pANO-F12: An atomic natural orbital-inspired route to more compact basis sets for F12 explicitly correlated methods
Abstract
Explicitly correlated methods such as MP2-F12 and CCSD(F12*) exhibit much faster basis set convergence (asymptotically ∝ L−7, with L the highest angular momentum) than orbital-only approaches. Yet it has been pointed out that cc-pVnZ-F12 basis sets themselves are substantially larger than the corresponding cc-pVnZ, and specifically that cc-pVDZ-F12 is the size of cc-pVTZ. One way to generate compact basis sets in an orbital-only context are Atomic Natural Orbital (ANO) basis sets [J. Almlöf and P. R. Taylor, JCP 86, 4070 (1987)]. However, obtaining the required first-order reduced density matrix while properly accounting for the F12 geminal is problematic. In this work, we show that an energy minimization-based contraction process under linear independence constraints yields `pseudo-ANO' (pANO) basis sets that are functionally equivalent in quality. Subsequently, we apply this recipe to obtain pANO-F12 basis sets from the same elements, then validate them for several thermochemical benchmarks and for the hypersensitive out-of-plane vibrations of benzene. We show that, unlike cc-pVnZ-F12, pANO-F12 exhibits the familiar shell structure seen in cc-pVnZ and ANO basis sets, and that pANO-F12 offers a route to more compact F12 basis sets more amenable to medium-sized systems, especially in conjunction with localized pair natural orbital approaches. Overall, the pANO approach is most beneficial for the smaller double-and triple-zeta basis sets, offering either superior performance to cc-pVnZ-F12 at same cost, or similar performance at lower cost.
Related
- A linear-scaling explicitly correlated local natural orbital CCSD(T) approach
- Target breadth and mutation resilience in African-natural-product-inspired antimalarial chemotypes: a computational analysis
- Brueckner Orbitals in Local Pair Natural Orbital Coupled-Cluster Theory: DLPNO-BCCD(T) and DLPNO-BCCD(T)_Lambda2
- Electron Density of Delocalized Bonds from Correlated One-Particle Density Matrices
- Local phase reconfiguration induced by laser-driven thermal cycles in a highly-correlated manganite
BibTeX
@misc{fishman2026panof12,
title = {{pANO-F12: An atomic natural orbital-inspired route to more compact basis sets for F12 explicitly correlated methods}},
author = {Vladimir Fishman and Jan M. L. Martin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.22543},
eprint = {2605.22543},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.22543},
}
RIS
TY - UNPB
TI - pANO-F12: An atomic natural orbital-inspired route to more compact basis sets for F12 explicitly correlated methods
AU - Vladimir Fishman
AU - Jan M. L. Martin
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2605.22543
UR - https://arxiv.org/abs/2605.22543
AB - Explicitly correlated methods such as MP2-F12 and CCSD(F12*) exhibit much faster basis set convergence (asymptotically ∝ L^−7, with L the highest angular momentum) than orbital-only approaches. Yet it has been pointed out that cc-pVnZ-F12 basis sets themselves are substantially larger than the corresponding cc-pVnZ, and specifically that cc-pVDZ-F12 is the size of cc-pVTZ. One way to generate compact basis sets in an orbital-only context are Atomic Natural Orbital (ANO) basis sets [J. Almlöf and P. R. Taylor, JCP 86, 4070 (1987)]. However, obtaining the required first-order reduced density matrix while properly accounting for the F12 geminal is problematic. In this work, we show that an energy minimization-based contraction process under linear independence constraints yields `pseudo-ANO' (pANO) basis sets that are functionally equivalent in quality. Subsequently, we apply this recipe to obtain pANO-F12 basis sets from the same elements, then validate them for several thermochemical benchmarks and for the hypersensitive out-of-plane vibrations of benzene. We show that, unlike cc-pVnZ-F12, pANO-F12 exhibits the familiar shell structure seen in cc-pVnZ and ANO basis sets, and that pANO-F12 offers a route to more compact F12 basis sets more amenable to medium-sized systems, especially in conjunction with localized pair natural orbital approaches. Overall, the pANO approach is most beneficial for the smaller double-and triple-zeta basis sets, offering either superior performance to cc-pVnZ-F12 at same cost, or similar performance at lower cost.
ER -