Reduced scaling CASPT2 using supporting subspaces and tensor hyper-contraction.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Complete Active Space Second-Order Perturbation (CASPT2) is a powerful method for electronic structure calculations.
• Conventional CASPT2 methods face computational scaling challenges (O(N^4) operations, O(N^2) memory) limiting their application to larger systems.

Purpose of the Study:

• To develop a reduced scaling formulation of CASPT2.
• To enable accurate electronic structure calculations for larger molecular systems.

Main Methods:

• Introduced the supporting subspace technique (SST) to decompose CASPT2 equations.
• Combined SST with Laplace quadrature and tensor hyper-contraction (THC) approximation.
• Utilized graphical processing units (GPUs) and exploited spatial sparsity for efficient implementation.

Main Results:

• Achieved reduced computational scaling (O(N^4) operations, O(N^3) for remainder).
• Demonstrated the feasibility of CASPT2 calculations for systems with approximately 100 atoms.
• Validated accuracy against conventional CASPT2 for gas-phase reactions.

Conclusions:

• The new formulation significantly enhances the efficiency of CASPT2 calculations.
• This advancement opens possibilities for studying complex chemical reactions in large systems, such as S_N2 reactions in carbon nanotubes.