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Ludwik Adamowicz - One of the best experts on this subject based on the ideXlab platform.
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universal all particle explicitly correlated gaussians for non born oppenheimer calculations of molecular rotationless states
Chemical Physics Letters, 2016Co-Authors: Sergiy Bubin, Martin Formanek, Ludwik AdamowiczAbstract:Abstract Complex explicitly correlated one-center all-particle Gaussian functions (CECGs) are tested as basis functions for molecular non-Born–Oppenheimer (non-BO) calculations. The tests concern the complete spectrum of the 23 bound pure vibrational states of the HD + ion. The tests show that CECGs are very effective in representing both the nuclear-nuclear correlation and the vibrational oscillation of the wave functions in terms of the Internuclear Distance. This finding is important because it paves the way for high-accuracy non-BO calculations of bound vibrational states of molecules with more than two nuclei that have never been performed before.
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complete pure vibrational spectrum of hd calculated without the born oppenheimer approximation and including relativistic corrections
Physical Review A, 2011Co-Authors: Sergiy Bubin, Monika Stanke, Ludwik AdamowiczAbstract:All 18 bound pure vibrational levels of the HD molecule have been calculated within the framework that does not assume the Born-Oppenheimer (BO) approximation. The nonrelativistic energies of the states have been corrected for the relativistic effects of the order of ${\ensuremath{\alpha}}^{2}$ (where $\ensuremath{\alpha}$ is the fine structure constant), calculated using the perturbation theory with the nonrelativistic non-BO wave functions being the zero-order approximation. The calculations were performed by expanding the non-BO wave functions in terms of one-center explicitly correlated Gaussian functions multiplied by even powers of the Internuclear Distance and by performing extensive optimization of the Gaussian nonlinear parameters. Up to 10 000 basis functions were used for each state.
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lower vibrational transitions of the 3he4he ion calculated without the born oppenheimer approximation and with leading relativistic corrections
Chemical Physics Letters, 2010Co-Authors: Sergiy Bubin, Monika Stanke, Ludwik AdamowiczAbstract:Abstract Very accurate variational calculations of the five lowest vibrational states of the 3He4He+ ion are carried out within a framework that does not assume the Born–Oppenheimer (BO) approximation, i.e., treating the two nuclei and three electrons forming the system on an equal footing. The non-BO wave functions are expanded in terms of one-center explicitly correlated Gaussian functions multiplied by even powers of the Internuclear Distance. The wave functions are used to calculate the leading relativistic corrections. The approach reproduces the experimental 3He4He+ fundamental transition within 0.055 cm−1 and similar accuracy is expected for the higher yet unmeasured vibrational transitions determined in the present calculations.
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Darwin and mass-velocity relativistic corrections in non-Born-Oppenheimer variational calculations
The Journal of chemical physics, 2006Co-Authors: Dariusz Kędziera, Monika Stanke, Sergiy Bubin, Maria Barysz, Ludwik AdamowiczAbstract:The Pauli approach to account for the mass-velocity and Darwin relativistic corrections has been applied to the formalism for quantum mechanical molecular calculations that does not assume the Born-Oppenheimer (BO) approximation regarding separability of the electronic and nuclear motions in molecular systems. The corrections are determined using the first order perturbation theory and are derived for the non-BO wave function of a diatomic system expressed in terms of explicitly correlated Gaussian functions with premultipliers in the form of even powers of the Internuclear Distance. As a numerical example we used calculations of the transition energies for pure vibrational states of the HD+ ion.
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Darwin and mass-velocity relativistic corrections in the non-Born-Oppenheimer calculations of pure vibrational states of H2.
The Journal of chemical physics, 2006Co-Authors: Dariusz Kȩdziera, Sergiy Bubin, Monika Stanke, Maria Barysz, Ludwik AdamowiczAbstract:The Darwin and mass-velocity relativistic corrections have been calculated for all pure vibrational states of the H2 using the perturbation theory and very accurate variational wave functions obtained without assuming the Born-Oppenheimer (BO) approximation. Expansions in terms of explicitly correlated Gaussians with premultipliers in the form of even powers of the Internuclear Distance were used for the wave functions. With the inclusion of the two relativistic corrections to the non-BO energies the transition energies for the highest states agree more with the experimental results.
