The Regularized Frozen Natural Orbital approach to CASPT2: extension to Restricted Active Space wave functions, different multiplicities and assessment of correlation effects
- 1Instituto de Ciencia Molecular, Universitat de Valencia, P.O. Box 22085, Valencia, Spain, ES-46071
- 2National Centre for Computational Design and Discovery of Novel Materials (MARVEL
- 3École Polytechnique Fédérale de Lausanne
Abstract
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.
Related
- Maximum-Entropy Extension of Quantum Correlation Functions from Short Real-Time Dynamics
- Non-orthogonal extension of Graspg - dynamic electron correlation for large and compact active spaces
- alpha_s from hadron multiplicities: an updated analysis
- Search for new physics using single-lepton events with high multiplicities of jets and b jets in proton-proton collisions at √s = 13 TeV
- Revisiting Unidentified Charged-Hadron Fragmentation Functions with Modern COMPASS SIDIS Multiplicities
BibTeX
@misc{cuellarzuquin2026regularized,
title = {{The Regularized Frozen Natural Orbital approach to CASPT2: extension to Restricted Active Space wave functions, different multiplicities and assessment of correlation effects}},
author = {Juliana Cuéllar-Zuquin and Javier Segarra-Martí and Francesco Aquilante},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15007726/v2},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15007726/v2},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - The Regularized Frozen Natural Orbital approach to CASPT2: extension to Restricted Active Space wave functions, different multiplicities and assessment of correlation effects
AU - Juliana Cuéllar-Zuquin
AU - Javier Segarra-Martí
AU - Francesco Aquilante
PY - 2026
DA - 2026/10/16
PB - ChemRxiv
DO - 10.26434/chemrxiv.15007726/v2
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15007726/v2
AB - 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.
ER -