Evaluation of Energy Gradients and Infrared Vibrational Spectra through Molecules-in-Molecules Fragment-Based Approach

Molecules-in-Molecules (MIM) is a general hybrid fragment-based extrapolation approach for calculating accurate total energies of large molecules, similar in spirit to the popular ONIOM methodology. In this work, the MIM model is extended for the precise evaluation of the energy gradients and infrared (IR) vibrational spectra of large molecules. The overlapping subsystems in this work are constructed from nonoverlapping fragments using a number-based scheme, and the dangling bonds are saturated with link-hydrogen atoms. Independent fragment calculations are performed to evaluate the energies and its gradients. Subsequently, the link-atom energy gradient components are projected back onto the corresponding host and supporting atoms, through the Jacobian projection method, as in the ONIOM approach. After geometry optimization, the Jacobian link-atom projection method is also employed for the precise evaluation of the force constants and dipole derivatives of the full molecule. The performance of the MIM model is benchmarked on 25 small-to-large peptides, with inevitable weak long-range intramolecular interactions. Upon accounting these long-range interactions through a second layer, at an inexpensive low-level of theory (MIM2), the energy accuracy improve by 80%, compared to MIM with one layer (MIM1). The MIM2 IR frequencies and intensities have an similar to 75% improvement, compared to the corresponding values at the MIM1 level of theory. A similar improvement is also observed for anion, cation, and radical systems constructed from the neutral benchmark molecules. The accuracy and performance of the benchmark systems validate the MIM model for exploring the vibrational infrared spectra of large molecules.