Local physical quantities for spin based on the relativistic quantum field theory in molecular systems

Local physical quantities for spin are investigated on the basis of the four‐ and two‐component relativistic quantum theory. In the quantum field theory, local physical quantities for spin such as the spin angular momentum density, spin torque density, zeta force density, and zeta potential play important roles in spin dynamics. We discuss how to calculate these local physical quantities based on the two‐component relativistic quantum theory. Some different types of relativistic numerical calculations of local physical quantities in Li atom and C₆H₆ are demonstrated and compared. Local physical quantities for each orbital are also discussed, and it is seen that a total local zeta potential is given as a result of some cancellation of large contributions from each orbital. © 2016 Wiley Periodicals, Inc.     

Relativistic Jahn-Teller effects in the photoelectron spectra of tetrahedral P4, As4, Sb4, and Bi4

The group-V tetrahedral cluster cations P(4)(+), As(4)(+), Sb(4)(+), and Bi(4)(+) are known to exhibit exceptionally strong Jahn-Teller (JT) effects of electrostatic origin in their (2)E ground states and (2)T(2) excited states. It has been predicted that there exist, in addition, JT couplings of relativistic origin (arising from the spin-orbit (SO) operator) in (2)E and (2)T(2) states of tetrahedral systems, which should become relevant for the heavier elements. In the present work, the JT and SO couplings in the group-V tetramer cations have been analyzed with ab initio relativistic electronic structure calculations. The vibronic line spectra and the band shapes of the photoelectron spectra were simulated with time-dependent quantum wave-packet methods. The results provide insight into the interplay of electrostatic and relativistic JT couplings and SO splittings in the complex photoelectron spectra of these systems.     

Relativistic quantum chemistry and rigorous variational analysis

A brief review of relativistic quantum chemistry is given here. Relativistic effects and their importance in chemistry are discussed. An outline of different theoretical aspects is presented. Aspects of variation techniques relevant to relativistic calculations are discussed in detail. These involve the derivation of min-max theorems for Dirac, Dirac-Hartree-Fock and Dirac-Coulomb calculations. The consequence of relativistic Hamiltonians being unbounded are also discussed for other lines of investigation. The upper bounds derived are physically interpreted. Sample Dirac-Hartree-Fock results for the Be atom, calculated using both STO and GTO bases for the nonrelativistic orbitals and the upper components of the relativistic orbitals, are given. The inadequacy of the so-called kinetically balanced basis set is discussed and illustrated with these results. The importance of the variational or dynamical balance and hence the merit of the LCAS-MS scheme is pointed out. The possibility of calculating quantum electrodynamical pair energy from relativistic configuration interaction calculations on a two-electron atom is discussed and exemplified. The present status of relativistic molecular calculations is briefly reviewed. Conclusions on the aspects of variational analysis and molecular calculations are enclosed.     

Energies,fine structures,and radiative lifetimes for the multiexcited quartet states of B‐like oxygen

Energies for the multiexcited states 1s²2s2pnl and 1s²2p²nl ⁴P^e,o (n ≥ 2) of B‐like oxygen are calculated using Rayleigh–Ritz variation method with configuration interaction. The mass polarization and relativistic corrections are obtained with first‐order perturbation theory. Configuration structures of the high‐lying multiexcited series are identified by energies and contribution to normalization of angular‐spin components. These structures are further checked by calculations of relativistic corrections and fine structure splittings. Hyperfine parameters and hyperfine coupling constants are calculated for the first time. Wavelengths including quantum electrodynamic effect and higher‐order relativistic corrections and lifetimes are also calculated. These results are compared with available results in the literature. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Simulations of 129Xe NMR chemical shift of atomic xenon dissolved in liquid benzene

The isotropic ¹²⁹Xe NMR chemical shift of atomic Xe dissolved in liquid benzene was simulated by combining classical molecular dynamics and quantum chemical calculations of ¹²⁹Xe nuclear magnetic shielding. Snapshots from the molecular dynamics trajectory of xenon atom in a periodic box of benzene molecules were used for the quantum chemical calculations of isotropic ¹²⁹Xe chemical shift using nonrelativistic density functional theory as well as relativistic Breit?CPauli perturbation corrections. Thus, the correlation and relativistic effects as well as the temperature and dynamics effects could be included in the calculations. Theoretical results are in a very good agreement with the experimental data. The most of the experimentally observed isotropic ¹²⁹Xe shift was recovered in the nonrelativistic dynamical region, while the relativistic effects explain of about 8% of the total ¹²⁹Xe chemical shift.     

