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

• Published in: Journal of chemical theory and computation 2020-04, Vol.16 (6)
• Main Authors: Schwinn, Karno, Ferré, Nicolas, Huix-Rotllant, Miquel
• Format: Article
• Language: English
• Subjects: Chemical Sciences; or physical chemistry; Theoretical and
• ISSN: 1549-9618; 1549-9626
• DOI: 10.1021/acs.jctc.9b01145

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 effcient and easy to implement manner. To show the capabilities of our method, we compute the normal modes for the full 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 vibrationally resolved absorption spectrum of FAD in protein.