Water Dynamics: Vibrational Echo Correlation Spectroscopy and Comparison to Molecular Dynamics Simulations

Temperature dependence of the two-dimensional infrared spectrum of liquid H2O

Two-dimensional infrared photon-echo measurements of the OH stretching vibration in liquid H2O are performed at various temperatures. Spectral diffusion and resonant energy transfer occur on a time scale much shorter than the average hydrogen bond lifetime of approximately 1 ps. Room temperature measurements show a loss of frequency and, thus, structural correlations on a 50-fs time scale. Weakly hydrogen-bonded OH stretching oscillators absorbing at high frequencies undergo slower spectral diffusion than strongly bonded oscillators. In the temperature range from 340 to 274 K, the loss in memory slows down with decreasing temperature. At 274 K, frequency correlations in the OH stretch vibration persist beyond approximately 200 fs, pointing to a reduction in dephasing by librational excitations. Polarization-resolved pump-probe studies give a resonant intermolecular energy transfer time of 80 fs, which is unaffected by temperature. At low temperature, structural correlations persist longer than the energy transfer time, suggesting a delocalization of OH stretching excitations over several water molecules.

Confinement or the nature of the interface? Dynamics of nanoscopic water

The dynamics of water confined in two different types of reverse micelles are studied using ultrafast infrared pump-probe spectroscopy of the hydroxyl OD stretch of HOD in H2O. Reverse micelles of the surfactant Aerosol-OT (ionic head group) in isooctane and the surfactant Igepal CO 520 (nonionic head group) in 50/50 wt % cyclohexane/hexane are prepared to have the same diameter water nanopools. Measurements of the IR spectra and vibrational lifetimes show that the identity of the surfactant head groups affects the local environment experienced by the water molecules inside the reverse micelles. The orientational dynamics (time-dependent anisotropy), which is a measure of the hydrogen bond network rearrangement, are very similar for the confined water in the two types of reverse micelles. The results demonstrate that confinement by an interface to form a nanoscopic water pool is a primary factor governing the dynamics of nanoscopic water rather than the presence of charged groups at the interface.

Frequency-frequency correlation functions and apodization in two-dimensional infrared vibrational echo spectroscopy: a new approach

Ultrafast two-dimensional infrared (2D-IR) vibrational echo spectroscopy can probe structural dynamics under thermal equilibrium conditions on time scales ranging from femtoseconds to approximately 100 ps and longer. One of the important uses of 2D-IR spectroscopy is to monitor the dynamical evolution of a molecular system by reporting the time dependent frequency fluctuations of an ensemble of vibrational probes. The vibrational frequency-frequency correlation function (FFCF) is the connection between the experimental observables and the microscopic molecular dynamics and is thus the central object of interest in studying dynamics with 2D-IR vibrational echo spectroscopy. A new observable is presented that greatly simplifies the extraction of the FFCF from experimental data. The observable is the inverse of the center line slope (CLS) of the 2D spectrum. The CLS is the inverse of the slope of the line that connects the maxima of the peaks of a series of cuts through the 2D spectrum that are parallel to the frequency axis associated with the first electric field-matter interaction. The CLS varies from a maximum of 1 to 0 as spectral diffusion proceeds. It is shown analytically to second order in time that the CLS is the T(w) (time between pulses 2 and 3) dependent part of the FFCF. The procedure to extract the FFCF from the CLS is described, and it is shown that the T(w) independent homogeneous contribution to the FFCF can also be recovered to yield the full FFCF. The method is demonstrated by extracting FFCFs from families of calculated 2D-IR spectra and the linear absorption spectra produced from known FFCFs. Sources and magnitudes of errors in the procedure are quantified, and it is shown that in most circumstances, they are negligible. It is also demonstrated that the CLS is essentially unaffected by Fourier filtering methods (apodization), which can significantly increase the efficiency of data acquisition and spectral resolution, when the apodization is applied along the axis used for obtaining the CLS and is symmetrical about tau=0. The CLS is also unchanged by finite pulse durations that broaden 2D spectra.

On the ultrafast infrared spectroscopy of anion hydration shell hydrogen bond dynamics

Molecular Dynamics simulations are used to examine the title issue for the I-/HOD/D2O solution system in connection with recent ultrafast infrared spectroscopic experiments. It is argued that the long "modulation time" associated with the spectral diffusion of the OH frequency, extracted in these experiments, should be interpreted as reflecting the escape time of an HOD from the first hydration shell of the I- ion, i.e., the residence time of an HOD in this solvation shell. Shorter time features related to the oscillation of the OH ...I- hydrogen bond and the breaking and making of this bond are also discussed.

