Relativistic Energy Corrections Research Articles

Fine structure calculations, polarizability and oscillator strengths for C VI ion embedded in Debye plasma applying accurate Numerov method

The dipole polarizabilities, dipole and quadruple oscillator strengths and relativistic energy corrections are calculated for plasma embedded C VI ion which is of relevance in astrophysics and plasma physics. Numerical simulation of Numerov method is used to find the energy eigenvalues and eigenfunctions by solving the time-independent Schrodinger equation. The dependence of dipole and quadruple polarizabilities, oscillator strengths and relativistic energy corrections on Debye length is shown.

Single-photon ionization of SiC in the gas phase: experimental and ab initio characterization of SiC.

We report the first experimental observation of single-photon ionization transitions of the SiC radical between 8.0 and 11.0 eV performed on the DESIRS beamline at the SOLEIL synchrotron facility. The SiC radical, very difficult to synthesize in the gas phase, was produced through chemical reactions between CHx (x = 0-3) and SiHy (y = 0-3) in a continuous microwave discharge flow tube, the CHx and SiHy species being formed by successive hydrogen-atom abstractions induced by fluorine atoms on methane and silane, respectively. Mass-selected ion yield and photoelectron spectra were recorded as a function of photon energy using a double imaging photoelectron/photoion coincidence spectrometer. The photoelectron spectrum enables the first direct experimental determinations of the X+ 4Σ- ← X 3Π and 1+ 2Π ← X 3Π adiabatic ionization energies of SiC (8.978(10) eV and 10.216(24) eV, respectively). Calculated spectra based on Franck-Condon factors are compared with the experimental spectra. These spectra were obtained by solving the rovibrational Hamiltonian, using the potential energy curves calculated at the multireference single and double configuration interaction level with Davidson correction (MRCI + Q) and the aug-cc-pV5Z basis set. MRCI + Q calculations including the core and core-valence electron correlation were performed using the aug-cc-pCV6Z basis set to predict the spectroscopic properties of the six lowest electronic states of SiC+. Complete basis set extrapolations and relativistic energy corrections were also included in the determination of the energy differences characterizing the photoionization process. Using our experimental and theoretical results, we derived semi-experimental values for the five lowest ionization energies of SiC.

Theoretical analysis of relativistic energy corrections, partition function and thermodynamic properties of spherically confined hydrogen atom

Theoretical analysis of relativistic energy corrections, partition function and thermodynamic properties of spherically confined hydrogen atom

Threshold photoelectron spectroscopy of 9-methyladenine: theory and experiment.

We present a combined experimental and theoretical study of single-photon ionization of 9-methyladenine (9MA) in the gas phase. In addition to tautomerism, several rotamers due to the rotation of the methyl group may exist. Computations show, however, that solely one rotamer contributes because of low population in the molecular beam and/or unfavorable Franck-Condon factors upon ionization. Experimentally, we used VUV radiation available at the DESIRS beamline of the synchrotron radiation facility SOLEIL to record the threshold photoelectron spectrum of this molecule between 8 and 11 eV. This spectrum consists of a well-resolved band assigned mainly to vibronic levels of the D0 cationic state, plus a contribution from the D1 state, and two large bands corresponding to the D1, D2 and D3 electronically excited states. The adiabatic ionization energy of 9MA is measured at 8.097 ± 0.005 eV in close agreement with the computed value using the explicitly correlated coupled cluster approach including core valence, scalar relativistic and zero-point vibrational energy corrections. This work sheds light on the complex pattern of the lowest doublet electronic states of 9MA+. The comparison to canonical adenine reveals that methylation induces further electronic structure complication that may be important to understand the effects of ionizing radiation and the charge distribution in these biological entities at different time scales.