Sergiy Bubin - One of the best experts on this subject based on the ideXlab platform.
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universal all particle explicitly correlated gaussians for non born oppenheimer calculations of molecular rotationless states
Chemical Physics Letters, 2016Co-Authors: Sergiy Bubin, Martin Formanek, Ludwik AdamowiczAbstract:Abstract Complex explicitly correlated one-center all-particle Gaussian functions (CECGs) are tested as basis functions for molecular non-Born–Oppenheimer (non-BO) calculations. The tests concern the complete spectrum of the 23 bound pure vibrational states of the HD + ion. The tests show that CECGs are very effective in representing both the nuclear-nuclear correlation and the vibrational oscillation of the wave functions in terms of the Internuclear Distance. This finding is important because it paves the way for high-accuracy non-BO calculations of bound vibrational states of molecules with more than two nuclei that have never been performed before.
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Universal all-particle explicitly-correlated Gaussians for non-Born–Oppenheimer calculations of molecular rotationless states
Chemical Physics Letters, 2016Co-Authors: Sergiy Bubin, Bubin Sergiy, Formanek Martin, Adamowicz LudwikAbstract:Abstract Complex explicitly correlated one-center all-particle Gaussian functions (CECGs) are tested as basis functions for molecular non-Born–Oppenheimer (non-BO) calculations. The tests concern the complete spectrum of the 23 bound pure vibrational states of the HD+ ion. The tests show that CECGs are very effective in representing both the nuclear-nuclear correlation and the vibrational oscillation of the wave functions in terms of the Internuclear Distance. This finding is important because it paves the way for high-accuracy non-BO calculations of bound vibrational states of molecules with more than two nuclei that have never been performed before
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complete pure vibrational spectrum of hd calculated without the born oppenheimer approximation and including relativistic corrections
Physical Review A, 2011Co-Authors: Sergiy Bubin, Monika Stanke, Ludwik AdamowiczAbstract:All 18 bound pure vibrational levels of the HD molecule have been calculated within the framework that does not assume the Born-Oppenheimer (BO) approximation. The nonrelativistic energies of the states have been corrected for the relativistic effects of the order of ${\ensuremath{\alpha}}^{2}$ (where $\ensuremath{\alpha}$ is the fine structure constant), calculated using the perturbation theory with the nonrelativistic non-BO wave functions being the zero-order approximation. The calculations were performed by expanding the non-BO wave functions in terms of one-center explicitly correlated Gaussian functions multiplied by even powers of the Internuclear Distance and by performing extensive optimization of the Gaussian nonlinear parameters. Up to 10 000 basis functions were used for each state.
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lower vibrational transitions of the 3he4he ion calculated without the born oppenheimer approximation and with leading relativistic corrections
Chemical Physics Letters, 2010Co-Authors: Sergiy Bubin, Monika Stanke, Ludwik AdamowiczAbstract:Abstract Very accurate variational calculations of the five lowest vibrational states of the 3He4He+ ion are carried out within a framework that does not assume the Born–Oppenheimer (BO) approximation, i.e., treating the two nuclei and three electrons forming the system on an equal footing. The non-BO wave functions are expanded in terms of one-center explicitly correlated Gaussian functions multiplied by even powers of the Internuclear Distance. The wave functions are used to calculate the leading relativistic corrections. The approach reproduces the experimental 3He4He+ fundamental transition within 0.055 cm−1 and similar accuracy is expected for the higher yet unmeasured vibrational transitions determined in the present calculations.
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Darwin and mass-velocity relativistic corrections in non-Born-Oppenheimer variational calculations
The Journal of chemical physics, 2006Co-Authors: Dariusz Kędziera, Monika Stanke, Sergiy Bubin, Maria Barysz, Ludwik AdamowiczAbstract:The Pauli approach to account for the mass-velocity and Darwin relativistic corrections has been applied to the formalism for quantum mechanical molecular calculations that does not assume the Born-Oppenheimer (BO) approximation regarding separability of the electronic and nuclear motions in molecular systems. The corrections are determined using the first order perturbation theory and are derived for the non-BO wave function of a diatomic system expressed in terms of explicitly correlated Gaussian functions with premultipliers in the form of even powers of the Internuclear Distance. As a numerical example we used calculations of the transition energies for pure vibrational states of the HD+ ion.
