GVVPT2 energy gradient using a Lagrangian formulation.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Calculating nuclear gradients is crucial for understanding molecular properties and reaction pathways.
• Existing methods may have limitations in handling complex electronic structures or reference spaces.

Purpose of the Study:

• To develop accurate analytic formulas for GVVPT2 energy nuclear gradients.
• To enable the use of complete or incomplete model spaces in gradient calculations.
• To demonstrate the method's applicability to challenging systems, including state-averaged MCSCF and conical intersections.

Main Methods:

• A Lagrangian-based approach was employed to derive analytic formulas for GVVPT2 nuclear gradients.
• The methodology accommodates both complete and incomplete model spaces, limited only by MCSCF program capabilities.
• An efficient evaluation scheme for the gradient equations was developed and implemented.

Main Results:

• Demonstrative calculations show GVVPT2 gradients are accurate when compared to finite difference methods.
• The formalism successfully handles state-averaged MCSCF descriptions with arbitrary weights, demonstrated on LiH excited states.
• Calculations on O(3) conical intersections near C(2v) symmetry agree well with higher-level MRCISD theory.

Conclusions:

• The GVVPT2 gradient method provides an accurate and efficient approach for electronic structure calculations.
• The ability to use state-averaged MCSCF and handle arbitrary weights enhances its applicability to complex systems.
• The method is validated for accurately determining molecular geometries, including those at conical intersections.