Ludwik Adamowicz

University of Arizona

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Zdeněk Slanina

Huazhong University of Science and Technology

Sergiy Bubin

Nazarbayev University

Filip Uhlı́k

Charles University

Monika Stanke

Institute of Physics

S. G. Stepanian

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine

Andrzej Leś

University of Warsaw

Johan Smets

Procter & Gamble (Belgium)

Abraham F. Jalbout

Universidad de Sonora

Guido Maes

KU Leuven

Takeshi Akasaka

Huazhong University of Science and Technology

Cooperative Institutions

University of Arizona

101

National Academy of Sciences of Ukraine

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine

Polish Academy of Sciences

University of Warsaw

University College London

Institute of Physics

Centre National de la Recherche Scientifique

KU Leuven

University of Florida

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Explicitly correlated Gaussian functions with r factors for calculations of the ground state of the helium atom

Journal of Computational Chemistry (1994)

Zhenghong Zhang Ludwik Adamowicz

Abstract Explicitly correlated Gaussian functions with r exp( − β r ) factors have been used in variational calculations of the ground state of the helium atom. Additional correlation factors in the form of even powers of r ij were introduced to the Gaussian functions with exponential correlation components by differentiating these functions with respect to the correlation exponent β. The algorithm of this method and its computational implementation is described. A number of calculations were performed for the ground state of helium atom to test the performance of the basis sets comparising different numbers of the Gaussians with the exp( − β r ) and r exp( − β r ) correlation factors. The numerical results indicate that including functions with r factors does not lead to improved results, contrary to what was anticipated initially. © 1994 by John Wiley & Sons, Inc.

Helium atom

Exponent

Variational method

Electronic correlation

10.1002/jcc.540150810

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Citations (2)

Analytical energy gradient used in variational Born-Oppenheimer calculations with all-electron explicitly correlated Gaussian functions for molecules containing one π electron

The Journal of Chemical Physics (2013)

Wei-Cheng Tung Michele Pavanello Keeper L. Sharkey Nikita Kirnosov Ludwik Adamowicz

An algorithm for variational calculations of molecules with one π electron performed with all-electron explicitly correlated Gaussian (ECG) functions with floating centers is derived and implemented. The algorithm includes the analytic gradient of the Born-Oppenheimer electronic energy determined with respect to the ECG exponential parameters and the coordinates of the Gaussian centers. The availability of the gradient greatly accelerates the variational energy minimization. The algorithm is tested in calculations of four electronic excited states, c3Πu, C1Πu, i3Πg, and I1Πg, of the hydrogen molecule at a single internuclear distance specific to each state. With the use of the analytical energy gradient, the present calculations yield new, lowest-to-date, variational energy upper bounds for all four states.

Variational method

Born–Oppenheimer approximation

Energy minimization

10.1063/1.4795094

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Citations (3)

An algorithm for nonrelativistic quantum-mechanical finite-nuclear-mass variational calculations of nitrogen atom in L = 0, M = 0 states using all-electrons explicitly correlated Gaussian basis functions

The Journal of Chemical Physics (2014)

Keeper L. Sharkey Ludwik Adamowicz

An algorithm for quantum-mechanical nonrelativistic variational calculations of L = 0 and M = 0 states of atoms with an arbitrary number of s electrons and with three p electrons have been implemented and tested in the calculations of the ground (4)S state of the nitrogen atom. The spatial part of the wave function is expanded in terms of all-electrons explicitly correlated Gaussian functions with the appropriate pre-exponential Cartesian angular factors for states with the L = 0 and M = 0 symmetry. The algorithm includes formulas for calculating the Hamiltonian and overlap matrix elements, as well as formulas for calculating the analytic energy gradient determined with respect to the Gaussian exponential parameters. The gradient is used in the variational optimization of these parameters. The Hamiltonian used in the approach is obtained by rigorously separating the center-of-mass motion from the laboratory-frame all-particle Hamiltonian, and thus it explicitly depends on the finite mass of the nucleus. With that, the mass effect on the total ground-state energy is determined.

Hamiltonian (control theory)

Variational method

10.1063/1.4873916

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Citations (17)

Analytic first derivatives for explicitly correlated, multicenter, Gaussian geminals

International Journal of Quantum Chemistry (1997)

D. W. Gilmore Pawel M. Kozlowski Donald B. Kinghorn Ludwik Adamowicz

Variational calculations utilizing the analytic gradient of explicitly correlated Gaussian molecular integrals are presented for the ground state of the hydrogen molecule. Preliminary results serve to motivate the need for general formulas for analytic first derivatives of molecular integrals involving multicenter, explicitly correlated Gaussian geminals with respect to Gaussian exponents and coordinates of the orbital centers. Explicit formulas for analytic first derivatives of Gaussian functions containing correlation factors of the form exp(-βrij2) are derived and discussed. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 991–999, 1997

Hydrogen molecule

10.1002/(sici)1097-461x(1997)63:5<991::aid-qua8>3.0.co;2-r

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Citations (10)

Structure and energy of nucleic acid base–amino acid complexes: 1. 1-methyl-uracil-acrylamide