Monika Stanke - One of the best experts on this subject based on the ideXlab platform.
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complete pure vibrational spectrum of hd calculated without the born oppenheimer approximation and including relativistic corrections
Physical Review A, 2011Co-Authors: Sergiy Bubin, Monika Stanke, Ludwik AdamowiczAbstract:All 18 bound pure vibrational levels of the HD molecule have been calculated within the framework that does not assume the Born-Oppenheimer (BO) approximation. The nonrelativistic energies of the states have been corrected for the relativistic effects of the order of ${\ensuremath{\alpha}}^{2}$ (where $\ensuremath{\alpha}$ is the fine structure constant), calculated using the perturbation theory with the nonrelativistic non-BO wave functions being the zero-order approximation. The calculations were performed by expanding the non-BO wave functions in terms of one-center explicitly correlated Gaussian functions multiplied by even powers of the Internuclear Distance and by performing extensive optimization of the Gaussian nonlinear parameters. Up to 10 000 basis functions were used for each state.
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lower vibrational transitions of the 3he4he ion calculated without the born oppenheimer approximation and with leading relativistic corrections
Chemical Physics Letters, 2010Co-Authors: Sergiy Bubin, Monika Stanke, Ludwik AdamowiczAbstract:Abstract Very accurate variational calculations of the five lowest vibrational states of the 3He4He+ ion are carried out within a framework that does not assume the Born–Oppenheimer (BO) approximation, i.e., treating the two nuclei and three electrons forming the system on an equal footing. The non-BO wave functions are expanded in terms of one-center explicitly correlated Gaussian functions multiplied by even powers of the Internuclear Distance. The wave functions are used to calculate the leading relativistic corrections. The approach reproduces the experimental 3He4He+ fundamental transition within 0.055 cm−1 and similar accuracy is expected for the higher yet unmeasured vibrational transitions determined in the present calculations.
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Darwin and mass-velocity relativistic corrections in non-Born-Oppenheimer variational calculations
The Journal of chemical physics, 2006Co-Authors: Dariusz Kędziera, Monika Stanke, Sergiy Bubin, Maria Barysz, Ludwik AdamowiczAbstract:The Pauli approach to account for the mass-velocity and Darwin relativistic corrections has been applied to the formalism for quantum mechanical molecular calculations that does not assume the Born-Oppenheimer (BO) approximation regarding separability of the electronic and nuclear motions in molecular systems. The corrections are determined using the first order perturbation theory and are derived for the non-BO wave function of a diatomic system expressed in terms of explicitly correlated Gaussian functions with premultipliers in the form of even powers of the Internuclear Distance. As a numerical example we used calculations of the transition energies for pure vibrational states of the HD+ ion.
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Darwin and mass-velocity relativistic corrections in the non-Born-Oppenheimer calculations of pure vibrational states of H2.
The Journal of chemical physics, 2006Co-Authors: Dariusz Kȩdziera, Sergiy Bubin, Monika Stanke, Maria Barysz, Ludwik AdamowiczAbstract:The Darwin and mass-velocity relativistic corrections have been calculated for all pure vibrational states of the H2 using the perturbation theory and very accurate variational wave functions obtained without assuming the Born-Oppenheimer (BO) approximation. Expansions in terms of explicitly correlated Gaussians with premultipliers in the form of even powers of the Internuclear Distance were used for the wave functions. With the inclusion of the two relativistic corrections to the non-BO energies the transition energies for the highest states agree more with the experimental results.
C. W. Mccurdy - One of the best experts on this subject based on the ideXlab platform.
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Multiconfiguration time-dependent Hartree-Fock treatment of electronic and nuclear dynamics in diatomic molecules
Physical Review A, 2011Co-Authors: Daniel J. Haxton, Keith V. Lawler, C. W. MccurdyAbstract:The multiconfiguration time-dependent Hartree-Fock (MCTDHF) method is formulated for treating the coupled electronic and nuclear dynamics of diatomic molecules without the Born-Oppenheimer approximation. The method treats the full dimensionality of the electronic motion, uses no model interactions, and is in principle capable of an exact nonrelativistic description of diatomics in electromagnetic fields. An expansion of the wave function in terms of configurations of orbitals whose dependence on Internuclear Distance is only that provided by the underlying prolate spheroidal coordinate system is demonstrated to provide the key simplifications of the working equations that allow their practical solution. Photoionization cross sections are also computed from the MCTDHF wave function in calculations using short pulses.
