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.     

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.     

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.     

Ultrafast Vibrational Dynamics of Membrane‐Bound Peptides at the Lipid Bilayer/Water Interface

Vibrational energy transfer (VET) of proteins at cell membrane plays critical roles in controlling the protein functionalities, but its detection is very challenging. By using a surface‐sensitive femtosecond time‐resolved sum‐frequency generation vibrational spectroscopy with infrared pump, the detection of the ultrafast VET in proteins at cell membrane has finally become possible. The vibrational relaxation time of the N−H groups is determined to be 1.70(±0.05) ps for the α‐helix located in the hydrophobic core of the lipid bilayer and 0.9(±0.05) ps for the membrane‐bound β‐sheet structure. The N−H groups with strong hydrogen bonding gain faster relaxation time. By pumping the amide A band and probing amide I band, the vibrational relaxation from N−H mode to C=O mode through two pathways (direct coupling and through intermediate states) is revealed. The ratio of the pathways depends on the NH⋅⋅⋅O=C hydrogen‐bonding strength. Strong hydrogen bonding favors the coupling through intermediate states.     

Vibrational energy relaxation of the bend fundamental of dilute water in liquid chloroform and d-chloroform

The population lifetimes of the bend fundamental of dilute water in liquid chloroform (8.5 ps) and d-chloroform (28.5 ps) display an interesting solvent isotope effect. As the lowest excited vibrational state of the molecule, the water bend fundamental relaxes directly to the ground state with about 1600 cm-1 of energy released to the other degrees of freedom. The strong solvent isotope effect along with the large energy gap indicates the participation of solvent vibrational modes in this vibrational energy relaxation process. We calculate the vibrational energy relaxation rates of the water bend in chloroform and d-chloroform using the Landau-Teller formula with a new potential model developed and parametrized self-consistently to describe the chloroform-water interaction. The computed values are in reasonable agreement with the experimental results, and the trend for the isotope effect is correct. It is found that energy transfer to the solvent vibrations does indeed play an important role. Nevertheless, no single dominant solvent accepting mode can be identified; the relaxation appears to involve both the bend and the C-Cl stretches, and frequency changes of all of these modes upon deuteration contribute to the observed solvent isotope effect.     

Vibrational dynamics of deoxyguanosine 5'-monophosphate following UV excitation

The relaxation dynamics of the DNA nucleotide deoxyguanosine 5'-monophosphate (dGMP) following 266 nm photoexcitation has been studied by transient IR spectroscopy with femtosecond time resolution. The induced dynamics of the amide I (carbonyl) stretch, the asymmetric guanine ring stretch and the phosphate asymmetric stretch are monitored in the region 1000-1800 cm(-1). Excitation and subsequent rapid internal conversion to a "hot" ground state is reflected by depletion of the vibrational ground states of the amide I stretch and guanine ring stretch. However, the vibrational ground state of the phosphate is left unperturbed, indicating the absence of vibrational coupling between the guanine ring system and the phosphate group. The vibrational ground state of the amide I is repopulated in 2.5 ps (±0.2 ps) while it takes 3.7 ps (±0.5 ps) to repopulate the guanine ring vibration. This article discusses two possible relaxation pathways of dGMP, as well as the implications of the weak phosphate dynamics.     

Ultrafast vibrational energy relaxation of the water bridge

We report the energy relaxation of the OH stretch vibration of HDO molecules contained in an HDO:D(2)O water bridge using femtosecond mid-infrared pump-probe spectroscopy. We found that the vibrational lifetime is shorter (~630 ± 50 fs) than for HDO molecules in bulk HDO:D(2)O (~740 ± 40 fs). In contrast, the thermalization dynamics following the vibrational relaxation are much slower (~1.5 ± 0.4 ps) than in bulk HDO:D(2)O (~250 ± 90 fs). These differences in energy relaxation dynamics strongly indicate that the water bridge and bulk water differ on a molecular scale.     

