Quasi-four-component method with numeric atom-centered orbitals for relativistic density functional simulations of molecules and solids

We describe and benchmark the quasi-four-component (Q4C) approach to relativistic density functional simulations of molecules and solids, using precise, numerically tabulated atom-centered orbital (NAO) basis sets to discretize Dirac's equation. The Q4C approach initially projects the atomic solution to (electron-only) positive-energy states and eventually deals with only two components but retains the precision of traditional four-component (4C) relativistic methods. While Q4C inherently reduces the dimension of the Hamiltonian matrix in diagonalization, the adoption of localized NAO basis functions in solids further limits the computational demand in real space operations, promising a pathway to investigate large and complex systems containing heavy elements with the precision of a 4C method. Here, we first perform validation and benchmark calculations for cohesive properties of a set of diatomic molecules and of previously established periodic model systems (i.e., silver halides). Then we report Q4C relativistic energy band structure benchmarks for a series of 103 periodic materials, including chemical elements up to Bi, and providing quantitative comparisons with more approximate scalar-relativistic and spin-orbit coupled treatments. Finally, we demonstrate the applicability of the method to band structure calculations of simple and complex hybrid organic-inorganic perovskites containing Pb and Bi, i.e., Cs2AgBiCl6 and a larger system (containing 94 atoms per unit cell), (4-FPEA)2PbI4. The effect of full Q4C, compared with scalar relativity, on binding energies can be significant even for relatively light p-orbital bonded main group elements such as Br and I - i.e., 0.3 and 0.6 eV for Br2 and I2 binding energies, respectively.