Linear-Scaling Systematic Molecular Fragmentation Approach for Perturbation Theory and Coupled-Cluster Methods.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Method Development

Background:

• The coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method is the gold standard but computationally expensive (O(N^7)).
• High computational cost limits CCSD(T) applications to small molecular systems.
• Systematic molecular fragmentation (SMF) offers a path to linear-scaling coupled-cluster methods.

Purpose of the Study:

• To develop and validate a revised linear-scaling systematic molecular fragmentation (LSSMF) approach for coupled-cluster (CC) methods.
• To introduce a new fragmentation algorithm for smaller fragments suitable for high-level CC.
• To enhance existing algorithms with a modified nonbonded fragmentation scheme.

Main Methods:

• Implementation of revised nonbonded interaction handling in SMF, termed LSSMF, to achieve exact linear scaling.
• Development of a novel fragmentation algorithm producing smaller fragments for improved CC compatibility.
• Performance comparison of LSSMF-CC methods (e.g., LSSMF-CCSD(T), LSSMF-MP2) against canonical versions using alkane datasets of varying sizes.

Main Results:

• LSSMF-CCSD(T) demonstrated negligible errors (MAE 0.20-0.59 kcal mol⁻¹) compared to canonical methods for CnH2n+2 (n=6-10).
• LSSMF(6,2)-MP2 achieved high accuracy (MAE 0.32 kcal mol⁻¹) for larger alkanes (n=50-70), showing a 26-fold error reduction over LSSMF(3,1).
• LSSMF-CCSD(T) successfully computed energies for a 10,004-atom alkane in ~24 hours and a 10,488-atom biomolecular complex in ~7 days.

Conclusions:

• LSSMF-CC methods are efficient and reliable for large-scale chemical systems where canonical methods are computationally prohibitive.
• Bonded level 3 accuracy is insufficient for large systems; higher levels (≥5) with nonbonded level 2 are recommended for high accuracy.
• The LSSMF approach offers substantial improvements over the original SMF, enabling accurate computational chemistry for significantly larger systems.