Inclusion Of Relativistic Effects Research Articles

Comparativeab initiostudies on the molecular structure and spectroscopic properties of FeF2: Single reference versus multireference methods

The electronic excitation energies, molecular geometry, quadratic force fields, and vibrational frequencies in the ground (5)Delta(g) and low-lying excited (5)Sigma(g) (+) and (5)Pi(g) electronic states of iron difluoride are studied at sophisticated levels of theory. Two families of basis sets, nonrelativistic and Douglas-Kroll-Hess relativistic, are used that range in quality from triple-zeta to quintuple-zeta. These are augmented by additional diffuse functions (on fluorine atoms) and tight functions (on all atoms) for the description of core-valence correlation and utilized to determine complete basis set molecular properties. The quality of electron correlation treatment using conventional single reference coupled cluster methods CCSD and CCSD(T) is compared to that attained at the multiconfigurational quasidegenerate second-order perturbation theory (CASSCF+MCQDPT2) and the electron attachment equation-of-motion coupled cluster (EOMEA-CCSD) levels. Spin-orbit coupling effects are studied by the SO-MCQDPT2 method using the full Breit-Pauli spin-orbit operator. Effects of spin contamination in the coupled cluster molecular calculations are carefully analyzed. Results of the single reference CCSD(T) and multireference calculations are found to be in a remarkable agreement. The calculations indicate that the EOMEA-CC approach provides a suitable tool for an accurate treatment of FeF(2) and other systems where delicate electron correlation effects have to be carefully dealt with. The inclusion of relativistic effects is shown to be necessary for an accurate description of the molecular geometry and excitation energies of FeF(2). The results of calculations are in good agreement with the experimental data available. The predicted FeF(2) molecular properties are compared to those of the related FeF(3).

Calculations of nuclear quadrupole coupling in noble gas–noble metal fluorides: Interplay of relativistic and electron correlation effects

The nuclear quadrupole coupling constants (NQCCs) of noble gas and noble metal nuclei in the recently found noble gas-noble metal fluorides (NgMF, where Ng=Ar,Kr,Xe and M=Cu,Ag,Au) are obtained theoretically by high-level ab initio calculations, where both relativistic and electron correlation effects are included, and compared to experimental results. Fully relativistic four-component Dirac-Hartree-Fock (DHF) calculations are carried out at the basis set limit for electric field gradient that couples with the electric quadrupole moment of the nucleus, and uncorrelated relativistic effects are extracted by comparing DHF results to nonrelativistic (NR) HF calculations. Electron correlation effects are investigated both at fully relativistic second-order Moller-Plesset (DMP2) and at NR MP2 levels of theory, as well as at the NR coupled-cluster singles and doubles with perturbational triples [CCSD(T)] level. The validity of the approximation where relativistic effects, on the one hand, and nonrelativistically obtained correlation effects, on the other hand, are evaluated separately and assumed to be additive, is investigated by comparison with the DMP2 results. Inclusion of relativistic effects is shown to be necessary for obtaining the correct NQCC trends as the nucleus of interest and/or its neighbors become heavier. Electron correlation treatment is needed for approaching quantitative agreement with the experimental NQCCs. The assumption of additive electron correlation and relativistic effects, corresponding to the NR correlation treatment added on top of relativistic DHF data, gives qualitatively correct noble gas NQCCs. For noble metal NQCCs, correlation treatment at the relativistic level of theory is mandatory for reaching agreement with experimental results. Current work also confirms the experimental trends of NQCCs, which have been taken as an indication of nearly covalent interaction between noble gas and noble metal in the heaviest present systems, especially in XeAuF.

Explicitly correlated potential energy surface of , including relativistic and adiabatic corrections

After a short historical account of the theory of the H3+ ion, two ab initio methods are reviewed that allow the computation of the ground-state potential energy surface (PES) of H3+ in the Born-Oppenheimer (BO) approximation, with microhartree or even sub-microhartree accuracy, namely the R12 method and the method of explicitly correlated Gaussians. The BO-PES is improved by the inclusion of relativistic effects and adiabatic corrections. It is discussed how non-adiabatic effects on rotation and vibration can be simulated by corrections to the moving nuclear masses. The importance of the appropriate analytic fit to the computed points of the PES for the subsequent computation of the rovibronic spectrum is addressed. Some recent extensions of the computed PES in the energy region above the barrier to linearity are reviewed. This involves a large set of input geometries and the correct treatment of the dissociation asymptotics, including the coupling with the first excited singlet state. Some comments on this state as well as on the lowest triplet state of H3+ are made. The paper ends with a few remarks on the ion H5+.