Journal of Molecular Structure (1999)

И. К. Галетич М. В. Косевич Vadim S. Shelkovsky S. G. Stepanian Yu. P. Blagoı̆

Uracil

Quantum chemical

10.1016/s0022-2860(98)00756-x

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Citations (16)

Eu@C₈₆ isomers: Calculated relative populations

Fullerenes Nanotubes and Carbon Nanostructures (2020)

Zdeněk Slanina Filip Uhlı́k Lipiao Bao Takeshi Akasaka Xing Lü

Relative populations of four energy-lowest IPR (isolated-pentagon-rule) isomers of Eu@C86 are computed using the Gibbs energy based on characteristics from density functional theory calculations (M06-2X/3-21G ∼ SDD entropy term, M06-2X/6-31G*∼SDD or B2PLYP(D)/6-31G*∼SDD energetics). The calculations confirm that the recently isolated Eu@C1(7)-C86 species is a major isomer in a relevant temperature region. Relationship to the empty C86 cages is discussed, too.

Energetics

Total energy

10.1080/1536383x.2020.1724104

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Citations (7)

Fine structure of the beryllium P3 states calculated with all-electron explicitly correlated Gaussian functions

Physical review. A/Physical review, A (2022)

Monika Stanke Andrzej Kȩdziorski Ludwik Adamowicz

The recently presented general algorithm for calculating an atomic fine structure [K\ifmmode \mbox{\k{e}}\else \k{e}\fi{}dziorski et al., Chem. Phys. Lett. 751, 137476 (2020)] is employed to study the fine splitting of the lowest eight $^{3}P$ states of beryllium, i.e., the $1{s}^{2}\phantom{\rule{0.28em}{0ex}}2s\phantom{\rule{0.28em}{0ex}}np$, $n=2,\ensuremath{\cdots},9$, $^{3}P$ states. All-electron explicitly correlated Gaussian functions and a finite-nuclear-mass variational method are used in the calculations. The energies of the states are augmented with the leading ${\ensuremath{\alpha}}^{2}$ relativistic and ${\ensuremath{\alpha}}^{3}$ (and approximate ${\ensuremath{\alpha}}^{4}$) QED corrections ($\ensuremath{\alpha}=\frac{1}{c}$ is the fine-structure constant, and $c$ is the speed of light in atomic units). The calculated results are compared with the available experimental data.

10.1103/physreva.105.012813

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Citations (3)

Corrigendum to “Quantum states of a confined hydrogen atom calculated in a basis of explicitly correlated Gaussians” [Chemical Physics Letters, Volume 790, March 2022, 139358]

Chemical Physics Letters (2022)

Arunima Coomar Keith Jones Ludwik Adamowicz

Basis (linear algebra)

Hydrogen atom

Quantum chemical

10.1016/j.cplett.2022.139486

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Citations (0)

Nucleoside conformers in low-temperature argon matrices: Fourier transform IR spectroscopy of isolated thymidine and deuterothymidine molecules and quantum-mechanical calculations

Low Temperature Physics (2019)

A. Yu. Ivanov S. G. Stepanian V. А. Karachevtsev Ludwik Adamowicz

The conformational equilibrium of thymidine and deuterothymidine molecules in low-temperature Ar matrices has been studied using low-temperature matrix-isolation Fourier IR spectroscopy and quantum-chemical calculations by the DFT/B3LYP and MP2 methods. It has been found that two anti-conformers ta2_0 and ta3_0 with different structures of the sugar ring, C2′-endo and C3′-endo, predominate in low-temperature matrices. In isolated state, each of these conformers has a few low-barrier satellites that can fully pass into more stable structures when a molecule enters the matrix. The main syn conformer ts2_0 is stabilized by an intramolecular hydrogen bond between the O5′H group of the sugar and the C2O group of the base (O5′H⋅⋅⋅O2), while C2′-endo is the predominant conformation of the deoxyribose ring. The considerably lower population of ts2_0 compared to the anti-conformers ta2_0, ta3_0 can be explained by the smaller population of satellite conformations. It has been shown that the absorption band of νN3D stretching vibration is split by the Fermi resonance.

Conformational isomerism

Matrix Isolation

Deoxyribose

10.1063/1.5121271

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Citations (9)

Stabilization of an excess electron on uracil by water. Ab initio study

Physical Chemistry Chemical Physics (2004)

Claudio A. Morgado Kostyantyn Pichugin Ludwik Adamowicz

Experiments performed on the uracil anion in the gaseous phase indicated that in this system the excess electron is dipole-bound. The experiments, however, also indicated that water solvation changes the character of the anion from dipole-bound to covalent. In this work we have used ab initio theoretical calculations to investigate the stabilization effect that the attachment of one or two water molecules has on the electron attached to uracil. The calculations concern both dipole-bound and covalently-bound electrons and reveal rich configurational isomerism of the complex of the uracil anion with H2O molecules. The systems differ in terms of the structure of the solvation cluster formed around the excess electron.

Uracil

Solvated electron

Bound water

10.1039/b316910c

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Citations (25)