A four-index transformation in Dirac's four-component relativistic theory

On the Utmost Importance of the Basis Set Choice for the Calculations of the Relativistic Corrections to NMR Shielding Constants

The investigation of the sensitivity of the relativistic corrections to the NMR shielding constants (σ) to the configuration of angular spaces of the basis sets used on the atoms of interest was carried out within the four-component density functional theory (DFT). Both types of relativistic effects were considered, namely the so-called heavy atom on light atom and heavy atom on heavy atom effects, though the main attention was paid to the former. As a main result, it was found that the dependence of the relativistic corrections to σ of light nuclei (exemplified here by 1H and 13C) located in close vicinity to a heavy atom (exemplified here by In, Sn, Sb, Te, and I) on the basis set used on the light spectator atom was very much in common with that of the Fermi-contact contribution to the corresponding nonrelativistic spin-spin coupling constant (J). In general, it has been shown that the nonrelativistic J-oriented and σ-oriented basis sets, artificially saturated in the tight s-region, provided much better accuracy than the standard nonrelativistic σ-oriented basis sets when calculating the relativistic corrections to the NMR shielding constants of light nuclei at the relativistic four-component level of the DFT theory.

Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method

A second-order many-body perturbation correction to the relativistic Dirac-Hartree-Fock energy is evaluated stochastically by integrating 13-dimensional products of four-component spinors and Coulomb potentials. The integration in the real space of electron coordinates is carried out by the Monte Carlo (MC) method with the Metropolis sampling, whereas the MC integration in the imaginary-time domain is performed by the inverse-CDF (cumulative distribution function) method. The computational cost to reach a given relative statistical error for spatially compact but heavy molecules is observed to be no worse than cubic and possibly quadratic with the number of electrons or basis functions. This is a vast improvement over the quintic scaling of the conventional, deterministic second-order many-body perturbation method. The algorithm is also easily and efficiently parallelized with demonstrated 92% strong scalability going from 64 to 4096 processors for a fixed job size.

Significance of Non-Linear Terms in the Relativistic Coupled-Cluster Theory in the Determination of Molecular Properties

The relativistic coupled-cluster (RCC) theory has been applied recently to a number of heavy molecules to determine their properties very accurately. Since it demands large computational resources, the method is often approximated to single and double excitations (RCCSD method). The effective electric fields ( E e f f ) and molecular permanent electric dipole moments (PDMs) of SrF, BaF, and mercury monohalides (HgX with X = F, Cl, Br, and I) molecules are of immense interest for probing fundamental physics. In our earlier calculations of E e f f and PDMs for the above molecules, we neglected the non-linear terms in the property evaluation expression of the RCCSD method. In this work, we demonstrate the roles of these terms in determining the above quantities and their computational time scalability with the number of processors of a computer. We also compare our results with previous calculations that employed variants of RCC theory, as well as other many-body methods and available experimental values.

The Role of Relativistic Many-Body Theory in Electron Electric Dipole Moment Searches Using Cold Molecules

In this review article, we survey some of our results pertaining to the search for the electric dipole moment of the electron (eEDM), using heavy polar molecules. In particular, we focus on the relativistic coupled cluster method (RCCM) and its applications to eEDM searches in YbF, HgX (X = F, Cl, Br, and I), BaF, HgA (A = Li, Na, and K), and YbOH. Our results are presented in a systematic manner, by first introducing the eEDM and its measurement using molecules, the importance of relativistic many-body theory, and finally our results, followed by future prospects.

Mercury monohalides: suitability for electron electric dipole moment searches

Heavy polar diatomic molecules are the primary tools for searching for the T-violating permanent electric dipole moment of the electron (eEDM). Valence electrons in some molecules experience extremely large effective electric fields due to relativistic interactions. These large effective electric fields are crucial to the success of polar-molecule-based eEDM search experiments. Here we report on the results of relativistic ab initio calculations of the effective electric fields in a series of molecules that are highly sensitive to an eEDM, the mercury monohalides (HgF, HgCl, HgBr, and HgI). We study the influence of the halide anions on E_{eff}, and identify HgBr and HgI as attractive candidates for future electric dipole moment search experiments.

Ligand effect on uranium isotope fractionations caused by nuclear volume effects: An ab initio relativistic molecular orbital study

We have calculated the nuclear volume term (ln K(nv)) of the isotope fractionation coefficient (epsilon) between (235)U-(238)U isotope pairs by considering the effect of ligand coordination in a U(IV)-U(VI) reaction system. The reactants were modeled as [UO(2)Cl(3)](-) and [UO(2)Cl(4)](2-) for U(VI), and UCl(4) for U(IV). We adopted the Dirac-Coulomb Hartree-Fock method with the Gaussian-type finite nucleus model. The result obtained was ln K(nv)=0.001 90 at 308 K, while the experimentally estimated value of ln K(nv) is 0.002 24. We also discuss how the ligand affects the value of ln K(nv), especially for the various structures of different compounds, and different ligands within the halogen ion series (F, Cl, and Br).

The relativistic complete active-space second-order perturbation theory with the four-component Dirac Hamiltonian

The relativistic complete active-space second-order perturbation theory (CASPT2) is developed for the four-component relativistic Hamiltonian. The present method can describe the near-degenerated and dissociated electronic states of molecules involving atoms of heavy elements. The present approach is less expensive than the relativistic multireference configuration interaction method. The ground and low-lying excited states of TlH, Tl(2), and PtH molecules are calculated with the Dirac-Coulomb (DC) CASPT2 method and their spectroscopic constants are obtained. These spectroscopic constants are compared with experimental findings and previous theoretical work. For all the molecules, the spectroscopic constants of DC-CASPT2 show good agreement with the experimental or previous theoretical spectroscopic constants. The present theory provides accurate descriptions of bonding or dissociation states and of ground and excited states in a well-balanced way.