Ultrafast anisotropy dynamics of water molecules dissolved in acetonitrile

Infrared pump-probe experiments are performed on isolated H(2)O molecules diluted in acetonitrile in the spectral region of the OH stretching vibration. The large separation between water molecules excludes intermolecular interactions, while acetonitrile as a solvent provides substantial hydrogen bonding. Intramolecular coupling between symmetric and asymmetric modes results in the anisotropy decay to the frequency-dependent values of approximately 0-0.2 with a 0.2 ps time constant. The experimental data are consistent with a theoretical model that includes intramolecular coupling, anharmonicity, and environmental fluctuations. Our results demonstrate that intramolecular processes are essential for the H(2)O stretching mode relaxation and therefore can compete with the intermolecular energy transfer in bulk water.

Neuroglobin dynamics observed with ultrafast 2D-IR vibrational echo spectroscopy

Neuroglobin (Ngb), a protein in the globin family, is found in vertebrate brains. It binds oxygen reversibly. Compared with myoglobin (Mb), the amino acid sequence has limited similarity, but key residues around the heme and the classical globin fold are conserved in Ngb. The CO adduct of Ngb displays two CO absorption bands in the IR spectrum, referred to as N(3) (distal histidine in the pocket) and N(0) (distal histidine swung out of the pocket), which have absorption spectra that are almost identical with the Mb mutants L29F and H64V, respectively. The Mb mutants mimic the heme pocket structures of the corresponding Ngb conformers. The equilibrium protein dynamics for the CO adduct of Ngb are investigated by using ultrafast 2D-IR vibrational echo spectroscopy by observing the CO vibration's spectral diffusion (2D-IR spectra time dependence) and comparing the results with those for the Mb mutants. Although the heme pocket structure and the CO FTIR peak positions of Ngb are similar to those of the mutant Mb proteins, the 2D-IR results demonstrate that the fast structural fluctuations of Ngb are significantly slower than those of the mutant Mbs. The results may also provide some insights into the nature of the energy landscape in the vicinity of the folded protein free energy minimum.

What nonlinear-IR experiments can tell you about water that the IR spectrum cannot

Frequently, the IR spectrum of water is used to characterize the structure and strength of the associated hydrogen bond network. Here, we use nonlinear-IR spectroscopy to investigate the dynamics of four aqueous systems that have very similar absorption spectra. We address the question: to what extent can the dynamics of water vary in systems with very similar absorption spectra? The results illustrate that the vibrational lifetimes and orientational relaxation time scales vary dramatically between the four samples and do not correlate with the amount of water relative to surfactant or solute in solution. Nonlinear-IR spectroscopies are therefore important for providing detailed information necessary to understand hydrogen bonded systems.

Relaxation and anharmonic couplings of the O-H stretching vibration of asymmetric strongly hydrogen-bonded complexes

We present infrared transient grating measurements of complexes of formic acid with pyridine and pyrazine at four excitation frequencies within the broad proton-stretching band. These experiments investigate the mechanism of the line broadening of the O-H stretching vibration. The transients show coherent oscillations that decay within a few hundred femtoseconds and population relaxation on two time scales. We fit the data using a simple model of three coupled oscillators that relax via sequential kinetics through an intermediate state. Based on this model, we conclude that the coherent oscillations result from superpositions of Fermi-resonance-coupled states involving formic acid overtone and combination states.

Dynamics of a Multimode System Coupled to Multiple Heat Baths Probed by Two-Dimensional Infrared Spectroscopy

Reduced equation of motion for a multimode system coupled to multiple heat baths is constructed by extending the quantum Fokker-Planck equation with low-temperature correction terms (J. Phys. Soc. Jpn. 2005, 74, 3131). Unlike such common approaches used to describe intramolecular multimode vibration as a Bloch-Redfield theory and a stochastic theory, the present formalism is defined by the molecular coordinates. To explore the correlation among different modes through baths, we consider two cases of system-bath couplings. One is a correlated case in which two modes are coupled to a single bath, and the other is an uncorrelated case in which each mode is coupled to a different bath. We further classify the correlated case into two cases, the plus- and minus-correlated cases, according to distinct correlation manners. For these, one-dimensional and two-dimensional infrared (2D-IR) spectra are calculated numerically by solving the equation of motion. It is demonstrated that 2D-IR spectroscopy has the ability to analyze the correlation of fluctuation-dissipation processes among different modes.

