Monte Carlo MP2-F12 for Noncovalent Interactions: The C₆₀ Dimer

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Accurate calculation of intermolecular interaction energies is crucial for understanding noncovalent interactions in chemistry and biology.
• Explicitly correlated (F12) methods and second-order many-body perturbation theory (MP2) offer improved accuracy but can be computationally expensive.
• Stochastic methods, like Monte Carlo, provide a scalable alternative for evaluating complex energy calculations.

Purpose of the Study:

• To develop a scalable stochastic algorithm for evaluating explicitly correlated (F12) MP2 energies.
• To apply the algorithm to study weak, noncovalent, intermolecular interactions.
• To reduce the statistical uncertainty in binding energy calculations for such interactions.

Main Methods:

• Transformation of MP2-F12 energy difference formulas into high-dimensional integrals of Green's functions.
• Evaluation of integrals using Monte Carlo methods augmented with parallel execution and convergence acceleration techniques.
• Implementation of techniques such as redundant-walker convergence, direct-sampling autocorrelation elimination, and control-variate error reduction.
• Sharing of electron-pair walkers across supermolecules and subsystems to minimize statistical uncertainty.

Main Results:

• The algorithm successfully evaluates explicitly correlated (F12) MP2 energies for intermolecular interactions.
• Statistical uncertainty in MP2 binding energy calculations is reduced by one to two orders of magnitude.
• The method predicts a binding energy of 19.1 ± 4.0 kcal mol^-1 for the C₆₀ dimer at a specific distance.

Conclusions:

• The developed scalable stochastic algorithm provides an efficient and accurate approach for calculating MP2-F12 energies.
• The method significantly enhances the precision of binding energy calculations for noncovalent interactions.
• This approach offers a promising avenue for studying complex molecular systems where accurate interaction energies are required.