Electron Relativistic Effects Research Articles

Plane-wave pseudopotential study of the light actinides

Norm conserving pseudopotentials have been generated for the light actinides (Th-Np) and the plane waves + pseudopotential formalism has been used to study their crystal structures at zero temperature as a function of pressure. The often complex alpha phases of these elements have been fully relaxed, and we have used a thorough treatment of spin-orbit coupling. The zero-pressure zero-temperature equilibrium volumes and bulk moduli are consistent with previous all-electron full-potential calculations, and, up to uranium, in excellent agreement with experiment. This is also the case for cell parameters and pressure-induced phase transitions. It is likely that, from neptunium on, a more careful treatment of electronic correlations and/or relativistic effects is necessary to reproduce the experimental data with the same precision.

Plane-wave pseudopotential study on mechanical and electronic properties for IV and III-V crystalline phases with zinc-blende structure

Norm conserving pseudopotentials have been generated for the light actinides (Th-Np) and the plane waves + pseudopotential formalism has been used to study their crystal structures at zero temperature as a function of pressure. The often complex alpha phases of these elements have been fully relaxed, and we have used a thorough treatment of spin-orbit coupling. The zero-pressure zero-temperature equilibrium volumes and bulk moduli are consistent with previous all-electron full-potential calculations, and, up to uranium, in excellent agreement with experiment. This is also the case for cell parameters and pressure-induced phase transitions. It is likely that, from neptunium on, a more careful treatment of electronic correlations and/or relativistic effects is necessary to reproduce the experimental data with the same precision.

The influence of electron correlation and relativistic effects on the valence shellphotoelectron spectrum of iodothiophene

The valence shell photoelectron spectrum of 2-iodothiophene (2-I-Th) hasbeen studied experimentally and calculations have been carried out tocharacterize the main bands due to single-hole ionized states for both2- and 3-iodothiophene. The importance of electron correlation in theformation of satellite states has also been assessed. The vertical ionizationenergies and spectral intensities of the entire valence shell photoelectronspectrum have been computed using the third-order algebraic–diagrammaticconstruction approximation for the one-particle Green function. These theoreticalpredictions have allowed assignments to be proposed for all the prominentstructure observed in the experimental spectra, and have highlightedthe breakdown of the molecular orbital model of ionization for the π1-orbital.By comparing the present theoretical and experimental results for iodothiophenewith similar data for chloro-and bromothiophene, it has been found that thebinding energies and intensities of the satellites associated with the π1-orbitalform a pattern which is common to all three monohalothiophenes. RelativisticHartree–Fock calculations have been carried out to investigate the importance ofsuch effects on the valence shell ionization of iodothiophene. Synchrotron radiationhas been used to measure photoelectron angular distributions and branching ratios of2-I-Th. The spectral behaviour of the asymmetry parameters has provided anexperimental means of distinguishing photoelectron bands due to σ-orbitals from thoseassociated with π-orbitals.A high-resolution photoelectron spectrum of the outer valence shell of 2-I-Th hasbeen recorded using HeI radiation, and vibrational structure has been observed andanalysed in the X̃ 2A′′, Ã 2A′′, B̃ 2A′ and C̃ 2A′′state bands.

Fully relativistic coupled-cluster static dipole polarizabilities of the positively charged alkali ions from Li+ to 119+

The static dipole polarizabilities of the positively charged alkali atoms from Li+ to 119+ (eka-Fr) were obtained from relativistic coupled-cluster theory using a scalar relativistic Douglas–Kroll Hamiltonian. Spin–orbit coupling effects were obtained from a fully relativistic four-component Dirac–Hartree–Fock scheme followed by a second-order many-body perturbation treatment to account for electron correlation. Electron correlation effects are found to be small for all ions, but become more sizable as the nuclear charge increases. Scalar relativistic effects dominate over electron correlation for Cs+, Fr+, and 119+. Spin–orbit coupling is non-negligible for the heaviest elements Fr+ and 119+, where they dominate over both electron correlation and scalar relativistic effects. Breit interactions obtained for Cs+ and Fr+ can safely be neglected. A relationship between dipole polarizabilities and second ionization potentials is established. The use of a basis set limit one-electron description and a high level treatment of electron correlation and relativistic effects makes our results the most accurate available for the stable dipole polarizabilities (1.00±0.04 a.u. for Na+, 5.52±0.04 a.u. for K+, 9.11±0.04 a.u. for Rb+, 15.8±0.1 a.u. for Cs+, 20.4±0.2 a.u. for Fr+, and 32±1 a.u. for 119+).