Vibrational spectral diffusion of azide in water

Vibrational spectral diffusion denotes the time-dependent fluctuations of a solute's vibrational frequencies due to local environmental dynamics. Vibrational line shapes are weakly sensitive to spectral diffusion, whereas three-pulse vibrational echoes are much more sensitive. We report here on theoretical studies of spectral diffusion of the asymmetric stretch of the azide anion in heavy water. We run a classical molecular dynamics simulation of rigid azide in rigid water, and at every time step we calculate the azide's anharmonic asymmetric stretch frequency using an optimized quantum mechanics/molecular mechanics method developed earlier. This generates a frequency trajectory, which we use to calculate the absorption line shape and integrated three-pulse echo intensity. Our results for both the line width and the integrated echo intensity are in excellent agreement with experiment. Our calculated frequency time-correlation function is in excellent agreement with experiment for long times (greater than 250 fs) but differs considerably from experiment at short times; our theoretical correlation function has a very pronounced oscillation, presumably due to intermolecular azide-water hydrogen-bond stretching dynamics.

Approaches for the calculation of vibrational frequencies in liquids: comparison to benchmarks for azide/water clusters

Ultrafast vibrational spectroscopy experiments, together with molecular-level theoretical interpretation, can provide important information about the structure and dynamics of complex condensed phase systems, including liquids. The theoretical challenge is to calculate the instantaneous vibrational frequencies of a molecule in contact with a molecular environment, accurately and quickly, and to this end a number of different methods have been developed. In this paper we critically analyze these different methods by comparing their results to accurate benchmark calculations on azide/water clusters. We also propose an optimized quantum mechanics/molecular mechanics method, which for this problem is superior to the other methods.

Hydrogen bonding definitions and dynamics in liquid water

X-ray and neutron diffractions, vibrational spectroscopy, and x-ray Raman scattering and absorption experiments on water are often interpreted in terms of hydrogen bonding. To this end a number of geometric definitions of hydrogen bonding in water have been developed. While all definitions of hydrogen bonding are to some extent arbitrary, those involving one distance and one angle for a given water dimer are unnecessarily so. In this paper the authors develop a systematic procedure based on two-dimensional potentials of mean force for defining cutoffs for a given pair of distance and angular coordinates. They also develop an electronic structure-based definition of hydrogen bonding in liquid water, related to the electronic occupancy of the antibonding OH orbitals. This definition turns out to be reasonably compatible with one of the distance-angle geometric definitions. These two definitions lead to an estimate of the number of hydrogen bonds per molecule in liquid simple point charge/extended (SPC/E) water of between 3.2 and 3.4. They also used these and other hydrogen-bond definitions to examine the dynamics of local hydrogen-bond number fluctuations, finding an approximate long-time decay constant for SPC/E water of between 0.8 and 0.9 ps, which corresponds to the time scale for local structural relaxation.

Three-dimensional-IR spectroscopy: beyond the two-point frequency fluctuation correlation function

Three-dimensional-IR spectroscopy is proposed as a new spectroscopic technique that is sensitive to three-point frequency fluctuation correlation functions. This will be important when the statistics of the underlying stochastic process is non-Gaussian, and hence when the system does not follow the linear response hypothesis. Furthermore, a very general classification of nonlinear spectroscopy in terms of higher order frequency fluctuation correlation functions is introduced, according to which certain moments of a multidimensional spectrum are related to certain frequency fluctuation correlation functions. The classification is rigorous in the so-called inhomogeneous limit, but remains valid approximately also when motional narrowing becomes important. The work also puts a recent paper [J. Bredenbeck et al., Phys. Rev. Lett. 95, 083201 (2005)] onto solid theoretical grounds, where we have shown for the first time that fifth-order spectroscopy--in this case transient two-dimensional spectroscopy--is indeed sensitive to the three-point frequency fluctuation correlation function.

Dynamical properties of liquid water from ab initio molecular dynamics performed in the complete basis set limit

Dynamical properties of liquid water were studied using Car-Parrinello [Phys. Rev. Lett. 55, 2471 (1985)] ab initio molecular dynamics (AIMD) simulations within the Kohn-Sham (KS) density functional theory employing the Becke-Lee-Yang-Parr exchange-correlation functional for the electronic structure. The KS orbitals were expanded in a discrete variable representation basis set, wherein the complete basis set limit can be easily reached and which, therefore, provides complete convergence of ionic forces. In order to minimize possible nonergodic behavior of the simulated water system in a constant energy (NVE) ensemble, a long equilibration run (30 ps) preceded a 60 ps long production run. The temperature drift during the entire 60 ps trajectory was found to be minimal. The diffusion coefficient [0.055 A2/ps] obtained from the present work for 32 D2O molecules is a factor of 4 smaller than the most up to date experimental value, but significantly larger than those of other recent AIMD studies. Adjusting the experimental result so as to match the finite-sized system used in the present study brings the comparison between theory and experiment to within a factor of 3. More importantly, the system is not observed to become "glassy" as has been reported in previous AIMD studies. The computed infrared spectrum is in good agreement with experimental data, especially in the low frequency regime where the translational and librational motions of water are manifested. The long simulation length also made it possible to perform detailed studies of hydrogen bond dynamics. The relaxation dynamics of hydrogen bonds observed in the present AIMD simulation is slower than those of popular force fields, such as the TIP4P potential, but comparable to that of the TIP5P potential.

