Simulation of vibrational energy transfer in two-dimensional infrared spectroscopy of amide I and amide II modes in solution

Population transfer between vibrational eigenstates is important for many phenomena in chemistry. In solution, this transfer is induced by fluctuations in molecular conformation as well as in the surrounding solvent. We develop a joint electrostatic density functional theory map that allows us to connect the mixing of and thereby the relaxation between the amide I and amide II modes of the peptide building block N-methyl acetamide. This map enables us to extract a fluctuating vibrational Hamiltonian from molecular dynamics trajectories. The linear absorption spectrum, population transfer, and two-dimensional infrared spectra are then obtained from this Hamiltonian by numerical integration of the Schrodinger equation. We show that the amide I/amide II cross peaks in two-dimensional infrared spectra in principle allow one to follow the vibrational population transfer between these two modes. Our simulations of N-methyl acetamide in heavy water predict an efficient relaxation between the two modes with a time scale of 790 fs. This accounts for most of the relaxation of the amide I band in peptides, which has been observed to take place on a time scale of 450 fs in N-methyl acetamide. We therefore conclude that in polypeptides, energy transfer to the amide II mode offers the main relaxation channel for the amide I vibration.     

Conformational preferences and vibrational frequency distributions of short peptides in relation to multidimensional infrared spectroscopy.

Molecular dynamics simulations of the structural distributions and the associated amide-I vibrational modes are carried out for dialanine peptide in water and carbon tetrachloride. The various manifestations in nonlinear-infrared spectroscopic experiments of the distributions of conformations of solvated dialanine are examined. The two-dimensional infrared (2D-IR) spectrum of dialanine exhibits the coupling between the amide oscillators and the correlations of the frequency fluctuations. An internally hydrogen-bonded conformation exists in CCl(4) but not in H(2)O where two externally hydrogen-bonded forms are preferred. Simulations of solvated dialanine show how the 2D-IR spectra expose the underlying structural distributions and dynamics that are not deducible from linear-infrared spectra. In H(2)O the 2D-IR shows cross-peaks from large coupling in the alpha-helical conformer and an elongated higher frequency diagonal peak, reflecting the broader distribution of structures for the more flexible acetyl end. In CCl(4), the computed cross-peak portion of the 2D-IR shows evidence of two amide-I transitions in the high-frequency region which are not apparent from the diagonal peak profile. The vibrational frequency inhomogeneity of the amide-I band arises from fluctuations of the instantaneous normal modes of these conformers rather than the shifts induced by hydrogen bonding. The simulation shows that there are correlations between fluctuations of the acetyl and amino end frequencies in H(2)O that arise from mechanical coupling and not from hydrogen bonding at the two ends of the molecule. The angular relationships between the two amide units which also show up in 2D-IR were computed, and spectral manifestations of them are discussed. The simulations also permit a calculation of the rate of energy transfer from one side of the molecule to the other. From these calculations, 2D-IR spectroscopy in conjunction with simulations is seen to be a promising tool for determining dynamics of structure changes in dipeptides.     

Two-dimensional infrared spectral signature and hydration of the oxalate dianion

Ultrafast vibrational spectra of the aqueous oxalate ion in the region of its carboxylate asymmetric stretch modes show novel relaxation processes. Two-dimensional infrared vibrational echo spectra and the vibrational dynamics obtained from them along with measurements of the anisotropy decay provide a picture in which the localization of the oxalate vibrational excitation onto the carboxylate groups occurs in ~450 fs. Molecular dynamics simulations are used to characterize the vibrational dynamics in terms of dihedral angle motion between the two carboxylate planes and solvation dynamics. The localization of the oxalate vibrational excitation onto the carboxylates is induced by the fluctuations in the carboxylate vibrational frequencies which are shown by theory and experiment to have a similar correlation time as the anisotropy decay.     

Signatures of beta-peptide unfolding in two-dimensional vibrational echo spectroscopy: a simulation study.

An ensemble of exciton Hamiltonians for the amide-I band of the folded and unfolded states of a helical beta-heptapeptide is generated using a molecular dynamics (MD) simulation. The correlated fluctuations of its parameters and their signatures in two-dimensional (2D) vibrational echo spectroscopy are computed. This technique uses infrared pulse sequences to provide ultrafast snapshots of molecular structural fluctuations, in analogy with multidimensional NMR. The present study demonstrates that, by combining a method of calculating the vibrational Hamiltonian from MD snapshots and the nonlinear exciton equations (NEE), it may be possible to simulate realistic multidimensional IR spectra of chemically and biologically interesting systems.     

