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Yunlong Xiao - One of the best experts on this subject based on the ideXlab platform.
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Relativistic Theory of nuclear spin rotation tensor with kinetically balanced rotational london orbitals
Journal of Chemical Physics, 2014Co-Authors: Yunlong XiaoAbstract:Both kinetically balanced (KB) and kinetically unbalanced (KU) rotational London orbitals (RLO) are proposed to resolve the slow basis set convergence in Relativistic calculations of nuclear spin-rotation (NSR) coupling tensors of molecules containing heavy elements [Y. Xiao and W. Liu, J. Chem. Phys. 138, 134104 (2013)]. While they perform rather similarly, the KB-RLO Ansatz is clearly preferred as it ensures the correct nonRelativistic limit even with a finite basis. Moreover, it gives rise to the same “direct Relativistic mapping” between nuclear magnetic resonance shielding and NSR coupling tensors as that without using the London orbitals [Y. Xiao, Y. Zhang, and W. Liu, J. Chem. Theory Comput. 10, 600 (2014)].
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body fixed Relativistic molecular hamiltonian and its application to nuclear spin rotation tensor
Journal of Chemical Physics, 2013Co-Authors: Yunlong XiaoAbstract:A Relativistic molecular Hamiltonian that describes electrons fully Relativistically and nuclei quasi-Relativistically is proposed and transformed from the laboratory to the body-fixed frame of reference. As a first application of the resulting body-fixed Relativistic molecular Hamiltonian, the long anticipated Relativistic Theory of nuclear spin-rotation (NSR) tensor is formulated rigorously. A “Relativistic mapping” between experimental NSR and NMR is further proposed, which is of great value in establishing high-precision absolute NMR shielding scales.
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four component Relativistic Theory for nuclear magnetic shielding magnetically balanced gauge including atomic orbitals
Journal of Chemical Physics, 2009Co-Authors: Lan Cheng, Yunlong Xiao, Wenjian LiuAbstract:It is recognized only recently that the incorporation of the magnetic balance condition is absolutely essential for four-component Relativistic theories of magnetic properties. Another important issue to be handled is the so-called gauge problem in calculations of, e.g., molecular magnetic shielding tensors with finite bases. It is shown here that the magnetic balance can be adapted to distributed gauge origins, leading to, e.g., magnetically balanced gauge-including atomic orbitals (MB-GIAOs) in which each magnetically balanced atomic orbital has its own local gauge origin placed on its center. Such a MB-GIAO scheme can be combined with any level of Theory for electron correlation. The first implementation is done here at the coupled-perturbed Dirac–Kohn–Sham level. The calculated molecular magnetic shielding tensors are not only independent of the choice of gauge origin but also converge rapidly to the basis set limit. Close inspections reveal that (zeroth order) negative energy states are only importan...
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four component Relativistic Theory for nuclear magnetic shielding constants critical assessments of different approaches
Journal of Chemical Physics, 2007Co-Authors: Yunlong Xiao, Lan Cheng, Wenjian Liu, Daoling PengAbstract:Both formal and numerical analyses have been carried out on various exact and approximate variants of the four-component Relativistic Theory for nuclear magnetic shielding constants. These include the standard linear response Theory (LRT), the full or external field-dependent unitary transformations of the Dirac operator, as well as the orbital decomposition approach. In contrast with LRT, the latter schemes take explicitly into account both the kinetic and magnetic balances between the large and small components of the Dirac spinors, and are therefore much less demanding on the basis sets. In addition, the diamagnetic contributions, which are otherwise “missing” in LRT, appear naturally in the latter schemes. Nevertheless, the definitions of paramagnetic and diamagnetic terms are not the same in the different schemes, but the difference is only of O(c−2) and thus vanishes in the nonRelativistic limit. It is shown that, as an operator Theory, the full field-dependent unitary transformation approach cannot...
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four component Relativistic Theory for nuclear magnetic shielding constants the orbital decomposition approach
Journal of Chemical Physics, 2007Co-Authors: Yunlong Xiao, Daoling Peng, Wenjian LiuAbstract:The authors present a scheme to simplify four-component Relativistic calculations of nuclear magnetic shielding constants. The central idea is to decompose each first order orbital into two terms, one is magnetically balanced and directly leads to the diamagnetic term, and the other is, to leading order of relativity, kinetically balanced and can therefore simply be represented in the basis of unperturbed positive energy states. As a matrix formulation, the present approach is far simpler than other operator theories. Combined with the Dirac-Kohn-Sham ansatz, the nuclear magnetic shielding constants for the Kr, Xe, and Rn atoms as well as the HBr and HI molecules are calculated, and the results compare favorably with those of other schemes.
