Frequency-frequency Correlation Function Research Articles

A new method based on pseudo-Zernike polynomials to analyze and extract dynamical and spectral information from the 2DIR spectra.

Ultrafast two-dimensional infrared (2DIR) spectroscopy is a relatively new methodology, which has now been widely used to study the molecular structure and dynamics of molecular processes occurring in solution. Typically, in 2DIR spectroscopy the dynamics of a system is inferred from the evolution of 2DIR spectral features over waiting times. One of the most important metrics derived from the 2DIR is the frequency-frequency correlation function (FFCF), which can be extracted using different methods, including center and nodal line slope. However, these methods struggle to correctly describe the dynamics in 2DIR spectra with multiple and overlapping transitions. Here, a new approach, utilizing pseudo-Zernike moments, is introduced to retrieve the FFCF dynamics of each spectral component from complex 2DIR spectra. The results show that this new method not only produces equivalent results to more established methodologies in simple spectra but also successfully extracts the FFCF dynamics of individual component from very congested and unresolved 2DIR spectra. In addition, this new methodology can be used to locate the individual frequency components from those complex spectra. Overall, a new methodology for analyzing the 2D spectra is presented here, which allows us to retrieve previously unattainable spectral features from the 2DIR spectra.

2D-IR Spectroscopy of Nitrosyl Stretch of Sodium Nitroprusside Reveals the Elusive Two Anomalous Regions in the DMSO–Water Mixture

DMSO-water mixtures provide an intriguing hydrogen-bonding environment which has been a subject of various theoretical and experimental investigations. The structural dynamics of aqueous DMSO solutions has been investigated, using nitrosyl stretch of sodium nitroprusside (SNP, Na2[Fe(CN)5NO]) as a local vibrational probe, with the help of infrared (IR) absorption spectroscopy, vibrational pump-probe spectroscopy, and two-dimensional IR spectroscopy (2D-IR). Fourier transform infrared spectra of the nitrosyl stretch of SNP reveals that both the peak position and spectral broadening are very sensitive to the composition of the DMSO-water mixture and the subsequent structural changes occurring due to the addition of DMSO to water. The vibrational lifetime of the nitrosyl stretch displays two different linear variation regimes as a function of mole fraction of DMSO which has been assigned presumably to two different predominant structures at these compositions. However, the rotational depolarization measurements show that the reorientational times follow a bell-shaped profile, imitating the changes in the composition-dependent physical properties (viscosity) of DMSO-water solvent mixtures. To get a holistic picture of the system, 2D-IR spectroscopy of the NO stretch of SNP has been employed to study time scales of hydrogen-bond reorganization dynamics existing at different compositions. The analysis of frequency-frequency correlation function (FFCF) decay times reveal that the dynamics gets slower in intermediate DMSO concentrations than that of pure DMSO or pure water. A careful analysis reveals two anomalous regions of hydrogen-bond dynamics: XDMSO ∼0.2 and 0.4, which indicates that different hydrogen-bonded structures exist in these regions that can be effectively probed by SNP which has remained mostly elusive to previous vibrational probe-based investigations.

Molecular Simulation-Guided Spectroscopy of Imidazolium-Based Ionic Liquids and Effects of Methylation on Ion-Cage and -Pair Dynamics.

