Inclusion Of Relativistic Effects Research Articles

Assessing the performance of ΔSCF and the diagonal second-order self-energy approximation for calculating vertical core excitation energies.

Vertical core excitation energies are obtained using a combination of the ΔSCF method and the diagonal second-order self-energy approximation. These methods are applied to a set of neutral molecules and their anionic forms. An assessment of the results with the inclusion of relativistic effects is presented. For core excitations involving delocalized symmetry orbitals, the applied composite method improves upon the overestimation of ΔSCF by providing approximate values close to experimental K-shell transition energies. The importance of both correlation and relaxation contributions to the vertical core-excited state energies, the concept of local and nonlocal core orbitals, and the consequences of breaking symmetry are discussed.

Study of excitation energies of doubly excited states and identification of EUV, SXR and HXR spectral lines in M1 transitions of W LXXIII and Au LXXVIII

We present excitation energies, wavelength of emitted photon during the transition from upper level to lower level, transitions rates and other transition parameters for doubly excited states of W LXXIII and Au LXXVIII by employing Multi-Configuration Dirac-Fock (MCDF) scheme with the inclusion of relativistic effects. We endorse that contribution of QED and Breit corrections in energies of levels is significant. We have also shown that our results of energies from both, FAC and GRASP matches with each other. We have predicted that 37 Hard X-ray (HXR), 25 Soft X-ray (SXR) and 20 Extreme Ultraviolet (EUV) magnetic dipole (M1) transitions among relativistic levels generated from doubly excited states in W LXXIII and Au LXXVIII. Further, we have studied the convergence in excitation energies and lifetime of excited states and analysed the improvement in accuracy of results by estimation of uncertainty percentage in line strength. Besides, fresh atomic data of W LXXIII and Au LXXVII which is not published in the literature have been reported and can be advantageous in diagnosis and modelling of fusion and astrophysical plasmas.

Relativistic four-component MRCISD+Q calculations of the six lowest valence states of molecular F[Formula: see text] anion including Breit interactions.

In this study, the potential energy curves of the ground and the excited states of molecular fluorine anion (F[Formula: see text]) were investigated at multireference configuration interaction (MRCISD) with Davidson size-extensivity correction (denoted as +Q) within fully relativistic four-component relativistic framework including Breit interaction. Spectroscopic constants (Re, ωe, ωexe, ωeye, De,D0,Be, αe, βe, γe ), accurate extended Rydberg analytical form and rovibrational levels for ground state X:[Formula: see text] are presented, as well as spectroscopic constants for non dissociative excited states. For most states these spectroscopic constants are presented for the first time in literature and they are of interest for experimental studies, specially regarding electron attachment of F2. Results suggest that inclusion of relativistic effects at 4-component level and correlation effects treated at MRCISD+Q level are needed to obtain reliable results, which we report for X:[Formula: see text] ground state's Re, ωe and De the values of 1.999 Å, 391 cm- 1 and 1.22 eV, respectively.

The Chronus Quantum software package

AbstractThe Chronus Quantum (ChronusQ) software package is an open source (under the GNU General Public License v2) software infrastructure which targets the solution of challenging problems that arise in ab initio electronic structure theory. Special emphasis is placed on the consistent treatment of time dependence and spin in the electronic wave function, as well as the inclusion of relativistic effects in said treatments. In addition, ChronusQ provides support for the inclusion of uniform finite magnetic fields as external perturbations through the use of gauge‐including atomic orbitals. ChronusQ is a parallel electronic structure code written in modern C++ which utilizes both message passing implementation and shared memory (OpenMP) parallelism. In addition to the examination of the current state of code base itself, a discussion regarding ongoing developments and developer contributions will also be provided.This article is categorized under: Software > Quantum Chemistry Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Density Functional Theory

Molecular QTAIM Topology Is Sensitive to Relativistic Corrections.

The topology of the molecular electron density of benzene dithiol gold cluster complex Au4 -S-C6 H4 -S'-Au'4 changed when relativistic corrections were made and the structure was close to a minimum of the Born-Oppenheimer energy surface. Specifically, new bond paths between hydrogen atoms on the benzene ring and gold atoms appeared, indicating that there is a favorable interaction between these atoms at the relativistic level. This is consistent with the observation that gold becomes a better electron acceptor when relativistic corrections are applied. In addition to relativistic effects, here, we establish the sensitivity of molecular topology to basis sets and convergence thresholds for geometry optimization.