Ab initio rotation–vibration energy levels of triatomics to spectroscopic accuracy

The factors that need to be taken into account to achieve spectroscopic accuracy for triatomic molecules are considered focusing on H 3 + and water as examples. The magnitude of the adiabatic and non-adiabatic corrections to the Born–Oppenheimer approximation is illustrated for both molecules, and methods of including them ab initio are discussed. Electronic relativistic effects are not important for H 3 +, but are for water for which the magnitude of the various effects is discussed. For H 3 + inclusion of rotational non-adiabatic effects means that levels can be generated to an accuracy approaching 0.01 cm −1; for water the error is still dominated by the error in the correlation energy in the electronic structure calculation. Prospects for improving this aspect of the calculation are discussed.

Theoretical study of electron correlation and relativistic effects on spectroscopic constants of hydrogen halides HX (X=F, Cl, Br, I)

Analytical computations of the first-order relativistic correction in the framework of direct perturbation theory (DPT) have recently become available at the level of coupled cluster theory with singles and doubles excitations (CCSD). At this level, large-scale calculations were performed on the hydrogen halides HX (X=F, Cl, Br, I) including core- and core-valence correlation effects and a perturbative correction for connected triples excitations [CCSD(T)]. Potential energy curves were computed and spectroscopic constants (re, ωe, ωexe, Be) were derived.

Theoretical study of valence photoelectron spectrum of OsO4: A spin-orbit RESC-CASPT2 study

The valence photoelectron spectrum (bands from A to E) of OsO4 is studied by second-order complete active space perturbation theory (CASPT2). The relativistic effects are included by the relativistic elimination of the small components (RESC) scheme. Spin-orbit coupling is also considered. Both the electron correlation and relativistic effects are significant on the peak position and intensity of valence photoelectron spectrum of OsO4. RESC-CASPT2 gives values for the peak position and intensity in reasonable agreement with the resolved photoelectron spectrum data. The state ordering is predicted as T12(1t1)>2T2(3t2)>2A1(2a1)>2T2(2t2)>2E2(1e). Electron correlation shifts all peak positions by 2.5–3.5 eV to the high-energy side. Spin-free relativistic effects shift the band D by 0.8 eV again to the high-energy side due to the stabilization of Os 6s orbital. The present study confirms that the band C arises from the spin-orbit coupling in the ionic T22(3t2) state. Under the E band, there are many two-electron shake-up peaks in addition to the two one-electron ionization peaks. The broad feature of the E band is due to the satellite peaks and can be well explained through the introduction of the relativistic effects.

The correlation, relativistic, and vibrational contributions to the dipole moments, polarizabilities, and first and second hyperpolarizabilities of ZnS, CdS, and HgS

The dipole moments, dipole polarizabilities, and the first and second hyperpolarizabilities of the Group IIb sulfides have been calculated by using different high-level-correlated methods and including both the relativistic and vibrational contributions. The electron correlation effects have been studied at the levels of the second-order Møller–Plesset perturbation theory and the coupled-cluster methods. The relativistic contributions and the interference relativistic-correlation effects have been accounted for by using the spin-averaged Douglas–Kroll approximation. The vibrational properties (pure vibrational contributions and the zero-point vibrational averaging corrections) have been computed using CCSD(T) theory with and without relativistic corrections. The present pure electronic nonrelativistic results exhibit essentially the same pattern as that observed for similar molecules studied earlier. Most of the relativistic effects on dipole moments and dipole polarizabilities is accounted for at the level of the SCF approximation and rapidly increases with the nuclear charge of the heavy atom. The contribution of the relativistic-correlation interference terms has been found to be quite significant for axial components of the first and second dipole hyperpolarizabilities. All the properties reported here are static. This is the first study which reports on the relativistic contributions to hyperpolarizabilities as well as on vibrational effects upon both polarizabilities and hyperpolarizabilities of heavy metal (Group IIb) involving compounds. Thus the reported results add to the knowledge and understanding of the importance of the electron correlation, relativistic, and vibrational effects on electric properties of heavy molecules and extend the corresponding data beyond the linear response approximation. The reliability of the computed data is discussed in terms of the underlying approximations and limitations of methods used in this study.

