The Experts below are selected from a list of 222 Experts worldwide ranked by ideXlab platform
Jacek Komasa - One of the best experts on this subject based on the ideXlab platform.
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rovibrational energy levels of the Hydrogen Molecule through nonadiabatic perturbation theory
Physical Review A, 2019Co-Authors: Jacek Komasa, Mariusz Puchalski, Pawel Czachorowski, Grzegorz łach, Krzysztof PachuckiAbstract:We present an accurate theoretical determination of rovibrational energy levels of the Hydrogen Molecule and its isotopologues in its electronic ground state. We consider all significant corrections to the Born-Oppenheimer approximation, obtained within nonadiabatic perturbation theory, including the mixed nonadiabatic-relativistic effects. Quantum electrodynamic corrections in the leading ${\ensuremath{\alpha}}^{5}\phantom{\rule{0.16em}{0ex}}m$ and the next-to-leading ${\ensuremath{\alpha}}^{6}\phantom{\rule{0.16em}{0ex}}m$ orders, as well as finite nuclear size effect, are also taken into account but within the Born-Oppenheimer approximation only. Final results for the transition wavelength between rovibrational levels achieve accuracy of the order of ${10}^{\ensuremath{-}3}$--${10}^{\ensuremath{-}7}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, and are provided by simple to use computer code.
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nonadiabatic qed correction to the dissociation energy of the Hydrogen Molecule
Physical Review Letters, 2019Co-Authors: Mariusz Puchalski, Jacek Komasa, Pawel Czachorowski, Krzysztof PachuckiAbstract:The quantum electrodynamic correction to the energy of the Hydrogen Molecule has been evaluated without expansion in the electron-proton mass ratio. The obtained results significantly improve the accuracy of theoretical predictions reaching the level of 1 MHz for the dissociation energy, in very good agreement with the parallel measurement [Holsch et al., Phys. Rev. Lett. 122, 103002 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.103002]. Molecular Hydrogen has thus become a cornerstone of ultraprecise quantum chemistry, which opens perspectives for determination of fundamental physical constants from its spectra.
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nonadiabatic rotational states of the Hydrogen Molecule
Physical Chemistry Chemical Physics, 2018Co-Authors: Krzysztof Pachucki, Jacek KomasaAbstract:We present a new computational method for the determination of energy levels in four-particle systems like H2, HD, and HeH+ using explicitly correlated exponential basis functions and analytic integration formulas. In solving the Schrodinger equation, no adiabatic separation of the nuclear and electronic degrees of freedom is introduced. We provide formulas for the coupling between the rotational and electronic angular momenta, which enable calculations of arbitrary rotationally excited energy levels. To illustrate the high numerical efficiency of the method, we present the results for various states of the Hydrogen Molecule. The relative accuracy to which we determined the nonrelativistic energy reached the level of 10−12–10−13, which corresponds to an uncertainty of 10−7–10−8 cm−1.
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nonadiabatic rotational states of the Hydrogen Molecule
arXiv: Chemical Physics, 2017Co-Authors: Krzysztof Pachucki, Jacek KomasaAbstract:We present a new computational method for the determination of energy levels in four-particle systems like H$_2$, HD, and HeH$^+$ using explicitly correlated exponential basis functions and analytic integration formulas. In solving the Schr\"odinger equation, no adiabatic separation of the nuclear and electronic degrees of freedom is introduced. We provide formulas for the coupling between the rotational and electronic angular momenta, which enable calculations of arbitrary rotationally excited energy levels. To illustrate the high numerical efficiency of the method, we present results for various states of the Hydrogen Molecule. The relative accuracy to which we determined the nonrelativistic energy reached the level of $10^{-12}$-$10^{-13}$, which corresponds to an uncertainty of $10^{-7}$-$10^{-8}$ cm$^{-1}$.
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schrodinger equation solved for the Hydrogen Molecule with unprecedented accuracy
Journal of Chemical Physics, 2016Co-Authors: Krzysztof Pachucki, Jacek KomasaAbstract:The Hydrogen Molecule can be used for determination of physical constants, including the proton charge radius, and for improved tests of the hypothetical long range force between hadrons, which require a sufficiently accurate knowledge of the molecular levels. In this work, we perform the first step toward a significant improvement in theoretical predictions of H2 and solve the nonrelativistic Schrodinger equation to the unprecedented accuracy of 10−12. We hope that it will inspire a parallel progress in the spectroscopy of the molecular Hydrogen.