Nuclear Fusion Research and Development Need New Relativistic Mass and Energy Corrections Given by the Information Relativity Theory

Hundred years after the conjecture of the British astronomer Eddington that the sun is powered by nuclear fusion of hydrogen, new physics theory may help make energy harvesting by nuclear fusion soon a reality. Researchers as well as investors funding fusion megaprojects are asked to deal with new relativistic corrections for mass and energy proposed by Suleiman in his Information Relativity Theory (IRT). These corrections were calculated in this contribution. It will help to decide whether a venture will be successful and to save big investments when in doubt. The assumed optimal kinetic energy for controlled nuclear fusion must be corrected to a somewhat higher level. At very high kinetic energy in the upper GeV range, it remains not enough baryonic mass to be transformed in energy. The fusion probability faded out to zero already at the golden limit of the recession speed of between target nucleon and projectile nucleon. Cold nuclear fusion, if ever possible, is recommended for protons rather than deuterons at highest experimental possible temperatures around 1000 (K) and needs fine-tuned kinetic nucleon energy. It would be also of interest whether a golden ratio based nuclear fuel confinement chamber could be beneficial. In this connection, also cold nuclear fusion setups should be discussed. Nature is governed by the golden ratio and criticality of physical systems influenced by it, and nuclear physics is not an exception. Computer simulations of the underlying controlled nuclear fusion processes should gain profit from IRT corrected starting information and may tackle anew possible low energy nuclear transmutations considering the wave-like dark components of matter and energy.

High-accuracy calculations of the lowest eleven Rydberg 2 P states of the Li atom

Highly accurate calculations are reported for the eleven lowest states of the 2 P Rydberg series (1s 2 np 1, n = 2, …, 12) of the lithium atom. The nonrelativistic wave functions of the states are expanded in terms of up to 16 000 all-electron explicitly correlated Gaussian (ECG) basis functions. The ECG exponential parameters are variationally optimized using a method that employs the analytical energy gradient determined for the parameters. The finite-nuclear-mass effects of the 6Li and 7Li isotopes are explicitly included in the nonrelativistic variational calculations. The results also include the leading relativistic and quantum electrodynamics energy corrections computed using the framework of perturbation theory. The calculated interstate transition energies are compared with the available experimental data. The 6Li–7Li isotope shifts of the transition energies are determined.

ExoMol line lists XXXI: spectroscopy of lowest eights electronic states of C2

Accurate line lists for the carbon dimer, C2, are presented. These line lists cover rovibronic transitions between the eight lowest electronic states: |$X\, {}^{1}\Sigma _{g}^{+}$|⁠, |$a\, {}^{3}\Pi _{u}$|⁠, |$A\, {}^{1}\Pi _{u}$|⁠, |$b\, ^{3}\Sigma _{g}^{-}$|⁠, |$c\, ^{3}\Sigma _{u}^{+}$|⁠, |$d\, {}^{3}\Pi _{g}$|⁠, |$B\, {}^{1}\Delta _{g}$|⁠, and |$B^\prime \, {}^{1}\Sigma _{g}^{+}$|⁠. Potential energy curves (PECs) and transition dipole moment curves are computed on a large grid of geometries using the aug-cc-pwCVQZ-DK/MRCI level of theory including core and core–valence correlations and scalar relativistic energy corrections. The same level of theory is used to compute spin-orbit and electronic angular momentum couplings. The PECs and couplings are refined by fitting to the empirical (MARVEL) energies of 12C2 using the nuclear-motion program Duo. The transition dipole moment curves are represented as analytical functions to reduce the numerical noise when computing transition line strengths. Partition functions, full line lists, Landé-factors, and lifetimes for three main isotopologues of C2 (12C2, 13C2, and 12C13C) are made available in electronic form from the CDS (http://cdsarc.u-strasbg.fr) and ExoMol (www.exomol.com) data bases.

Two-Dimensional Hydrogen-like Atom: Photon Emission and Relativistic Energy Corrections

Using the well-known solution Ψ S of the Schrodinger equation for an electron in the field of a nucleus (Ze) in polar coordinates, via which the spin-state-dependent Dirac spinor Ψ± obtained here is expressed, and by extending the QED methods to subspace {0; 1, 2}, we have calculated the probability of single-photon emission by a two-dimensional hydrogen-like atom with allowance made for the polarization and spin states. Relativistic energy corrections ∼(Zα)4 to the energy value have also been found. We show that the so-called contact interaction typical of a three-dimensional hydrogen-like atom also takes place in the twodimensional case, while the ordinary three-dimensional spin–orbit interaction is absent altogether.