N-乙基丙酰胺的飞秒二维红外光谱

利用飞秒二维红外实验方法, 结合稳态红外光谱实验和计算化学手段, 对β-肽模型分子N-乙基丙酰胺(NEPA)的超快结构动力学进行了研究. 结果表明, 在水溶液中, NEPA具有类α-肽酰胺-I 带的振动特征, 并表现出对分子结构和化学环境的灵敏性. 二维红外光谱动力学结果揭示了一个1 ps 左右的光谱扩散时间, 与酰胺-水之间的氢键结构动力学时间尺度一致.     

Simulations of vibrational spectra from classical trajectories: calibration with ab initio force fields

An algorithm allowing simulating vibrational spectra from classical time-dependent trajectories was applied for infrared absorption, vibrational circular dichroism, Raman, and Raman optical activity of model harmonic systems. The implementation of the theory within the TINKER molecular dynamics (MD) program package was tested with ab initio harmonic force fields in order to determine the feasibility for more extended MD simulations. The results suggest that sufficiently accurate frequencies can be simulated with integration time steps shorter than about 0.5 fs. For a given integration time step, lower vibrational frequencies ( approximately 0-2000 cm(-1)) could be reproduced with a higher accuracy than higher-frequency vibrational modes (e.g., O-H and C-H stretching). In principle, the algorithm also provides correct intensities for ideal systems. In applied simulations, however, the intensity profiles are affected by an unrealistic energy distribution between normal modes and a slow energy relaxation. Additionally, the energy fluctuations may cause weakening of the intensities on average. For ab initio force fields, these obstacles could be overcome by an arbitrary normal mode energy correction. For general MD simulations, averaging of many shorter MD trajectories started with randomly distributed atomic velocities provided the best spectral shapes. alpha-pinene, D-gluconic acid, formaldehyde dimer, and the acetylprolineamide molecule were used in the tests.     

Anharmonicity of amide modes

The principal contributions to the anharmonic coupling of amide vibrations are explored with the objective of comparing recent experiments with density functional theory and evaluating simple models of mode coupling. Experimental information obtained by means of two-dimensional infrared spectroscopy (2D IR) is reasonably well predicted by the computed one- and two-quantum anharmonic modes of amide-A, -I, and -II types in mono-, di- and tripeptides. The expansion of the vibrational energy up to the cubic and quartic coupling of harmonic modes suggested criteria to assess how localized are the forces determining the anharmonicity. The off-diagonal anharmonicity between an amide-A and one other amide mode was shown to be mainly determined by forces involving only these two modes, whereas the off-diagonal anharmonicity of two amide-I modes in peptides depended significantly on forces due to motions other than those of the amide-I type. Both the diagonal and off-diagonal anharmonicities exhibit sensitivity to peptide structures. These results should prove useful in linking 2D IR experimental results to secondary structure. Further, the results are used to evaluate the vibrational exciton model for the mixed-mode anharmonicities of the amide-I transitions.     

Motional narrowing in the time-averaging approximation for simulating two-dimensional nonlinear infrared spectra

The diagonal linewidth in two-dimensional infrared spectra is often narrower than the distribution of transition frequencies. The width along the antidiagonal is broader than predicted by the lifetime broadening. These effects arise from time-dependent fluctuations of the transition frequencies. They can be accounted for with a semiclassical approach. For systems with many coupled vibrational modes, this approach, however, becomes computationally too demanding to be practically applicable. A time-averaging approximation was suggested for linear infrared absorption spectra. In this paper, we demonstrate that the averaging can be optimized to fit a broader scale of frequency fluctuations by using a Gaussian weight function instead of the originally proposed box function. We further generalize the time-averaging method to allow the simulation of two-dimensional infrared spectra and demonstrate the method on a simple system. The approximation delivers a large speed-up of the calculation without losing significant accuracy.     

Dynamics of amide-I modes of the alanine dipeptide in D2O

The equilibrium dynamics of the acetyl and amino amide-I groups of the alanine dipeptide were examined separately using (13)C isotopic selection and 2D IR. The population relaxation times of the amide transitions were measured to be in the range 500 fs by means of heterodyne transient grating methods. The vibrational frequency correlation functions consisted in all cases of a motionally narrowed part, a component near 800 fs, and a constant part representing a distribution of structures that is static on the few ps time scale. The intermediate time scale is attributed to fluctuations in the stretching and bending of hydrogen bonds between the carbonyl and water.     

Characterization of spectral diffusion from two-dimensional line shapes

The analysis of line shapes in two-dimensional optical and infrared spectroscopies is a powerful approach to characterizing the dynamics of molecules in the condensed phase. Changes in line shape from diagonally elongated to symmetric as a function of waiting time arise from evolution of the transition frequency. We describe a number of quantitative measures of frequency fluctuations and spectral diffusion through the analysis of two-dimensional (2D) line shapes. These metrics are identical to the system's frequency correlation function and independent of population relaxation in the limit of a short time approximation for the 2D response. We also test the broader applicability of these expressions for analyzing three-level vibrational systems and experiments with finite pulses.     