Hydrogen bonding and Raman, IR, and 2D-IR spectroscopy of dilute HOD in liquid D2O

We present improvements on our previous approaches for calculating vibrational spectroscopy observables for the OH stretch region of dilute HOD in liquid D2O. These revised approaches are implemented to calculate IR and isotropic Raman spectra, using the SPC/E simulation model, and the results are in good agreement with experiment. We also calculate observables associated with three-pulse IR echoes: the peak shift and 2D-IR spectrum. The agreement with experiment for the former is improved over our previous calculations, but discrepancies between theory and experiment still exist. Using our proposed definition for hydrogen bonding in liquid water, we decompose the distribution of frequencies in the OH stretch region in terms of subensembles of HOD molecules with different local hydrogen-bonding environments. Such a decomposition allows us to make the connection with experiments and calculations on water clusters and more generally to understand the extent of the relationship between transition frequency and local structure in the liquid.

Picosecond water dynamics adjacent to charged paramagnetic ions measured by magnetic relaxation dispersion

Measurements of water-proton spin-lattice relaxation rate constants as a function of magnetic field strength [magnetic relaxation dispersion (MRD)] in aqueous solutions of paramagnetic solutes reveal a peak in the MRD profile. These previously unobserved peaks require that the time correlation functions describing the water-proton-electron dipolar coupling have a periodic contribution. In aqueous solutions of iron(III) ion the peak corresponds to a frequency of 8.7 cm-1, which the authors ascribe to the motion of water participating in the second coordination sphere of the triply charged solute ion. Similar peaks of weaker intensity in the same time range are observed for aqueous solutions of chromium(III) chloride as well as for ion pairs formed by ammonium ion with trioxalatochromate(III) ion. The widths of the dispersion peaks are consistent with a lifetime for the periodic motion in the range of 5 ps or longer.

Excited state dynamics of liquid water: Insight from the dissociation reaction following two-photon excitation

The authors use transient absorption spectroscopy to monitor the ionization and dissociation products following two-photon excitation of pure liquid water. The primary decay mechanism changes from dissociation at an excitation energy of 8.3 eV to ionization at 12.4 eV. The two channels occur with similar yield for an excitation energy of 9.3 eV. For the lowest excitation energy, the transient absorption at 267 nm probes the geminate recombination kinetics of the H and OH fragments, providing a window on the dissociation dynamics. Modeling the OH geminate recombination indicates that the dissociating H atoms have enough kinetic energy to escape the solvent cage and one or two additional solvent shells. The average initial separation of H and OH fragments is 0.7+/-0.2 nm. Our observation suggests that the hydrogen bonding environment does not prevent direct dissociation of an O-H bond in the excited state. We discuss the implications of our measurement for the excited state dynamics of liquid water and explore the role of those dynamics in the ionization mechanism at low excitation energies.

Hydrogen bond lifetimes and energetics for solute/solvent complexes studied with 2D-IR vibrational echo spectroscopy

Weak pi hydrogen-bonded solute/solvent complexes are studied with ultrafast two-dimensional infrared (2D-IR) vibrational echo chemical exchange spectroscopy, temperature-dependent IR absorption spectroscopy, and density functional theory calculations. Eight solute/solvent complexes composed of a number of phenol derivatives and various benzene derivatives are investigated. The complexes are formed between the phenol derivative (solute) in a mixed solvent of the benzene derivative and CCl4. The time dependence of the 2D-IR vibrational echo spectra of the phenol hydroxyl stretch is used to directly determine the dissociation and formation rates of the hydrogen-bonded complexes. The dissociation rates of the weak hydrogen bonds are found to be strongly correlated with their formation enthalpies. The correlation can be described with an equation similar to the Arrhenius equation. The results are discussed in terms of transition state theory.

Probing dynamics of complex molecular systems with ultrafast 2D IR vibrational echo spectroscopy

Ultrafast 2D IR vibrational echo spectroscopy is described and a number of experimental examples are given. Details of the experimental method including the pulse sequence, heterodyne detection, and determination of the absorptive component of the 2D spectrum are outlined. As an initial example, the 2D spectrum of the stretching mode of CO bound to the protein myoglobin (MbCO) is presented. The time dependence of the 2D spectrum of MbCO, which is caused by protein structural evolution, is presented and its relationship to the frequency-frequency correlation function is described and used to make protein structural assignments based on comparisons to molecular dynamics simulations. The 2D vibrational echo experiments on the protein horseradish peroxidase are presented. The time dependence of the 2D spectra of the enzyme in the free form and with a substrate bound at the active site are compared and used to examine the influence of substrate binding on the protein's structural dynamics. The application of 2D vibrational echo spectroscopy to the study of chemical exchange under thermal equilibrium conditions is described. 2D vibrational echo chemical exchange spectroscopy is applied to the study of formation and dissociation of organic solute-solvent complexes and to the isomerization around a carbon-carbon single bond of an ethane derivative.

