Relativistic Kramers-Unrestricted Exact-Two-Component Density Matrix Renormalization Group

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Relativistic Quantum Mechanics

Background:

• Accurate calculation of electronic structures in heavy elements is challenging due to significant relativistic effects, particularly spin-orbit coupling.
• Traditional methods struggle with systems requiring large determinantal spaces, limiting their applicability.
• The Density Matrix Renormalization Group (DMRG) is a powerful method for strongly correlated systems, but its relativistic application is complex.

Purpose of the Study:

• To develop and validate a variational relativistic Density Matrix Renormalization Group (DMRG) approach within the exact-two-component (X2C) framework (X2C-DMRG).
• To investigate the accuracy of X2C-DMRG for fine-structure splittings of p- and d-block atoms and excitation energies of monohydride molecules.
• To assess symmetry breaking and electron correlation convergence in relativistic calculations.

Main Methods:

• Development of the variational relativistic X2C-DMRG method.
• Optimization of spinor orbitals using the two-component relativistic complete active space self-consistent field (X2C CASSCF).
• Application of an all-electron relativistic Hamiltonian in a Kramers-unrestricted basis for calculations.

Main Results:

• X2C-DMRG accurately predicts 2P and 2D fine-structure splittings for atoms (Ga, In, Tl, Sc, Y, La), comparable to multireference configuration interaction with singles and doubles (MRCISD).
• The method effectively recovers symmetry breaking in atomic multiplets by increasing the number of renormalized block states (m).
• Electron correlation convergence in X2C-DMRG approaches MRCISDTQ5 quality, outperforming traditional configuration interaction (CI) for systems with up to 10^19 determinants.

Conclusions:

• The developed X2C-DMRG approach is a significant advancement for relativistic quantum chemistry, particularly for systems with strong spin-orbit coupling.
• This method enables accurate calculations for systems previously intractable with traditional CI methods due to their large size.
• X2C-DMRG provides a computationally feasible pathway to quantitatively correct fine-structure splittings and other relativistic effects.