We report the development of a real time propagation method for solving the time-dependent relativistic exact two-component density functional theory equations (RT-X2C-TDDFT). The method is fundamentally non-perturbative and may be employed to study nonlinear responses for heavy elements which require a relativistic Hamiltonian. We apply the method to several group 12 atoms as well as heavy-element hydrides, comparing with the extensive theoretical and experimental studies on this system, which demonstrates the correctness of our approach. Because the exact two-component Hamiltonian contains spin-orbit operators, the method is able to describe the non-zero transition moment of otherwise spin-forbidden processes in non-relativistic theory. Furthermore, the two-component approach is more cost effective than the full four-component approach, with similar accuracy. The RT-X2C-TDDFT will be useful in future studies of systems containing heavy elements interacting with strong external fields.

The Chronus Quantum (ChronusQ) software package is an open source (under the GNU General Public License v2) software infrastructure which targets the solution of challenging problems that arise in ab initio electronic structure theory. Special emphasis is placed on the consistent treatment of time dependence and spin in the electronic wave function, as well as the inclusion of relativistic effects in said treatments. In addition, ChronusQ provides support for the inclusion of uniform finite magnetic fields as external perturbations through the use of gauge‐including atomic orbitals. ChronusQ is a parallel electronic structure code written in modern C++ which utilizes both message passing implementation and shared memory (OpenMP) parallelism. In addition to the examination of the current state of code base itself, a discussion regarding ongoing developments and developer contributions will also be provided. This article is categorized under: Software > Quantum Chemistry Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Density Functional Theory

The multiconfiguration nature of late-row (≥4th) elements and their molecular complexes, combined with significant relativistic effects, present large challenges for the accurate description of their electronic structure. To address these challenges and incorporate both relativistic and electron correlation effects, we present a two-component Kramers-unrestricted multireference configuration interaction method where relativistic effects are included variationally at the molecular orbital level via use of the “exact two-component” transformation of the solution of the one-electron modified Dirac equation. This method is developed within the restricted active space framework, allowing flexibility in both the choice of correlation space and the level of truncation of the excitation operator, as well as promoting the efficiency of generating and book-keeping unique electronic configurations. This method is applied to the study of fine structure splitting in selected p-block and d-block elements and is further applied to the study of the open-shell heavy-element uranium­(V) ion.

X-ray absorption spectroscopy is a powerful technique to probe local electronic and nuclear structure. There has been extensive theoretical work modeling K-edge spectra from first principles. However, modeling L-edge spectra directly with density functional theory poses a unique challenge requiring further study. Spin-orbit coupling must be included in the model, and a noncollinear density functional theory is required. Using the real-time exact two-component method, we are able to variationally include one-electron spin-orbit coupling terms when calculating the absorption spectrum. The abilities of different basis sets and density functionals to model spectra for both closed- and open-shell systems are investigated using SiCl and three transition metal complexes, TiCl, CrOCl, and [FeCl]. Although we are working in the real-time framework, individual molecular orbital transitions can still be recovered by projecting the density onto the ground state molecular orbital space and separating contributions to the time evolving dipole moment.

The accurate description of the electronic structure of transition metals and their compounds can be complicated by both the large number of close-lying states that often have multiconfigurational nature and significant relativistic effects. In order to address these challenges we present a two-component complete-active-space self-consistent field method that includes scalar relativistic effects and one-electron spin−orbit coupling during the self-consistent wave function optimization procedure. These relativistic effects are included via an "exact two-component" transformation of the solution of the one-electron modified Dirac equation. The method is applied to the study of spin−orbit splitting of ground and low-lying excited states of main group elements and selected transition metals.