Classical molecular dynamics simulations were performed to assess an atomistic interpretation of the ion-probe structural interactions in two typical ionic liquids (ILs), 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [BMIm][NTf2] and 1-butyl-2,3-dimethylimidazolium bis(trifluoromethylsulfonyl)imide [BDimIm][NTf2] through computational ultrafast spectroscopy. The nitrile stretching vibrations of the thiocyanate anion, [SCN]-, serve as the local mode of the ultrafast system dynamics within the imidazolium-based ionic liquid environment. The wavelet transform of classical trajectories determines the time-varying fluctuating frequencies and the stretch spectral signatures of SCN- in the normalized distribution. However, computational modeling of the two-dimensional (2D) spectra from the wavelet-derived vibrational frequencies yields time evolution of the local molecular structure along with the varied time-dependent dynamics of the spectral diffusion process. We calculated the frequency-frequency correlation functions (FFCFs), time correlations associated with the ion-pair and -cage dynamics, and mean square displacements as a function of time, depicting diffusive dynamics. The calculated results based on the pair correlation functions and the distribution of atomic density suggest that the hydrogen and methylated carbon at the two-position of the imidazolium ring of [BMIm] and [BDimIm] cations, respectively, strongly interact with the probe through the N of the thiocyanate anion rather than the S atom. The center-of-mass center-of-mass (COM-COM) cation-probe radial distribution functions (RDFs) in conjunction with the site-specific structural analysis further reveal well-structured interactions of the thiocyanate ion and [BMIm]+ cation rather than the [BDimIm] cation. In contrast, the anion-probe COM-COM RDFs depict weak interactive associations within the vibrational probe [SCN]- and [NTf2]- ions. Methylation at the two-position of the imidazolium ring predicts slower structural reorganization and breaking and reformation dynamics of the ion pairs and cages within the ionic liquid framework.

Vibrational dynamics of the OD stretch in an atomistic simulation of HDO in H2O

An all-atom molecular dynamics (MD) simulation of dilute HDO in H2O was used to obtain vibrational frequency spectra from the classical MD trajectories and a wavelet-based method was developed to obtain the frequency-frequency correlation functions (FFCFs) of the OD stretch vibrations. Time constants were obtained on the order of 30 fs, 150–260 fs and 3.2–3.6 ps. An OD covalent bond length correlation function was calculated and a long-timescale decay constant of 1.73 ps was obtained, similar to experimental values that range from 1.45 ps to 1.8 ps. An O-O hydrogen bond length correlation function was calculated and found to exhibit an oscillation at 150 fs and a long-timescale decay time of 3.47 ps, both in good agreement with the FFCFs. Such results suggest that the spectral diffusion observed in FFCFs can be primarily attributed to fluctuations in O-O distances. An OD stretch energy correlation function was calculated, which consists of exponential decay with a time constant of 1.13 ps. The energy correlation function also exhibits two oscillations that are indicative of resonant energy transfer processes involving the OD stretch.

Multiple Ensembles of the Hydrogen-bonded Network in Ethylammonium Nitrate versus Water from Vibrational Spectral Dynamics of SCN- Probe.

We performed classical molecular dynamics simulations to monitor the structural interactions and ultrafast dynamical and spectral response in the protic ionic liquid, ethylammonium nitrate (EAN) and water using the nitrile stretching mode of thiocyanate ion (SCN- ) as the vibrational probe. The normalized frequency distribution of the nitrile stretch in SCN- attains an asymmetric shape in EAN, indicating the existence of more than one hydrogen-bonding environment in EAN. Further, we computed the 2D IR spectrum from classical trajectories, applying the response function formalism. Spectral diffusion dynamics in EAN undergo an initial rattling of the SCN- inside the local ion-cage occurring at a timescale of 0.10 ps, followed by the breakup of the ion-cage activating molecular diffusion at 7.86 ps timescale. In contrast, the dynamics of structural reorganization occur at a timescale of 0.58 ps in H2 O. Hence, the time dependence of the frequency-frequency correlation function decay hints at the local molecular structure and ultrafast ion dynamics of the SCN- probe. The loss of frequency correlation read from the peak shape changes in the 2D correlation spectrum as a function of waiting time is faster in H2 O than in EAN due to the enhanced structural ordering and higher viscosity of the latter. We provide an atomic-level interpretation of the solvation environment around SCN- in EAN and water, which indicates multiple ensembles of the hydrogen bond network in EAN.

Ultrafast vibrational dynamics of the tyrosine ring mode and its application to enkephalin insertion into phospholipid membranes as probed by two-dimensional infrared spectroscopy.