Multidimensional infrared spectroscopy of water. I. Vibrational dynamics in two-dimensional IR line shapes

In this and the following paper, we describe the ultrafast structural fluctuations and rearrangements of the hydrogen bonding network of water using two-dimensional (2D) infrared spectroscopy. 2D IR spectra covering all the relevant time scales of molecular dynamics of the hydrogen bonding network of water were studied for the OH stretching absorption of HOD in D2O. Time-dependent evolution of the 2D IR line shape serves as a spectroscopic observable that tracks how different hydrogen bonding environments interconvert while changes in spectral intensity result from vibrational relaxation and molecular reorientation of the OH dipole. For waiting times up to the vibrational lifetime of 700 fs, changes in the 2D line shape reflect the spectral evolution of OH oscillators induced by hydrogen bond dynamics. These dynamics, characterized through a set of 2D line shape analysis metrics, show a rapid 60 fs decay, an underdamped oscillation on a 130 fs time scale induced by hydrogen bond stretching, and a long time decay constant of 1.4 ps. 2D surfaces for waiting times larger than 700 fs are dominated by the effects of vibrational relaxation and the thermalization of this excess energy by the solvent bath. Our modeling based on fluctuations with Gaussian statistics is able to reproduce the changes in dispersed pump-probe and 2D IR spectra induced by these relaxation processes, but misses the asymmetry resulting from frequency-dependent spectral diffusion. The dynamical origin of this asymmetry is discussed in the companion paper.     

Two-dimensional Infrared Spectroscopy of a Model Peptide Homodimer

A pair of peptide groups in space, as modeled by formamide dimer, was used to evaluate vibrational coupling between the amide-I modes and the spatial behavior of the coupling using ab initio quantum chemical calculations. It was found that the coupling between two C=O groups, which is electrostatic in nature, is still quite signiˉcant as the intermolecular distance reaches 10 oA. One- and two-dimensional infrared spectra of the dimer at several conˉgurations were calculated using a vibrational exciton model that utilizes the abinitio computation-obtained parameters. The distance dependence of the coupling is dramatically shown in both the 1D and 2D infrared spectral features. The results suggest that the C=O stretching modes in polypeptide can be coupled and their states can be delocalized over quite a long distance in space.     

Ultrafast intermolecular dynamics of liquid water: a theoretical study on two-dimensional infrared spectroscopy

Physical and chemical properties of liquid water are dominated by hydrogen bond structure and dynamics. Recent studies on nonlinear vibrational spectroscopy of intramolecular motion provided new insight into ultrafast hydrogen bond dynamics. However, our understanding of intermolecular dynamics of water is still limited. We theoretically investigated the intermolecular dynamics of liquid water in terms of two-dimensional infrared (2D IR) spectroscopy. The 2D IR spectrum of intermolecular frequency region (<1000 cm(-1)) is calculated by using the equilibrium and nonequilibrium hybrid molecular dynamics method. We find the ultrafast loss of the correlation of the libration motion with the time scale of approximately 110 fs. It is also found that the energy relaxation from the libration motion to the low frequency motion takes place with the time scale of about 180 fs. We analyze the effect of the hindered translation motion on these ultrafast dynamics. It is shown that both the frequency modulation of libration motion and the energy relaxation from the libration to the low frequency motion significantly slow down in the absence of the hindered translation motion. The present result reveals that the anharmonic coupling between the hindered translation and libration motions is essential for the ultrafast relaxation dynamics in liquid water.     

Long-Lived Coherence Originating from Electronic-Vibrational Couplings in Light-Harvesting Complexes

We theoretically investigate the evolutions of two-dimensional, third-order, nonlinear pho-ton echo rephasing spectra with population time by using an exact numerical path integral method. It is shown that for the same system, the coherence time and relaxation time of excitonic states are short, however, if the couplings of electronic and intra-pigment vibra-tional modes are considered, the coherence time and relaxation time of this vibronic states are greatly extended. It means that the couplings between electronic and vibrational modes play important roles in keeping long-lived coherence in light-harvesting complexes. Particularly, by using the method we can fix the transition path of the energy transfer in bio-molecular systems.     