An NMR and relativistic DFT investigation of one-bond nuclear spin–spin coupling in solid triphenyl group-14 chlorides

A solid-state nuclear magnetic resonance and zeroth-order regular approximation density functional theory, ZORA-DFT, study of one-bond nuclear spin-spin coupling between group-14 nuclei and quadrupolar 35/37Cl nuclei in triphenyl group-14 chlorides, Ph3XCl (X = C, Si, Ge, Sn and Pb), is presented. This represents the first combined experimental and theoretical systematic study of spin-spin coupling involving spin-pairs containing quadrupolar nuclei. Solid-state NMR spectra have been acquired for all compounds in which X has a spin-1/2 isotope--13C, 29Si, [117/119]Sn and 207Pb-at applied magnetic fields of 4.70, 7.05 and 11.75 T. From simulations of these spectra, values describing the indirect spin-spin coupling tensor-the isotropic indirect spin-spin coupling constant, 1J(X, 35/37Cl)iso and the anisotropy of the J tensor, Delta1J(X, 35/37Cl)--have been determined for all but the lead-chlorine spin-pair. To better compare the indirect spin-spin coupling parameters between spin-pairs, 1J(iso) and Delta1J values were converted to their reduced coupling constants, 1K(iso) and Delta1K. From experiment, the sign of 1K(iso) was found to be negative while the sign of Delta1K is positive for all spin-pairs investigated. The magnitude of both 1K(iso) and Delta1K was found to increase as one moves down group-14. Theoretical values of the magnitude and sign of 1K(iso) and Delta1K were obtained from ZORA-DFT calculations and are in agreement with the available experimental data. From the calculations, the Fermi-contact mechanism was determined to provide the largest contribution to 1K(iso) for all spin-pairs while spin-dipolar and paramagnetic spin-orbit mechanisms make significant contributions to the anisotropy of K. The inclusion of relativistic effects was found to influence K(Sn,Cl) and K(Pb,Cl).

A Computational and Experimental Study of the Structures and Raman and 77Se NMR Spectra of SeX3+ and SeX2 (X = Cl, Br, I): FT-Raman Spectrum of (SeI3)[AsF6

The ability of MP2, B3PW91 and PBE0 methods to produce reliable predictions in structural and spectroscopic properties of small selenium-halogen molecules and cations has been demonstrated by using 6-311G(d) and cc-pVTZ basis sets. Optimized structures and vibrational frequencies agree closely with the experimental information, where available. Raman intensities are also well reproduced at all levels of theory. Calculated GIAO isotropic shielding tensors yield a reasonable linear correlation with the experimental chemical shift data at each level of theory. The largest deviations between calculated and experimental chemical shifts are found for selenium-iodine species. The agreement between observed and calculated chemical shifts for selenium-iodine species can be improved by inclusion of relativistic effects using the ZORA method. The best results are achieved by adding spin-orbit correction terms from ZORA calculations to nonrelativistic GIAO isotropic shielding tensors. The calculated isotropic shielding tensors can be utilized in the spectroscopic assignment of the 77Se chemical shifts of novel selenium-halogen molecules and cations. The experimental FT-Raman spectra of (SeI3)[AsF6] in the solid state and in SO2(l) solution are also reported.

A Theoretical Investigation of One-Bond Phosphorus−Phosphorus Indirect Nuclear Spin−Spin Coupling Tensors, 1J(31P,31P), Using Density Functional Theory