Enkephalins are small opioid peptides whose binding conformations are catalyzed by phospholipid membranes. Binding to opioid receptors is determined by the orientation of tyrosine and phenylalanine side chains. In this work, we investigate the effects of different charged phospholipid headgroups on the insertion of the tyrosine side chain into a lipid bilayer using a combination of 2D IR spectroscopy, anharmonic DFT calculations, and third order response function modeling. The insertion is probed by using the ∼1515cm-1 tyrosine ring breathing mode, which we found exhibits rich vibrational dynamics on the picosecond timescale. These dynamics include rapid intramolecular vibrational energy redistribution (IVR), where some of the energy ends up in a dark state that shows up as an anharmonically shifted combination band. The waiting-time dependent 2D IR spectra also show an unusual line shape distortion that affects the extraction of the frequency-frequency correlation function (FFCF), which is the dynamic observable of interest that reflects the tyrosine side chain's insertion into the lipid bilayer. We proposed three models to account for this distortion: a hot-state exchange model, a local environment dependent IVR model, and a coherence transfer model. A qualitative analysis of these models suggests that the local environment dependent IVR rate best explains the line shape distortion, while the coherence transfer model best reproduced the effects on the FFCF. Even with these complex dynamics, we found that the tyrosine ring mode's FFCF is qualitatively correlated with the degree of insertion expected from the different phospholipid headgroups.

Two-Dimensional Electronic-Vibrational Spectroscopy Reveals Cross-Correlation between Solvation Dynamics and Vibrational Spectral Diffusion.

Two-dimensional electronic-vibrational spectroscopy (2DEVS) is a useful technique for studying the structure and dynamics of photoexcited molecules via monitoring of the vibrational spectrum in real-time. However, quantitative modeling or prediction of experimental spectra has been hampered by the lack of a firm theoretical basis for this quantity. Here, we develop a useful theory of 2DEVS and show that the time-dependent line shape of the 2DEVS spectrum provides invaluable information on the cross-correlation function of the solvation dynamics and vibrational spectral diffusion. The center and nodal line slopes of each 2DEVS peak are determined by the associated cross-electronic-vibrational frequency-frequency correlation function, which is shown to be related to the intermolecular interactions and vibrational anharmonicities. The present theory of 2DEVS would thus be of use for a refined understanding of the 2DEVS spectra of reactive chemical and biological systems. We anticipate that further development of the expressions developed here will illuminate the application of 2DEVS studies of vibronically induced energy and electron transfer in functional materials.

Probing the vibrational dynamics of amide bands of N-methylformamide, N, N-dimethylacetamide, and N-methylacetamide in water

We report the vibrational dynamics of amide modes of N-methylformamide (NMF), N-methylacetamide (NMA), and N, N-dimethylacetamide (DMA) in water using first principles molecular dynamics simulations. The solvent-mediated dynamics and stretching profile of CO, NH, and CN modes of amide molecules were analyzed in terms of vibrational spectral and second-order reorientational dynamical properties. The maximum redshift is observed for the amide I band of DMA due to stronger DMA-water hydrogen bonding interaction; a blue shift is observed for NMF. The calculations also reveal that the amide-A band of NMF exhibits a redshift as compared to NMA. Multiple peaks are located for the CN band of DMA, and this feature gradually decreases for NMA and NMF. Spectral dynamics of amide bands were investigated by calculating the frequency-frequency correlation functions. Slowest spectral diffusion is found for the CO band of DMA. However, NMA shows slower dynamics for NH band than that of NMF.

CLS Next Gen: Accurate Frequency-Frequency Correlation Functions from Center Line Slope Analysis of 2D Correlation Spectra Using Artificial Neural Networks.

The center line slope (CLS) observable has become a popular method for characterizing spectral diffusion dynamics in two-dimensional (2D) correlation spectroscopy because of its ease of implementation, robustness, and clear theoretical relationship to the frequency-frequency correlation function (FFCF). The FFCF relates the frequency fluctuations of an ensemble of chromophores to coupled bath modes of the chemical system and is used for comparison to molecular dynamics simulations and for calculating 2D spectra. While in the appropriate limits, the CLS can be shown to be the normalized FFCF, from which the full FFCF can be obtained, in practice the assumptions that relate the CLS to the normalized FFCF are frequently violated. These violations are due to the presence of homogeneous broadening and motional narrowing. The generalized problem of relating the CLS to the FFCF is reanalyzed by introducing a new set of dimensionless parameters for both the CLS and FFCF. A large data set was generated of CLS parameters derived from numerically modeled 2D line shapes with known FFCF parameters. This data set was used to train feedforward artificial neural networks that act as functions, which take the CLS parameters as inputs and return FFCF parameters. These neural networks were deployed in an algorithm that is able to quickly and accurately determine FFCF parameters from experimental CLS parameters and the fwhm of the absorption line shape. The method and necessary inputs to accurately obtain the FFCF from the CLS are presented.