Classical and quantum mechanical infrared echoes from resonantly coupled molecular vibrations

The nonlinear response function associated with the infrared vibrational echo is calculated for a quantum mechanical model of resonantly coupled, anharmonic oscillators at zero temperature. The classical mechanical response function is determined from the quantum response function by setting variant Planck's over 2pi-->0, permitting the comparison of the effects of resonant vibrational coupling among an arbitrary number of anharmonic oscillators on quantum and classical vibrational echoes. The quantum response function displays a time dependence that reflects both anharmonicity and resonant coupling, while the classical response function depends on anharmonicity only through a time-independent amplitude, and shows a time dependence controlled only by the resonant coupling. In addition, the classical response function grows without bound in time, a phenomenon associated with the nonlinearity of classical mechanics, and absent in quantum mechanics. This unbounded growth was previously identified in the response function for a system without resonant vibrational energy transfer, and is observed to persist in the presence of resonant coupling among vibrations. Quantitative agreement between classical and quantum response functions is limited to a time scale of duration inversely proportional to the anharmonicity.

Phenol-benzene complexation dynamics: Quantum chemistry calculation, molecular dynamics simulations, and two dimensional IR spectroscopy

Molecular dynamics (MD) simulations and quantum mechanical electronic structure calculations are used to investigate the nature and dynamics of the phenol-benzene complex in the mixed solvent, benzene/CCl4. Under thermal equilibrium conditions, the complexes are continuously dissociating and forming. The MD simulations are used to calculate the experimental observables related to the phenol hydroxyl stretching mode, i.e., the two dimensional infrared vibrational echo spectrum as a function of time, which directly displays the formation and dissociation of the complex through the growth of off-diagonal peaks, and the linear absorption spectrum, which displays two hydroxyl stretch peaks, one for the complex and one for the free phenol. The results of the simulations are compared to previously reported experimental data and are found to be in quite reasonable agreement. The electronic structure calculations show that the complex is T shaped. The classical potential used for the phenol-benzene interaction in the MD simulations is in good accord with the highest level of the electronic structure calculations. A variety of other features is extracted from the simulations including the relationship between the structure and the projection of the electric field on the hydroxyl group. The fluctuating electric field is used to determine the hydroxyl stretch frequency-frequency correlation function (FFCF). The simulations are also used to examine the number distribution of benzene and CCl4 molecules in the first solvent shell around the phenol. It is found that the distribution is not that of the solvent mole fraction of benzene. There are substantial probabilities of finding a phenol in either a pure benzene environment or a pure CCl4 environment. A conjecture is made that relates the FFCF to the local number of benzene molecules in phenol's first solvent shell.

Effects of Hydrogen Bonding on the Ring Stretching Modes of Pyridine

The effects of hydrogen bonding on the ring stretching modes (both ring breathing and triangle) of pyridine are experimentally investigated using noisy light based coherent Raman scattering spectroscopy. Three systems, pyridine/formamide, pyridine/water, and pyridine/acetic acid, provide varying degrees of strength for the diluent-pyridine hydrogen bond complex. Formamide forms a relatively weaker hydrogen bond, while acetic acid essentially fully transfers a proton to pyridine. Both dilution studies and temperature studies are performed on the three systems. Together, these provide a broad context in which a very simple model for the electronic behavior of pyridine is formulated. This model is based on a molecular orbital picture and electrostatic arguments, and it well explains the observed experimental results. Additionally, a new mechanism for the line broadening of the ring breathing mode for the pyridine-water hydrogen bonded complex is proposed.

Multidimensional infrared spectroscopy of water. II. Hydrogen bond switching dynamics

We use multidimensional infrared spectroscopy of the OH stretch of HOD in D2O to measure the interconversion of different hydrogen bonding environments. The OH stretching frequency distinguishes hydrogen bonded (HB) and non-hydrogen-bonded (NHB) configurations by their absorption on the low (red) and high (blue) sides of the line shape. Measured asymmetries in the two dimensional infrared OH line shapes are manifestations of the fundamentally different spectral relaxations of HB and NHB. HB oscillators exhibit coherent oscillations within the hydrogen-bonded free energy well before undergoing activated barrier crossing, resulting in the exchange of hydrogen bonded partners. Conversely, NHB oscillators rapidly return to HB frequencies within 150 fs. These results support a picture where NHB configurations are only visited transiently during large fluctuations about a hydrogen bond or during the switching of hydrogen bonding partners. The results are not consistent with the presence of entropically stabilized dangling hydrogen bonds or a conceptual picture of water as a mixture of environments with varying hydrogen bond strength separated by barriers >kT.