Electron correlation and relativistic effects in electric properties of the alkali metal fluorides

The major electric properties in the series of the alkali metal fluorides are calculated with the purpose of investigating the electron correlation and relativistic contributions. The reported results for KF, RbF, CsF, and FrF correspond to three different levels of approximation concerning the treatment of the electron correlation contribution to the investigated properties. The relativistic effects are studied by using the scalar Pauli approximation and the Douglas—Kroll method. The calculated dipole moments are in agreement with available experimental data. In the case of the quadrupole moment of KF, the discrepancy between the experimental and theoretical values is interpreted in favour of the theoretical result. The electron correlation contribution to electric properties of the alkali metal fluorides is relatively small. The only truly ‘relativistic’ molecule in the series is FrF. Both the electron correlation and relativistic contributions to dipole and quadrupole moments and dipole polarizabilities in this series of ionic diatoms can be qualitatively interpreted in terms of a very simple model of polarizable charges.

Electron correlation and relativistic effects in electric properties of the alkali metal fluorides

Electron correlation and relativistic effects in electric properties of the alkali metal fluorides

Ab initio calculations on cis-[ PtCl2(PMe3)2] : Search for a model chemistry for platinum(II) complexes

The capacity of Hartree-Fock (HF), Moller-Plesset second order perturbation (MP2), and density functional (DF) calculations to predict the experimental dipole moment and the metal-ligand bond lengths of a planar platinum(II) complex, cis-[ PtCl2 (PMe3 )2 ] , was investigated. Highly erroneous results were obtained from uncorrelated HF calculations and from MP2 and DF calculations which included the 5s and 5p electrons of platinum in a frozen core or in an effective core potential. DF calculations including these (n-1)s and (n-1)p electrons in the valence space are shown to have the ability to correctly reproduce the platinum-ligand bond lengths and the dipole moment, provided that sufficiently large basis sets including polarization functions are used. MP2 calculations yielded dipole moments comparable to those obtained from DF calculations with the same basis set and reproduced better the difference between the Pt-Cl and Pt-P bond lengths, but required 2-6 times more computer time. The best agreement between calculated and experimental dipole moment and bond length values was obtained with DF calculations using the program ADF, provided that the scalar relativistic terms were included in the hamiltonian. Our results indicate that the mutual influence of the platinum-ligand bonds in trans-position (the so-called trans -influence) involves both electron correlation and relativistic effects.

Bonding of transition metal atoms on the Al(100) surface from density functional calculations: I. Anomalous work function change as relativistic effect

For the series Ni, Pd, Pt, Cu, Ag, and Au, we have studied the interaction of transition metal (TM) atoms with the (100) surface of Al by means of cluster models and density functional calculations. Adsorption of K has also been considered for comparison. This study aims at analyzing the inter-metallic bond. In particular, we have correlated the adsorbate-induced changes in the surface dipole with the measured change in the work function of the bimetallic system. We find that, differently from K which is characterized by a charge transfer interaction, TM atoms form largely covalent bonds accompanied by only small charge displacements which, in turn, induce small surface dipoles. The sign of these dipoles, hence the expected change in the work function, is different for Pt and Au; this “anomalous” behavior of Pt and Au relative to the other members of the TM series is clearly due to intra-atomic electronic relativistic effects.

