Relativistic Ab Initio Calculations Research Articles

Fermi surface of2H−NbSe2and its implications on the charge-density-wave mechanism

We report a detailed experimental and theoretical investigation of the Fermi-surface topology of the layered transition-metal dichalcogenide $2H\ensuremath{-}{\mathrm{NbSe}}_{2},$ which undergoes a second-order phase transition into an incommensurate two-dimensional charge-density-wave phase at 33.5 K. High-resolution angle-resolved photoemission with synchrotron radiation yields two Nb $4d$-related Fermi-surface cylinders and a Se ${4p}_{z}$-derived pocket around the center of the Brillouin zone, in good agreement with the results of fully relativistic ab initio calculations within the local-density approximation of density-functional theory. The measurements were carried out at 50 K to identify characteristic features in the electronic structure of the normal phase that can give important clues as to the origins of the phase transition, and to achieve high resolution, at the same time. The implications of our results on the charge-density-wave mechanism in $2H\ensuremath{-}{\mathrm{NbSe}}_{2}$ are discussed. Our results together with previous data from the literature seem to rule out the saddle-point mechanism, but they reveal at the same time that the driving mechanism for the transition into the charge-density-wave state is not a simple Fermi-surface nesting, as recently suggested by Straub et al. [Phys. Rev. Lett. $82,$ 4504 (1999)].

Interpretation of the spectrum of Pb(II). Theoretical transition probabilities and lifetimes

Radiative transition probabilities for 190 lines arising from the ns 2S1/2, np 2P1/2,3/2, nd 2D3/2,5/2, nf 2F5/2,7/2, and 6p2 (4P1/2,3/2,5/2, 2D3/2,5/2, 2P1/2,3/2, and 2S1/2) levels of Pb(II) have been calculated. Lifetimes of the above mentioned levels have been determined from the present transition probabilities. These values were obtained in intermediate coupling (IC) and using ab initio relativistic Hartree-Fock calculations. For the IC calculations, we use the standard method of least-square fitting of experimental energy levels by means of computer codes from Cowan. The results of calculations for radiative transition probabilities and excited states lifetimes are presented and compared with the experimental results present in the literature and with other theoretical values. There is generally good agreement between our values and the experimental data available. Analysis of the interaction shows that the level 4P5/2 of the 6s6p2 configuration presents a large contribution to the 2D5/2 level of the 6s26d configuration. This result explains the good agreement between our result and the experimental values obtained to the observed as the 6s6p2 4P5/2 – 6s 25f2F7/2 dipole-forbidden transition. PACS Nos.: 32.70^*, 32.70Fw, 32.70Cs

Many-body calculations of electric-dipole amplitudes for transitions between low-lying levels of Mg, Ca, and Sr

To support efforts on cooling and trapping of alkaline-earth atoms and designs of atomic clocks, we performed ab initio relativistic many-body calculations of electric-dipole transition amplitudes between low-lying states of Mg, Ca, and Sr. In particular, we report amplitudes for ^1P_1 --> ^1S_0, ^3S_1, ^1D_2$, for ^3P_1 --> ^1S_0, ^1D_2, and for ^3P_2 --> ^1D_2 transitions. For Ca, the reduced matrix element <4s4p, ^1P_1 ||D|| 4s^2, ^1S_0> is in a good agreement with a high-precision experimental value deduced from photoassociation spectroscopy [Zinner et al., Phys.Rev.Lett., v.85, 2292 (2000)]. An estimated uncertainty of the calculated lifetime of the (3s3p ^1P_1) state of Mg is a factor of three smaller than that of the most accurate experiment. Calculated binding energies reproduce experimental values within 0.1-0.2%.

