Analytic second derivatives for the efficient electrostatic embedding in the fragment molecular orbital method.

The analytic second derivatives of the energy with respect to nuclear coordinates are developed for restricted Hartree-Fock and density functional theory, based on the two-body fragment molecular orbital method (FMO) and combined with the electrostatic embedding potential, self-consistently determined by point charges for far separated fragments and electron densities for near fragments. The accuracy of the method is established with respect to FMO using the exact embedding potential based on electron densities and to full calculations without fragmentation. The computational efficiency of parallelization is measured on the K supercomputer and the method is applied to simulate infrared spectra of two proteins, Trp-cage (PDB: 1L2Y) and crambin (1CRN). The nature of the vibrations in the Amide I peak of crambin and the Tyr symmetric stretch peak in Trp-cage are analyzed in terms of localized vibrations. © 2018 Wiley Periodicals, Inc.