Structure and stretching dynamics of water molecules around an amphiphilic amide from FPMD simulations: A case study of N,N-dimethylformamide

N,N-Dimethylformamide (DMF) is a unique tertiary amphiphilic amide, where the presence of a hydrophilic aldehyde group favors hydrogen bond acceptance, but two hydrophobic methyl substituents inhibit interaction with water molecules. As a result, the water molecules encounter two different environments in the vicinity of DMF molecule: around the hydrophobic nitrogen site; and near the hydrophilic carbonyl oxygen. We employ first principles molecular dynamics methods to simulate an aqueous solution of DMF using PBE functional with Grimme's D3 dispersion correction at 330 K. Investigations on the liquid structure to understand inter-atomic interactions in amides attract much attention. We calculated various structural and dynamical properties along with vibrational stretching frequency of water molecules to understand heterogeneously affected water molecules by an amphiphilic amide molecule. In solvated DMF, the first peak minimum of the N-OW and OC-OW radial distribution functions (‘w’ subscript denotes atoms of water) are located at 5.72 and 3.16 Å, respectively. These distance cutoffs decide the boundary of the solvation shell. At OC-HW distance 2.45 Å, the deep peak minimum indicates stable OC … HW hydrogen bond. Previous Monte Carlo simulations reported the presence of hydrogen bonds between the oxygen site of DMF and hydrogen of water. The time-series wavelet method was used to compute the time-dependent frequencies of the hydroxyl groups of water. The average frequency of the OH modes inside the CO solvation shell (~3364 cm−1) in DMF is higher than bulk (~3337 cm−1), and the trend matches with an aqueous solution of acetone. In nitrogen hydration shell, the intense band resembles the bulk frequency distribution, and a narrow distinctive peak at the high-frequency side (range ~3650–3750 cm−1) represents the non‑hydrogen bonded or dangling OH groups. Raman spectroscopy in hydrophobic TBA and air/water interface displayed dangling OH stretch peak at ~3660 cm−1 and ~3710 cm−1, respectively. Our calculation of the frequency distribution, frequency-frequency correlation function, and hydrogen bond dynamics show the water molecules at bulk behave as in pure water. Inside the solvation shell of aminic nitrogen, non‑hydrogen bonded OH modes with a dangling lifetime ~0.38 ps dominates over the water-water hydrogen bonds. The time-dependent decay of the frequency correlation inside CO solvation shell has three decay components, a rapid decay, then, an intermediate component (~1.52 ps) corresponding to the lifetime of the carbonyl-water hydrogen bond, and the longer timescale ~11.97 ps representing the residence time of water molecules in the vicinity of carbonyl oxygen. We find that the carbonyl-water hydrogen bond (OC … HW) is stronger than the water-water hydrogen bond. The methyl substituents on the nitrogen of DMF impose weak hydrophobic interaction, and the hydrophilic carbonyl oxygen forms a strong hydrogen bond with the neighboring water resulting in localized dynamics.

Dynamics of Water Molecules and Ions in Concentrated Lithium Chloride Solutions Probed with Ultrafast 2D IR Spectroscopy.