Temperature-dependent electronicstructure, spin-resolved photoemission, and magnetic dichroism ofultrathin ferromagnetic films: Co/Cu(001)

The temperature dependences of the electronic structure,spin-resolved photoemission, and magnetic linear dichroism of theprototypical system 2 ML Co on Cu(001) (ML stands for monolayer(s))are presented in a detailed theoretical study. Relativistic ab initio electronic structure calculations were carried out withinthe framework of multiple-scattering theory; the spin-resolvedphotoemission was calculated within the one-step model. Thetemperature dependence was taken into account within the disorderedlocal moment picture.The spectral features show a distinct dispersion and broadening withtemperature, in particular those derived from quantum-well states inthe Co film. These findings can be traced back to the layer- andspin-resolved Bloch spectral function. Further, Co-derived maximain the photoemission intensities behave significantly differently withtemperature to Cu-derived ones. The spin-resolved photoemissionintensities compare well with experimental data and with theoreticaldata obtained within the fluctuating local moment picture. Magneticlinear dichroism in spin-resolved photoemission is discussed interms of asymmetries which are related to the spin polarizations.

Measurement of atomic L shell fluorescence (ω 1, ω 2, ω 3) and Auger ( a1, a2 and a3) yields for some elements in the atomic number range 59≤ Z≤85

A comprehensive set of theoretical Coster–Kronig and fluorescence yields are presented for atomic numbers 18≤ Z≤100. These quantities are based on ab initio relativistic calculations. Agreement with experimental values is fair for ω 1 and generally good for ω 2, ω 3 ( Z≥54) [1]. Therefore, atomic L shell fluorescence (ω 1, ω 2, ω 3) and Auger yields ( a 1, a 2 and a 3) for some elements in the atomic number range 59≤ Z≤85 were determined. These selected measured semi-empirical values were also fitted by least squares to polynomials in the Z of the form ∑ n a n Z n and compared with theoretical and with earlier fitted values.

Highly accurate relativistic gaussian basis sets for closed-shell atoms from He through to No

We have used the generator coordinate Dirac–Fock method for closed shell atoms, to generate accurate adapted Gaussian basis sets for ab initio relativistic self-consistent field calculations of some atoms from He ( Z=2) through to No ( Z=102). For all atoms studied, our Dirac–Fock–Coulomb and Dirac–Fock–Breit total energies are better than the corresponding ones obtained with previous larger Gaussian basis sets. Except for the Hg atom, our Dirac–Fock–Coulomb total energies are always equal to or lower than those calculated with the numerical finite-difference method (GRASP2 package). For No, we compare our Dirac–Fock–Coulomb and Dirac–Fock–Breit orbital energies with the corresponding values obtained with other approaches.

Density functional calculations of nuclear quadrupole coupling constants in the zero-order regular approximation for relativistic effects

The zeroth-order regular approximation (ZORA) is used for the evaluation of the electric field gradient, and hence nuclear quadrupole coupling constants, in some closed shell molecules. It is shown that for valence orbitals the ZORA-4 electron density, which includes a small component density (“picture-change correction”), very accurately agrees with the Dirac electron density. For hydrogen-like atoms exact relations between the ZORA-4 and Dirac formalism are given for the calculation of the electric field gradient. Density functional (DFT) calculations of the electric field gradients for a number of diatomic halides at the halogen nuclei Cl, Br, and I and at the metallic nuclei Al, Ga, In, Th, Cu, and Ag are presented. Scalar relativistic effects, spin–orbit effects, and the effects of picture-change correction, which introduces the small component density, are discussed. The results for the thallium halides show a large effect of spin–orbit coupling. Our ZORA-4 DFT calculations suggest adjustment of some of the nuclear quadrupole moments to Q(79Br)=0.30(1) barn, Q(127I)=−0.69(3) barn, and Q(115In)=0.74(3) barn, which should be checked by future highly correlated ab initio relativistic calculations. In the copper and silver halides the results with the used gradient corrected density functional are not in good agreement with experiment.

Theoretical analysis of parity-violating energy differences between the enantiomers of chiral molecules

Fully relativistic four-component electronic structure ab initio calculations including neutral current corrections are reported for a number of small chiral molecules that are of interest in the experimental search for differences in the vibrational spectra of the two enantiomers of handed molecules. The largest vibrational energy differences, of the order 0.2 Hz, are found in chiral methane derivatives which include an iodine substituent. The vibrational energy differences in CHBrClF are 7 and 2 mHz for the carbon-chlorine and carbon-fluorine stretching modes, respectively, which are 3 to 4 orders of magnitude smaller than the precision reported in recent experiments.