Transition Metal Cation−π Interactions: Complexes Formed by Fe2+, Co2+, Ni2+, Cu2+, and Zn2+ Binding with Benzene Molecules

A computational investigation of the structures and interaction energies of complexes formed by Fe2+, Co2+, Ni2+, Cu2+, and Zn2+ binding with benzene (Bz) molecules is performed employing high level ab initio quantum chemical methods, such as the second-order perturbation theory (MP2), coupled-cluster singles and doubles (CCSD), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)] methods, along with the 6-311++G(2d,2p) and 6-311++G(d,p) basis sets. As far as we know, the present work is the first to study the structures and energetics of Bz-M2+ and Bz-M2+-Bz type complexes (M = Co, Ni, Cu, and Zn). Relativistic effects are also investigated via Douglas-Kroll-Hess second-order scalar relativistic computations for the complexes considered. Our results demonstrate that there are strong bindings between transition metal cations and benzene molecules. The computed interaction energies, including relativistic energy corrections, for the Bz-M2+ type complexes at the CCSD(T)/6-311++G(2d,2p) level are -131.9 (Bz-Fe2+), -172.6 (Bz-Co2+), -189.8 (Bz-Ni2+), -181.1 (Bz-Cu2+), and -158.2 (Bz-Zn2+) kcal mol-1. Similarly, interaction energies for the Bz-M2+-Bz type complexes at the CCSD(T)/6-311++G(d,p) level are -206.4 (Bz-Fe2+-Bz), -213.4 (Bz-Co2+-Bz), -249.7 (Bz-Ni2+-Bz), -258.6 (Bz-Cu2+-Bz), and -235.2 (Bz-Zn2+-Bz) kcal mol-1. Further, our results also demonstrate that the relativistic effects are very important in accurate computations of interaction energies. The predicted relativistic energy corrections to interaction energies, using the ωB97X-D functional, are between -1.9 and -7.7 kcal mol-1. The transition metal cation-π interactions investigated in this study prove significantly larger binding energies compared to arbitrary π-π interactions and main group cation-π interactions. We believe that the present study may open new avenues in cation-π interactions.

Interplay between relativistic energy corrections and resonant excitations in x-ray multiphoton ionization dynamics of Xe atoms

In this paper, we theoretically study x-ray multiphoton ionization dynamics of heavy atoms taking into account relativistic and resonance effects. When an atom is exposed to an intense x-ray pulse generated by an x-ray free-electron laser (XFEL), it is ionized to a highly charged ion via a sequence of single-photon ionization and accompanying relaxation processes, and its final charge state is limited by the last ionic state that can be ionized by a single-photon ionization. If x-ray multiphoton ionization involves deep inner-shell electrons in heavy atoms, energy shifts by relativistic effects play an important role in ionization dynamics, as pointed out in Phys. Rev. Lett. 110, 173005 (2013). On the other hand, if the x-ray beam has a broad energy bandwidth, the high-intensity x-ray pulse can drive resonant photoexcitations for a broad range of ionic states and ionize even beyond the direct one-photon ionization limit, as first proposed in Nat. Photon. 6, 858 (2012). To investigate both relativistic and resonance effects, we extend the xatom toolkit to incorporate relativistic energy corrections and resonant excitations in x-ray multiphoton ionization dynamics calculations. Charge-state distributions are calculated for Xe atoms interacting with intense XFEL pulses at a photon energy of 1.5 keV and 5.5 keV, respectively. For both photon energies, we demonstrate that the role of resonant excitations in ionization dynamics is altered due to significant shifts of orbital energy levels by relativistic effects. Therefore, it is necessary to take into account both effects to accurately simulate multiphoton multiple ionization dynamics at high x-ray intensity.

Lowest ^{2}S Electronic Excitations of the Boron Atom.

A theoretical abinitio approach for calculating bound states of small atoms is developed and implemented. The approach is based on finite-nuclear-mass [non-Born-Oppenheimer (non-BO)] nonrelativistic variational calculations performed with all-particle explicitly correlated Gaussian functions and includes the leading relativistic and quantum electrodynamics energy corrections determined using the non-BO wave functions. The approach is applied to determine the total and transition energies for the lowest four ^{2}S electronic excitations of the boron atom. The transition energies agree with the available experimental values within 0.2-0.3 cm^{-1}. Previously, such accuracy was achieved for three- and four-electron systems.