Theoretical study of internal field effects on peptide amide I modes

Charged terminal groups or polar side chains of amino acids create spatially nonuniform electrostatic potential around intramolecular peptide bonds and induce amide I mode frequency shifts in polypeptides. By carrying out a series of quantum chemistry calculation studies of various ionic di- and tripeptides as well as dipeptides of 20 different amino acids, these internal field effects on vibrational properties are theoretically investigated. The amide I local and normal mode frequencies and dipole and rotational strengths determining IR and vibrational circular dichroism intensities, respectively, are found to depend on the polar nature of side chains, whereas the vibrational coupling strength weakly does so. The empirical correction and fragment analysis methods were used to theoretically calculate the amide I local mode frequencies and dipole and rotational strengths. These values were directly compared with ab initio and density functional theory calculation results, and the agreements were found to be quantitative.     

Molecular dynamics simulations and instantaneous normal-mode analysis of the vibrational relaxation of the C-H stretching modes of N-methylacetamide-d in liquid deuterated water

Nonequilibrium molecular dynamics (MD) simulations and instantaneous normal mode (INMs) analyses are used to study the vibrational relaxation of the C-H stretching modes (ν(s)(CH?)) of deuterated N-methylacetamide (NMAD) in aqueous (D2O) solution. The INMs are identified unequivocally in terms of the equilibrium normal modes (ENMs), or groups of them, using a restricted version of the recently proposed Min-Cost assignment method. After excitation of the parent ν(s)(CH?) modes with one vibrational quantum, the vibrational energy is shown to dissipate through both intramolecular vibrational redistribution (IVR) and intermolecular vibrational energy transfer (VET). The decay of the vibrational energy of the ν(s)(CH?) modes is well fitted to a triple exponential function, with each characterizing a well-defined stage of the entire relaxation process. The first, and major, relaxation stage corresponds to a coherent ultrashort (τ(rel) = 0.07 ps) energy transfer from the parent ν(s)(CH?) modes to the methyl bending modes δ(CH?), so that the initially excited state rapidly evolves into a mixed stretch-bend state. In the second stage, characterized by a time of 0.92 ps, the vibrational energy flows through IVR to a number of mid-range-energy vibrations of the solute. In the third stage, the vibrational energy accumulated in the excited modes dissipates into the bath through an indirect VET process mediated by lower-energy modes, on a time scale of 10.6 ps. All the specific relaxation channels participating in the whole relaxation process are properly identified. The results from the simulations are finally compared with the recent experimental measurements of the ν(s)(CH?) vibrational energy relaxation in NMAD/D?O(l) reported by Dlott et al. (J. Phys. Chem. A 2009, 113, 75.) using ultrafast infrared-Raman spectroscopy.     

Empirical solvent correction for multiple amide group vibrational modes

Previously proposed solvent correction to the amide I peptide vibration was extended so that it can be applied to a general solvated chromophore. The combined molecular and quantum mechanics (MMQM) method is based on a linear dependence of harmonic force field and intensity tensor components of the solute on solvent electrostatic field. For N-methylacetamide, realistic solvent frequency and intensity changes as well as inhomogeneous band widths were obtained for amide A, I, II , and III modes. A rather anomalous basis set size dependence was observed for the amide A and I vibrations, when bigger basis lead to narrowing of spectral bands and lesser molecular sensibility to the environment. For a model alpha-helical peptide, a W-shape of the vibrational circular dichroism signal observed in deuterated solvent for the amide I band was reproduced correctly, unlike with previous vacuum models.     

Vibrational energy relaxation of isotopically labeled amide I modes in cytochrome c: theoretical investigation of vibrational energy relaxation rates and pathways

With use of a time-dependent perturbation theory, vibrational energy relaxation (VER) of isotopically labeled amide I modes in cytochrome c solvated with water is investigated. Contributions to the VER are decomposed into two contributions from the protein and water. The VER pathways are visualized by using radial and angular excitation functions for resonant normal modes. Key differences of VER among different amide I modes are demonstrated, leading to a detailed picture of the spatial anisotropy of the VER. The results support the experimental observation that amide I modes in proteins relax with subpicosecond time scales, while the relaxation mechanism turns out to be sensitive to the environment of the amide I mode.     