Krzysztof Pachucki - One of the best experts on this subject based on the ideXlab platform.
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long range asymptotics of exchange energy in the Hydrogen Molecule
Journal of Chemical Physics, 2020Co-Authors: Michal Silkowski, Krzysztof PachuckiAbstract:The exchange energy, i.e., the splitting ΔE between gerade and ungerade states in the Hydrogen Molecule, has proven very difficult in numerical calculation at large internuclear distances R, while the known results are sparse and highly inaccurate. On the other hand, there are conflicting analytical results in the literature concerning its asymptotics. In this work, we develop a flexible and efficient numerical approach using explicitly correlated exponential functions and demonstrate highly accurate exchange energies for internuclear distances as large as 57.5 a.u. This approach may find further applications in calculations of inter-atomic interactions. In particular, our results support the asymptotics form ΔE ∼ R5/2e-2R, but with the leading coefficient being 2σ away from the analytically derived value.
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long range asymptotics of exchange energy in the Hydrogen Molecule
arXiv: Atomic Physics, 2020Co-Authors: Michal Silkowski, Krzysztof PachuckiAbstract:The exchange energy, i.e. the splitting $\Delta E$ between gerade and ungerade states in the Hydrogen Molecule has proven very difficult in numerical calculation at large internuclear distances $R$, while known results are sparse and highly inaccurate. On the other hand, there are conflicting analytical results in the literature concerning its asymptotics. In this work we develop a flexible and efficient numerical approach using explicitly correlated exponential functions and demonstrate highly accurate exchange energies for internuclear distances as large as 57.5 au. This approach may find further applications in calculations of inter-atomic interactions. In particular, our results support the asymptotics form $\Delta E \sim R^{5/2}e^{-2R}$, but with the leading coefficient being $2\,\sigma$ away from the analytically derived value.
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rovibrational energy levels of the Hydrogen Molecule through nonadiabatic perturbation theory
Physical Review A, 2019Co-Authors: Jacek Komasa, Mariusz Puchalski, Pawel Czachorowski, Grzegorz łach, Krzysztof PachuckiAbstract:We present an accurate theoretical determination of rovibrational energy levels of the Hydrogen Molecule and its isotopologues in its electronic ground state. We consider all significant corrections to the Born-Oppenheimer approximation, obtained within nonadiabatic perturbation theory, including the mixed nonadiabatic-relativistic effects. Quantum electrodynamic corrections in the leading ${\ensuremath{\alpha}}^{5}\phantom{\rule{0.16em}{0ex}}m$ and the next-to-leading ${\ensuremath{\alpha}}^{6}\phantom{\rule{0.16em}{0ex}}m$ orders, as well as finite nuclear size effect, are also taken into account but within the Born-Oppenheimer approximation only. Final results for the transition wavelength between rovibrational levels achieve accuracy of the order of ${10}^{\ensuremath{-}3}$--${10}^{\ensuremath{-}7}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, and are provided by simple to use computer code.
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nonadiabatic qed correction to the dissociation energy of the Hydrogen Molecule
Physical Review Letters, 2019Co-Authors: Mariusz Puchalski, Jacek Komasa, Pawel Czachorowski, Krzysztof PachuckiAbstract:The quantum electrodynamic correction to the energy of the Hydrogen Molecule has been evaluated without expansion in the electron-proton mass ratio. The obtained results significantly improve the accuracy of theoretical predictions reaching the level of 1 MHz for the dissociation energy, in very good agreement with the parallel measurement [Holsch et al., Phys. Rev. Lett. 122, 103002 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.103002]. Molecular Hydrogen has thus become a cornerstone of ultraprecise quantum chemistry, which opens perspectives for determination of fundamental physical constants from its spectra.
