Analytical energy gradients for second-order multireference perturbation theory using density fitting.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Accurate calculation of molecular properties requires computationally intensive methods.
• Analytical energy gradients are crucial for geometry optimization and reaction pathway analysis.
• Multi-configuration self-consistent field (MCSCF) and complete active space second-order perturbation theory (CASPT2) are powerful but costly quantum chemistry methods.

Purpose of the Study:

• To develop and implement efficient algorithms for analytical energy gradients in MCSCF and CASPT2.
• To accelerate CASPT2 gradient calculations using density fitting (DF) approximations.
• To validate the accuracy and performance of the new DF-based methods.

Main Methods:

• Implementation of analytical energy gradient algorithms for MCSCF and partially internally contracted CASPT2.
• Application of density fitting (DF) techniques to approximate integrals.
• Calculation of molecular structures and excitation energies using the developed methods.

Main Results:

• The developed algorithms enable accurate analytical energy gradients for single- and multi-state CASPT2.
• Density fitting (DF) effects on optimized structures and relative energies were found to be negligible.
• DF-CASPT2 gradient calculations showed significant speedups (3-5x with triple-ζ, ~10x with quadruple-ζ basis sets) compared to conventional methods.

Conclusions:

• The new DF-based analytical gradient methods provide a computationally efficient approach for CASPT2 calculations.
• These methods are accurate and suitable for studying molecular properties, including electronic states and energy splittings.
• The implementation offers substantial performance gains, making larger and more complex systems tractable.