Nanna Holmgaard List - One of the best experts on this subject based on the ideXlab platform.
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beyond the electric dipole approximation in simulations of x ray absorption spectroscopy lessons from Relativistic Theory
Journal of Chemical Physics, 2020Co-Authors: Nanna Holmgaard List, Timothe Romain Leo Melin, Martin Van Horn, Trond SaueAbstract:: We present three schemes to go beyond the electric-dipole approximation in x-ray absorption spectroscopy calculations within a four-component Relativistic framework. The first is based on the full semi-classical light-matter interaction operator and the two others on a truncated interaction within the Coulomb gauge (velocity representation) and multipolar gauge (length representation). We generalize the derivation of the multipolar gauge to an arbitrary expansion point and show that the potentials corresponding to different expansion points are related by a gauge transformation, provided that the expansion is not truncated. This suggests that the observed gauge-origin dependence in the multipolar gauge is more than just a finite-basis set effect. The simplicity of the Relativistic formalism enables arbitrary-order implementations of the truncated interactions, with and without rotational averaging, allowing us to test their convergence behavior numerically by comparison to the full formulation. We confirm the observation that the oscillator strength of the electric-dipole allowed ligand K-edge transition of TiCl4, when calculated to the second order in the wave vector, becomes negative but also show that inclusion of higher-order contributions allows convergence to the result obtained using the full light-matter interaction. However, at higher energies, the slow convergence of such expansions becomes dramatic and renders such approaches at best impractical. When going beyond the electric-dipole approximation, we therefore recommend the use of the full light-matter interaction.
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beyond the electric dipole approximation in simulations of x ray absorption spectroscopy lessons from Relativistic Theory
arXiv: Chemical Physics, 2020Co-Authors: Nanna Holmgaard List, Timothe Romain Leo Melin, Martin Van Horn, Trond SaueAbstract:We present three schemes to go beyond the electric-dipole approximation in X-ray absorption spectroscopy calculations within a four-component Relativistic framework. The first is based on the full semi-classical light-matter interaction operator, and the two others on a truncated interaction within Coulomb gauge (velocity representation) and multipolar gauge (length representation). We generalize the derivation of multipolar gauge to an arbitrary expansion point and show that the potentials corresponding to different expansion point are related by a gauge transformation, provided the expansion is not truncated. This suggests that the observed gauge-origin dependence in multipolar gauge is more than just a finite-basis set effect. The simplicity of the Relativistic formalism enables arbitrary-order implementations of the truncated interactions, with and without rotational averaging, allowing us to test their convergence behavior numerically by comparison to the full formulation. We confirm the observation that the oscillator strength of the electric-dipole allowed ligand K-edge transition of TiCl$_4$, when calculated to second order in the wave vector, become negative, but also show that inclusion of higher-order contributions allows convergence to the result obtained using the full light-matter interaction. However, at higher energies, the slow convergence of such expansions becomes dramatic and renders such approaches at best impractical. When going beyond the electric-dipole approximation, we therefore recommend the use of the full light-matter interaction.
Constantinos Skordis - One of the best experts on this subject based on the ideXlab platform.
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new Relativistic Theory for modified newtonian dynamics
Physical Review Letters, 2021Co-Authors: Constantinos Skordis, Tom ZlośnikAbstract:We propose a Relativistic gravitational Theory leading to modified Newtonian dynamics, a paradigm that explains the observed universal galactic acceleration scale and related phenomenology. We discuss phenomenological requirements leading to its construction and demonstrate its agreement with the observed cosmic microwave background and matter power spectra on linear cosmological scales. We show that its action expanded to second order is free of ghost instabilities and discuss its possible embedding in a more fundamental Theory.
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a new Relativistic Theory for modified newtonian dynamics
arXiv: General Relativity and Quantum Cosmology, 2020Co-Authors: Constantinos Skordis, Tom ZlosnikAbstract:We propose a Relativistic gravitational Theory leading to Modified Newtonian Dynamics, a paradigm that explains the observed universal acceleration and associated phenomenology in galaxies. We discuss phenomenological requirements leading to its construction and demonstrate its agreement with the observed Cosmic Microwave Background and matter power spectra on linear cosmological scales. We show that its action expanded to 2nd order is free of ghost instabilities and discuss its possible embedding in a more fundamental Theory.