Energy levels and radiative transitions of the core-excited high-spin states in boron atom (ion)

Energy levels of the core-excited high-spin Rydberg states (4,5,6L, L = S, P) in boron atom (ion) are calculated by the Rayleigh-Ritz variation method with using large-scale multi-configuration wave functions. The important orbital-spin angular momentum partial waves are selected based on the rule of configuration interaction. The computational convergence is discussed by the example of the contribution from each partial wave in the non-relativistic energy calculations of the high-spin state 1s2s2p2 5Pe in B+ ion. To saturate the wave functional space and improve the non-relativistic energy, the restricted variational method is used to calculate the restricted variational energy. Furthermore, the mass polarization effect and relativistic energy correction are included by using a first-order perturbation theory. The quantum electrodynamic effects and higher-order relativistic contributions to the energy levels are also calculated by the screened hydrogenic formula. Then, the accurate relativistic energy levels of these high-spin states of B atom (ion) are obtained by adding the non-relativistic energy and all corrections. The fine structure splitting of these high-spin states is also calculated by the Breit-Pauli operators in the first-order perturbation theory. Compared with other theoretical results, our calculation results are in good accordance with the experimental data. The absorption oscillator strengths, emission oscillator strengths, absorption rates, emission rates, and transition wavelengths of the electric-dipole transitions between these high-spin states of B atom (ions) are systematically calculated by using the optimized wave functions. The oscillator strengths and transition rates are obtained in both the length and velocity gauges. By comparing the two gauge results of oscillator strength, we find that there is a good consistency between them when fl 0.3, and a reasonable consistency is obtained when fl 0.3. The accordance between the length and the velocity gauge results reflects that the calculated wave functions in this work are reasonably accurate. The calculated transition data are also compared with the corresponding experimental and other theoretical data. Good agreement is obtained except the wavelengths for two transitions: 1s2p4p 4Se1s2p3d 4P and 1s2p4d 4P1s2p3p 4Pe. The relative differences between our theoretical results and experimental data are 0.7% and 0.3%, respectively. They need to be verified by further theoretical and experimental studies. For some core-excited high-spin states, the related energy levels and transition data are reported for the first time. Our calculation results will provide valuable data for calculating the spectral lines in the relevant experiments.

Global spectroscopy of the water monomer

Given the large energy required for its electronic excitation, the most important properties of the water molecule are governed by its ground potential energy surface (PES). Novel experiments are now able to probe this surface over a very extended energy range, requiring new theoretical procedures for their interpretation. As part of this study, a new, accurate, global spectroscopic-quality PES and a new, accurate, global dipole moment surface are developed. They are used for the computation of the high-resolution spectrum of water up to the first dissociation limit and beyond as well as for the determination of Stark coefficients for high-lying states. The water PES has been determined by combined ab initio and semi-empirical studies. As a first step, a very accurate, global, ab initio PES was determined using the all-electron, internally contracted multi-reference configuration interaction technique together with a large Gaussian basis set. Scalar relativistic energy corrections are also determined in order to move the energy determinations close to the relativistic complete basis set full configuration interaction limit. The electronic energies were computed for a set of about 2500 geometries, covering carefully selected configurations from equilibrium up to dissociation. Nuclear motion computations using this PES reproduce the observed energy levels up to 39 000 cm(-1) with an accuracy of better than 10 cm(-1). Line positions and widths of resonant states above dissociation show an agreement with experiment of about 50 cm(-1). An improved semi-empirical PES is produced by fitting the ab initio PES to accurate experimental data, resulting in greatly improved accuracy, with a maximum deviation of about 1 cm(-1) for all vibrational band origins. Theoretical results based on this semi-empirical surface are compared with experimental data for energies starting at 27 000 cm(-1), going all the way up to dissociation at about 41 000 cm(-1) and a few hundred wavenumbers beyond it.

LOCV calculation of nuclear matter with relativistic Hamiltonian

The equation of state of symmetric nuclear matter is calculated using the relativistic Hamiltonian (HR) with potentials which have been fitted with the N -N scattering data using the relativistic two-body Hamiltonian ( \( \tilde{{v}}_{{14}}^{}\) and the non-relativistic two-body Hamiltonian, i.e. the Argonne V14 interaction. The boost interaction corrections as well as the relativistic one-body and two-body kinetic energy corrections in cluster expansion energy within the lowest-order-constrained variational method are calculated. It is shown that the relativistic corrections reduce the binding energy by 1.5MeV for \( \tilde{{v}}_{{14}}^{}\) and AV14 interactions. The symmetric nuclear-matter saturation energy is about -16.43 MeV at \( \rho\) = 0.253 (fm-3) with \( \tilde{{v}}_{{14}}^{}\) interaction plus relativistic corrections. Finally, various properties of the symmetric nuclear matter are given and a comparison is made with the other many-body calculations.