Water and ion dynamics in concentrated LiCl solutions were studied using ultrafast 2D IR spectroscopy with the methyl thiocyanate (MeSCN) CN stretch as the vibrational probe. The IR absorption spectrum of MeSCN has two peaks, one peak for water associated with the nitrogen lone pair of MeSCN (W) and the other peak corresponding to Li+ associated with the lone pair (L). To extract the spectral diffusion (structural dynamics) of W and L species, we developed a method that isolates the peak of interest by subtracting the 2D Gaussian proxies of multiple interfering peaks. Center line slope data (normalized frequency-frequency correlation function) for 2D bands from the W and L are fit with triexponential functions. The fastest component (1.1-1.6 ps) is assigned to local hydrogen bond length fluctuations. The intermediate timescale (∼4.0 ps) corresponds to the hydrogen bond network rearrangement. The slowest component decays in ∼40 ps and corresponds to ion pair and ion cluster dynamics. The very similar W and L spectral diffusion indicates that the motions of the water and ions are strongly coupled. Orientational relaxations of the W and L species were extracted using a new method to eliminate the effects of overlapping peaks. The results show that MeSCN bound to water undergoes orientational relaxation significantly faster than MeSCN bound to Li+. The orientational and spectral diffusion results are compared. A Stark coupling model is used to extract the root mean square average electric field caused by the ion clouds along the CN moiety as a function of concentration.

Vibration Spectral Dynamics of Weakly Coordinating Water Molecules near an Anion: FPMD Simulations of an Aqueous Solution of Tetrafluoroborate.

The extent to which the ions affect the nearby water molecules will decide the structure-making or breaking nature of those ions in aqueous solutions. The effects of a weakly coordinating anion on the structure, dynamics, and vibrational properties of water molecules are not so significant as compared to an anion capable of making strong ion-water hydrogen bonds. The present work deals with the first-principles molecular dynamics study of an aqueous solution of such a weakly coordinating anion, tetrafluoroborate (BF4-), using dispersion-corrected DFT-based first-principles molecular dynamics (FPMD) simulations. Various structural, dynamical, and spectral properties, such as radial distribution functions (RDFs), rotational dynamics, vibrational density of states (VDOS), hydrogen bond as well as dangling OH autocorrelation functions, and residence dynamics, were calculated to investigate the effects of the anion on nearby water molecules. The process of spectral diffusion was assessed through a time series wavelet transformation of trajectories obtained from FPMD simulations. The first ion-water solvation shell extends up to 5.5 Å, containing around 20 water molecules. The lifetime of the ion-water hydrogen bond is found to be 1.19 ps, whereas the water-water hydrogen bond lifetime is found to be 1.13 ps. Inside the solvation shell, the persistence time of dangling OH chromophores and the average frequency of OH modes inside the solvation shell are found to be more compared to bulk. Three time scales are found for solvation shell OH modes from the frequency-frequency correlation function. A very short time scale is found for the intact ion-water interaction; the short time scale is for the ion-water hydrogen bond, and the long time scale is for escape dynamics of water molecules from the ion solvation shell. From the mean squared displacement, it is found that solvation water molecules diffuse slower than the bulk. However, solvation shell water molecules show faster relaxation from the analysis of rotational anisotropy. Within the longer time scale of spectral diffusion, this process (which is related to various dynamics of the molecules) is not yet complete, as compared to fast anisotropic decay. This fact is similar to the experimental finding of spectral diffusion and anisotropy time scales in the aqueous solution of borohydride anion. The calculated results are also compared with available experimental data wherever possible.

Vibrational heavy atom effect controls relaxation and spectral diffusion in triphenyl hydride complexes

A series of three triphenyl hydride compounds was investigated in a range of solvents by Fourier transform infrared (FTIR), IR pump-probe, and two-dimensional IR (2D-IR) spectroscopies. The mass of the central atom of the three compounds was varied systematically down the group 14 elements of silicon, germanium, and tin. FTIR studies provided evidence that the solvent perturbs the three hydride modes in a similar manner, as indicated by identical solvatochromic and broadening trends. IR pump-probe measurements showed that the vibrational lifetime of the hydride stretch increased when the mass of the central atom increased. Density functional theory calculations asserted that the vibrational modes of the three compounds are nearly identical except for the hydride stretching and wagging modes. Interestingly, frequency-frequency correlation functions obtained from 2D-IR spectra indicated that an increasingly large central atom produces small, but measurable changes in the dynamics of the solvation shell surrounding each compound.