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role of nuclear motion in double ionization of molecular hydrogen by a single photon
Physical Review Letters, 2007Co-Authors: Daniel A Horner, Wim Vanroose, T N Rescigno, F Martin, C. W. MccurdyAbstract:We examine the origin of recently observed variations with Internuclear Distance (R) of the fully differential cross sections for double ionization of aligned H2 by absorption of a single photon. Using the results of fully converged numerical solutions of the Schrodinger equation, we show that these variations arise primarily from pronounced differences in the R dependence of the parallel and perpendicular components of the ionization amplitude. We also predict that R dependences should be readily observable in the asymmetry parameter for photodouble ionization, even in experimental measurements that are not differential in the energy sharings between ejected photoelectrons.
S Magnier - One of the best experts on this subject based on the ideXlab platform.
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electronic transition dipole moment and radiative lifetime calculations of sodium dimer ion pair states
Journal of Chemical Physics, 2015Co-Authors: Aydin Sanli, B Beser, John R Edwardson, S Magnier, Ergin Ahmed, Marjatta A LyyraAbstract:We report here ab initio calculated electronic transition dipole moments for the sodium dimer ion pair states of 1Σg+ symmetry. They vary strongly as a function of Internuclear Distance because of the effect of the Na+ + Na− ion pair potential, which also causes the formation of additional wells and shoulders in the molecular potential energy curves. We also present a computational study of the transition dipole moment matrix elements and lifetimes for these ion-pair states.
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measurement of the electronic transition dipole moment by autler townes splitting comparison of three and four level excitation schemes for the na2 a 1sigma u x 1sigma g system
Journal of Chemical Physics, 2006Co-Authors: Ergin Ahmed, S Magnier, A Hansson, T Kirova, A Lazoudis, Svetlana Kotochigova, A M LyyraAbstract:We present a fundamentally new approach for measuring the transition dipole moment of molecular transitions, which combines the benefits of quantum interference effects, such as the Autler-Townes splitting, with the familiar R-centroid approximation. This method is superior to other experimental methods for determining the absolute value of the R-dependent electronic transition dipole moment function mu(e)(R), since it requires only an accurate measurement of the coupling laser electric field amplitude and the determination of the Rabi frequency from an Autler-Townes split fluorescence spectral line. We illustrate this method by measuring the transition dipole moment matrix element for the Na2 A 1Sigma(u)+ (v' = 25, J' = 20e)-X 1Sigma(g)+ (v" = 38, J" = 21e) rovibronic transition and compare our experimental results with our ab initio calculations. We have compared the three-level (cascade) and four-level (extended Lambda) excitation schemes and found that the latter is preferable in this case for two reasons. First, this excitation scheme takes advantage of the fact that the coupling field lower level is outside the thermal population range. As a result vibrational levels with larger wave function amplitudes at the outer turning point of vibration lead to larger transition dipole moment matrix elements and Rabi frequencies than those accessible from the equilibrium Internuclear Distance of the thermal population distribution. Second, the coupling laser can be "tuned" to different rovibronic transitions in order to determine the Internuclear Distance dependence of the electronic transition dipole moment function in the region of the R-centroid of each coupling laser transition. Thus the Internuclear Distance dependence of the transition moment function mu(e)(R) can be determined at several very different values of the R centroid. The measured transition dipole moment matrix element for the Na2 A 1Sigma(u)+ (v' = 25, J' = 20e)-X 1Sigma(g)+ (v" = 38, J" = 21e) transition is 5.5+/-0.2 D compared to our ab initio value of 5.9 D. By using the R-centroid approximation for this transition the corresponding experimental electronic transition dipole moment is 9.72 D at Rc = 4.81 A, in good agreement with our ab initio value of 10.55 D.
