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Two-dimensional infrared spectroscopy of amide I vibrations is increasingly being used to study the structure and dynamics of proteins and peptides. Amide I, a primarily carbonyl stretching vibration of the protein backbone, provides information on secondary structures as a result of vibrational couplings and on hydrogen-bonding contacts when isotope labeling is used to isolate specific sites. In parallel with experiments, computational models of amide I spectra that use atomistic structures from molecular dynamics simulations have evolved to calculate experimental spectra. Mixed quantum-classical models use spectroscopic maps to translate the structural information into a quantum-mechanical Hamiltonian for the spectroscopically observed vibrations. This allows one to model the spectroscopy of large proteins, disordered states, and protein conformational dynamics. With improvements in amide I models, quantitative modeling of time-dependent structural ensembles and of direct feedback between experiments and simulations is possible. We review the advances in developing these models, their theoretical basis, and current and future applications.
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