Putting PASPT2 on a Firmer Basis
Abstract
The recently proposed partial-active-space (PAS) multi-state second-order perturbation theory (PASPT2) [Precis. Chem. 4, 997 (2026)] features connected amplitudes and a connected, closed intermediate Hamiltonian. Despite these hallmarks, PASPT2 (denoted as PASPT2H from now on) is not strictly size-extensive, as originally thought (and numerically confirmed), albeit strictly size-consistent. Nevertheless, PASPT2 is near-extensive for the states with major projections on the chosen PAS ℳ0. This becomes more transparent upon introducing PASPT2X, a strictly size-extensive variant. Compared with the intruder-prone PASPT2X, the intruder-free PASPT2H merely neglects the second-order corrections that are important only for those states with major projections on the orthogonal complement ℛX of ℳ0 within the closed space ℳX (=ℳ0⊕ℛX); however, such states are not supported by the chosen finite one-particle basis set. The weak violation of size-extensivity is therefore numerically insignificant for the target states supported by ℳ0, reinforcing the theoretical basis of PASPT2H.
Versions
Related
- Putting a Temperature on Electron Correlation
- Biosolids in Washington State: Putting per- and poly-fluorinated alkyl substances concerns into a real-world context.
- Structural basis of interaction between Pol1 and DnaN from Mycobacterium tuberculosis
- Making Complete-Basis-Set Extrapolation Visible: A Spreadsheet-Based Activity for Upper-Division Computational Chemistry
- Structural basis for oxidation-coupled isomerization by ApnO
BibTeX
@misc{liu2026putting,
title = {{Putting PASPT2 on a Firmer Basis}},
author = {Chunzhang Liu and Ning Zhang and Wenjian Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.22152},
eprint = {2607.22152},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.22152},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Putting PASPT2 on a Firmer Basis
AU - Chunzhang Liu
AU - Ning Zhang
AU - Wenjian Liu
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2607.22152
UR - https://arxiv.org/abs/2607.22152
AB - The recently proposed partial-active-space (PAS) multi-state second-order perturbation theory (PASPT2) [Precis. Chem. 4, 997 (2026)] features connected amplitudes and a connected, closed intermediate Hamiltonian. Despite these hallmarks, PASPT2 (denoted as PASPT2H from now on) is not strictly size-extensive, as originally thought (and numerically confirmed), albeit strictly size-consistent. Nevertheless, PASPT2 is near-extensive for the states with major projections on the chosen PAS ℳ_0. This becomes more transparent upon introducing PASPT2X, a strictly size-extensive variant. Compared with the intruder-prone PASPT2X, the intruder-free PASPT2H merely neglects the second-order corrections that are important only for those states with major projections on the orthogonal complement ℛ_X of ℳ_0 within the closed space ℳ_X (=ℳ_0⊕ℛ_X); however, such states are not supported by the chosen finite one-particle basis set. The weak violation of size-extensivity is therefore numerically insignificant for the target states supported by ℳ_0, reinforcing the theoretical basis of PASPT2H.
ER -