Imaginary Shift in CASPT2 Nuclear Gradient and Derivative Coupling Theory.

Area of Science:

• Quantum chemistry
• Computational chemistry
• Theoretical chemistry

Background:

• Complete active space second-order perturbation theory (CASPT2) is crucial for accurate electronic structure calculations.
• Divergence in perturbation expressions can limit the applicability of CASPT2.
• Imaginary shift is a common technique to stabilize CASPT2 calculations.

Purpose of the Study:

• To develop and implement analytical nuclear gradient theory for CASPT2 with an imaginary shift.
• To extend existing CASPT2 gradient formalisms to incorporate imaginary shift stabilization.
• To assess the accuracy and efficiency of the new method for molecular geometry optimizations and conical intersection calculations.

Main Methods:

• Formulation of analytical nuclear gradients using the Lagrangian approach.
• Extension of existing CASPT2 gradient algorithms to include imaginary shift.
• Implementation into an efficient parallel computational program.
• Application to ground- and excited-state calculations of molecular systems.

Main Results:

• The developed theory provides accurate analytical nuclear gradients for CASPT2 with imaginary shift.
• Numerical examples for a green fluorescent protein model chromophore (p-HBDI-) show improved accuracy in energies and geometries.
• Timing benchmarks on adenine, p-HBDI-, and iron porphyrin demonstrate computational efficiency.
• The imaginary shift improves accuracy with only a minor increase in computational cost.

Conclusions:

• The analytical nuclear gradient theory for CASPT2 with imaginary shift is a robust and efficient method.
• This approach enhances the reliability of CASPT2 calculations, particularly for systems prone to divergence.
• The method is suitable for studying molecular properties like geometries and conical intersections.