Performance of relativistic density functional and ab initio pseudopotential approaches for systems with high-spin multiplicities: Gadolinium diatomics GdX (X=H, N, O, F, P, S, Cl, Gd)

Gadolinium high-spin diatomics with first- and second-row elements of groups 15–17 as well as the gadolinium dimer were studied by fully relativistic density functional and scalar relativistic ab initio pseudopotential configuration interaction calculations. Bond lengths, binding energies, vibrational frequencies, dipole moments, and charge distributions are presented for the ground and low-lying excited states. In addition, the different contributions of the 4f shell to chemical bonding in wave-function-based and density-based calculations are investigated. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 359–370, 2000

Electronic structure and bonding in the platinum–silylene complex [PtSiH 2

Relativistic ab initio molecular orbital calculations have been performed on the monoligated neutral complex [PtSiH 2] in order to investigate the nature and energetics of the interaction between the metal and SiH 2 ligand. The results suggest that the silylene ligand acts as both a σ-donor and π-acceptor but is a relatively better π-acceptor. The electronic structure of [PtSiH 2] is analyzed in detail as measured by Wiberg’s bond indices, charge distributions and orbital populations.

Electronic structure and coordinate bonding nature of manganese(I) disulfur monoxide complex [MnS2O

Relativistic ab initio molecular orbital calculations have been performed on S2O and [MnS2O]+ in order to investigate the nature and energetics of the interaction between the metal and S2O ligand. The results suggest that the main bonding interactions between the fragment Mn+ and S2O is the σ and π-donative interactions and there is no π back transfer from the disulfur monoxide ligand to manganese. The interactions of π type are weaker. For the coordinated S2O moiety, the unsubstituted sulfur S2 is the electrophilic sile and the exocyclic oxygen and substituted sulfur S1 are nucleophilic sites. The electronic structure of [MnS2O]+ is analyzed in detail as measured by Wiberg's bond indices, charge distributions and orbital populations.

Relativistic ab initio and density functional theory calculations on the mercury fluorides: Is HgF4 thermodynamically stable?

Structural and energetic properties of the experimentally yet unknown gas-phase molecule mercury(IV) fluoride HgF4 have been calculated with three independent quantum-chemical approaches accounting for relativistic and electron correlation effects. All-electron 4-component density functional and scalar relativistic direct perturbation theory as well as valence-only quasi-relativistic pseudopotential calculations predict HgF4 to be thermodynamically stable by at least 19 kJ/mol with respect to HgF2 and F2, and by at least 690 kJ/mol with respect to atomization. The Hg–F bond length and the totally symmetric Hg–F stretching mode are predicted to be 1.910±0.015 Å and 565±25 cm−1, respectively. HgCl4 is predicted to be unstable with respect to HgCl2 and Cl2. The ionization potentials and excitation energies of the Hg atom and its cations are presented.

Absolute Metal−Ligand σ Bond Enthalpies in Group 4 Metallocenes. A Thermochemical, Structural, Photoelectron Spectroscopic, and ab Initio Quantum Chemical Investigation