Enhanced vibrational solvatochromism and spectral diffusion by electron rich substituents on small molecule silanes.

Fourier transform infrared and two-dimensional IR (2D-IR) spectroscopies were applied to two different silanes in three different solvents. The selected solutes exhibit different degrees of vibrational solvatochromism for the Si-H vibration. Density functional theory calculations confirm that this difference in sensitivity is the result of higher mode polarization with more electron withdrawing ligands. This mode sensitivity also affects the extent of spectral diffusion experienced by the silane vibration, offering a potential route to simultaneously optimize the sensitivity of vibrational probes in both steady-state and time-resolved measurements. Frequency-frequency correlation functions obtained by 2D-IR show that both solutes experience dynamics on similar time scales and are consistent with a picture in which weakly interacting solvents produce faster, more homogeneous fluctuations. Molecular dynamics simulations confirm that the frequency-frequency correlation function obtained by 2D-IR is sensitive to the presence of hydrogen bonding dynamics in the surrounding solvation shell.

Water-anion hydrogen bonding dynamics: Ultrafast IR experiments and simulations.

Many of water's remarkable properties arise from its tendency to form an intricate and robust hydrogen bond network. Understanding the dynamics that govern this network is fundamental to elucidating the behavior of pure water and water in biological and physical systems. In ultrafast nonlinear infrared experiments, the accessible time scales are limited by water's rapid vibrational relaxation (1.8 ps for dilute HOD in H2O), precluding interrogation of slow hydrogen bond evolution in non-bulk systems. Here, hydrogen bonding dynamics in bulk D2O were studied from the perspective of the much longer lived (36.2 ps) CN stretch mode of selenocyanate (SeCN-) using polarization selective pump-probe (PSPP) experiments, two-dimensional infrared (2D IR) vibrational echo spectroscopy, and molecular dynamics simulations. The simulations make use of the empirical frequency mapping approach, applied to SeCN- for the first time. The PSPP experiments and simulations show that the orientational correlation function decays via fast (2.0 ps) restricted angular diffusion (wobbling-in-a-cone) and complete orientational diffusive randomization (4.5 ps). Spectral diffusion, quantified in terms of the frequency-frequency correlation function, occurs on two time scales. The initial 0.6 ps time scale is attributed to small length and angle fluctuations of the hydrogen bonds between water and SeCN-. The second 1.4 ps measured time scale, identical to that for HOD in bulk D2O, reports on the collective reorganization of the water hydrogen bond network around the anion. The experiments and simulations provide details of the anion-water hydrogen bonding and demonstrate that SeCN- is a reliable vibrational probe of the ultrafast spectroscopy of water.

Direct observation of dynamic crossover in fragile molecular glass formers with 2D IR vibrational echo spectroscopy.

The dynamics of supercooled liquids of the molecular glass formers benzophenone and ortho-terphenyl were investigated with 2D IR spectroscopy using long-lived vibrational probes. The long lifetimes of the probes enabled structural dynamics of the liquids to be studied from a few hundred femtoseconds to a nanosecond. 2D IR experiments measured spectraldiffusion of a vibrational probe, which reports on structural fluctuations of the liquid. Analysis of the 2D IR data provides the frequency-frequency correlation function (FFCF). Two vibrational probes were examined with equivalent results, demonstrating the observed liquid dynamics are not significantly influenced by the probe molecules. At higher temperatures, the FFCF is a biexponential decay. However, at mild supercooling, the biexponential decay is no longer sufficient, indicating a dynamic crossover. The crossover occurs at a temperature well above the mode-coupling theory critical temperature for the given liquid, indicating dynamic heterogeneity above the critical temperature. Examination of the low temperature data with lifetime density analysis shows that the change is best described as an additional, distinct relaxation that shows behavior consistent with a slow β-process.