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nonadiabatic rotational states of the Hydrogen Molecule
Physical Chemistry Chemical Physics, 2018Co-Authors: Krzysztof Pachucki, Jacek KomasaAbstract:We present a new computational method for the determination of energy levels in four-particle systems like H2, HD, and HeH+ using explicitly correlated exponential basis functions and analytic integration formulas. In solving the Schrodinger equation, no adiabatic separation of the nuclear and electronic degrees of freedom is introduced. We provide formulas for the coupling between the rotational and electronic angular momenta, which enable calculations of arbitrary rotationally excited energy levels. To illustrate the high numerical efficiency of the method, we present the results for various states of the Hydrogen Molecule. The relative accuracy to which we determined the nonrelativistic energy reached the level of 10−12–10−13, which corresponds to an uncertainty of 10−7–10−8 cm−1.
Jacek Rychlewski - One of the best experts on this subject based on the ideXlab platform.
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The nuclear magnetic shielding and spin-rotation constants of the Hydrogen Molecule
Chemical Physics Letters, 1995Co-Authors: Jacek Komasa, Jacek Rychlewski, William T. RaynesAbstract:Abstract The variation-perturbation method, employing an explicitly correlated basis set in the form of Gaussian functions with exponential correlation factors, has been used to calculate the paramagnetic component of the nuclear magnetic shielding and the electronic contribution to the spin-rotation constant for the Hydrogen Molecule in its ground state. The diamagnetic components of the shielding tensor have also been computed. The computations have been performed for three internuclear distances in the vicinity of equilibrium. A comparison of the calculated quantities, which are of high accuracy, with the experimental data reveals a small but significant discrepancy between theory and experiment.
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configuration interaction and hylleraas configuration interaction methods in valence bond theory calculation of the nuclear shielding constant for the ground state of the Hydrogen Molecule
Physical Review A, 1992Co-Authors: Jacek Komasa, Wojciech Cencek, Jacek RychlewskiAbstract:Values of the magnetic shielding constant in the ground state of the Hydrogen Molecule are calculated using explicitly correlated Gaussian functions. The total shielding at equilibrium amounts to 26.73 ppm.
Alejandro López-castillo - One of the best experts on this subject based on the ideXlab platform.
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Semiclassical study of the one-dimensional Hydrogen Molecule
Chaos (Woodbury N.Y.), 2008Co-Authors: Alejandro López-castilloAbstract:The Hydrogen Molecule, as a restricted four-body problem, is a mixed chaotic system and is studied in this work as an extension of the helium atom. Several types of one-dimensional periodic orbits have been studied for this two-fixed-center system starting from some known orbits for the one-fixed-center system (helium atom). The Hydrogen Molecule has been studied by means of a semiclassical formalism. The single quantization of some periodic orbits are shown. These orbits are used to form a global quantization of the Hydrogen Molecule. Electronic energies of this nonintegrable molecular system are obtained with nonsingle semiclassical quantization.
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Classical and semiclassical studies of the Hydrogen Molecule
arXiv: Chaotic Dynamics, 2003Co-Authors: Alejandro López-castilloAbstract:The Hydrogen Molecule contains the basic ingredients to understand the chemical bond, i.e, a pair of electrons. We show a step to understand The Correspondence Principle for chaotic system in the Chemical World. The Hydrogen Molecule is studied classically as an extension of the helium atom. Several types of orbits were found for two-fixed-centers system (Hydrogen Molecule) starting from some known orbits for one-fixed center one (helium atom), e.g., one dimension orbits as pendulum and axial and also Bohr and Langmuir's orbits. The classical stability and the single quantization of some one-dimensional periodic orbits are shown. These orbits are used to make a global quantization of that molecular chaotic system. We discuss the importance of those periodic orbits in the comprehension of the nature of chemical bond.
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Nonlinear dynamics of the Hydrogen Molecule
Physical Review A, 1998Co-Authors: Alejandro López-castilloAbstract:The Hydrogen Molecule $({\mathrm{H}}_{2})$ contains the basic ingredients for understanding the chemical bond, even more so than the Hydrogen Molecule ion. ${\mathrm{H}}_{2}$ is studied in the context of nonlinear dynamics. The classical mechanics of ${\mathrm{H}}_{2}$ is studied in three dimensions with nine, six, and three degrees of freedom and in one dimension (two degrees of freedom). The semiclassical quantization is made using the Bohr-Sommerfeld rules and the Gutzwiller formula to calculate the eigenvalues of the doubly occupied symmetric excited states of ${\mathrm{H}}_{2}.$ An ab initio quantum calculation is performed and compared with semiclassical results. The difficulties that appear in those calculations are discussed, and a proposal of the experimental measure is made.
