Analytic First and Second Derivatives for the Fragment Molecular Orbital Method Combined with Molecular Mechanics

TL;DR

This paper develops analytic derivatives for the fragment molecular orbital method combined with molecular mechanics, enabling accurate vibrational analysis of complex biological molecules.

Contribution

It introduces analytic first and second derivatives for the FMO method with MM, incorporating orbital response and electrostatic effects at Hartree-Fock and DFT levels.

Findings

Orbital response terms are crucial for accurate derivatives.

Electrostatic embedding influences vibrational frequencies.

The method reproduces experimental IR frequencies within 17 cm$^{-1}$.

Abstract

Analytic first and second derivatives of the energy are developed for the fragment molecular orbital method interfaced with molecular mechanics in the electrostatic embedding scheme at the level of Hartree-Fock and density functional theory. The importance of the orbital response terms is demonstrated. The role of the electrostatic embedding upon molecular vibrations is analyzed, comparing force field and quantum-mechanical treatments for an ionic liquid and a solvated protein. The method is applied for 100 protein conformations sampled in MD to take into account the complexity of a flexible protein structure in solution, and a good agreement to experimental data is obtained: frequencies from an experimental IR spectrum are reproduced within 17 cm$^{-1}$.