Computational Vibrational Spectroscopy of Peptides and Proteins in One and Two Dimensions

Abstract

Vibrational spectroscopy provides direct information on molecular environment and motions but, its interpretation is often hampered by band broadening. Over the past decade, two-dimensional (2D) vibrational spectroscopy has emerged as a promising technique to overcome a number of difficulties associated with linear spectroscopy and provided significantly detailed information on the structure and dynamics of complex molecules in condensed phases. This Account reviews recently developed computational methods used to simulate 1D and 2D vibrational spectra. The central quantity to calculate in computational spectroscopy is the spectroscopic response function, which is the product of many contributing factors such as vibrational transition energies, transition moments, and their modulations by fluctuating local environment around a solute. Accurate calculations of such linear and nonlinear responses thus require a concerted effort employing a wide range of methods including electronic structure calculation (ESC) and molecular dynamics (MD) simulation. The electronic structure calculation can provide fundamental quantities such as normal-mode frequencies and transition multipole strengths. However, since the treatable system size is limited with this method, classical MD simulation has also been used to account for the dynamics of the solvent environment. To achieve chemical accuracy, these two results are combined to generate time series of fluctuating transition frequencies and transition moments with the distributed multipole analysis, and this particular approach has been known as the hybrid ESC/MD method. For coupled multichromophore systems, vibrational properties of each chromophore such as a peptide are individually calculated by electronic structure methods and the Hessian matrix reconstruction scheme was used to obtain local mode frequencies and couplings of constituting anharmonic oscillators. The spectra thus obtained, especially for biomolecules including polypeptides and proteins, have proven to be reliable and in good agreement with experimental spectra. An alternative to the hybrid method has also been developed, where the classical limit of the vibrational response function was considered. Its main attraction is the capability to obtain the spectra directly from a set of MD trajectories. A novel development along this direction has been achieved by using quantum mechanical/molecular mechanical (QM/MM) force fields for the accurate description of vibrational anharmonicity and chromophore polarization effects. The latter aspects are critical in the 2D case because classical force fields employing harmonic intramolecular potential cannot produce reliable 2D signal. We anticipate that the computational methods presented here will continue to evolve along with experimental advancements and will be of use to further elucidate ultrafast dynamics of chemical and biological systems.

Molecular quantum mechanical gradients within the polarizable embedding approach—Application to the internal vibrational Stark shift of acetophenone

“…Whenever a highresolution structure of the protein is available, computations constitute a complementary tool that allows a direct evaluation of the internal electric fields. 24 Correlating the computed fields with the vibrational frequency of the probe (experimental or calculated), one obtains a calibration curve that provides a quantitative mapping of the electrostatic landscape in other complex environments based on the vibrational frequency of the probe.…”

MOVIPAC: Vibrational spectroscopy with a robust meta‐program for massively parallel standard and inverse calculations

“…More accurate methods for the variational calculation of molecular vibrations including anharmonic effects [2][3][4][5][6][7] are under constant development but can hardly be applied to truly large molecules containing on the order of 100 atoms and more. Hence, molecular dynamics approaches are often used as a means to include anharmonic effects on the motion of atomic nuclei [8,9] but suffer from the neglect of quantum effects on the nuclear motion. Moreover, they necessitate force-field approximations or require tremendous resources for the generation of trajectories if the potential energy surface is calculated with first-principles methods.…”

Vibrational coherence and energy transfer in two-dimensional spectra with the optimized mean-trajectory approximation

“…One successful strategy is to treat a subsystem of interest with an implementation of quantum dynamics and to treat the rest of the system with classical or semiclassical mechanics. [24][25][26][27][28][29][30][31][32][33] An alternative approach is to treat all degrees of freedom consistently with a semiclassical approximation to quantum dynamics. 19,20,[34][35][36][37][38][39][40] Kryvohuz and Cao 41 have developed a semiclassical approximation of response functions in terms of classical dynamics in action-angle variables 42 with action variables subject to quantization conditions.…”