Hyperfine Coupling Constants in Local Exact Two-Component Theory

We
present a highly efficient implementation of the electron–nucleus
hyperfine coupling matrix within the one-electron exact two-component
(X2C) theory. The complete derivative of the X2C Hamiltonian is formed,
that is, the derivatives of the unitary decoupling transformation
are considered. This requires the 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 ωB97X-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-ζ 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 results with the spin−orbit
DLU-X2C Hamiltonian are in an excellent agreement with the experimental
findings of all Pt, La, Lu, and Tb molecules.