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.

Microscopic Inhomogeneity and Ultrafast Orientational Motion in an Organic Photovoltaic Bulk Heterojunction Thin Film Studied with 2D IR Vibrational Spectroscopy

Two-dimensional infrared vibrational spectroscopy is used to examine conformational inhomogeneity and ultrafast orientational motion within local environments of an organic photovoltaic bulk heterojunction thin film. The bulk heterojunction material consists of a mixture of the electron donor poly[2-methoxy-5-(2'-ethylhexyloxy)-1,4-(1-cyanovinylene)phenylene] (CN-MEH-PPV) and the electron acceptor [6,6]-phenyl-C(61)-butyric acid methyl ester (PCBM). PCBM species reside in a distribution of environments within large domains of the molecules that cause their C=O stretch modes to be inhomogeneously broadened. The molecular inhomogeneity also results in frequency dependent vibrational relaxation dynamics. The butyric acid methyl ester group of PCBM undergoes ultrafast wobbling-in-the-cone orientational motion on the 110 fs time scale within a cone semiangle of 29 degrees . The vibrational dynamics are sensitive metrics of molecular order in the material and have implications for charge mobility and degradation phenomena in organic photovoltaic devices. This report represents the first study of organic photovoltaic materials using ultrafast two-dimensional infrared vibrational spectroscopy.

Multidimensional infrared spectroscopy of the N-H bond motions in formamide

The heterodyned two-dimensional (2D) IR spectra and equilibrium dynamics of the N-H stretching motion of DCONHD in deuterated formamide, DCOND(2), were studied with 80 fs pulses at 3 microm. The time evolution of the heterodyned 2D IR spectra, pump-probe spectra, and photon echo peak shift demonstrate that interstate dynamics is occurring by relaxation of the original N-H excitation. The N-H vibrational frequency correlation function can be expressed as a sum of three exponentials with correlation times 0.24 ps, 0.8 ps, and 11 ps. The intermediate component is attributed to motions of the N-Hcdots, three dots, centeredO unit involving only slight angular variations of the N-H bond. The slow component is attributed to the structure breaking and making. The anisotropy decay confirmed that the significant angular N-H bond motion occurs on the 11 ps time scale. The fast component, which is the least well determined, might correspond to the modulation of the H-bond distance without angular motion. The correlation coefficient between the pumped and relaxed state distributions was +0.51, implying that the excited state phase memory is only slightly diminished by the relaxation of the N-H excitation. The relaxed modes are concluded to be local to the driven N-H mode.

Modeling vibrational dephasing and energy relaxation of intramolecular anharmonic modes for multidimensional infrared spectroscopies

Starting from a system-bath Hamiltonian in a molecular coordinate representation, we examine an applicability of a stochastic multilevel model for vibrational dephasing and energy relaxation in multidimensional infrared spectroscopy. We consider an intramolecular anharmonic mode nonlinearly coupled to a colored noise bath at finite temperature. The system-bath interaction is assumed linear plus square in the system coordinate, but linear in the bath coordinates. The square-linear system-bath interaction leads to dephasing due to the frequency fluctuation of system vibration, while the linear-linear interaction contributes to energy relaxation and a part of dephasing arises from anharmonicity. To clarify the role and origin of vibrational dephasing and energy relaxation in the stochastic model, the system part is then transformed into an energy eigenstate representation without using the rotating wave approximation. Two-dimensional (2D) infrared spectra are then calculated by solving a low-temperature corrected quantum Fokker-Planck (LTC-QFP) equation for a colored noise bath and by the stochastic theory. In motional narrowing regime, the spectra from the stochastic model are quite different from those from the LTC-QFP. In spectral diffusion regime, however, the 2D line shapes from the stochastic model resemble those from the LTC-QFP besides the blueshifts caused by the dissipation from the colored noise bath. The preconditions for validity of the stochastic theory for molecular vibrational motion are also discussed.

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.