In the present study, one-bond 3 1 P, 3 1 P indirect nuclear spin-spin coupling tensors, 1 J( 3 1 P, 3 1 P), are calculated using nonrelativistic and relativistic zeroth-order regular approximation (ZORA) density functional theory (DFT) methods for the following model molecules and ions: P 2 , cis-MeP=PMe, trans-RP=PR (R = H, Me, Ph), (cis-η 1 -PhP=PPh)Cr(CO) 5 , (cis- and trans-η 1 -MeP=PMe)Cr(CO) 5 , H 2 P-PH 2 , H 2 P-PF 2 , cis- and trans-diphosphetes, a phosphole tetramer, [O 3 P-PO 3 ] 4 - , [HO 3 P-PO 3 H] 2 - , [FO 2 P-PO 2 F] 2 - , Me 2 (S)P-P(S)Me 2 , [MeN≡P-PMe 3 ] + , and Me 3 P-PF 5 . These compounds have been chosen because the values of 1 J( 3 1 P, 3 1 P) i s o in these systems vary from approximately -480 to +770 Hz, thereby spanning the known range of experimentally measured one-bond 3 1 P, 3 1 P indirect nuclear spin-spin coupling constants. However, in many cases, the sign of 1 J( 3 1 P, 3 1 P) i s o has not been determined by experiment. Our DFT results for 1 J( 3 1 P, 3 1 P) i s o and the anisotropy of J are in qualitative agreement with experimental values; furthermore, our calculations provide the absolute sign of 1 J( 3 1 P, 3 1 P) i s o in cases where it is unknown experimentally. A number of empirical trends between 1 J( 3 1 P, 3 1 P) i s o and various structural parameters have been reproduced by our calculations. Inspection of the mechanisms which contribute to 1 J( 3 1 P, 3 1 P) i s o indicates that the Fermi contact (FC) mechanism dominates in all cases where formal single P,P bonds exist and that the paramagnetic spin-orbit mechanism is of equal or greater importance in comparison with the FC mechanism in cases where formal multiple P,P bonds exist. Results from relativistic ZORA DFT calculations differ from the nonrelativistic calculations by less than 10%, indicating that inclusion of relativistic effects is not crucial, as anticipated, given that the systems investigated herein contain relatively light atoms (Z ≤ 24).

Expectation values ofrqbetween Dirac and quasirelativistic wave functions in the quantum-defect approximation

A search is conducted for the determination of expectation values of r{sup q} between Dirac and quasirelativistic radial wave functions in the quantum-defect approximation. The phenomenological and supersymmetry-inspired quantum-defect models, which have proven so far to yield accurate results, are used. The recursive structure of formulas derived on the basis of the hypervirial theorem enables us to develop explicit relations for arbitrary values of q. Detailed numerical calculations concerning alkali-metal-like ions of the Li, Na, and Cu isoelectronic sequences confirm the superiority of supersymmetry-based quantum-defect theory over quantum-defect orbital and exact orbital quantum number approximations. It is also shown that relativistic rather than quasirelativistic treatment may be used for consistent inclusion of relativistic effects.

Relativistic effects in lanthanides and actinides

The Judd–Ofelt theory of f↔f transitions was originally developed as a non-relativistic theory nearly 40 years ago. Modifications to include the effects of spin–orbit effects have been developed by various researchers. The inclusion of relativistic effects both for the Judd–Ofelt theory of intensities and for crystal field effects has been hindered, until recent times, by the lack of adequate relativistic radial integrals. It is now possible to obtain reliable relativistic integrals and we show how both the Judd–Ofelt theory and crystal field theory may be modified to accommodate relativistic effects. These extensions involve new effective operators. We include some historical remarks on the development of the Judd–Ofelt theory.

Orbital and dipolar contributions to the hyperfine fields in bulk bcc Fe, hcp Co, and at the Fe/Ag(100) interface: The inclusion of orbital polarization

First-principles calculations can make quantitative predictions of many properties of solids including magnetic hyperfine fields (hf). The inclusion of relativistic effects becomes important in this case. We have selected to study three systems in order to assess the importance of orbital and dipolar contributions to the Bhf and its anisotropies: bulk bcc Fe, hcp Co, and the Fe/Ag~100! interface. For the last two, in-plane ~parallel to the hexagonal planes and to the interface, respectively! and perpendicular magnetizations were considered. The influence of different exchange-correlation potentials ~local density and generalized gradient approximation! and the inclusion of the orbital polarization term ~known to improve the evaluation of orbital moments! in the Hamiltonian is reported. A comparison is made with other theoretical studies and to experiment when possible.

