Hyperfine Coupling Constants in Local Exact Two-Component Theory

We present a highly efficient implementation of the electron-nucleus hyperfine coupling matrix within one-electron exact two-component (X2C) theory. The complete derivative of the X2C Hamiltonian is formed, i.e. the derivatives of the unitary decoupling transformation are considered. This requires solution of the response and Sylvester equations, consequently increasing the computational costs. Therefore, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The finite nucleus model is employed for both the scalar potential and the vector potential. Two-electron picture-change effects are modeled with the (modified) screened-nuclear spin--orbit approach. Our implementation is fully integral direct and OpenMP-parallelized. An extensive benchmark study regarding the Hamiltonian, the basis set, and the density functional approximation is carried out for a set of 12--17 transition-metal compounds. The error introduced by DLU is negligible and the DLU-X2C Hamiltonian accurately reproduces its four-component ``fully'' relativistic parent results. Functionals with a large amount of Hartree--Fock exchange such as CAM-QTP-02 and omega-B97X-D are generally favorable. The pure density functional r2SCAN performs remarkably and even outperforms the common hybrid functionals TPSSh and CAM-B3LYP. Fully uncontracted basis sets or contracted quadruple-zeta bases are required for accurate results. The capability of our implementation is demonstrated for [Pt(C6Cl5)4]- with more than 4700 primitive basis functions and four rare-earth single molecule magnets: [La(OAr*)3]-, [Lu(NR2)3]-, [Lu(OAr*)3]-, and [TbPc2]-. Here, the spin--orbit DLU-X2C Hamiltonian results in an excellent agreement with the experimental findings of all Pt, La, Lu, and Tb molecules.

Hyperfine Coupling Constants in Local Exact Two-Component Theory

We present a highly efficient implementation of the electron-nucleus hyperfine coupling matrix within one-electron exact two-component (X2C) theory. The complete derivative of the X2C Hamiltonian is formed, i.e. the derivatives of the unitary decoupling transformation are considered. This requires solution of the response and Sylvester equations, consequently increasing the computational costs. Therefore, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The finite nucleus model is employed for both the scalar potential and the vector potential. Two-electron picture-change effects are modeled with the (modified) screened-nuclear spin--orbit approach. Our implementation is fully integral direct and OpenMP-parallelized. An extensive benchmark study regarding the Hamiltonian, the basis set, and the density functional approximation is carried out for a set of 12--17 transition-metal compounds. The error introduced by DLU is negligible and the DLU-X2C Hamiltonian accurately reproduces its four-component ``fully'' relativistic parent results. Functionals with a large amount of Hartree--Fock exchange such as CAM-QTP-02 and omega-B97X-D are generally favorable. The pure density functional r2SCAN performs remarkably and even outperforms the common hybrid functionals TPSSh and CAM-B3LYP. Fully uncontracted basis sets or contracted quadruple-zeta bases are required for accurate results. The capability of our implementation is demonstrated for [Pt(C6Cl5)4]- with more than 4700 primitive basis functions and four rare-earth single molecule magnets: [La(OAr*)3]-, [Lu(NR2)3]-, [Lu(OAr*)3]-, and [TbPc2]-. Here, the spin--orbit DLU-X2C Hamiltonian results in an excellent agreement with the experimental findings of all Pt, La, Lu, and Tb molecules.

Influence of surface effects on neutron skin in atomic nuclei

The influence of the diffuse surface layer of a finite nucleus on the mean square radii and their isotopic shift is investigated. We present the calculations within the Gibbs - Tolman approach using the experimental values of the nucleon separation energies. Results are compared with that obtained by means of a direct variational method based on Fermi-like trial functions.

A bridge between finite and infinite Nuclear matter

The bridge between finite and infinite nuclear system is analyzed for the fundamental quantities such as binding energy, incompressibility and giant monopole excitation energy using relativistic mean-field formalism. The well known Thomas-Fermi, extended Thomas-Fermi and Hartree approximations are used to evaluate the observables. A parametric form of the density is used to convert the infinite nuclear matter density to the mean density of a finite nucleus. The present analysis shows an estimation of finite nucleus properties from information of the corresponding infinite nuclear matter quantities only approximately. In other words, it is not quite obvious to get the observables of finite nuclei by converting the corresponding entities of the nuclear matter system or vice versa. If at all one can achieved, it can be done only approximately.

Finite nucleus effects, relativistic effects and picture change error in the IOTC/DKH2 contact spin densities of Cu, Ag, Au atoms

Sensitivity of contact spin density as well as electron density to the size of nucleus is investigated using the Gaussian model of nucleus and the point charge nucleus model. Scalar Infinite Order Two Component and scalar second order Douglas-Kroll-Hess quasirelativistic contact spin densities (spin densities at the nucleus) of Cu, Ag and Au atoms are considered. The non-relativistic contact spin densities and the valence s-orbital contact densities of Kramers restricted orbitals (Cu, Ag, Au atoms) are presented as well. The picture change error in the quasirelativistic calculations of spin densities is corrected by analytic means. Uncontracted triple-zeta UTZ+Ns basis sets are employed, where N is the number of additional tight s Gaussians. In addition, the impact of tight p and d Gaussians is briefly discussed.

Charge exchange response functions of finite nucleus by an extended Skyrme interaction

The charge exchange resonances in finite nucleus, such as Gamow–Teller (GT) and Spin-Dipole (SD) resonances, have been studied in a self-consistent Hartree–Fock (HF) plus random phase approximation (RPA) approach by employing an extended Skyrme interaction with spin-density dependent terms. The calculations are performed within the KDE0v1 and KDE0v1st Skyrme interactions. The peak energy of GT response function is increased by about 1.4 MeV when the spin-density dependent terms are included. For total response function of SD resonance, the spin-density dependent terms give an overall repulsive contribution to the strength. The specific effect for each multipole presents a multipole dependence.