Analytical Nuclear Gradients for State-Averaged Configuration Interaction Singles Variants: Application to Conical...

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Accurate prediction of molecular geometries and reaction pathways is crucial in chemistry.
• Minimum-energy conical intersections (MECXs) play a vital role in understanding photochemical reactions and excited-state dynamics.
• Existing methods often struggle to accurately describe conical intersections, especially within cost-effective computational frameworks.

Purpose of the Study:

• To derive analytical nuclear gradients for state-averaged orbital-optimized configuration interaction singles (SACIS) and its spin-projected extension (SAECIS).
• To enable efficient geometry optimization and MECX searches using these low-cost methods.
• To assess the accuracy and reliability of SACIS and SAECIS for describing conical intersections.

Main Methods:

• Development of analytical nuclear gradients using a Lagrangian approach.
• Explicit removal of null-space contributions in coupled-perturbed equations for numerical stability.
• Application of SACIS and SAECIS to twisted-pyramidalized ethylene and benchmark calculations on 12 MECXs.

Main Results:

• SACIS and SAECIS qualitatively reproduce correct conical intersection topology, outperforming conventional CIS and ECIS.
• Benchmark calculations show mean RMSDs below 0.1 Å compared to high-level references for both methods.
• SACIS effectively incorporates static correlation via variational orbital relaxation, mitigating ground-state Hartree-Fock orbital bias.
• Spin projection was found to be nonessential for the qualitative description of these intersections.

Conclusions:

• SACIS and SAECIS provide qualitatively reliable conical intersection descriptions at mean-field computational cost.
• SACIS offers a better cost-performance balance for general applications due to its comparable accuracy and lower computational overhead.
• SAECIS may be advantageous for systems involving higher excited states with significant double-excitation character.