Multi-state local complete active space second-order perturbation theory using pair natural orbitals (PNO-MS-CASPT2)

A multistate complete active space second-order perturbation theory (CASPT2) method is presented, which utilizes domains of pair natural orbitals and projected atomic orbitals for the virtual space to achieve linear scaling of the computational effort with the number of inactive orbitals. The method is applied to compute excitation energies of medium size aromatic molecules, and it is shown that the impact of the local approximations on the computed excitation energies is negligible. The applicability and efficiency of the method are demonstrated for two large molecular systems with up to 400 correlated electrons, nearly 3000 basis functions, and 45 electronic states. Furthermore, some approximations in the CASPT2 zeroth-order Hamiltonian, which decouple different configuration spaces, are proposed and tested. These approximations allow us to reuse many integrals and amplitudes from the ground state in the excited states, thereby significantly reducing the computational effort for calculations with many states. Using appropriate correction terms, the impact of these approximations is shown to be small.