Asymptotic Expansion for Electrostatic Embedding Integrals in QM/MM Calculations

Area of Science:

• Computational Chemistry
• Biomolecular Simulations

Background:

• Quantum Mechanics/Molecular Mechanics (QM/MM) methods are crucial for studying large molecular systems.
• Calculating electrostatic embedding integrals poses a significant computational challenge in QM/MM, especially with extensive molecular mechanics (MM) regions.

Purpose of the Study:

• To develop a computationally efficient algorithm for electrostatic embedding integrals in QM/MM.
• To accelerate long-range QM/MM interactions by employing asymptotic expansions and multipole moment-like expansions.

Main Methods:

• An asymptotic expansion for nuclear attraction-type integrals was developed.
• A spatial division algorithm and a cutoff radius for multipole expansions were implemented.
• The method was validated using deMon2k/CHARMM QM/MM on a large RNA polymerase II model.

Main Results:

• Long-range QM/MM interactions were approximated by atom-centered multipole expansions.
• Computational time for embedding integrals was reduced to under 200 seconds on an 8-core system for a 350,000-atom model.
• No loss of accuracy was observed compared to standard methods.

Conclusions:

• The developed method offers a substantial speedup for QM/MM calculations involving large MM regions.
• This advancement enables more efficient and accurate simulations of complex biological systems.
• The approach effectively addresses the computational bottleneck in electrostatic embedding integral calculations.