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Hydrogen Molecule as a Classical Restricted Four-Body Problem
Physical review letters, 1996Co-Authors: Alejandro López-castilloAbstract:Bohr was the first to use an orbit to describe the chemical bond of the Hydrogen Molecule. In this Letter the Hydrogen Molecule was studied classically as an extension of the helium atom. Various types of symmetric orbits like Bohr{close_quote}s and Langmuir{close_quote}s orbits for the helium atom were found and their stability indexes computed. The importance of these orbits in the semiclassical quantization of the Hydrogen Molecule is presented. {copyright} {ital 1996 The American Physical Society.}
L. Wolniewicz - One of the best experts on this subject based on the ideXlab platform.
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excited states and the transition moments of the Hydrogen Molecule
Journal of Molecular Spectroscopy, 2003Co-Authors: L. Wolniewicz, G. StaszewskaAbstract:Abstract Accurate Born–Oppenheimer energies and adiabatic corrections are computed for the Hydrogen Molecule for the four lowest electronic states of 1 Π u symmetry for internuclear distances, 0.5⩽R⩽100 bohr. Computed term values of the D′(4p)1Πu− state of D2 compare favorably with experiment. The determined electronic wavefunctions are used to evaluate 1 Π u →X 1 Σ g + dipole transition moments.
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transition moments for the Hydrogen Molecule
Journal of Molecular Spectroscopy, 2003Co-Authors: L. Wolniewicz, G. StaszewskaAbstract:Abstract Electronic moments are given for internuclear distances, 0.5⩽R⩽50.0 bohr, for transitions connecting the six lowest 1 Σ u + states and the 1 Σ g + ground state of the Hydrogen Molecule. Except for the two lowest transitions, the computed moments show—due to avoided crossings—very strong R-dependence; especially at R below 0.7 bohr. This effect is also clearly visible in the adiabatic corrections that are computed for 0.5⩽R⩽0.8.
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adiabatic energies of excited 1σu states of the Hydrogen Molecule
Journal of Molecular Spectroscopy, 2002Co-Authors: G. Staszewska, L. WolniewiczAbstract:Abstract Accurate Born–Oppenheimer potential energy curves and adiabatic corrections are computed for the six lowest 1Σu states of the Hydrogen Molecule. For the 41Σu–61Σu states adiabatic term values of the vibrational levels supported by the potentials and the corresponding rotational constants are given. For the outer potential well of the 61Σu state, Franck–Condon factors are listed for the possible transitions to the HH1Σg state.
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The HH̄1Σg state of the Hydrogen Molecule
The Journal of Chemical Physics, 1998Co-Authors: L. WolniewiczAbstract:Born–Oppenheimer potential and adiabatic corrections for the HH1Σg+ state of the Hydrogen Molecule are given for internuclear distances up to 80 a.u. Term values in the outer well are computed for J⩽5. A comparison with experiment shows that the theoretical total energies are too low by about 1 cm−1. The source of this discrepancy is briefly discussed.
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NONADIABATIC ENERGIES OF THE GROUND STATE OF THE Hydrogen Molecule
The Journal of Chemical Physics, 1995Co-Authors: L. WolniewiczAbstract:Possible sources of residual errors in the theoretical energies of the Hydrogen Molecule are investigated. Nonadiabatic corrections are computed for all bound, J≤10 X 1Σg+ ro‐vibrational states of the six isotopic Hydrogen Molecules. The new results improve significantly the overall agreement with accurate experimental transition frequencies. In order to estimate the convergence errors of the Born–Oppenheimer energies generalized James–Coolidge functions with powers of the interelectronic distance, r12, up to 6 are used and the precision of the computations is increased. Except for the equilibrium separation, R=1.4011 bohr, the obtained potential energy curve is lower by a few thousandths of a wave number than any other reported variational result. This lowers the v=0 vibrational levels by 0.009 cm−1 and results in a dissociation energy of H2, D0=36118.069 cm−1.