On the energy integral for first post-Newtonian approximation

The post-Newtonian approximation for general relativity is widely adopted by the geodesy and astronomy communities. It has been successfully exploited for the inclusion of relativistic effects in practically all geodetic applications and techniques such as satellite/lunar laser ranging and very long baseline interferometry. Presently, the levels of accuracy required in geodetic techniques require that reference frames, planetary and satellite orbits and signal propagation be treated within the post-Newtonian regime. For arbitrary scalar W and vector gravitational potentials \(W^j (j=1,2,3)\), we present a novel derivation of the energy associated with a test particle in the post-Newtonian regime. The integral so obtained appears not to have been given previously in the literature and is deduced through algebraic manipulation on seeking a Jacobi-like integral associated with the standard post-Newtonian equations of motion. The new integral is independently verified through a variational formulation using the post-Newtonian metric components and is subsequently verified by numerical integration of the post-Newtonian equations of motion.

Many-Electron Theory

A conference on the advances in many-electron theory was held recently. The meeting was attended by renowned experts in the field, including 40 senior faculty from India and abroad, and about 25 students from India. Several topics concerning many-body structure with emphasis on multi-reference theories and inclusion of relativistic effects, dynamics with special emphasis on non-adiabatic effects as well on density functional theory and some applications of the theory were covered during the conference.

On the atomic-number similarity of the binding energies of electrons in filled shells of elements of the periodic table

An expression for the binding energies of electrons in the ground state of an atom is derived on the basis of the Bohr–Sommerfeld quantization rule within the Thomas–Fermi model. The validity of this relation for all elements from neon to uranium is tested within a more perfect quantum-mechanical model with and without the inclusion of relativistic effects, as well as with experimental binding energies. As a result, the ordering of electronic levels in filled atomic shells is established, manifested in an approximate atomic-number similarity. It is proposed to use this scaling property to analytically estimate the binding energies of electrons in an arbitrary atom.

Ion-acoustic envelope modes in a degenerate relativistic electron-ion plasma

A self-consistent relativistic two-fluid model is proposed for one-dimensional electron-ion plasma dynamics. A multiple scales perturbation technique is employed, leading to an evolution equation for the wave envelope, in the form of a nonlinear Schrödinger type equation (NLSE). The inclusion of relativistic effects is shown to introduce density-dependent factors, not present in the non-relativistic case—in the conditions for modulational instability. The role of relativistic effects on the linear dispersion laws and on envelope soliton solutions of the NLSE is discussed.

Stability of Brillouin flow in planar, conventional, and inverted magnetrons

The Brillouin flow is the prevalent flow in crossed-field devices. We systematically study its stability in the conventional, planar, and inverted magnetron geometry. To investigate the intrinsic negative mass effect in Brillouin flow, we consider electrostatic modes in a nonrelativistic, smooth bore magnetron. We found that the Brillouin flow in the inverted magnetron is more unstable than that in a planar magnetron, which in turn is more unstable than that in the conventional magnetron. Thus, oscillations in the inverted magnetron may startup faster than the conventional magnetron. This result is consistent with simulations, and with the negative mass property in the inverted magnetron configuration. Inclusion of relativistic effects and electromagnetic effects does not qualitatively change these conclusions.

Lattice dynamics and chemical bonding in Sb2Te3 from first-principles calculations.

Pressure effects on the lattice dynamics and the chemical bonding of the three-dimensional topological insulator, Sb2Te3, have been studied from a first-principles perspective in its rhombohedral phase. Where it is possible to compare, theory agrees with most of the measured phonon dispersions. We find that the inclusion of relativistic effects, in terms of the spin-orbit interaction, affects the vibrational features to some extend and creates large fluctuations on phonon density of state in high frequency zone. By investigations of structure and electronic structure, we analyze in detail the semiconductor to metal transition at ∼2 GPa followed by an electronic topological transition at a pressure of ∼4.25 GPa.

Chemical-shift tensors of heavy nuclei in network solids: a DFT/ZORA investigation of (207)Pb chemical-shift tensors using the bond-valence method.