Peptide bond vibrational coupling

Neutral trialanine (Ala3), which is geometrically constrained to have its peptide bond at Phi and Psi angles of alpha-helix and PPII-like conformers, are studied at the B3LYP/6-31+G(d,p) level of theory to examine vibrational interactions between adjacent peptide units. Delocalization of the amide I, amide II, and amide III3 vibrations are analyzed by calculating their potential energy distributions (PED). The vibrational coupling strengths are estimated from the frequency shifts between the amide vibrations of Ala3 and the local amide bond vibrations of isotopically substituted Ala3 derivatives. Our calculations show the absence of vibrational coupling of the amide I and amide II bands in the PPII conformations. In contrast, the alpha-helical conformation shows strong coupling between the amide I vibrations due to the favorable orientation of the C=O bonds and the strong transitional dipole coupling. The amide III3 vibration shows weak coupling in both the alpha-helix and PPII conformations; this band can be treated as a local independent vibration. Our calculated results in general agree with our previous experimental UV Raman studies of a 21-residue mainly alanine-based peptide (AP).     

Single-conformation infrared spectra of model peptides in the amide I and amide II regions: Experiment-based determination of local mode frequencies and inter-mode coupling

Single-conformation infrared spectra in the amide I and amide II regions have been recorded for a total of 34 conformations of three α-peptides, three β-peptides, four α∕β-peptides, and one γ-peptide using resonant ion-dip infrared spectroscopy of the jet-cooled, isolated molecules. Assignments based on the amide NH stretch region were in hand, with the amide I∕II data providing additional evidence in favor of the assignments. A set of 21 conformations that represent the full range of H-bonded structures were chosen to characterize the conformational dependence of the vibrational frequencies and infrared intensities of the local amide I and amide II modes and their amide I∕I and amide II∕II coupling constants. Scaled, harmonic calculations at the DFT M05-2X∕6-31+G(d) level of theory accurately reproduce the experimental frequencies and infrared intensities in both the amide I and amide II regions. In the amide I region, Hessian reconstruction was used to extract local mode frequencies and amide I∕I coupling constants for each conformation. These local amide I frequencies are in excellent agreement with those predicted by DFT calculations on the corresponding (13)C = (18)O isotopologues. In the amide II region, potential energy distribution analysis was combined with the Hessian reconstruction scheme to extract local amide II frequencies and amide II∕II coupling constants. The agreement between these local amide II frequencies and those obtained from DFT calculations on the N-D isotopologues is slightly worse than for the corresponding comparison in the amide I region. The local mode frequencies in both regions are dictated by a combination of the direct H-bonding environment and indirect, "backside" H-bonds to the same amide group. More importantly, the sign and magnitude of the inter-amide coupling constants in both the amide I and amide II regions is shown to be characteristic of the size of the H-bonded ring linking the two amide groups. These amide I∕I and amide II∕II coupling constants remain similar in size for α-, β-, and γ-peptides despite the increasing number of C-C bonds separating the amide groups. These findings provide a simple, unifying picture for future attempts to base the calculation of both nearest-neighbor and next-nearest-neighbor coupling constants on a joint footing.     

Vibrational relaxation of CH3I in the gas phase and in solution

Transient electronic absorption measurements reveal the vibrational relaxation dynamics of CH(3)I following excitation of the C-H stretch overtone in the gas phase and in liquid solutions. The isolated molecule relaxes through two stages of intramolecular vibrational relaxation (IVR), a fast component that occurs in a few picoseconds and a slow component that takes place in about 400 ps. In contrast, a single 5-7 ps component of IVR precedes intermolecular energy transfer (IET) to the solvent, which dissipates energy from the molecule in 50 ps, 44 ps, and 16 ps for 1 M solutions of CH(3)I in CCl(4), CDCl(3), and (CD(3))(2)CO, respectively. The vibrational state structure suggests a model for the relaxation dynamics in which a fast component of IVR populates the states that are most strongly coupled to the initially excited C-H stretch overtone, regardless of the environment, and the remaining, weakly coupled states result in a secondary relaxation only in the absence of IET.     