Accelerated electrons as the source of Auroral Kilometric Radiation

Data from the Fast Auroral Snapshot Explorer (FAST) have confirmed that Auroral Kilometric Radiation (AKR) is generated by the accelerated electrons in the auroral density cavity. FAST observations of the electron distribution within the AKR source region show a characteristic horse-shoe distribution expected from the parallel electric field acceleration and magnetic mirroring of the electrons, the precipitating portion of which constitute the auroral electrons. Within the density cavity it is likely that the hot electrons carry most, if not all, of the plasma density. The AKR wave characteristics within the source region show that the lower frequency cut-off is below the cold electron gyro-frequency, and near the cut-off, the wave electric and magnetic field polarization is consistent with perpendicularly propagating X-mode waves. Taken together these observations are consistent with the cyclotron maser instability, but with the inclusion of relativistic effects in the wave dispersion, as well as the resonance condition. This allows the accelerated electrons to generate AKR, and further the replenishment of the distribution by the parallel electric field ensures that AKR can be generated over a large altitude range on auroral zone field lines

RelativisticRmatrix with pseudostates calculations for electron scattering from cesium atoms

The R matrix with pseudostates (RMPS) method was used with inclusion of relativistic effects to calculate differential cross sections and several spin asymmetries for elastic electron scattering from Cs atoms in the theoretically most difficult ``intermediate energy regime'' between one and five times the ionization threshold. Comparison of the RMPS predictions with experimental benchmark data for 7, 13, and 20 eV is satisfactory, thereby indicating the applicability of the method to collision systems involving heavy targets. Furthermore, justification for the apparent success of nonrelativistic calculations for the differential cross sections and the exchange asymmetry is given.

Trends in back-bonding in the series trans-[M(CCR)Cl(PH 3) 4] (M=Fe, Ru, Os; R=H, Ph, C 6H 4NO 2-4)

The electronic structure of the complexes trans-[M(CCR)Cl(PH 3) 4] (M=Fe, Ru, Os; R=H, Ph, C 6H 4NO 2-4) has been investigated using approximate density functional theory in order to examine the MC back-bonding interaction. For all three metal systems, the π back-bonding increases in the order R=H<Ph<C 6H 4-4-NO 2, indicating that the π acceptor character of the acetylide ligand increases with the electron-withdrawing ability of the substituent. The inclusion of relativistic effects in the calculations results in a metal dependence of Fe∼Ru<Os for the back-bonding, consistent with the observed trend in quadratic hyperpolarizabilities, β.

Inclusion of relativistic effects in Gaussian-basis density functional calculations for extended systems

Non-perturbative calculation of the scalar relativistic contributions to the density functional total energy and one-electron energies of extended systems until recently has been via exploitation of the features of cellular basis sets (the Koelling–Harmon scheme and cousins) to achieve the decoupling of large and small components. Cellular basis sets are relatively uncommon in quantum chemistry codes; Gaussian-type orbitals are the de facto standard. Among the various order-by-order decouplings used for molecular calculations in quantum chemistry, the Douglas–Kroll transformation has advantages which have brought it to prominence. Here we review the first extension of that procedure to an all-electron, linear combination of Gaussian-type-orbitals, fitting function (LCGTO-FF) methodology for DFT calculations on crystals and ordered films. To show the power and accuracy of the method, we summarize results for Au, Mo, Th, and Pu. In general, values from the Gaussian methodology and from cellular-basis, all-electron, scalar-relativistic density functional codes are essentially indistinguishable. In every case of a difference compared to previously published results, the prediction of the Gaussian methodology has been confirmed by an independent high-quality cellular-based calculation. These outcomes verify that, for the first time, a single, consistent, systematic, first-principles, all-electron, full-potential DFT technique is available for prediction of the properties of complex crystalline, slab, ordered polymer, and cluster/molecule systems that contain heavy elements, all devoid of potentially troublesome algorithmic inconsistencies.

The Adiabatic Exponent in the Solar Core

We present helioseismic inversions of solar p-mode frequencies obtained by the Michelson Doppler Imager instrument of the Solar Oscillation Investigation project on board SOHO, which indicate a lower central value for the adiabatic exponent Γ1 in the Sun than in current models. We show how the inclusion of relativistic effects in the equation of state removes the discrepancy and allows almost perfect agreement in Γ1 between the models and the Sun. This increases our confidence both in the reliability of the equation-of-state calculation and the determination of solar p-mode frequencies.

Precipitation of magnetospheric electrons caused by relativistic effect‐enhanced chaotic motion in the whistler wave fields

In the magnetosphere, energetic electrons in the radiation belts are trapped by the Earth's dipole magnetic field and undergo bounce motion about the geomagnetic equator. It is shown that the trajectories of some of the trapped particles can in the presence of a whistler wave become chaotic and wander into the loss cone. Comparing the surface of section plots obtained from the both relativistic equations of motion and from the nonrelativistic ones, the effect of the relativistic correction to the electron motion are shown. The threshold field for the commencement of chaos in the trajectories of electrons with energies of a few hundred keV is found to be lowered by the inclusion of relativistic effects by about an order of magnitude. Waves with these smaller magnetic field amplitudes (about 1% of the geomagnetic field) have been observed propagating between hemispheres. Since this chaotic scattering process does not have a directional preference, it offers a plausible explanation for the simultaneous observation of electron precipitation into the upper atmosphere at geomagnetically conjugate regions because of a single lightning flash [Burgess and Inan, 1990].

