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

2018 ◽  
Vol 74 (5) ◽  
pp. 524-536 ◽  
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).

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.

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

2021 ◽  
Vol 77 (10) ◽  
pp. 1292-1304 ◽  
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.

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.

Fast analytical evaluation of intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density. II. The Fourier transform method

2019 ◽  
Vol 75 (3) ◽  
pp. 448-464 ◽  
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.

Computational Investigation of the Asymmetry in Photosynthetic Reaction Center Models from First Principles

2020 ◽  
Author(s):  
Denis Artiukhin ◽  
Patrick Eschenbach ◽  
Johannes Neugebauer
Keyword(s):  
Spin Density ◽  
Reaction Center ◽  
Density Functional ◽  
Photosynthetic Reaction Center ◽  
Chem Phys ◽  
Molecular Structures ◽  
Error Characteristic ◽  
Molecular Systems ◽  
Density Distributions ◽  
The Asymmetry

We present a computational analysis of the asymmetry in reaction center models of photosystem I, photosystem II, and bacteria from <i>Synechococcus elongatus</i>, <i>Thermococcus vulcanus</i>, and <i>Rhodobacter sphaeroides</i>, respectively. The recently developed FDE-diab methodology [J. Chem. Phys., 148 (2018), 214104] allowed us to effectively avoid the spin-density overdelocalization error characteristic for standard Kohn–Sham Density Functional Theory and to reliably calculate spin-density distributions and electronic couplings for a number of molecular systems ranging from dimeric models in vacuum to large protein including up to about 2000 atoms. The calculated spin densities showed a good agreement with available experimental results and were used to validate reaction center models reported in the literature. We demonstrated that the applied theoretical approach is very sensitive to changes in molecular structures and relative orientation of molecules. This makes FDE-diab a valuable tool for electronic structure calculations of large photosynthetic models effectively complementing the existing experimental techniques.

Perangkat keras komputer

2020 ◽  
Author(s):  
Roudati jannah
Keyword(s):  
Data Storage ◽  
Central Processing Unit ◽  
External Memory ◽  
Storage Device ◽  
Input Device ◽  
Processing Unit ◽  
Central Processing ◽  
Output Device

Perangkat keras komputer adalah bagian dari sistem komputer sebagai perangkat yang dapat diraba, dilihat secara fisik, dan bertindak untuk menjalankan instruksi dari perangkat lunak (software). Perangkat keras komputer juga disebut dengan hardware. Hardware berperan secara menyeluruh terhadap kinerja suatu sistem komputer. Prinsipnya sistem komputer selalu memiliki perangkat keras masukan (input/input device system) – perangkat keras premprosesan (processing/central processing unit) – perangkat keras luaran (output/output device system) – perangkat tambahan yang sifatnya opsional (peripheral) dan tempat penyimpanan data (storage device system/external memory).

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