Comparative Study of Electron Correlation and Relativistic Effects in CuF, AgF, and AuF

Spectroscopic and electric properties of the series of diatomic molecules FCu, FAg, and FAu are calculated using the coupled cluster CCSD(T) method and considering relativistic effects by the no-pair one-component Douglas−Kroll−Hess approximation. The correlation and relativistic effects in the FM series (M = Cu, Ag, Au) are compared with these effects in the AlM series. Differences in the bonding character and consequently also in molecular properties in FM and AlM are primarily due to different relativistic effects in both series. Relativity destabilized all bonds in the FM series but led to the increase of bond energy in all AlM diatomics. At the same time correlation effects were similar in all FM and AlM molecules, making all bonds considerably stronger. The different influences of relativistic effects on the bond energy are interpreted in traditional terms of electronegativities of constituent atoms supplemented by the comparative analysis of correlation and relativistic effects on electric properties in both the FM and the AlM series. The polarity of FM and AlM molecules is opposite and the dipole polarizabilities in the FM series are much lower than those in the AlM series.

ENERGY-LOSS EFFECT IN K-SHELL IONIZATION

The energy-loss effect of the projectile for direct inner-shell ionization cross sections by charged-particle impact has been examined. The relativistic and nonrelativistic calculations for K-shell ionization with and without the energy-loss effect are made in the plane-wave Born approximation and compared with the Brandt-Lapicki theory for the corrections of the relativistic and energy-loss effect. It is demonstrated that the Brandt-Lapicki method gives a good approximation to both relativistic and nonrelativistic cross sections, which implicitly take into account the energy-loss effect. However, the use of the Brandt-Lapicki relativistic correction method in the nonrelativistic theory with the exact integration limits for energy and momentum transfer overestimates the relativistic calculations for low-energy projectiles. This indicates that the Brandt-Lapicki method for correction of the electronic relativistic effect should be used only with their energy-loss correction method.

Binding of aluminium to coinage metals: electron correlation and relativistic effects

Binding of aluminium to coinage metals: electron correlation and relativistic effects

Binding of aluminium to coinage metals: electron correlation and relativistic effects

Relativistic coupled cluster calculations have been carried out for diatomic molecules formed by aluminium and the coinage metal atoms (Me). The relativistic effects are accounted for by using the spin-free Douglas–Kroll formalism while the electron correlation contribution is calculated at the level of the CCSD(T) method. The theoretical data are in satisfactory agreement with the known experimental values and available results of other calculations. The AlAu molecule with the calculated relativistic dissociation energy of 3·41 eV is the most stable species in the series. The spectroscopic parameters determined are analysed in terms of the electron correlation and relativistic contributions to their values. These results parallel those obtained recently for a similar series of boron compounds. Dipole and quadrupole moments also were investigated as was the parallel component of the dipole polarizability of all three AlMe molecules, with particular attention given to their decomposition into electron correlation and relativistic contributions. Within the one electron non-relativistic approximation all these molecules turn out to have negative dipole moments (polarity Al(-) Me(-)) whose sign is changed already by taking into account the electron correlation. The relativistic effects enhance the positive dipole moment values and make AlAu the most polar molecule in the series, with a dipole moment of about 1·58 D. Similarly, due to both electron correlation and relativistic contributions, the quadrupole moment of AlAu is positive and differs by more than 7 au from the value calculated in the one-electron non-relativistic approach. The present results obtained without the spin-free Douglas–Kroll formalism are compared with those calculated by using the spin-free (MVD) Pauli correction for relativistic effects. It follows that for systems as heavy as AlAu the MVD correction to non-relativistic results becomes insufficient. This is partly because of the violation of the low-order perturbation treatment of relativistic effects and partly due to the increasing importance of non-additive relativistic-correlation contributions.