Smooth relativistic Hartree-Fock pseudopotentials for H to Ba and Lu to Hg

We report smooth relativistic Hartree-Fock pseudopotentials (also known as averaged relativistic effective potentials) and spin-orbit operators for the atoms H to Ba and Lu to Hg. We remove the unphysical extremely nonlocal behavior resulting from the exchange interaction in a controlled manner, and represent the resulting pseudopotentials in an analytic form suitable for use within standard quantum chemistry codes. These pseudopotentials are suitable for use within Hartree-Fock and correlated wave function methods, including diffusion quantum Monte Carlo calculations.     

Economical treatments of relativistic effects and electron correlation in WH6

The equilibrium geometries and relative stabilities of several structural isomers of tungsten hexahydride, WH₆, have been obtained at different levels of quantum chemical calculations. The performance of various strategies to (i) include electron correlation, viz. density functional theory based approaches, Møller/Plesset perturbation and coupled cluster theory, and to (ii) account for scalar relativistic effects, viz. various relativistic effective core potentials, first order perturbation theory, a quasi-relativistic treatment employing a Pauli Hamiltonian, and use of the Douglas/Kroll operator, are compared to the best theoretical data available. It is shown that relativistic and electron correlation effects are most important for the high-symmetry species, that these effects give rise to opposite trends in relative energies, and that overall the relativistic effects dominate. The most efficient way to incorporate relativistic effects appears to be via the use of relativistic effective core potentials, while the correlation energies are best taken account of using a conventional method such as CCSD(T). © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1604–1611, 1998     

Quantum and classical dynamics of wave packets in an electromagnetic plane wave

Dynamics of a charged particle in a plane wave electromagnetic field is analyzed using the relativistic quantum and classical theory. Relativistic quantum dynamics is based on the Klein-Gordon equation. It is shown that the classical theory reproduces quantum results almost exactly.     

Relativistic contributions to single and double core electron ionization energies of noble gases

We have performed relativistic calculations of single and double core 1s hole states of the noble gas atoms in order to explore the relativistic corrections and their additivity to the ionization potentials. Our study unravels the interplay of progression of relaxation, dominating in the single and double ionization potentials of the light elements, versus relativistic one-electron effects and quantum electrodynamic effects, which dominate toward the heavy end. The degree of direct relative additivity of the relativistic corrections for the single electron ionization potentials to the double electron ionization potentials is found to gradually improve toward the heavy elements. The Dirac-Coulomb Hamiltonian is found to predict a scaling ratio of ～4 for the relaxation induced relativistic energies between double and single ionization. Z-scaling of the computed quantities were obtained by fitting to power law. The effects of nuclear size and form were also investigated and found to be small. The results indicate that accurate predictions of double core hole ionization potentials can now be made for elements across the full periodic table.     

Generalized spherical functions in the theory of many-electron atoms

A new method for finding non-relativistic and relativistic wave-functions of an electron moving in the field of a nuclear charge in the jj coupling scheme is proposed. It is based on the usage of generalized spherical functions. The mathematical apparatus necessary to find the expressions for matrix elements of the non-relativistic and relativistic energy or electron transition operators is developed. The formulas obtained for these matrix elements are more convenient than those usually used in jj coupling scheme; only their radial integrals and some phase multipliers depend on orbital quantum numbers.     

Spectroscopic constants and molecular properties of the X2Π and a4Σ− electronic states of the SiF radical

The potential energy curves (PECs) of the X²Π and a⁴Σ^? electronic states of the SiF radical have been studied by an ab initio quantum chemical method. The calculations have been made using the complete active space self‐consistent field (CASSCF) method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with several correlation‐consistent basis sets. The effects on the PECs by the core‐valence correlation and relativistic corrections are included. The way to consider the relativistic correction is to use the third‐order Douglas–Kroll Hamiltonian approximation. The relativistic corrections are made at the level of cc‐pV5Z basis set. The core‐valence correlation corrections are performed using the cc‐pCV5Z basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are also corrected for size‐extensivity errors by means of the Davidson modification (MRCI+Q). These PECs are extrapolated to the complete basis set limit by the total‐energy extrapolation scheme. Using these PECs, the spectroscopic parameters are determined and compared with those reported in the literature. With these PECs obtained by the MRCI+Q/CV+DK+56 calculations, the vibrational levels, inertial rotation, and centrifugal distortion constants of the first 20 vibrational state of each electronic state are calculated when the rotational quantum number J equals zero. Comparison with the Rydberg‐Klein‐Rees (RKR) data shows that the present results are reliable and accurate. The molecular constants of the X²Π and a⁴Σ^? electronic states determined by the MRCI+Q/CV+DK+56 calculations should be good prediction for future laboratory experiment. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