Absolute metal−ligand σ bond enthalpies have been determined for a series of titanocene, zirconocene, and hafnocene halides and dimethyls by iodinolytic titration calorimetry. Absolute metal−iodine bond disruption enthalpies were measured by iodination of the monomeric trivalent group 4 metallocenes Cptt2TiI, (Me5C5)2TiI, Cptt2ZrI, and Cptt2HfI (Cptt = η5-1,3-di-tert-butylcyclopentadienyl). Iodinolysis of Cptt2ZrMe2 and Cptt2HfMe2 in turn yields absolute Zr−Me and Hf−Me bond enthalpies. Derived values (kcal/mol) are D[Cptt2Ti(I)−I] = 40.6(5); D[(Me5C5)2Ti(I)−I] = 52.3(6); D[Cptt2Zr(I)−I] = 58.0(5); D[Cptt2Hf(I)−I] = 61.2(4); D̄[Cptt2Zr-Me2] = 43(1); and D̄[Cptt2Hf−Me2] = 47.6(9). That D[Cptt2Zr(I)−(I)] ≈ D(I3Zr−I) and D[(Me5C5)2Ti(I)−I] ≈ D(I3Ti−I), while D[Cptt2Ti(I)−I] ≈ D(I3Ti−I) − 12 kcal/mol, argues for more reliable transferability of D(MIV−I) in sterically less congested metallocenes. The molecular structures of Cp2ttZrI2, Cp2ttZrI, and Cp2ttHfI were determined by X-ray diffraction. In Cptt2ZrI2, the Zr ligation is pseudotetrahedral, and the ring tert-butyl groups “straddle” the Zr−I bonds to minimize steric interactions. The geometry about Zr in Cptt2ZrI is pseudotrigonal, with contracted Zr−ring centroid and Zr−I distances versus Cptt2ZrI2, primarily reflecting substantially diminished ligand−ligand repulsive nonbonded interactions in the latter. Cptt2HfI is isomorphous with Cptt2ZrI, and the slightly different metrical parameters are in accord with Hf vs Zr ionic radii. The significant differences in interligand repulsive interactions in the trivalent versus tetravalent complexes are confirmed by van der Waals calculations. High-resolution UV PE spectra combined with ab initio relativistic effective core potential calculations provide details of electronic structure. Absolute ionization energy values indicate that iodine behaves as both a strong σ and π donor. Trends in the large Cp2MXn structural database can be understood in terms of the interplay between electronic and molecular structure factors, which are highly sensitive to the substitution patterns of the cyclopentadienyl ligands and, in particular, to competing σ vs π M−X bonding.

Relativistic ab initio calculations of oscillator strengths and hyperfine structure constants in Tl II

We present accurate calculations of oscillator strengths and hyperfine structure splitting for a set of transitions in Tl II, and discuss how they can be used in stellar atmosphere models of chemically peculiar stars. The results are in good agreement with recent experiments. The predicted uncertainty for oscillator strengths ranges from about 5 to 20% and in most cases less than 10% for hyperfine structure constants.

Fine-structure effects in the antisymmetric stretching vibrational spectrum of FeH2 and FeD2

Relativistic ab initio calculations have been performed for the 5Δ, 5Π, and 5Σ+ electronic states of iron dihydride. We have determined potential energies along the antisymmetric stretching coordinate and coupling matrix elements including spin-orbit and rotational interactions. Vibrational excitation energies are in good agreement with recent gas phase experiments. We determine a first-order spin-orbit parameter of A SO,e = −104.2cm-1 in the 5Δ ground state with the fine-structure splitting only slightly reduced by higher-order spin–orbit interaction with the 5Π and 5Σ+ states. The higher-order effects are found to be mass dependent resulting in different spin–orbit splittings for FeH2 and FeD2. The 5Π and 5Σ+ states are strongly coupled by both spin-orbit and rotational interaction rendering the definition of a first-order spin-orbit parameter for the 5Π state meaningless.

Ab initio relativistic all-electron calculation of the Ar–I2 ground state potential

Correlated relativistic all-electron supermolecular ab initio calculations of the ground state potential of the Ar–I2 molecule are presented. The role of differential intramonomer spin–orbit and correlation effects in the interaction energy is investigated and found to be only of minor importance. Two energetically very similar minima of the Ar–I2 complex are found, corresponding to a linear and a T-shaped geometry of the monomers. The comparatively large isomerization barrier for the two conformations indicates the existence of two stable isomers at very low temperatures.