Ionization potentials and electron affinities of Cu, Ag, and Au: Electron correlation and relativistic effects

The electron correlation and relativistic effects on ionization potentials and electron affinities of Cu, Ag, and Au are investigated in the framework of the coupled cluster method and different 1-component approximations to the relativistic Dirac-Coulomb Hamiltonian. The first-order perturbation approach based on the massvelocity and Darwin terms is found to be sufficiently accurate for Cu and Ag while it fails for Au. The spin-averaged Douglas-Kroll no-pair method gives excellent results for the studied atomic properties. The ionization potentials obtained within this method and the coupled cluster scheme for the electron correlation effects are 7.733(7.735) eV for Cu, 7.461(7.575) eV for Ag, and 9.123(9.225) eV for Au (experimental values given in parentheses). The calculated (experimental) electron affinity results for Cu, Ag, and Au are 1.236(1.226), 1.254(1.303), and 2.229(2.309) eV, respectively. There is a marked relativistic effect on both the ionization potential and electron affinity of Ag which sharply increases for Au while Cu exhibits only a little relativistic character. A similar pattern of relativistic effects is also observed for electric dipole polarizabilities of the coinage metal atoms and their ions. The coupled cluster dipole polarizabilities of the coinage metal atoms calculated in this article in the Douglas-Kroll no-pair formalism (Cu: 46.50 au; Ag: 52.46 au; Au: 36.06 au) are compared with our earlier data for their singly positive and singly negative ions. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 557–565, 1997

Electric dipole polarizabilities of negative ions of the coinage metal atoms

The dipole polarizability of the coinage metal anions is calculated in different approximations for both the electron correlation and relativistic effects. The large polarizabilities of these ions give a good illustration of the performance of different computational methods. The spin-averaged Douglas-Kroll no-pair scheme combined with the CCSD(T) treatment of the electron correlation predict the following values of polarizabilities: 243 au for Cu −, 213 au for Ag − and only about 93 au for Au −. The non-relativistic CCSD(T) results are 278, 299 and 256 au, respectively. Both the non-relativistic and relativistic results agree with the QCISD(T) pseudopotential data, though serious discrepancies occur at the level of the QCISD approximation. The use of the scalar Pauli approximation for the estimation of the relativistic contribution to the dipole polarizabilities of the coinage metal ions is limited to Cu − and Ag −. For Au − this approximation strongly overestimates the magnitude of the relativistic effect.

Electron correlation and relativistic effects in the coinage metal compounds

The first-order polarized basis sets of the coinage metal atoms have been used to perform high-level-correlated calculations of the dipole moment in the series of the MeH (Me=Cu, Ag, Au) molecules. The relativistic effects were accounted for by using the quasirelativistic approach based on the mass-velocity and Darwin terms in both the SCF HF and correlated level approximations. The non-relativistic coupled cluster calculations with complete treatment of one- and two-body clusters and perturbative correction for the three-body terms (CCSD(T) predict the following sequence of the dipole moment data: 1.13 a.u. for CuH, 1.35 a.u. for AgH, and 1.21 a.u. for AuH. Upon including the relativistic correction the calculated dipole moments turn out to be 1.05 a.u. for CuH, 1.14 for AgH, and 0.64 a.u. for AuH. The influence of the electron correlation and relativistic effects on the electronic distribution in the MeH molecules is discussed. A comparison of calculations with different number of explicitly correlated electrons gives an approximate scheme for the estimation of the core polarization/correlation contribution.

Electron correlation and relativistic effects in the coinage metal compounds. II. Heteronuclear dimers: CuAg, CuAu, and AgAu

Electric properties of heteronuclear dimers of the coinage metals are calculated at the level of the CCSD(T) approximation applied to 38 electrons of the valence and next-to-valence atomic shells. The relativistic effects are accounted for by using the scalar approximation to the Pauli hamiltonian. Both the pure relativistic and mixed relativistic-correlation contributions to energies and electric properties are computed. All calculations have been carried out by using the recently developed first-order polarized basis sets of the coinage metal atoms. In the non-relativistic approximation all studied dimers show only a moderate degree of polarity; the non-relativistic CuAg turns out to be the most polar dimer with the Cu(−)Ag(+) polarity. The relativistic effects considerably reduce the negative value of the CuAg dipole moment, change the sign of the CuAu dipole moment, and make the AgAu molecule the most polar species in the series. Simultaneously, the parallel component of the dipole polarizability shows only a small relativistic contraction. The calculated quasirelativistic interaction potentials have a correct behavior in the vicinity of their minima and give the Re and ωe values in complete agreement with experiment. Much less satisfactory are the dissociation energy data which seem to suffer from the single reference configuration approximation.