用相对论效应解释第二周期性

本文介绍了相对论效应的主要定性结论，并用以解释“第二周期性”     

Perspective: relativistic effects

This perspective article discusses some broadly-known and some less broadly-known consequences of Einstein's special relativity in quantum chemistry, and provides a brief outline of the theoretical methods currently in use, along with a discussion of recent developments and selected applications. The treatment of the electron correlation problem in relativistic quantum chemistry methods, and expanding the reach of the available relativistic methods to calculate all kinds of energy derivative properties, in particular spectroscopic and magnetic properties, requires on-going efforts.     

Thirty years of relativistic self-consistent field theory for molecules: relativistic and electron correlation effects for atomic and molecular systems of transactinide superheavy elements up to ekaplutonium E126 with g-atomic spinors in the ground state configuration

Relativistic Hartree–Fock–Roothaan (RHFR) self-consistent field theory for molecules developed by Malli and Oreg (J Chem Phys 63, 830, 1975) is reviewed. Ab initio all-electron fully relativistic Dirac–Fock and the corresponding nonrelativistic Hartree–Fock calculations for a number of molecular systems of heavy and superheavy elements are discussed in order to asecrtain relativistic effects. It is pointed out for the first time that there are dramatic antibinding effects of relativity for diatomics of the superheavy elements ekagold and ekaastatine. These are first results of antibinding effects of relativity in relativistic quantum chemistry. Moreover, in order to take into account the relativistic and electron correlation effects simultaneously for these systems, relativistic Moeller Plesset second order (RMP2), coupled-cluster singles doubles (RCCSD) and RCCSD with inclusion of triple corrections perturbationally (RCCSD(T)) calculations performed by the author for a number of atomic and molecular systems of superheavy elements (SHE) including the primordial SHE ekaplutonium E126 (Z = 126) (with g atomic spinors occupied in the ground state atomic configuration) are reported. Such calculations and results have not been reported before for systems of superheavy elements. Contribution to the Serafin Fraga Memorial Issue. An erratum to this article can be found at     

Triplet-triplet transitions in zinc-like ions

Theoretical oscillator strengths are reported for the lines of the 4s4p ³ P-4s4d ³ D transition in some ions of the zinc isoelectronic sequence, which are of interest in fusion plasma research. The calculations have been performed with the relativistic quantum defect orbital (RQDO) method. A core-polarization to the dipole transitions moment has also been included in the formalism. A comparative study with other theoretical results and the scarce experimental measurements has also been carried out. Systematic trends of individual oscillator strengths along the isoelectronic sequence are also shown in a graphical form.     

A relativistic C.I. study on theJ=1/2 even spectrum of Sr II

We present a method for performing relativistic CI calculations in ground and excited atomic and ionic levels. An electron occupying a relativistic shellnκ in a given electronic configuration is described by a single numerical four-component Dirac-Fock orbital having the samen and κ quantum numbers to those of the shellnκ. Application of this method yields estimates for the I.P. (88 741 cm^?1) and the core correlation energy (?30916 cm^?1) for Sr II and for the total correlation energy in Sr III (?30916 cm^?1). Core-valence correlation energies for the |core 5s〉 (?4379 cm^?1), |core 6s〉 (?1191 cm^?1) and |core 13s〉 (?32 cm^?1) levels have been calculated for Sr II. Estimates for the total relativistic, Breit, vacuum polarization and self energy corrections for these levels are also reported. Configurations in which the core is not fully occupied have been found to yield significant contributions to the correlation energies of both ground and excited levels. Our results show that full scale relativistic CI calculations using numerical four-component Dirac-Fock orbitals are feasible and provide a useful ab-initio tool for the investigation of atomic properties within the framework of fully relativistic theories.