Reduced scaling implementation of the coupled cluster-based static embedding method, MPCC with density fitting
Abstract
An improved algorithm to implement our previously proposed static quantum embedding method MPCC (J. Chem. Phys. 161, 164107 (2024)) is presented. It uses the density-fitting (DF) approximation for the electron-repulsion integrals (ERIs) across all layers of the embedding method: the low-level method, the screened interaction, and the high-level method. Additionally, an approximate factorized solution of the Sylvester equation is employed based on the Laplace transformation for the low-level method. To build the screened interaction, we have explored an approximate construction of it based on the distinguishable cluster approximation (DCA) by Kats and Manby (J. Chem. Phys. 141, 061101 (2014)), which amounts to neglecting certain higher-order exchange and ladder diagrams. Combining all these techniques, we have obtained an 𝒪(N4) algorithm for the low-level method; a non-iterative Nfrag 𝒪(N4) algorithm for the screened interaction; and an iterative 𝒪(Nfrag6) algorithm for the fragment solver, where Nfrag is the number of fragment orbitals and N is the total number of orbitals. The resulting low-scaling implementation of the MPCC method is applied to trans polyacetylenes, that is, C2nH2n+2 molecules for chain lengths n=1−8, and the timing and accuracy of the method are compared to the original unfactorized implementation. Moreover, the approximations are further validated by applying the method to the potential energy surface of the \ce{O3} molecule. Finally, we apply the method to the selected molecules in the S22 dataset for which the performance of the MP2 method is known to be poor. The results demonstrate that the DF-based implementation of the MPCC method provides a significant reduction in computational cost while maintaining accuracy comparable to that of the original implementation.
Related
- Bringing coupled‑cluster theory to the strong-correlation frontier
- Examining Convergence of Cluster Perturbation Theory and Cluster Coupled Cluster for J1-J2 Heisenberg Spin Lattices
- Coupled Cluster Amplitude Extrapolation in Geometry Optimization
- Coupled cluster theory for multireference and open-shell molecules
- Cavity Loss in QED Coupled-Cluster Theory: Polariton Linewidths, Driven Steady States, and the Rabi Splitting
BibTeX
@misc{shee2026reduced,
title = {{Reduced scaling implementation of the coupled cluster-based static embedding method, MPCC with density fitting}},
author = {Avijit Shee and Fabian M. Faulstich and K. Birgitta Whaley and Lin Lin and Martin Head-Gordon},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.32884},
eprint = {2609.32884},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32884},
}
RIS
TY - UNPB
TI - Reduced scaling implementation of the coupled cluster-based static embedding method, MPCC with density fitting
AU - Avijit Shee
AU - Fabian M. Faulstich
AU - K. Birgitta Whaley
AU - Lin Lin
AU - Martin Head-Gordon
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2609.32884
UR - https://arxiv.org/abs/2609.32884
AB - An improved algorithm to implement our previously proposed static quantum embedding method MPCC (J. Chem. Phys. 161, 164107 (2024)) is presented. It uses the density-fitting (DF) approximation for the electron-repulsion integrals (ERIs) across all layers of the embedding method: the low-level method, the screened interaction, and the high-level method. Additionally, an approximate factorized solution of the Sylvester equation is employed based on the Laplace transformation for the low-level method. To build the screened interaction, we have explored an approximate construction of it based on the distinguishable cluster approximation (DCA) by Kats and Manby (J. Chem. Phys. 141, 061101 (2014)), which amounts to neglecting certain higher-order exchange and ladder diagrams. Combining all these techniques, we have obtained an 𝒪(N^4) algorithm for the low-level method; a non-iterative N_frag 𝒪(N^4) algorithm for the screened interaction; and an iterative 𝒪(N_frag^6) algorithm for the fragment solver, where N_frag is the number of fragment orbitals and N is the total number of orbitals. The resulting low-scaling implementation of the MPCC method is applied to trans polyacetylenes, that is, C_2nH_2n+2 molecules for chain lengths n=1−8, and the timing and accuracy of the method are compared to the original unfactorized implementation. Moreover, the approximations are further validated by applying the method to the potential energy surface of the \ce{O3} molecule. Finally, we apply the method to the selected molecules in the S22 dataset for which the performance of the MP2 method is known to be poor. The results demonstrate that the DF-based implementation of the MPCC method provides a significant reduction in computational cost while maintaining accuracy comparable to that of the original implementation.
ER -