Relativistic corrections for a two-dimensional hydrogen-like atom in the presence of a constant magnetic field

In this paper, we study the relativistic corrections to energy eigenvalues of a 2D hydrogen atom in an external magnetic field. Using the power series expansion method, we have solved the nonrelativistic eigenvalue problem for arbitrary magnetic field strength. The first-order relativistic energy correction is calculated in the framework of the perturbation approach to the Dirac equation for the ground state and a few low-lying excited states.

A relativistic quark-diquark model for the nucleon

We developed a constituent quark-diquark model for the nucleon and its resonances using a harmonic oscillator potential for the interaction. The effects due to relativistic kinetic energy correction are studied. Finally, charge form factor of the model is calculated and compared with experimental data.

Oscillator strengths and radiative lifetimes for C2: Swan, Ballik-Ramsay, Phillips, and dΠg3←cΣu+3 systems

High level ab initio calculations, using multireference configuration interaction (MRCI) techniques, have been carried out to investigate the spectroscopic properties of the singlet A 1Piu<--X 1Sigmag+ Phillips, the triplet d 3Pig<--a 3Sigmau Swan, the b 3Sigmag-<--a 3Piu Ballik-Ramsay, and the d 3Pig<--c 3Sigmau+ transitions of C2. The MRCI expansions are based on full-valence complete active space self-consistent-field reference states and utilize the aug-cc-pV6Z basis set to resolve valence electron correlation. Core and core-valence correlations and scalar relativistic energy corrections were also incorporated in the computed potential energy surfaces. Nonadiabatic and spin-orbit effects were explored and found to be of negligible importance in the calculations. Harmonic frequencies and rotational constants are typically within 0.1% of experiment. The calculated radiative lifetimes compare very well with the available experimental data. Oscillator strengths are reported for all systems: fv'v", where 0<or=v<or=5.

On the acceleration of the convergence of singular operators in Gaussian basis sets

Gaussian type wave functions do not reproduce the interparticle cusps which result in a slow convergence of the expectation values of the operators involved in calculations of the relativistic and QED energy corrections. Methods correcting this deficiency are the main topic discussed in this paper. Benchmark expectation values of the singular operators for several few-electron systems are presented.

RELATIVISTIC CORRECTIONS TO THE NUCLEAR AND NEUTRON MATTER ENERGY IN THE LOCV FRAMEWORK

We calculate the two-body relativistic boost interaction corrections as well as relativistic one-body and two-body kinetic energy corrections in cluster expansion of energy with AV18 and the new charge dependent Reid93 potentials within the lowest order constrained variational (LOCV) method. The equation of state of symmetric nuclear matter and pure neutron matter are calculated using the non-relativistic (H NR ), non-relativistic plus boost interaction corrections [Formula: see text] and [Formula: see text] plus kinetic energy corrections [Formula: see text] Hamiltonians. The relativistic boost interaction effects reduce the binding energies of symmetric nuclear matter for the AV18 interaction by ~3 MeV .

A closed-shell coupled-cluster treatment of the Breit-Pauli first-order relativistic energy correction.

First-order relativistic corrections to the energy of closed-shell molecular systems are calculated, using all terms in the two-component Breit-Pauli Hamiltonian. In particular, we present the first implementation of the two-electron Breit orbit-orbit integrals, thus completing the first-order relativistic corrections within the two-component Pauli approximation. Calculations of these corrections are presented for a series of small and light molecules, at the Hartree-Fock and coupled-cluster levels of theory. Comparisons with four-component Dirac-Coulomb-Breit calculations demonstrate that the full Breit-Pauli energy corrections represent an accurate approximation to a fully relativistic treatment of such systems. The Breit interaction is dominated by the spin-spin interaction, the orbit-orbit interaction contributing only about 10% to the total two-electron relativistic correction in molecules consisting of light atoms. However, the relative importance of the orbit-orbit interaction increases with increasing nuclear charge, contributing more than 20% in H(2)S.