Energetics of Metal−Ligand Multiple Bonds. A Combined Solution Thermochemical and ab Initio Quantum Chemical Study of MO Bonding in Group 6 Metallocene Oxo Complexes

In this paper, we report a synthetic, molecular structure, thermochemical, and ab initio Hartree−Fock/Moller−Plesset level study of bonding and bonding energetics in the group 6 metallocene oxo series Cp2Mo/(MeCp)2MO, M = Cr, Mo, W. Efficient, high-yield syntheses of the pairs Cp2MH2/(MeCp)2MH2, Cp2MCl2/(MeCp)2MCl2, and Cp2MO/(MeCp)2MO where M = Mo or W are reported. The molecular structure of (MeCp)2WO features a “bent sandwich” geometry with a WO distance of 2.04(1) A and an average WC(Cp) distance of 2.371(8) A. Thus, WC(Cp) exhibits a ∼0.07 A elongation over the corresponding distance in typical Cp2WX2 complexes and a WO distance which appears to be elongated versus what might be expected for a formal triple bond. D(MO) values obtained from (MeCp)2MO silanolytic (Me3SiCl, Me3SiI) batch titration calorimetry are very large: 110(11) kcal/mol (M = Mo) and 132(10) kcal/mol (M = W). The corresponding D(WOTMS) value is determined to be 65(18) kcal/mol. Ab initio relativistic core potential calculations rev...

Relativistic study of nuclear magnetic shielding constants: tungsten hexahalides and tetraoxide

Relativistic ab initio calculations of the 183W magnetic shielding constant and the chemical shift of WX 6(X = F and Cl) and WO 4 2− are presented. The computational method is a combination of the relativistic spin-free no-pair theory and the spin-orbit unrestricted Hartree-Fock method, which has been applied previously to 199Hg magnetic shielding constants. The spin-tree relativistic (SFR) terms, involving the mass velocity and Darwin terms, are shown to be important for 183W shielding constants. The spin-orbit interaction, which is smaller than the SFR term, works differently on WCl 6 and WO 4 2−. The effects of relaxing the inner s and p orbitals of W are investigated.

Relativistic study of nuclear magnetic shielding constants: mercury dihalides

Relativistic ab initio calculations of the 199Hg nuclear magnetic shielding constant and the chemical shift of HgX 2 (XCl, Br, I) are presented. The method is a combination of the relativistic spin-free no-pair theory of Sucher and Hess and the spin-orbit unrestricted Hartree-Fock (SO-UHF) method reported previously. For the 199Hg shileding constant, both the spin-free relativistic (SFR) term, like mass-velocity and Darwin terms, and the SO term are important and they strongly couple with each other. Without them the experimental trend in mercury dihalides cannot be explained even qualitatively. Since these relativistic terms stabilize the orbitals closer to the nucleus, a basis set having larger freedom near the nucleus is appropriate.

Electronic Structure and Photoelectron Spectroscopy of the Monomeric Uranium(III) Alkyl [η5-(CH3)5C5]2UCH[Si(CH3)3]2,

The ground state configuration and the electronic structure of the title compound have been investigated by relativistic effective core potential configuration interaction ab initio calculations and He I/He II UV photoelectron spectroscopy. It has been found that the 4A‘‘ [(a‘)1 (a‘‘)1 (a‘)1] state, associated with the 5f3 uranium configuration, represents the molecular ground state and is close in energy to the higher-lying 4A‘‘ (5f2 6d1) state. The comparison of the present photoelectron data and theoretical results with those reported for analogous lanthanide complexes indicates close similarities in metal−ligand bonding between the 4f and 5f M(III) organometallics. The relative stability of the 5f3 versus 5f2 6d1 uranium ion configuration correlates with the inherent chemical stability of U(III) organometallics, compared to that of the Th(III) (6d1) analogues. The easier M(IV) → M(III) reduction for U(IV) relative to Th(IV), the numerous examples of reductive elimination processes in U(IV) organometallic chemistry, and the greater Th−R versus U−R experimental homolytic bond disruption energies in cyclopentadienylactinide(IV) alkyls can all be rationalized in terms of the differing electronic stabilities of the U(III) and Th(III) ground states.