Nonlinear Exciton Annihilation and Local Heating Effects in Photosynthetic Antenna Systems

Abstract— Generation of the nonequilibrium distribution of excited vibrational modes stimulated by electronic energy relaxation in pigment-protein complexes of the light-harvesting antenna of some photosynthetic systems is discussed in this paper. It is shown that the simplest approach to this problem can be achieved by introducing a local temperature, which is a good parameter for describing the nonequilibrium distribution of the local vibrational modes of the pigment molecules and its nearest protein surroundings. Then the transient absorption kinetics is determined by the kinetics of the excitation relaxation as I well as the heating/cooling of the local vibrational modes. Experimentally, this process can be investigated in the i singlet-singlet annihilation conditions that create the i greatest amount of local heating. The systems under in-: vestigation are trimers of bacteriochlorophyll a contain- i ing pigment-protein complexes from the green sulfur i bacterium Chlorobium tepid urn (so-called FMO complexes) and aggregates of the light-harvesting complexes of photosystem II (LHC2) from higher plants containing chlorophyll alb. It was shown that at 77 K the heat redistribution kinetics in LHC2 is on the order of 3040 ps and in FMO it is approximately equal to 26 ps. The local heating effect at room temperature is less pronounced; however, by using longer pulses and at higher excitation energies (on the order of a magnitude higher), an additional kinetics of hundreds of ps, also related to the heating/cooling process, was observed.     

Vibrational energy relaxation of large-amplitude vibrations in liquids

Given the limited intermolecular spaces available in dense liquids, the large amplitudes of highly excited, low frequency vibrational modes pose an interesting dilemma for large molecules in solution. We carry out molecular dynamics calculations of the lowest frequency ("warping") mode of perylene dissolved in liquid argon, and demonstrate that vibrational excitation of this mode should cause identifiable changes in local solvation shell structure. But while the same kinds of solvent structural rearrangements can cause the non-equilibrium relaxation dynamics of highly excited diatomic rotors in liquids to differ substantially from equilibrium dynamics, our simulations also indicate that the non-equilibrium vibrational energy relaxation of large-amplitude vibrational overtones in liquids should show no such deviations from linear response. This observation seems to be a generic feature of large-moment-arm vibrational degrees of freedom and is therefore probably not specific to our choice of model system: The lowest frequency (largest amplitude) cases probably dissipate energy too quickly and the higher frequency (more slowly relaxing) cases most likely have solvent displacements too small to generate significant nonlinearities in simple nonpolar solvents. Vibrational kinetic energy relaxation, in particular, seems to be especially and surprisingly linear.     

Vibrational energy relaxation of benzene dimer and trimer in the CH stretching region studied by picosecond time-resolved IR-UV pump-probe spectroscopy

Vibrational energy relaxation (VER) of the Fermi polyads in the CH stretching vibration of the benzene dimer (Bz(2)) and trimer (Bz(3)) has been investigated by picosecond (ps) time-resolved IR-UV pump-probe spectroscopy in a supersonic beam. The vibrational bands in the 3000-3100 cm(-1) region were excited by a ps IR pulse and the time evolutions at the pumped and redistributed (bath) levels were probed by resonance enhanced multiphoton ionization with a ps UV pulse. For Bz(2), a site-selective excitation in the T-shaped structure was achieved by using the isotope-substituted heterodimer hd, where h = C(6)H(6) and d = C(6)D(6), and its result was compared with that of hh homodimer. In the hd heterodimer, the two isomers, h(stem)d(top) and h(top)d(stem), show remarkable site-dependence of the lifetime of intracluster vibrational energy redistribution (IVR); the lifetime of the Stem site [h(stem)d(top), 140-170 ps] is ~2.5 times shorter than that of the Top site [h(top)d(stem), 370-400 ps]. In the transient UV spectra, a broad electronic transition due to the bath modes emerges and gradually decays with a nanosecond time scale. The broad transition shows different time profile depending on UV frequency monitored. These time profiles are described by a three-step VER model involving IVR and vibrational predissociation: initial → bath1(intramolecular) → bath2(intermolecular) → fragments. This model also describes well the observed time profile of the Bz fragment. The hh homodimer shows the stepwise VER process with time constants similar to those of the hd dimer, suggesting that the excitation-exchange coupling of the vibrations between the two sites is very weak. Bz(3) also exhibited the stepwise VER process, though each step is faster than Bz(2).     