Cluster models are used in calculation of (207)Pb NMR magnetic-shielding parameters of α-PbO, β-PbO, Pb3O4, Pb2SnO4, PbF2, PbCl2, PbBr2, PbClOH, PbBrOH, PbIOH, PbSiO3, and Pb3(PO4)2. We examine the effects of cluster size, method of termination of the cluster, charge on the cluster, introduction of exact exchange, and relativistic effects on calculation of magnetic-shielding tensors with density functional theory. Proper termination of the cluster for a network solid, including approximations such as compensation of charge by the bond-valence (BV) method, is essential to provide results that agree with experiment. The inclusion of relativistic effects at the spin-orbit level for such heavy nuclei is an essential factor in achieving agreement with experiment.

E1 oscillator strengths and transition rates among levels of Cl I

We present oscillator strengths and transition rates of E1 transitions between the fine-structure levels belonging to the configurations 3s23p5, 3s3p6, and 3s23p4nl, where nl= 4s, 5s, 6s, 4p, 5p, 3d, 4d. The calculations have used extensive configuration interaction (CI) wavefunctions, with the associated Hamiltonian matrix adjusted to ensure that the eigenenergies agree with experimental energy level data (‘fine tuning’). There are consequential small changes in the CI mixing coefficients from their ab initio values and these corrected coefficients are used in the calculation of the transition data. The method of optimization of the orbital radial functions (expressed in terms of Slater-type orbitals) is described and the radial function parameters are also presented. We show some comparisons between our work and those of earlier calculations and demonstrate how the inclusion of relativistic effects (which we achieve through the use of the Breit–Pauli approximation) can result in a substantial redistribution of the oscillator strength from the LS calculation. We also demonstrate that the fine-tuning process can make, particularly for intercombination lines, a substantial improvement in the agreement between theoretical and experimental oscillator strengths.

Spin–orbit effects on a gold-based superatom: a relativistic Jellium model

The inclusion of relativistic effects always brings to the scientific community great and stimulating surprises. To consider the spin-orbit term, which accounts for the interaction between the spatial and spin coordinates, requires the use of double point groups of symmetry in order to solve the Dirac equation or the two component approximation to it, leading to total angular momenta (j) functions, atomic or molecular spinors, instead of pure orbital angular momenta (l), atomic or molecular orbitals. Large and small components, derived from the Dirac treatment, depict wavefunctions corresponding to fermions, electrons, which are described for the first time for a superatom case. In addition, their behavior is revisited in order to clarify the effects of the inclusion of the spin-orbit coupling into the electronic structure calculations, which can be extended to other superatoms, clusters, molecules and atoms.

Exact decoupling of the relativistic Fock operator

It is generally acknowledged that the inclusion of relativistic effects is crucial for the theoretical description of heavy-element-containing molecules. Four-component Dirac-operator-based methods serve as the relativistic reference for molecules and highly accurate results can be obtained—provided that a suitable approximation for the electronic wave function is employed. However, four-component methods applied in a straightforward manner suffer from high computational cost and the presence of pathologic negative-energy solutions. To remove these drawbacks, a relativistic electron-only theory is desirable for which the relativistic Fock operator needs to be exactly decoupled. Recent developments in the field of relativistic two-component methods demonstrated that exact decoupling can be achieved following different strategies. The theoretical formalism of these exact-decoupling approaches is reviewed in this paper followed by a comparison of efficiency and results.

Electron loss from fast heavy ions: Target-scaling dependence

The target dependence for projectile electron loss is investigated using experimental data taken from the literature. Impact energies range from a few tens of eV/u to tens of MeV/u. For energies less than several MeV/u, the target dependences are shown to be very similar, independent of projectile species and charge state. Overall, however, with increasing impact energy the cross-section dependence on the target nuclear charge systematically increases. It is shown that none of the existing cross-section target scaling models reproduce these features. A model, based on Born scaling and including both the antiscreening and screening contributions to projectile electron loss, is developed. With the inclusion of relativistic effects, which increase the contribution from both channels at high energies, and ''target saturation'' effects, which reduce the contribution from the screening term for heavy targets and lower impact energies, this model describes quite reasonably all available experimental data. A simple scaling formula that reproduces the measured atomic number and impact velocity dependences is provided. This formula is applicable for projectile electron loss in collisions with either atomic or molecular targets and for impact energies ranging from a few to tens of MeV/u.

