A Green's-Function Approach to Exchange Spin Coupling As a New Tool for Quantum Chemistry

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Density Functional Theory

Background:

• Exchange spin coupling is typically calculated using the energy difference between high-spin and Broken-Symmetry (BS) determinants within Kohn-Sham density functional theory (KS-DFT).
• This standard method, based on Noodleman's work, can be computationally intensive.
• An alternative, efficient approximate approach using Green's functions, originating from solid-state physics, has been proposed but not extensively tested for molecular systems.

Purpose of the Study:

• To rederive and systematically test a Green's function-based approach for evaluating exchange spin coupling in molecular systems.
• To provide a simpler, more efficient postprocessing procedure for KS-DFT calculations.
• To compare the performance of the Green's function method against the conventional BS energy-difference approach.

Main Methods:

• A Green's function approach is derived using local projection operators, a common technique in quantum chemistry for defining local properties.
• This derivation avoids the dual basis set used in the original Han-Ozaki-Yu approach.
• The method is applied as a postprocessing step to existing KS-DFT calculations, requiring the electronic structure of only a single spin state.

Main Results:

• The rederived Green's function method provides a computationally efficient alternative to the BS energy-difference approach.
• The method yields qualitatively consistent results with the BS energy-difference approach for various molecular systems, including small molecules, diradicals, and dinuclear transition metal complexes.
• Consistency is observed when the Green's function method is applied to high-spin determinants and when structural relaxation effects between spin states are negligible.

Conclusions:

• The Green's function-based method offers a viable and efficient alternative for calculating exchange spin coupling in molecular systems.
• This approach simplifies the computational workflow by requiring only one spin state calculation.
• The method's accuracy is comparable to the traditional BS approach under specific conditions, making it a valuable tool for computational chemists.