Theoretical study of the metathesis-like reaction between ditungsten hexaalkoxides and alkynes †

Density-functional calculations have been carried out on a metathesis-like reaction between W2(OR)6 (R = alkyl) and alkynes to give tungsten alkylidyne complexes. Two possible pathways have been taken into consideration: (i) a parallel approach between the reactants to give 1,2-ditungstenacyclobutadiene; (ii) a perpendicular approach to yield a ditungstenatetrahedrane which then flattens giving a 1,3-ditungstenacyclobutadiene. The electronic structure of the compounds involved in the reaction, as well as several energy profiles corresponding to the formation and decomposition of these species, have been investigated in order to study the thermodynamics and kinetics of the metathesis-like reaction. The inclusion of relativistic effects is crucial in order to understand how the reaction proceeds.

The structure of dichromium tetraformate

Second-order perturbation theory (CASPT2) calculations using large basis sets have been used to study the CrCr bond in dichromium tetraformate, Cr 2(O 2CH) 4 The CrCr potential was found to have a double minimum with one short equilibrium at 1.94 Å, exhibiting considerable 3d-3d bonding, and a long equilibrium at 2.50 Å, which is essentially determined by the structure of the bridging ligands. The energy difference between the two minima is small (of the order of 0.1 eV) and the relative order depends on the level of theory used. Inclusion of relativistic effects and 3s,3p correlation (estimated from the corresponding effect in the 3 Σ u + state of Cr 2 locates the inner minimum 0.07 eV below the outer. The measured distance in Cr 2(O 2CCH 3) 4 is 1.966 Å. It is likely that addition of axial ligands like water will make the outer minimum more stable, thus explaining the variations in Cr{inCr} distances in dichromium complexes. The DFr approach is also applied and long, 2.296 and 2.487 \\rA, CrCr bond distances are found for Cr{in2}(O{in2}CH){in4} and Cr{in2}(O{in2}CCH{in3}){in4}, respectively. Addition of axial water ligands increases the CrCr distance by about 0.19 and 0.07 \\rA, respectively, for these two systems.

Core and valence spectra of TaS2 and WS2. Experimental and theoretical studies

The study of two dichalcogenides 1T-TaS2 and 2H-WS2 by X-ray photoelectron spectroscopy is described with an investigation of both core and valence spectra. A theoretical model has been used (MSXα method) with inclusion of relativistic effects in order to describe precisely the electronic structure of the two disulfides.

The 4s2 1S0 -4s4p 3P1o intercombination line in the zinc-like ions: Ga II, Kr VII, Sr IX, Nb XII, Mo XIII, Rh XVI and Ag XVIII

Transition probabilities are calculated for the 4s2 1S0 -4s4p 3P1o intercombination line in the zinc-like ions Ga II, Kr VII, Sr IX, Nb XII, Mo XIII, Rh XVI and Ag XVIII using the configuration interaction (CI) code CIV3. The calculation involves valence shell correlation, use of model potentials to account for core polarization and the inclusion of relativistic effects. Adjustments are made to the diagonal elements of the Hamiltonian matrix so that eigenvalue differences agree with experimental energy differences, so effectively experimental energies are used for transition energies and to refine the CI mixing coefficients of the wave functions. Both the A-values and the lifetimes of the transition for the various ions are compared with recent experimental and other theoretical results. The present results are sufficiently accurate to provide a benchmark for the analysis of the experimental data.

The self-consistent fully relativistic SKKR Green function method: applications to the (100), (110) and (111) surfaces of Au and Pt

The fully relativistic version of the screened Korringa-Kohn-Rostoker (SKKR) method is discussed and applied charge self-consistently to the (100), (110) and (111) surfaces of Au and Pt. In comparison to corresponding semi-relativistic calculations for Au it is found that spectral densities depend very crucially on the inclusion of relativistic effects. In terms of work functions, however, the difference between the semi-relativistic and the relativistic calculations is rather small.