Theoretical calculations of infrared absorption, vibrational circular dichroism, and two-dimensional vibrational spectra of acetylproline in liquids water and chloroform

Infrared absorption, vibrational circular dichroism, and two-dimensional infrared pump-probe and photon echo spectra of acetylproline solutions are theoretically calculated and directly compared with experiments. In order to quantitatively determine interpeptide interaction-induced amide I mode frequency shifts, high-level quantum chemistry calculations were performed. The solvatochromic amide I mode frequency shift and fluctuation were taken into account by carrying out molecular dynamics simulations of acetylproline dissolved in liquids water and chloroform and by using the extrapolation method developed recently. We first studied correlation time scales of the two amide I vibrational frequency fluctuations, cross correlation between the two fluctuating local mode frequencies, ensemble averaged conformations of the acetylproline molecule in liquids water and chloroform. The corresponding conformations of the acetylproline in liquids water and chloroform are close to the ideal 3(10) helix and the C(7) structure, respectively. A few methods proposed to determine the angle between the two transition dipoles associated with the amide I vibrations were tested and their limitations are discussed.     

Optimal control simulation of the Deutsch-Jozsa algorithm in a two-dimensional double well coupled to an environment

The quantum Deutsch-Jozsa algorithm is implemented by using vibrational modes of a two-dimensional double well. The laser fields realizing the different gates (NOT, CNOT, and HADAMARD) on the two-qubit space are computed by the multitarget optimal control theory. The stability of the performance index is checked by coupling the system to an environment. Firstly, the two-dimensional subspace is coupled to a small number Nb of oscillators in order to simulate intramolecular vibrational energy redistribution. The complete (2+Nb)D problem is solved by the coupled harmonic adiabatic channel method which allows including coupled modes up to Nb=5. Secondly, the computational subspace is coupled to a continuous bath of oscillators in order to simulate a confined environment expected to be favorable to achieve molecular computing, for instance, molecules confined in matrices or in a fullerene. The spectral density of the bath is approximated by an Ohmic law with a cutoff for some hundreds of cm(-1). The time scale of the bath dynamics (of the order of 10 fs) is then smaller than the relaxation time and the controlled dynamics (2 ps) so that Markovian dissipative dynamics is used.     

Vibrational relaxation pathways of AI and AII modes in N-methylacetamide clusters

We studied the pathways of vibrational energy relaxation of the amide I (~1660 cm?1) and amide II (~1560 cm?1) vibrational modes of N-methylacetamide (NMA) in CCl? solution using two-color femtosecond vibrational spectroscopy. We measured the transient spectral dynamics upon excitation of each of these amide modes. The results show that there is no energy transfer between the amide I (AI) and amide II (AII) modes. Instead we find that the vibrational energy is transferred on a picosecond time scale to a common combination tone of lower-frequency modes. By use of polarization-resolved femtosecond pump-probe measurements we also study the reorientation dynamics of the NMA molecules and the relative angle between the transition dipole moments of the AI and AII vibrations. The spectral dynamics at later times after the excitation (>40 ps) reveal the presence of a dissociation process of the NMA aggregates, trimers, and higher order structures into dimers and monomers. By measuring the dissociation kinetics at different temperatures, we determined the activation energy of this dissociation E(a) = 35 ± 3 kJ mol?1.     

Excitonic effects in two-dimensional vibrational spectra of liquid formamide

The linear and two-dimensional infrared (2DIR) responses of the amide I vibrational mode in liquid formamide are investigated experimentally and theoretically using molecular dynamics simulations. The recent method based on the numerical integration of the Schr?dinger equation is employed to calculate the 2DIR spectra. Special attention is devoted to the interplay of the structural dynamics and the excitonic nature of the amide I modes in determining the optical response of the studied system. In particular, combining experimental data, simulated spectra and analysis of the simulated atomic trajectory in terms of a transition dipole coupling model, we provide a convincing explanation of the peculiar features of the 2DIR spectra, which show a substantial increase of the antidiagonal bandwidth with increasing frequency. We point out that, at variance with liquid water, the 2DIR spectral profile of formamide is determined more by the excitonic nature of the vibrational states than by the fast structural dynamics responsible for the frequency fluctuations.     

The anharmonic vibrational potential and relaxation pathways of the amide I and II modes of N-methylacetamide

We investigate the influence of isotopic substitution and solvation of N-methylacetamide (NMA) on anharmonic vibrational coupling and vibrational relaxation of the amide I and amide II modes. Differences in the anharmonic potential of isotopic derivatives of NMA in D2O and DMSO-d6 are quantified by extraction of the anharmonic parameters and the transition dipole moment angles from cross-peaks in the two-dimensional infrared (2D-IR) spectra. To interpret the effects of isotopic substitution and solvent interaction on the anharmonic potential, density functional theory and potential energy distribution calculations are performed. It is shown that the origin of anharmonic variation arises from differing local mode contributions to the normal modes of the NMA isotopologues, particularly in amide II. The time domain manifestation of the coupling is the coherent exchange of excitation between amide modes seen as the quantum beats in femtosecond pump-probes. The biphasic behavior of population relaxation of the pump-probe and 2D-IR experiments can be understood by the rapid exchange of strongly coupled modes within the peptide backbone, followed by picosecond dissipation into weakly coupled modes of the bath.