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

Chad E Hoyer1, Hang Hu1, Lixin Lu1

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This summary is machine-generated.

This study introduces a new computational method, X2C-DMRG, for accurately calculating atomic and molecular properties. The method effectively handles complex systems with significant spin-orbit coupling, providing reliable fine-structure splittings.

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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.