Reduced scaling extended multi-state CASPT2 (XMS-CASPT2) using supporting subspaces and tensor hyper-contraction.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• The extended multi-state Complete Active Space second-order perturbation theory (XMS-CASPT2) method is crucial for studying excited states.
• Previous XMS-CASPT2 formulations faced significant computational scaling challenges, limiting their application to larger systems.

Purpose of the Study:

• To develop a reduced scaling formulation of the XMS-CASPT2 method.
• To improve the efficiency of excited state calculations through computational optimization.
• To enable accurate calculations for larger molecular systems and complex phenomena.

Main Methods:

• Implemented a reduced scaling formulation based on state-specific CASPT2 (SS-CASPT2) using supporting subspaces and tensor hyper-contraction (THC).
• Utilized Laplace quadrature for factorizing energy denominators, including negative values critical for excited state calculations.
• Developed an efficient implementation leveraging graphical processing units (GPUs) and exploiting spatial sparsity in tensor operations.

Main Results:

• Achieved O(N^4) computational scaling and O(N^2) memory requirements, a significant reduction compared to previous algorithms.
• The THC approximation introduced negligible errors (≈0.01 eV) compared to non-THC methods.
• Demonstrated efficient performance through scaling behavior and computational timings, with GPU acceleration.

Conclusions:

• The new reduced scaling XMS-CASPT2 method enables efficient and accurate calculation of excited states.
• The method is interfaced with quantum mechanics/molecular mechanics (QM/MM) for studying complex systems.
• An example study on green fluorescent protein highlights the method's capability for large QM regions (278 atoms, >2300 basis functions).