The Regularized Frozen Natural Orbital approach to CASPT2: extension to Restricted Active Space wave functions, different multiplicities and assessment of correlation effects

Résumé fourni par la source

The frozen natural orbital (FNO) method is a well-known approximation that significantly reduces the cost of many-body perturbation theory treatments for obtaining correlation energies in a systematic and controlled manner, enabling the simulation of larger and more realistic molecular systems. Here, we implement FNO on top of restricted active-space self-consistent field (RASSCF) wave function within second-order perturbation theory, leading to the FNO-RASPT2 method. To account for the additional approximations incurred when using restricted RASSCF wave functions, as well as to apply it to states of different molecular charge and spin multiplicity, we introduce a regularisation approach via a level-shift in the orbital deletion procedure, which helps avoid singularities resulting from vanishing denominators due to the reduced occupation of restricted (active) virtual orbitals and that we show does not significantly influence the final energies obtained. Numerical results on vertical excitation energies showcase the FNO to be up to ∼3.5 faster than the parent computation while retaining ∼95% of the dynamic correlation energy and being within 0.1 eV of the reference calculation, with the CASPT2 equations-the main bottleneck in large molecular systems-registering over an order of magnitude speed-up. An in-depth analysis shows the regularized FNO approach to retain electron correlation appropriately for internal and semi-internal contributions, while displaying larger deviations for the external term, which originates from the initial FNO truncation based on an approximated one-electron reduced density matrix. Ongoing efforts are directed towards improving and extending our current implementation to the calculation of analytic gradients and non-adiabatic couplings to enable faster non-adiabatic molecular dynamics simulations in larger and more realistic molecular systems.

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