Vibrational Relaxation in beta-Carotene Probed by Picosecond Stokes and Anti-Stokes Resonance Raman Spectroscopy

Picosecond time-resolved Stokes and anti-Stokes resonance Raman spectra of all-trans-beta-carotene are obtained and analyzed to reveal the dynamics of excited-state (S(1)) population and decay, as well as ground-state vibrational relaxation. Time-resolved Stokes spectra show that the ground state recovers with a 12.6 ps time constant, in agreement with the observed decay of the unique S(1) Stokes bands. The anti-Stokes spectra exhibit no peaks attributable to the S(1) (2A(g) (-)) state, indicating that vibrational relaxation in S(1) must be nearly complete within 2 ps. After photoexcitation there is a large increase in anti-Stokes scattering from ground-state modes that are vibrationally excited through internal conversion. The anti-Stokes data are fit to a kinetic scheme in which the C=C mode relaxes in 0.7 ps, the C-C mode relaxes in 5.4 ps and the C-CH(3) mode relaxes in 12.1 ps. These results are consistent with a model for S(1)-S(0) internal conversion in which the C=C mode is the primary acceptor, the C-C mode is a minor acceptor, and the C-CH(3) mode is excited via intramolecular vibrational energy redistribution.     

Hydrogen-bonding dynamics in aqueous solutions of amides and acids: monomer, dimer, trimer, and polymer

Hydrogen-bonding dynamics in aqueous solutions of series of amides and acids have been investigated by means of femtosecond Raman-induced Kerr effect spectroscopy and ab initio quantum chemistry calculation. The amides and acids studied here are acetamide, 1,3-propanedicarboxamide, 1,3,5-pentanetricaroxamide, polyacrylamide with Mw=1500, acetic acid, 1,3-propanedicarboxylic acid, 1,3,5-pentanetricarboxylic acid, and poly(acrylic acid) with Mw=2000. The femtosecond damped transient feature for aqueous amide solutions, which arises from the intermolecular hydrogen bonds of amide and water, becomes clearer with the larger molecular weight of amide. A characteristic vibrational band at about 100 cm(-1) is assigned as the hydrogen-bonding vibrational mode and the ab initio quantum chemistry calculation result indicates that at least two waters, which make up the hydrogen-bonding network with amide, are necessary for this mode. The hydrogen-bonding vibrational mode at about 100 cm(-1) in aqueous amide solutions shifts to the higher frequency with the larger molecular weight amide in consequence of the stronger intermolecular interaction between amide and water. The evidence likely comes from the stronger hydrophobic interaction for polymer than oligomers and monomer. In the picosecond time region, an extra slow relaxation process with a time constant of about 60 ps has been found in the aqueous polymer solutions. The relaxation is assigned as a local motion of the constitutional repeat unit of polymers from comparison with monomer and oligomers.     

Dependence of amide vibrations on hydrogen bonding

The effect of hydrogen bonding on the amide group vibrational spectra has traditionally been rationalized by invoking a resonance model where hydrogen bonding impacts the amide functional group by stabilizing its [(-)O-C=NH (+)] structure over the [O=C-NH] structure. However, Triggs and Valentini's UV-Raman study of solvation and hydrogen bonding effects on epsilon-caprolactum, N, N-dimethylacetamide (DMA), and N-methylacetamide (NMA) ( Triggs, N. E.; Valentini, J. J. J. Phys. Chem. 1992, 96, 6922-6931) casts doubt on the validity of this model by demonstrating that, contrary to the resonance model prediction, carbonyl hydrogen bonding does not impact the AmII' frequency of DMA. In this study, we utilize density functional theory (DFT) calculations to examine the impact of hydrogen bonding on the C=O and N-H functional groups of NMA, which is typically used as a simple model of the peptide bond. Our calculations indicate that, as expected, the hydrogen bonding frequency dependence of the AmI vibration predominantly derives from the C=O group, whereas the hydrogen bonding frequency dependence of the AmII vibration primarily derives from N-H hydrogen bonding. In contrast, the hydrogen bonding dependence of the conformation-sensitive AmIII band derives equally from both C=O and N-H groups and thus, is equally responsive to hydrogen bonding at the C=O or N-H site. Our work shows that a clear understanding of the normal mode composition of the amide vibrations is crucial for an accurate interpretation of the hydrogen bonding dependence of amide vibrational frequencies.