Efficient analytic second derivative of electrostatic embedding QM/MM energy: normal mode analysis of plant cryptochrome

TL;DR

This paper introduces an efficient analytic second derivative method for electrostatic embedding QM/MM energy calculations, enabling detailed vibrational analysis of complex biological systems like plant cryptochrome.

Contribution

The authors derive a full analytic second derivative for EE-QM/MM energy using the Q-vector method, improving computational efficiency and ease of implementation.

Findings

Normal modes of plant cryptochrome were computed.

Strong mixing between flavin vibrations and protein modes was observed.

Spectral densities and broadening of FAD absorption were estimated.

Abstract

Analytic second derivatives of electrostatic embedding (EE) quantum mechanics/molecular mechanics (QM/MM) energy are important for performing vibrational analysis and simulating vibrational spectra of quantum systems interacting with an environment represented as a classical electrostatic potential. The main bottleneck of EE-QM/MM second derivatives is the solution of coupled perturbed equations for each MM atom perturbation. Here, we exploit the Q-vector method {[J. Chem. Phys., 151, 041102 (2019)]} to workaround this bottleneck. We derive the full analytic second derivative of the EE-QM/MM energy, which allows to compute QM, MM and QM-MM Hessian blocks in an efficient and easy to implement manner. To show the capabilities of our method, we compute the normal modes for the full \textit{arabidopsis thaliana} plant cryptochrome. We show that the flavin adenine dinucleotide vibrations (QM subsystem) strongly mix with protein modes. We compute approximate vibronic couplings for the lowest bright transition, from which we extract spectral densities and the homogeneous broadening of FAD absorption spectrum in protein using vibrationally resolved electronic spectrum simulations.