Spin-Flip TDDFT within the Sternheimer Formulation: A Gaussian and Plane Wave Implementation

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Accurate calculation of electronic excited states is vital for understanding molecular properties and reactions.
• Existing methods often face challenges with computational cost and accuracy, particularly for excited-state properties.

Purpose of the Study:

• To implement and validate a noncollinear spin-flip time-dependent density functional theory (SF-TDDFT) within the Tamm-Dancoff approximation and Sternheimer formulation.
• To assess the accuracy of this new implementation for calculating vertical excitation energies and optimized molecular geometries.

Main Methods:

• Developed a stabilized noncollinear kernel for SF-TDDFT using a screening method for numerical integration.
• Employed generalized gradient approximation (GGA) functionals (PBE, PBE0) for calculations.
• Benchmarked results against high-level theoretical data (QUESTDB, CCSD, CISD, FCI) for vertical excitations and molecular geometries.
• Extended the implementation to include the auxiliary density matrix method (ADMM).

Main Results:

• The PBE and PBE0 functionals showed a slight underestimation of vertical excitation energies (average deviation of -0.3 eV).
• Optimized molecular geometries using the noncollinear PBE and PBE0 functionals closely matched high-level reference data (mean deviations of 0.010 Å and -0.004 Å, respectively).
• The ADMM extension with PBE0 yielded bond length deviations of approximately 0.003 Å.

Conclusions:

• The implemented noncollinear SF-TDDFT provides a robust and accurate scheme for excited-state and geometry calculations.
• The method shows promising accuracy for molecular structure optimization, outperforming previous collinear implementations.
• The extension to ADMM further enhances the accuracy for bond length calculations.