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tensor vector scalar cosmology covariant formalism for the background evolution and linear perturbation Theory
Physical Review D, 2006Co-Authors: Constantinos SkordisAbstract:A Relativistic Theory of gravity has recently been proposed by Bekenstein, where gravity is mediated by a tensor, a vector, and a scalar field, thus called TeVeS. The Theory aims at modifying gravity in such a way as to reproduce Milgrom's modified Newtonian dynamics (MOND) in the weak field, nonRelativistic limit, which provides a framework to solve the missing mass problem in galaxies without invoking dark matter. In this paper I apply a covariant approach to formulate the cosmological equations for this Theory, for both the background and linear perturbations. I derive the necessary perturbed equations for scalar, vector, and tensor modes without adhering to a particular gauge. Special gauges are considered in the appendixes.
Trond Saue - One of the best experts on this subject based on the ideXlab platform.
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beyond the electric dipole approximation in simulations of x ray absorption spectroscopy lessons from Relativistic Theory
Journal of Chemical Physics, 2020Co-Authors: Nanna Holmgaard List, Timothe Romain Leo Melin, Martin Van Horn, Trond SaueAbstract:: We present three schemes to go beyond the electric-dipole approximation in x-ray absorption spectroscopy calculations within a four-component Relativistic framework. The first is based on the full semi-classical light-matter interaction operator and the two others on a truncated interaction within the Coulomb gauge (velocity representation) and multipolar gauge (length representation). We generalize the derivation of the multipolar gauge to an arbitrary expansion point and show that the potentials corresponding to different expansion points are related by a gauge transformation, provided that the expansion is not truncated. This suggests that the observed gauge-origin dependence in the multipolar gauge is more than just a finite-basis set effect. The simplicity of the Relativistic formalism enables arbitrary-order implementations of the truncated interactions, with and without rotational averaging, allowing us to test their convergence behavior numerically by comparison to the full formulation. We confirm the observation that the oscillator strength of the electric-dipole allowed ligand K-edge transition of TiCl4, when calculated to the second order in the wave vector, becomes negative but also show that inclusion of higher-order contributions allows convergence to the result obtained using the full light-matter interaction. However, at higher energies, the slow convergence of such expansions becomes dramatic and renders such approaches at best impractical. When going beyond the electric-dipole approximation, we therefore recommend the use of the full light-matter interaction.
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beyond the electric dipole approximation in simulations of x ray absorption spectroscopy lessons from Relativistic Theory
arXiv: Chemical Physics, 2020Co-Authors: Nanna Holmgaard List, Timothe Romain Leo Melin, Martin Van Horn, Trond SaueAbstract:We present three schemes to go beyond the electric-dipole approximation in X-ray absorption spectroscopy calculations within a four-component Relativistic framework. The first is based on the full semi-classical light-matter interaction operator, and the two others on a truncated interaction within Coulomb gauge (velocity representation) and multipolar gauge (length representation). We generalize the derivation of multipolar gauge to an arbitrary expansion point and show that the potentials corresponding to different expansion point are related by a gauge transformation, provided the expansion is not truncated. This suggests that the observed gauge-origin dependence in multipolar gauge is more than just a finite-basis set effect. The simplicity of the Relativistic formalism enables arbitrary-order implementations of the truncated interactions, with and without rotational averaging, allowing us to test their convergence behavior numerically by comparison to the full formulation. We confirm the observation that the oscillator strength of the electric-dipole allowed ligand K-edge transition of TiCl$_4$, when calculated to second order in the wave vector, become negative, but also show that inclusion of higher-order contributions allows convergence to the result obtained using the full light-matter interaction. However, at higher energies, the slow convergence of such expansions becomes dramatic and renders such approaches at best impractical. When going beyond the electric-dipole approximation, we therefore recommend the use of the full light-matter interaction.
V P Nair - One of the best experts on this subject based on the ideXlab platform.
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remarks on the exotic central extension of the planar galilei group
Physics Letters B, 2003Co-Authors: R Jackiw, V P NairAbstract:Some issues in relating the central extensions of the planar Galilei group to parameters in the corresponding Relativistic Theory are discussed. Some issues in relating the central extensions of the planar Galilei group to parameters in the corresponding Relativistic Theory are discussed.
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remarks on the exotic central extension of the planar galilei group
arXiv: High Energy Physics - Theory, 2002Co-Authors: R Jackiw, V P NairAbstract:Some issues in relating the central extensions of the planar Galilei group to parameters in the corresponding Relativistic Theory are discussed.
