP/MM method. Charger has been incorporated into the MoProViewer software. Benchmark tests on a series of small molecules containing only C, H, N and O atoms show the efficiency of Charger in terms of execution time and accuracy. Charger is also powerful in a study of electrostatic symbiosis between a protein and a ligand. It determines reliable protein–ligand interaction energies even when both contain S atoms. It easily estimates the individual contribution of every residue to the total protein–ligand electrostatic binding energy. Glutathione transferase (GST) in complex with a benzophenone ligand was studied due to the availability of both structural and thermodynamic data. The resulting analysis highlights not only the residues that stabilize the ligand but also those that hinder ligand binding from an electrostatic point of view. This offers new perspectives in the search for mutations to improve the interaction between the two partners. A proposed mutation would improve ligand binding to GST by removing an electrostatic obstacle, rather than by the traditional increase in the number of favourable contacts.

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