Numerically stable resonating Hartree-Fock.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Electronic Structure Theory

Background:

• Simulating excited states efficiently is a significant challenge in electronic structure (ES) methods.
• Existing orthogonal ES methods have limitations, and nonorthogonal methods for excited states, especially with nonorthogonal orbital optimization, are less explored.
• Numerical instabilities often arise in methods dealing with nearly orthogonal orbitals.

Purpose of the Study:

• To develop a numerically stable formulation of the Resonating Hartree-Fock (ResHF) method for excited state calculations.
• To improve the wavefunction optimization process within the ResHF method.
• To benchmark the performance of the improved ResHF method against established methods like Complete Active Space Self-Consistent Field (CASSCF).

Main Methods:

• Introduced a numerically stable formulation of the Resonating Hartree-Fock (ResHF) method.
• Utilized the matrix adjugate to mitigate numerical instabilities caused by nearly orthogonal orbitals.
• Benchmarked ResHF against CASSCF for various chemical systems, including LiF avoided crossings, ethene torsional rotation, and singlet-triplet energy gaps in small molecules.

Main Results:

• Demonstrated significant improvements in ResHF wavefunction optimization due to the new formulation.
• ResHF accurately describes excited states, incorporating orbital relaxation while preserving correct state crossings.
• The open-source implementation, yucca, is available for broader use.

Conclusions:

• The stabilized ResHF method offers a promising, computationally efficient approach for excited state simulations.
• It combines the benefits of state-specific (orbital relaxation) and state-averaged (correct state crossings) methods.
• The developed ResHF implementation provides a valuable tool for electronic structure calculations.