Calculating fifth-order Raman signals for various molecular liquids by equilibrium and nonequilibrium hybrid molecular dynamics simulation algorithms

The fifth-order two-dimensional (2D) Raman signals have been calculated from the equilibrium and nonequilibrium (finite field) molecular dynamics simulations. The equilibrium method evaluates response functions with equilibrium trajectories, while the nonequilibrium method calculates a molecular polarizability from nonequilibrium trajectories for different pulse configurations and sequences. In this paper, we introduce an efficient algorithm which hybridizes the existing two methods to avoid the time-consuming calculations of the stability matrices which are inherent in the equilibrium method. Using nonequilibrium trajectories for a single laser excitation, we are able to dramatically simplify the sampling process. With this approach, the 2D Raman signals for liquid xenon, carbon disulfide, water, acetonitrile, and formamide are calculated and discussed. Intensities of 2D Raman signals are also estimated and the peak strength of formamide is found to be only five times smaller than that of carbon disulfide.

Local structure of beta-hairpin isotopomers by FTIR, 2D IR, and ab initio theory

The 12-residue tryptophan zipper beta-hairpin (SWTWENGKWTWK) and two (13)C-isotopomers were examined in the amide-I region using FTIR and femtosecond two-dimensional infrared (2D IR) spectroscopies. Spectroscopic features of the labeled transitions with (13)C-substituted amide unit present in the terminal or turn region of the hairpin, including their frequency shifts and distributions, line broadenings, orientations, and anharmonicities of diagonal peaks, allow the peptide local structure and local environment to be examined. The results suggest a larger structure fluctuation in the terminal region than in the turn region as a result of the side chain effect and solvent-peptide interaction. The results also suggest that the uncoupled amide-I modes are not degenerate and that this is likely to be a common situation for solvated polypeptides. In addition, the amide-I states in the terminal and turn regions were found to be delocalized over several neighboring amide units. Cross-peaks between the various labeled and unlabeled structural regions were clearly observed in the 2D IR correlation spectra, allowing them to be characterized for monitoring structural changes. These results illustrate the sensitivity of 2D IR to the local environment of solvated peptides. The simulated 1D and 2D IR spectra of the hairpin, obtained by using the vibrational exciton model incorporating coupling constants from quantum chemical computations and semiempirical calculations, were found to reproduce the essential features of the experimental results.

Aqueous Solvation Dynamics at Metal Oxide Surfaces

Broadband transient absorption (TA) spectroscopy, three-pulse photon echo peak shift (3PEPS), and anisotropy decay measurements were used to study the solvation dynamics in bulk water and interfacial water at ZrO(2) surfaces, using Eosin Y as a probe. The 3PEPS results show a multiexponential behavior with two subpicosecond components that are similar in bulk and interfacial water, while a third component of several picoseconds is significantly lengthened at the interface. The bandwidth correlation function from TA spectra exhibits the same behavior, and the TA spectra are well reproduced using the doorway-window picture with the time constants from PEPS. Our results suggest that interfacial water is restricted to a thickness of less than 5 A. Also the high-frequency collective dynamics of water does not seem to be affected by the interface. On the other hand, the increase of the third component may point to a slowing down of diffusional motion at the interface, although other effects, may play a role, which are discussed.

Testing the Core/Shell Model of Nanoconfined Water in Reverse Micelles Using Linear and Nonlinear IR Spectroscopy

A core/shell model has often been used to describe water confined to the interior of reverse micelles. The validity of this model for water encapsulated in AOT/isooctane reverse micelles ranging in diameter from 1.7 to 28 nm (w0 = 2-60) and bulk water is investigated using four experimental observables: the hydroxyl stretch absorption spectra, vibrational population relaxation times, orientational relaxation rates, and spectral diffusion dynamics. The time dependent observables are measured with ultrafast infrared spectrally resolved pump-probe and vibrational echo spectroscopies. Major progressive changes appear in all observables as the system moves from bulk water to the smallest water nanopool, w0 = 2. The dynamics are readily distinguishable for reverse micelle sizes smaller than 7 nm in diameter (w0 = 20) compared to the response of bulk water. The results also demonstrate that the size dependent absorption spectra and population relaxation times can be quantitatively predicted using a core-shell model in which the properties of the core (interior of the nanopool) are taken to be those of bulk water and the properties of the shell (water associated with the headgroups) are taken to be those of w0 = 2. A weighted sum of the core and shell components reproduces the size dependent spectra and the nonexponential population relaxation dynamics. However, the same model does not reproduce the spectral diffusion and the orientational relaxation experiments. It is proposed that, when hydrogen bond structural rearrangement is involved (orientational relaxation and spectral diffusion), dynamical coupling between the shell and the core cause the water nanopool to display more homogeneous dynamics. Therefore, the absorption spectra and vibrational lifetime decays can discern different hydrogen bonding environments whereas orientational and spectral diffusion correlation functions predict that the dynamics are size dependent but not as strongly spatially dependent within a reverse micelle.

