scholarly journals Calculation of electrostatic interaction energies in molecular dimers from atomic multipole moments obtained by different methods of electron density partitioning

2004 ◽  
Vol 25 (7) ◽  
pp. 921-934 ◽  
Author(s):  
Anatoliy Volkov ◽  
Philip Coppens
Keyword(s):  
Electron Density ◽  
Electrostatic Interaction ◽  
Interaction Energies ◽  
Multipole Moments

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

2020 ◽  
Vol 76 (6) ◽  
pp. 630-651
Author(s):  
Daniel Nguyen ◽  
Piero Macchi ◽  
Anatoliy Volkov
Keyword(s):  
Interaction Energy ◽  
Crystal Structures ◽  
Electron Density ◽  
Small Molecule ◽  
Electrostatic Interaction ◽  
Multipole Moment ◽  
Interaction Energies ◽  
Acta Cryst ◽  
Löwdin Α Function ◽  
Direct Summation

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.

Interplay of point multipole moments and charge penetration for intermolecular electrostatic interaction energies from the University at Buffalo pseudoatom databank model of electron density

2017 ◽  
Vol 73 (4) ◽  
pp. 598-609 ◽  
Author(s):  
Sławomir A. Bojarowski ◽  
Prashant Kumar ◽  
Paulina M. Dominiak
Keyword(s):  
Electrostatic Interaction ◽  
The Other ◽  
Continuous Representation ◽  
Interaction Energies ◽  
Multipole Moments ◽  
Equilibrium Distance ◽  
Energy Estimation ◽  
The University ◽  
Nonpolar Molecules

The strength of the University at Buffalo DataBank (UBDB) inEesestimation is mainly due to charge overlap effects because the UBDB offers continuous representation of charge density which allows for a direct account of charge penetration in the derivation of electrostatic energies. In the UBDB model, these effects begin to play an important role at distances below twice the equilibrium distance and significantly increase as distances decrease. At equilibrium distances they are responsible for 30–50% ofEesfor polar molecules and around 90% ofEesfor nonpolar molecules. When the energy estimation from the UBDB is reduced to point multipoles, the results are comparable to point charges fitted to electrostatic potentials. On the other hand, particular components of energy from point multipole moments from the UBDB model are sensitive to the type of interaction and might be helpful in the characterization of interactions.

Electron density based analysis of N–H⋯OC hydrogen bonds and electrostatic interaction energies in high-resolution secondary protein structures: insights from quantum crystallographic approaches

CrystEngComm ◽  
2020 ◽  
Vol 22 (26) ◽  
pp. 4363-4373 ◽  
Author(s):  
Suman K. Mandal ◽  
Benoît Guillot ◽  
Parthapratim Munshi
Keyword(s):  
High Resolution ◽  
Hydrogen Bonds ◽  
Electron Density ◽  
Electrostatic Interaction ◽  
Main Chain ◽  
Protein Structures ◽  
Interaction Energies ◽  
Topological Parameters ◽  
Limiting Values ◽  
Qualitative Analyses

Limiting values of the topological parameters and the electrostatic interaction energies to establish the presence of true N–H⋯OC H-bonds in protein main-chain have been identified using quantitative and qualitative analyses of electron densities.

Electrostatic interaction energies with overlap effects from a localized approach

2007 ◽  
Vol 445 (4-6) ◽  
pp. 315-320 ◽  
Author(s):  
Fazle Rob ◽  
Rafał Podeszwa ◽  
Krzysztof Szalewicz
Keyword(s):  
Electrostatic Interaction ◽  
Interaction Energies

Electron-density-based calculations of intermolecular energy: case of urea

1999 ◽  
Vol 55 (5) ◽  
pp. 821-827 ◽  
Author(s):  
Kyrill Yu. Suponitsky ◽  
Vladimir G. Tsirelson ◽  
Dirk Feil
Keyword(s):  
Interaction Energy ◽  
Electron Density ◽  
Theoretical Data ◽  
Multipole Moments ◽  
Intermolecular Interaction Energy ◽  
Hartree Fock ◽  
Intermolecular Energy ◽  
Crystalline Urea ◽  
To Come ◽  
Experimental Values

The intermolecular interaction energy in crystalline urea has been calculated both from diffraction data and from the Hartree–Fock crystalline electron-density distribution, using a modified atom–atom approximation scheme. The electrostatic part of this energy has been calculated from the atomic multipole moments, obtained by adjustment of the multipole model to experimental X-ray and to theoretical Hartree–Fock structure amplitudes. To obtain the induction energy, multipole moments were calculated from structure amplitudes for the crystalline electron density and from those that refer to the electron density of a superposition of isolated molecules. This worked well for the calculation of the interaction energy from Hartree–Fock data (6% difference from the sublimation-energy value), but not for the interaction energy from experimental data, where the moments of the superposition have to come from Hartree–Fock calculations: the two sets of multipole moments are far too different. The uncertainty of the phases of the structure amplitudes, combined with systematic errors in the theoretical data and noise in the experimental values, may account for the discrepancies. The nature of the different contributions to intermolecular interactions for urea is examined.

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

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.

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

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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