On the Cholesky decomposition for electron propagator methods: General aspects and application on C(60)

Area of Science:

• Computational chemistry
• Quantum chemistry
• Molecular modeling

Background:

• Electron propagator methods are crucial for understanding molecular electronic structure.
• Large molecules pose computational challenges for traditional methods.
• Efficient algorithms are needed to handle complex electronic structure calculations.

Purpose of the Study:

• To develop a parallel computer program (P-RICDSigma) for treating large molecules using electron propagator methods.
• To exploit sparsity in the two-electron integral matrix for computational efficiency.
• To assess the accuracy and applicability of the developed program.

Main Methods:

• Developed the parallel program P-RICDSigma.
• Utilized Cholesky decomposition techniques to exploit matrix sparsity.
• Investigated various decomposition schemes and their impact on accuracy.
• Tested the program on a representative large molecule (C(60)).

Main Results:

• P-RICDSigma effectively treats the electronic structure of large molecules.
• Cholesky decomposition offers controlled error with a single parameter.
• Electron propagator methods show tolerance to moderate decomposition thresholds.
• Maximal errors in electron affinities and ionization potentials are within a few meV, becoming negligible with smaller thresholds.

Conclusions:

• The P-RICDSigma program is a powerful tool for accurate electronic structure calculations of large molecules.
• Cholesky decomposition is a viable technique for improving the efficiency of electron propagator methods.
• The developed method provides reliable results for electron affinities and ionization potentials.