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.

Fluctuating turnover times of a single enzyme become observable with the advent of modern cutting-edge, single enzyme experimental techniques. Although the conventional chemical kinetics and its modern generalizations could provide a good quantitative description for the mean of the enzymatic turnover times, to our knowledge there has not yet been a successful quantitative interpretation for the variance or the randomness of the enzymatic turnover times. In this review, we briefly review several theories in this field, and compare predictions of these theories to the randomness parameter data reported for β-galactosidase enzyme. We find the recently proposed kinetics for renewal reaction processes could provide an excellent quantitative interpretation of the randomness parameter data. From the analysis of the randomness parameter data of the single enzyme reaction, one can extract quantitative information about the mean lifetime of enzyme-substrate complex; the success or the failure probability of the catalytic reaction per each formation of ES complex; and the non-Poisson character of the reaction dynamics of the ES complex (which is beyond reach of the long-standing paradigm of the conventional chemical kinetics).

We report a robust quadratic relation between the inverse substrate concentration and the second moment, , of the catalytic turnover time distribution for enzyme reactions. The results hold irrespective of the mechanism and dynamics of the enzyme reaction and suggest a novel single molecule experimental analysis that provides information about reaction processes of the enzyme-substrate complex and ergodicity of the enzyme reaction system, which is beyond the reach of the conventional analysis for the mean reaction time, . It turns out that - 2(2) is linear in inverse substrate concentration for an ergodic homogeneous enzyme system given that the enzyme substrate encounter is a simple rate process, and its value at the high substrate concentration limit provides direct information about if any non-Poisson reaction process of the enzyme-substrate complex. For a nonergodic heterogeneous reaction system, the corresponding quantity becomes a quadratic function of the inverse substrate concentration. This leads us to suggest an ergodicity measure for single enzyme reaction systems. We obtain a simple analytic expression of the randomness parameter for the single catalytic turnover time, which could provide a quantitative explanation about the previously reported randomness data of the beta-galactosidase enzyme. In obtaining the results, we introduce novel chemical kinetics applicable to a non-Poisson reaction network with arbitrary connectivity, as a generalization of the conventional chemical kinetics.

We applied the combined quantum mechanical (QM)/molecular mechanical (MM) molecular dynamics (MD) simulation method in assessing IR spectra of N-methylacetamide and its deuterated form in aqueous solutions. The model peptide is treated at the Austin Model 1 (AM1) level and the induced dipole effects by the solvent are incorporated in fluctuating solute dipole moments, which are calculated using partial charges from Mulliken population analyses without resorting to any available high-level ab initio dipole moment data. Fourier transform of the solute dipole autocorrelation function produces in silico IR spectra, in which the relative peak intensities and bandwidths of major amide bands are quantitatively compatible with experimental results only when both geometric and electronic polarizations of the peptide by the solvent are dealt with at the same quantum-mechanical level. We cast light on the importance of addressing dynamic charge fluctuations of the solute in calculating IR spectra by comparing classical and QM/MM MD simulation results. We propose the adjustable scaling factors for each amide mode to be directly compared with experimental data.

The vibrational absorption (IR) and vibrational circular dichroism (VCD) spectra of alanine dipeptide analog in water are directly calculated by Fourier transforming the time correlation functions of the electric and magnetic dipole moments, which are calculated using the dynamic partial charges and trajectory of the peptide generated from the quantum mechanical/molecular mechanical molecular dynamics simulations. The alanine dipeptide analog is treated at the Hartree-Fock level with 3-21G, 4-31G, 6-31G, and 6-31G(*) basis sets and the solvent H(2)O is modeled with the TIP3P water. The atomic partial charges are obtained from the Lowdin population analysis, which gives consistent IR spectral profiles irrespective of the basis sets used. The simulated VCD spectrum by a polyproline II(P(II))-dominant trajectory is compatible with the previous experimental results of the polyproline peptides, where the amide I and II VCD bands are negative couplets with a weak positive peak to the high frequency region. The sampling efficiency of the P(II) conformer is much lower than the other ones at all basis levels used. The simulated VCD spectrum of alpha-helix averaged over five trajectories has the reverse sign pattern compared to the P(II) spectrum and is found to be consistent with the previously observed spectral features of alpha-helical polypeptides. The sign patterns of the beta-strand VCD spectrum are qualitatively similar to the experimental spectra of beta-sheet rich proteins. The VCD spectra obtained from the trajectories containing several extended conformers such as beta and P(II) are not clearly distinguishable from the beta-strand-dominant spectra. It is interesting that the P(II) and the coil VCD spectra coincide in sign pattern and relative intensity for all amide modes. This demonstrates that the negative couplet structures of the amide I and II VCD spectra do not necessarily prove the dominance of either P(II) or coil conformation. We anticipate that the present method can be used to directly simulate the IR and VCD spectra of structurally heterogeneous biomolecules in condensed phases.