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

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