Calculation of the magnetic hyperfine structure constant of alkali metals and alkaline-earth-metal ions using the relativistic coupled-cluster method

Abstract

The Z-vector method in the relativistic coupled-cluster framework is used to calculate magnetic hyperfine structure constant (AJ ) of alkali metals and singly charged alkaline earth metals in their ground state electronic configuration. The Z-vector results are in very good agreement with the experiment. The AJ values of Li, Na, K, Rb, Cs, Be + , Mg + , Ca + , and Sr + obtained in the Z-vector method are compared with the extended coupled-cluster results taken from Phys. Rev. A 91, 022512 (2015). The same basis and cutoff are used for the comparison purpose. The comparison shows that Z-vector method with the singles and double approximation can produce more precise wavefunction in the nuclear region than the ECC method.

Hyperfine Structure Constants on the Relativistic Coupled Cluster Level with Associated Uncertainties

“…In recent years Sasmal and co-workers have reported the HFS constants of a large set of atoms and molecules on the CCSD level using the extended CC (ECC) and Z-vector frameworks. , The ECC uses a variational CC ansatz that allows for calculating HFS constants as expectation values. The Z-vector technique, however, is a way to evaluate the energy derivative of nonvariational CC energies.…”

“…These include the multi-reference configuration interaction (MR-CISD) method, 25 the restricted active space CI (RAS-CI) approach, 26 as well as the coupled cluster singles and doubles (CCSD) method. 26,27 In this work we investigate the performance of the relativistic coupled cluster (CC) method for calculating the HFS constants of atoms and molecules. Where applicable, this approach provides the highest level of theory, while still being feasible for computations on the heaviest elements.…”

“…For molecules, the situation becomes more complicated due to the lack of spherical symmetry and a limited number of implementations exist. These include the multireference configuration interaction (MR-CISD) method, the restricted active space CI (RAS-CI) approach, and the coupled cluster singles and doubles (CCSD) method. , …”

Relativistic coupled-cluster-theory analysis of the hyperfine interaction of Ra$^{+}$ isotopes

“…For 223 Ra + , the BW correction obtained by SP model of the five states in table are greater than those from the sphere model, so we take 50% of the total BW effect within the SP model as the conservatively estimated uncertainty. [13] 3567.26 77.1 −23.9 Z-vector [45] 3446.3 Expt.1987 [46] 667.1(2.1) 56.5(8) Expt.1988 [20] 3404.0(1.9)…”

“…The present CCSD, SDpT [42], CCSD(T) [13], Zvector [45] methods in Table IV are all based on relativistic coupled-cluster-theory, though they have some different treatments for electronic correlation effects. In the SDpT method, other nuclear magnetic distribution models are used to consider the BW correction, while there is no description of the BW effect in the CCSD(T) and Z-Vector methods, and none of these three methods evaluate the contribution of QED effect.…”