Electronic and transport properties of disordered transition‐metal alloys

AbstractWe present a first‐principles approach to describe electronic transport of disordered alloys in a material specific way. The electronic structure is represented in terms of the relativistic multiple scattering KKR‐Green function. Disorder with possible inclusion of short‐ranged order effects is taken into account by the coherent‐potential approximation or its non‐local formulation. A salient feature of the presented method is the possibility to combine it with a linear response Kubo framework, allowing for a detailed investigation of many transport phenomena which are of immediate relevance for applications in which electrons and/or their spin are manipulated. This is illustrated by several examples and developments, among them the description of the residual resistivity of K‐state‐ and ferromagnetic alloys. Inclusion of relativistic effects by using the Dirac‐formalism represents the basis to deal with the anomalous Hall effect and to derive a relativistic spin‐projection scheme for currents.

First-Principles Investigation of the Atomic and Electronic Structure and Magnetic Moments in Gold Nanoclusters

We determine the structure, energetics, and emerging magnetic propertiesof Aun clusters using first-principles plane-wave density functional theory. We compare and contrast the findings obtained with and without spin−orbit interaction in the gold clusters of sizes down to 0.5−1 nm. The shapes are chosen to be representative of spherical gold nanoparticles: (a) Au13 and Au12, with cuboctahedral, icosahedral, and decahedral structures, and (b) Au25 and Au24, with truncated octahedral structures. We find that the trends in the binding energies are unaltered with the choice of the exchange correlation (LDA or GGA) or the inclusion of relativistic effects. The cuboctahedral Au13 is found to have the lowest binding energy compared with others at a given level of theory. Within the scalar relativistic description, these gold clusters exhibit a wide variety of magnetic moments: the stability and magnetic properties can be readily understood in terms of degeneracies of the HOMO and LUMO levels. Further, there is evidence of Jahn−Teller activity in the cases of cuboctahedral Au12 and Au13 that leads to structural distortion, inducing magnetism in the 12-atom cluster. Analysis of electronic states with projection on atomic orbitals for the scalar relativistic case shows that the magnetism in these gold clusters has an sp rather than the otherwise believed s character. By employing a fully relativistic description with inclusion of spin−orbit interaction and noncollinear magnetization, the magnetic moment in the icosahedral-shaped clusters is found to reduce substantially and that in the 12- and 13-atom clusters with a cuboctahedral structure becomes vanishingly small. The loss of magnetism in Au12 and Au13 appears to originate from the splitting of degenerate HOMO states in these clusters and an overlap of the d and sp states, whereas the magnetic moment of around 1 μB in Au25 is mainly caused by the s states of the central atom.

On the efficient solution of the relativistic APW secular equation for both eigenvalues and eigenvectors

From international symposium on atomic, molecular, solidstate theory, and quantum statistics: Sanibel Island, Florida, USA (20 Jan 1974). The special problems introduced into the solution of the secular equation by the inclusion of relativistic effects are discussed. A method based on the use of linear combination of RAPW's is then described for solving the secular equation. This method greatly reduces the computer time and core space required to solve the secular problem and is particularly advantageous in large systems. (auth)

Electronic Structure and Chemical Bonding in the Lowest Electronic States of TcN

Multiconfiguration second-order perturbation theory, with the inclusion of relativistic effects and spin-orbit coupling, was employed to investigate the nature of the ground and low-lying Lambda-S and Omega states of the TcN molecule. Spectroscopic constants, effective bond order, and potential energy curves for 13 low-lying Lambda-S states and 5 Omega states are given. The computed ground state of TcN is of Omega = 3 symmetry (R(e) = 1.605 A and omega(e) = 1085 cm(-1)), originating mainly from the (3)Delta Lambda-S ground state. This result is contrasted with the nature of the ground state for other VIIB transtion-metal mononitrides, including X(3)Sigma(-) symmetry for MnN and Omega = 0(+) symmetry for ReN, derived also from a X(3)Sigma(-) state.