Reduced Scaling Formulation of CASPT2 Analytical Gradients Using the Supporting Subspace Method

29 October 2020, Version 1
This content is a preprint and has not undergone peer review at the time of posting.


We present a reduced scaling and exact reformulation of state specific CASPT2 analytical gradients in terms of the MP2 and Fock derivatives using the supporting subspace method. This work follows naturally from the supporting subspace formulation of the CASPT2 energy in terms of the MP2 energy using dressed orbitals and Fock builds. For a given active space configuration, the terms corresponding to the MP2-gradient can be evaluated with O(N5) operations, while the rest of the calculations can be computed with O(N3) operations using Fock builds, Fock gradients, and linear algebra. When tensor-hyper-contraction is applied simultaneously, the computational cost can be further reduced to O(N4) for a fixed active space size. The new formulation enables efficient implementation of CASPT2 analytical gradients by leveraging existing GPU-based MP2 and Fock routines. We present benchmark results that demonstrate the accuracy and performance of the new method. Example applications of the new method in ab initio molecular dynamics simulation and constrained geometry optimization are given.


analytical gradients
tensor hyper-contraction
supporting subspace

Supplementary materials



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