Evolution of Ultrafast Vibrational Dynamics During Sol–Gel Aging

A longitudinal 1D- and 2D-IR spectroscopy study is presented in which the homogeneous and inhomogeneous contributions to the line shape of a surface-bound Si—H vibration are monitored in a silica sol–gel while it ages. The vibrational data are complemented by time-lapse 29Si NMR and rheological measurements leading up to the gel point. The silane stretching frequency evolves continuously over the equivalent of several days, tracking the increase in tertiary and quaternary functionalized silicon atoms. The 1D-IR peak shape of the mode is static up until gelation, but then broadens continuously as the gel ages. A frequency–frequency correlation function (FFCF) extracted from 2D-IR spectra reveals that the line shape changes stem from an increase in inhomogeneity while the homogeneous dynamics remain unaffected by changes in silica cross-linking.

Critical Slowing of Density Fluctuations Approaching the Isotropic-Nematic Transition in Liquid Crystals: 2D IR Measurements and Mode Coupling Theory.

Two-dimensional infrared (2D IR) data are presented for a vibrational probe in three nematogens: 4-cyano-4'-pentylbiphenyl, 4-cyano-4'-octylbiphenyl, and 4-(trans-4-amylcyclohexyl)-benzonitrile. The spectral diffusion time constants in all three liquids in the isotropic phase are proportional to [T*/(T - T*)](1/2), where T* is 0.5-1 K below the isotropic-nematic phase transition temperature (TNI). Rescaling to a reduced temperature shows that the decays of the frequency-frequency correlation function (FFCF) for all three nematogens fall on the same curve, suggesting a universal dynamic behavior of nematogens above TNI. Spectral diffusion is complete before significant orientational relaxation in the liquid, as measured by optically heterodyne detected-optical Kerr effect (OHD-OKE) spectroscopy, and before any significant orientational randomization of the probe measured by polarization selective IR pump-probe experiments. To interpret the OHD-OKE and FFCF data, we constructed a mode coupling theory (MCT) schematic model for the relationships among three correlation functions: ϕ1, a correlator for large wave vector density fluctuations; ϕ2, the orientational correlation function whose time derivative is the observable in the OHD-OKE experiment; and ϕ3, the FFCF for the 2D IR experiment. The equations for ϕ1 and ϕ2 match those in the previous MCT schematic model for nematogens, and ϕ3 is coupled to the first two correlators in a straightforward manner. Resulting models fit the data very well. Across liquid crystals, the temperature dependences of the coupling constants show consistent, nonmonotonic behavior. A remarkable change in coupling occurs at ∼5 K above TNI, precisely where the rate of spectral diffusion in 5CB was observed to deviate from that of a similar nonmesogenic liquid.

A new interpretation of the meaning of the center of line slope from a two-dimensional infrared spectrum.

This article presents a new approximation to understand the connection between the center of line slope from a single peak of a two-dimensional (2D) infrared spectrum and the frequency-frequency correlation function. This approximation which goes beyond the short-time approximation includes explicitly pure dephasing mechanisms by introducing a time parameter that separates the fast fluctuations and slow fluctuations. While in the short-time approximation, the center of line slope is given by the normalized frequency fluctuations auto-correlation function, I show using this new approximation that the center of line slope measures on long time scales a shifted and scaled correlation function. The results present a new interpretation of the meaning of the center of line slope that allows for a better understanding of what 2D experiments can measure. To illustrate these findings, I compare this approximation with the short-time approximation for several examples of frequency-frequency correlation functions. I also give an estimate of the value of the time separation parameter for a correlation function with a simple exponential decay.

Quantifying spectral diffusion by the direct measurement of the correlation function for excitons in semiconductor quantum wells

The phenomenon of spectral diffusion is common to a variety of inhomogeneously broadened systems. Spectral diffusion can be quantified through the frequency–frequency correlation function (FFCF), which is often approximated using observables from a variety of experimental techniques. We present a direct measurement of the temperature-dependent FFCF for excitons in semiconductor quantum wells using two-dimensional coherent spectroscopy. This technique enables the FFCF to be quantified without making any assumptions of the FFCF dynamics. Our results show that the Gauss–Markov approximation, which assumes exponential decay dynamics of the FFCF, is only valid for sample temperatures above 50 K. We compare our results with those obtained by the ellipticity and center-line slope measurements.