Relativistic coupled-cluster

Eliav, E., Kaldor, U. and Ishikawa, Y. (1994) Open-shell relativistic coupled-cluster method with Dirac-Breit wave functions Energies of the gold atom and its cation. Physical Review Letters, 49, 1724—1729 Including newer unpublished results from this group. 

Schwerdtfeger, P., Bast, R., Gerry, M.C.L., Jacob, C.R., Jansen, M., Kelld, V., Mudring, A.V., Sadlej, A.J., Saue, T, Sdhnel, T. and Wagner, F.E. (2005) The quadrupole moment of the 3 /2 nuclear groimd state of Au from electric field gradient relativistic coupled cluster and density functional theory of small molecules and the solid slide. Journal of Chemical Physics, 122,124317-1-124317-9. 

Seth, M., Cooke, F., Pehssier, M., Heully J.-L. and Schwerdtfeger, P. (1998) The Chemistry of the Superheavy Elements II. The Stability of High Oxidation States in Group 11 Elements. Relativistic Coupled Cluster Calculations for the Fluorides of Cu, Ag, Au and Element 111. Journal of Chemical Physics, 109, 3935—3943. 

The relativistic coupled cluster method starts from the four-component solutions of the Drrac-Fock or Dirac-Fock-Breit equations, and correlates them by the coupled-cluster approach. The Fock-space coupled-cluster method yields atomic transition energies in good agreement (usually better than 0.1 eV) with known experimental values. This is demonstrated here by the electron affinities of group-13 atoms. Properties of superheavy atoms which are not known experimentally can be predicted. Here we show that the rare gas eka-radon (element 118) will have a positive electron affinity. One-, two-, and four-components methods are described and applied to several states of CdH and its ions. Methods for calculating properties other than energy are discussed, and the electric field gradients of Cl, Br, and I, required to extract nuclear quadrupoles from experimental data, are calculated. 

Of the five group-13 elements, only B and A1 have experimentally well characterized electron affinities. Lists of recommended EAs [50,51] show errors ranging from 50% to 100% for Ga, In, and T1. Very few calculations have appeared for the latter atoms. These include the multireference configuration interaction (MRCI) ofAmau etal. using pseudopotentials [52], our relativistic coupled cluster work on T1 [45], and the multiconfiguration Dirac-Fock (MCDF) computation of Wijesundera [53]. 

One method of determining nuclear quadrupole moment Q is by measuring the quadrupole coupling constant, given by eqQ/h, where e is the charge of the electron and q the electric field gradient due to the electrons at the atomic nucleus. The extraction of Q depends on an accurately calculated q. As a test of our finite-field relativistic coupled cluster approach, preliminary results for Cl, Br, and I are presented. 

In this paper, the main features of the two-step method are presented and PNC calculations are discussed, both those without accounting for correlation effects (PbF and HgF) and those in which electron correlations are taken into account by a combined method of the second-order perturbation theory (PT2) and configuration interaction (Cl), or PT2/CI [100] (for BaF and YbF), by the relativistic coupled cluster (RCC) method [101, 102] (for TIF, PbO, and HI+), and by the spin-orbit direct-CI method [103, 104, 105] (for PbO). In the ab initio calculations discussed here, the best accuracy of any current method has been attained for the hyperfine constants and P,T-odd parameters regarding the molecules containing heavy atoms. 

Results. Calculations were carried out at two internuclear separations, the equilibrium Re = 2.0844 A as in Ref. [89], and 2.1 A, for comparison with Ref. [127]. The relativistic coupled cluster (RCC) method [130, 131] with only single (RCC-S) or with single and double (RCC-SD) cluster amplitudes is used (for review of different coupled cluster approaches see also [132, 133] and references). The RCC-S calculations with the spin-dependent GRECP operator take into account effects of the spin-orbit interaction at the level of the one-configurational SCF-type method. The RCC-SD calculations include, in addition, the most important electron correlation effects. 

On the other hand, Gold shows large relativistic effects (the Gold maximum — see eg. [21]). In fact, it has been explicitly demonstrated that for Au relativistic and arc-effects are nonadditive [22]. This is most obvious for its electron affinity While a nonrelativistic Cl-calculation [23] gives a value of 1.02 eV and a fully relativistic Coupled-Cluster calculation [22] yields 2.28 eV, the corresponding nonrelativistic and relativistic Hartree-Fock values are 0.10 eV [22] and 0.67 eV, respectively. Thus immediately the question arises to which extent the GGA s failure for metallic Au is due to the neglect of relativistic arc-contributions in Exc[n. ... 

Fsrcc is a multi-reference Fock-space relativistic coupled-cluster program by Eliav and Kaldor for correlated calculations on the ground and excited states of molecules. 

A pilot calculation on CdH using one-, two- and four-component Fock space relativistic coupled-cluster methods has been published by Eliav et al. (1998b). The calculated values obtained were in very good agreement with experiment. While the four-component method gives the best results, one- and two-component calculations include almost all the relativistic effects. 

Lindgren, 1.(1989) A relativistic coupled-cluster approach with radiative corrections. In Kaldor (1989), pp. 293-306. 

Pempointner, M. and Vissdier, L. (2001b) Parallelization of the relativistic coupled cluster program Relccsd. NCF Technical Report NRG-1999-08, Vrije Universiteit Amsterdam, The Netherlands. 

M. Seth, P. Schwerdtfeger, M. Dolg, The chemistry of the superheavy elements. I. Pseudopotentials for 111 and 112 and relativistic coupled cluster calculations for... 

The all-orders relativistic many-body perturbation theory approach [82], [83], the combination of this approach with the multiconfiguration Dirac - Fock method [84] or the relativistic coupled-cluster approach [85] allow for the evaluation of the energy levels for valence electrons with accuracy of the order of... 

Figure 3. Relativistic Dirac-Hartree-Fock (DHF) and experimental (Exp.) term energies of LSI levels arising from the ns np configuration of the group 4 elements (J=0 solid lines, J=1 dotted lines, J=2 dashed lines). The experimental result for Eka-Pb actually corresponds to the result of a high level relativistic coupled-cluster calculation [79]. The corresponding results for the nonrelativistic P, and S states (dot-dashed lines) were obtained from Hartree-Fock (HF) calculations.

U. Kaldor, Relativistic coupled cluster method and applications, in R.J. Bartlett (Ed.), Recent advances in coupled-cluster methods, Recent advances in computational chemistry, Vol. 3, World Scientific Publishing, Singapore, 1997, pp. 125-153, and references 45-58 therein. 

Some work has been reported on relativistic coupled cluster methods most notably by Kaldor, Ishikawa and their collaborators.232 These calculations are carried out within the no virtual pair approximation and are therefore analogous to the non-relativistic formulation. Perturbative analysis of the relativistic electronic structure problem demonstrated the importance of the negative energy branch of the spectrum in the calculation of energies and other expectation values. 

J. Thyssen, J. Laerdahl, P. Schwerdtfeger, Fully relativistic coupled cluster treatment for parity-violating energy differences in molecules, Phys. Rev. Lett. 85 (2000) 3105-3108. 

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