Efficient frequency calculations in QM/MM using the Mobile Block Hessian method

Normal mode analysis (NMA) is a well-known technique which estimates the intrinsic frequencies of chemical systems by assuming a harmonic shape for the potential energy surface. Despite its simplicity, it is still a popular approach to predict vibrational IR and Raman spectra, to identify chemical groups [1], or to study the large motions involved in conformational changes of biomolecules [2]. The method is based on the diagonalization of the Hessian matrix, which contains the second derivatives of the potential energy with respect to the 3N nuclear coordinates. In extended QM/MM systems, however, its calculation, storage and diagonalization is an expensive computational task. Even in the case of a small QM region, the numerous derivatives of the QM/MM interaction terms still form a bottleneck in the frequency calculation: each MM atom displacement atom affects the charge distribution in the QM region, resulting in a large number of coupled perturbation self-consistent field (CPSCF) equations [3].