Vibrational dynamics of N–H, C–D, and CO modes in formamide

By means of heterodyned two-dimensional IR photon echo experiments on liquid formamide and isotopomers the vibrational frequency dynamics of the N-H stretch mode, the C-D mode, and the C=O mode were obtained. In each case the vibrational frequency correlation function is fitted to three exponentials representing ultrafast (few femtoseconds), intermediate (hundreds of femtoseconds), and slow (many picoseconds) correlation times. In the case of N-H there is a significant underdamped contribution to the correlation decay that was not seen in previous experiments and is attributed to hydrogen-bond librational modes. This underdamped motion is not seen in the C-D or C=O correlation functions. The motions probed by the C-D bond are generally faster than those seen by N-H and C=O, indicating that the environment of C-D interchanges more rapidly, consistent with a weaker C-D...O=C bond. The correlation decays of N-H and C=O are similar, consistent with both being involved in strong H bonding.

Two-dimensional Raman spectra of atomic solids and liquids

We calculate third- and fifth-order Raman spectra of simple atoms interacting through a soft-core potential by means of molecular-dynamics (MD) simulations. The total polarizability of molecules is treated by the dipole-induced dipole model. Two- and three-body correlation functions of the polarizability at various temperatures are evaluated from equilibrium MD simulations based on a stability matrix formulation. To analyze the processes involved in the spectroscopic measurements, we divide the fifth-order response functions into symmetric and antisymmetric integrated response functions; the symmetric one is written as a simple three-body correlation function, while the antisymmetric one depends on a stability matrix. This analysis leads to a better understanding of the time scales and molecular motions that govern the two-dimensional (2D) signal. The 2D Raman spectra show novel differences between the solid and liquid phases, which are associated with the decay rates of coherent motions. On the other hand, these differences are not observed in the linear Raman spectra.

Multidimensional infrared spectroscopy for molecular vibrational modes with dipolar interactions, anharmonicity, and nonlinearity of dipole moments and polarizability

We present an analytical expression for the linear and nonlinear infrared spectra of interacting molecular vibrational motions. Each of the molecular modes is explicitly represented by a classical damped oscillator on an anharmonic multidimensional potential-energy surface. The two essential interactions, the dipole-dipole (DD) and the dipole-induced-dipole (DID) interactions, are taken into account, and each dipole moment and polarizability are expanded to nonlinear order with respect to the nuclear vibrational coordinate. Our analytical treatment leads to expressions for the contributions of anharmonicity, DD and DID interactions, and the nonlinearity of dipole moments and polarizability elements to the one-, two-, and three-dimensional spectra as separated terms, which allows us to discuss the relative importance of these respective contributions. We can calculate multidimensional signals for various configurations of molecules interacting through DD and DID interactions for different material parameters over the whole range of frequencies. We demonstrate that contributions from the DD and DID interactions and anharmonicity are separately detectable through the third-order three-dimensional IR spectroscopy, whereas they cannot be distinguished from each other in either the linear or the second-order IR spectroscopies. The possibility of obtaining the intra- or intermolecular structural information from multidimensional spectra is also discussed.

Electric Field Fluctuations Drive Vibrational Dephasing in Water

We present a microscopic description of the vibrational spectroscopy of the OH stretch of HOD in liquid D(2)O. Our model predicts that OH frequency correlations decay with a sharp and rapid ( approximately 35 fs) decrease, followed by a beat at approximately 125 fs from intermolecular oxygen vibrations. On a short time scale ( approximately 200 fs), ultrafast infrared spectroscopy of the OH stretch is sensitive to localized intermolecular motions. For times longer than approximately 200 fs, cooperative molecular rearrangements drive dephasing. The interplay of electric field fluctuations, both local and cooperative, dictate vibrational frequency shifts and destroy vibrational coherence in water.

Stochastic Liouville equations for hydrogen-bonding fluctuations and their signatures in two-dimensional vibrational spectroscopy of water

The effects of hydrogen-bond forming and breaking kinetics on the linear and coherent third-order infrared spectra of the OH stretch of HOD in D2O are described by Markovian, not necessarily Gaussian, fluctuations and simulated using the stochastic Liouville equations. Slow (0.5 ps) fluctuations are represented by a collective electrostatic coordinate, whereas fast (<100 fs) frequency fluctuations are described using either a second collective electrostatic coordinate or a four-state jump (FSJ) model for hydrogen-bonding configurations. Parameters for both models were obtained using a 1-ns molecular-dynamics trajectory calculated using the TIP4P force field combined with an electrostatic ab initio map. The asymmetry of the photon-echo spectra (larger linewidth on the blue side than on the red side) predicted by the FSJ is in better agreement with recent experiments.