Reduced scaling formulation of CASPT2 analytical gradients using the supporting subspace method

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.
• Calculating analytical gradients in CASPT2 is computationally intensive, limiting its application.
• Existing methods require significant computational resources, especially for large systems.

Purpose of the Study:

• To reformulate and reduce the computational scaling of state-specific CASPT2 analytical gradients.
• To develop an efficient method for calculating CASPT2 gradients using the supporting subspace approach.
• To enable faster and more accessible CASPT2 gradient calculations for complex molecular systems.

Main Methods:

• Developed a reduced scaling and exact reformulation of CASPT2 analytical gradients.
• Utilized the supporting subspace method, building upon previous energy formulations.
• Leveraged MP2 and Fock derivatives, Fock builds, and Fock gradients for efficient computation.
• Incorporated tensor-hyper-contraction to further reduce computational cost.

Main Results:

• Achieved O(N^5) scaling for MP2-gradient terms and O(N^3) for remaining calculations.
• Demonstrated further cost reduction to O(N^4) with tensor-hyper-contraction for fixed active space sizes.
• Validated the accuracy and performance through benchmark calculations.
• Showcased applicability in ab initio molecular dynamics and constrained geometry optimization.

Conclusions:

• The new formulation significantly enhances the efficiency of CASPT2 analytical gradient calculations.
• This method effectively utilizes existing GPU-based MP2 and Fock routines.
• The improved computational performance opens new possibilities for advanced molecular simulations and analyses.