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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Materials Science

Background:

  • Many-body expansion (MBE) is crucial for fragment-based methods to reduce the computational cost of ab initio quantum chemistry.
  • The combinatorial complexity of higher-order terms (n ≥ 4) in MBE limits its practical application.
  • Accurate electronic structure calculations for large systems remain a significant challenge due to computational scaling.

Purpose of the Study:

  • To develop an efficient algorithm and software to overcome the combinatorial bottleneck in many-body expansion calculations.
  • To enable accurate ab initio electronic structure calculations for significantly larger systems than previously feasible.
  • To investigate the behavior and necessity of high-order terms in MBE.

Main Methods:

  • Developed a bottom-up energy-based screening algorithm to manage combinatorial growth.
  • Implemented the algorithm in an open-source software package, "Fragme∩t".
  • Integrated a lightweight semi-empirical method for subsystem culling and used graph-based calculation management.

Main Results:

  • Successfully performed four-body calculations on (H2O)64 clusters with high accuracy (within 0.1 kcal/mol/monomer of supersystem) using <10% of subsystems.
  • Executed n-body calculations up to n=8 for (H2O)20 clusters, demonstrating termination via screening.
  • Achieved the largest reported n-body calculations using ab initio electronic structure theory to date.

Conclusions:

  • The developed algorithm and software effectively mitigate combinatorial issues in MBE.
  • High-order n-body terms in MBE calculations are largely artifacts of basis-set superposition error.
  • This work significantly advances the feasibility of applying fragment-based methods to very large molecular systems.