Hybrid Quantum/Classical Simulations of the Vibrational Relaxation of the Amide I Mode of N-Methylacetamide in D₂O Solution

Abstract

Hybrid quantum/classical molecular dynamics (MD) is applied to simulate the vibrational relaxation (VR) of the amide I mode of deuterated N-methylacetamide (NMAD) in aqueous (D(2)O) solution. A novel version of the vibrational molecular dynamics with quantum transitions (MDQT) treatment is developed in which the amide I mode is treated quantum mechanically while the remaining degrees of freedom are treated classically. The instantaneous normal modes of the initially excited NMAD molecule (INM(0)) are used as internal coordinates since they provide a proper initial partition of the system in quantum and classical subsystems. The evolution in time of the energy stored in each individual normal mode is subsequently quantified using the hybrid quantum-classical instantaneous normal modes (INM(t)). The identities of both the INM(0)s and the INM(t)s are tracked using the equilibrium normal modes (ENMs) as templates. The results extracted from the hybrid MDQT simulations show that the quantum treatment of the amide I mode accelerates the whole VR process versus pure classical simulations and gives better agreement with experiments. The relaxation of the amide I mode is found to be essentially an intramolecular vibrational redistribution (IVR) process with little contribution from the solvent, in agreement with previous theoretical and experimental studies. Two well-defined relaxation mechanisms are identified. The faster one accounts for ≈40% of the total vibrational energy that flows through the NMAD molecule and involves the participation of the lowest frequency vibrations as short-life intermediate modes. The second and slower mechanism accounts for the remaining ≈60% of the energy released and is associated to the energy flow through specific mid-range and high-frequency modes.

Vibrational Energy Relaxation: A Benchmark for Mixed Quantum–Classical Methods

“…Here we treat the mode x 1 quantum mechanically, and all other bath modes ( x 2 , ..., x N ) are treated classically. Note that several quantum mechanical treatments of vibrational degrees of freedom have been performed in literature, including the work of Hammes-Schiffer and Tully, Bastida and co-workers, − and Schubert and co-workers …”

“…First consider FSSH. FSSH is a popular, stochastic tool for running dynamics that is a very rough, approximate solution to the quantum–classical Liouville equation (QCLE). , Nowadays, FSSH is one of the most popular choices for simulating mixed quantum–classical dynamics, and there is a significant literature calculating VER rates with FSSH (often obtaining rates within a factor of 2 compared to the experimental rates). − Theoretical investigations by Tully on reduced dimensional models have demonstrated that FSSH should capture VER rates qualitatively, and furthermore, Tully and co-workers , and Corcelli and co-workers have shown that FSSH obtains detailed balance approximately. Interestingly, however, Käb has argued that decoherence is essential for obtaining detailed balance when studying the vibrational relaxation of a harmonic oscillator bilinearly coupled to a bath of harmonic oscillators .…”

Vibrational Spectroscopy of N3– in the Gas and Condensed Phase

“…3,4 For example, the CO chromophore was used as a probe to investigate the solvation dynamics of N-Methylacetamide in water. 3,[5][6][7][8][9][10] Similarly, the CN − stretching frequency has been used as a probe to investigate its own solvation dynamics [11][12][13][14] and structural and energetic features of a protein-ligand complex by attaching the probe to benzene. 15,16 A versatile, spatially sensitive spectroscopic probe can also report on the dynamics of a system while minimizing the perturbations induced.…”

“…Using 2D IR spectroscopy, the coupling between inter- and intramolecular degrees of freedom, such as the hydrogen bonding network in solution or structural features of biological macromolecules, can be investigated by monitoring the fluctuation of fundamental vibrational frequencies of a probe molecule or a ligand attached to a complex or a biological macromolecule. For quite some time, the amide-I stretching frequency has been used for this and has provided fundamental, molecular level insight into the structural dynamics of small molecules and proteins alike. , For example, the CO chromophore was used as a probe to investigate the solvation dynamics of N -methylacetamide in water. ,− Similarly, the CN – stretching frequency has been used as a probe to investigate its own solvation dynamics − and structural and energetic features of a protein–ligand complex by attaching the probe to benzene. , …”

Vibrational mode assignment of finite temperature infrared spectra using the AMOEBA polarizable force field

“…28 pointed out some limitations, e.g. 37 Furthermore, INMA can be very time-consuming on large systems. [49][50][51] The instantaneous normal mode analysis (INMA) and its variants [31][32][33][34][35][36] are obtained by diagonalizing the Hessian matrix at each instantaneous configuration of the molecule.…”