Vibrational Spectroscopic Map, Vibrational Spectroscopy, and Intermolecular Interaction.

Vibrational spectroscopy is an essential tool in chemical analyses, biological assays, and studies of functional materials. Over the past decade, various coherent nonlinear vibrational spectroscopic techniques have been developed and enabled researchers to study time-correlations of the fluctuating frequencies that are directly related to solute-solvent dynamics, dynamical changes in molecular conformations and local electrostatic environments, chemical and biochemical reactions, protein structural dynamics and functions, characteristic processes of functional materials, and so on. In order to gain incisive and quantitative information on the local electrostatic environment, molecular conformation, protein structure and interprotein contacts, ligand binding kinetics, and electric and optical properties of functional materials, a variety of vibrational probes have been developed and site-specifically incorporated into molecular, biological, and material systems for time-resolved vibrational spectroscopic investigation. However, still, an all-encompassing theory that describes the vibrational solvatochromism, electrochromism, and dynamic fluctuation of vibrational frequencies has not been completely established mainly due to the intrinsic complexity of intermolecular interactions in condensed phases. In particular, the amount of data obtained from the linear and nonlinear vibrational spectroscopic experiments has been rapidly increasing, but the lack of a quantitative method to interpret these measurements has been one major obstacle in broadening the applications of these methods. Among various theoretical models, one of the most successful approaches is a semiempirical model generally referred to as the vibrational spectroscopic map that is based on a rigorous theory of intermolecular interactions. Recently, genetic algorithm, neural network, and machine learning approaches have been applied to the development of vibrational solvatochromism theory. In this review, we provide comprehensive descriptions of the theoretical foundation and various examples showing its extraordinary successes in the interpretations of experimental observations. In addition, a brief introduction to a newly created repository Web site (http://frequencymap.org) for vibrational spectroscopic maps is presented. We anticipate that a combination of the vibrational frequency map approach and state-of-the-art multidimensional vibrational spectroscopy will be one of the most fruitful ways to study the structure and dynamics of chemical, biological, and functional molecular systems in the future.

Direct comparison of amplitude and geometric measures of spectral inhomogeneity using phase-cycled 2D-IR spectroscopy.

Two-dimensional infrared (2D-IR) spectroscopy provides access to equilibrium dynamics with the extraction of the frequency-fluctuation correlation function (FFCF) from the measured spectra. Several different methods of obtaining the FFCF from experimental spectra, such as the center line slope (CLS), ellipticity, phase slope, and nodal line slope, all depend on the geometrical nature of the 2D line shape and necessarily require spectral extent in order to achieve a measure of the FFCF. Amplitude measures, on the other hand, such as the inhomogeneity index, rely only on signal amplitudes and can, in principle, be computed using just a single point in a 2D spectrum. With a pulse shaper-based 2D-IR spectrometer, in conjunction with phase cycling, we separate the rephasing and nonrephasing signals used to determine the inhomogeneity index. The same measured data provide the absorptive spectrum, needed for the CLS. Both methods are applied to two model molecular systems: tungsten hexacarbonyl (WCO6) and methylcyclopentadienyl manganese tricarbonyl [Cp'Mn(CO)3, MCMT]. The three degenerate IR modes of W(CO)6 lack coherent modulation or noticeable intramolecular vibrational redistribution (IVR) and are used to establish a baseline comparison. The two bands of the MCMT tripod complex include intraband coherences and IVR as well as likely internal torsional motion on a few-picosecond time scale. We find essentially identical spectral diffusion, but faster, non-equilibrium dynamics lead to differences in the FFCFs extracted with the two methods. The inhomogeneity index offers an advantage in cases where spectra are complex and energy transfer can mimic line shape changes due to frequency fluctuations.

Ultrafast vibrational dynamics of a solute correlates with dynamics of the solvent.

Two-dimensional infrared (2D-IR) spectroscopy is used to measure the spectral dynamics of the metal carbonyl complex cyclopentadienyl manganese tricarbonyl (CMT) in a series of linear alkyl nitriles. 2D-IR spectroscopy provides direct readout of solvation dynamics through spectral diffusion, probing the decay of frequency correlation induced by fluctuations of the solvent environment. 2D-IR simultaneously monitors intramolecular vibrational energy redistribution (IVR) among excited vibrations, which can also be influenced by the solvent through the spectral density rather than the dynamical friction underlying solvation. Here, we report that the CMT vibrational probe reveals solvent dependences in both the spectral diffusion and the IVR time scales, where each slows with increased alkyl chain length. In order to assess the degree to which solute-solvent interactions can be correlated with bulk solvent properties, we compared our results with low-frequency dynamics obtained from optical Kerr effect (OKE) spectroscopy-performed by others-on the same nitrile solvent series. We find excellent correlation between our spectral diffusion results and the orientational dynamics time scales from OKE. We also find a correlation between our IVR time scales and the amplitudes of the low-frequency spectral densities evaluated at the 90-cm-1 energy difference, corresponding to the gap between the two strong vibrational modes of the carbonyl probe. 2D-IR and OKE provide complementary perspectives on condensed phase dynamics, and these findings provide experimental evidence that at least at the level of dynamical correlations, some aspects of a solute vibrational dynamics can be inferred from properties of the solvent.

Ultrafast X-ray Absorption Near Edge Structure Reveals Ballistic Excited State Structural Dynamics.

Polarized ultrafast time-resolved X-ray absorption near edge structure (XANES) allows characterization of excited state dynamics following excitation. Excitation of vitamin B12, cyanocobalamin (CNCbl), in the αß-band at 550 nm and the γ-band at 365 nm was used to uniquely resolve axial and equatorial contributions to the excited state dynamics. The structural evolution of the excited molecule is best described by a coherent ballistic trajectory on the excited state potential energy surface. Prompt expansion of the Co cavity by ca. 0.03 Å is followed by significant elongation of the axial bonds (>0.25 Å) over the first 190 fs. Subsequent contraction of the Co cavity in both axial and equatorial directions results in the relaxed S1 excited state structure within 500 fs of excitation.

Polarized XANES Monitors Femtosecond Structural Evolution of Photoexcited Vitamin B12.

Ultrafast, polarization-selective time-resolved X-ray absorption near-edge structure (XANES) was used to characterize the photochemistry of vitamin B12, cyanocobalamin (CNCbl), in solution. Cobalamins are important biological cofactors involved in methyl transfer, radical rearrangement, and light-activated gene regulation, while also holding promise as light-activated agents for spatiotemporal controlled delivery of therapeutics. We introduce polarized femtosecond XANES, combined with UV-visible spectroscopy, to reveal sequential structural evolution of CNCbl in the excited electronic state. Femtosecond polarized XANES provides the crucial structural dynamics link between computed potential energy surfaces and optical transient absorption spectroscopy. Polarization selectivity can be used to uniquely identify electronic contributions and structural changes, even in isotropic samples when well-defined electronic transitions are excited. Our XANES measurements reveal that the structural changes upon photoexcitation occur mainly in the axial direction, where elongation of the axial Co-CN bond and Co-NIm bond on a 110 fs time scale is followed by corrin ring relaxation on a 260 fs time scale. These observations expose features of the potential energy surfaces controlling cobalamin reactivity and deactivation.

Dynamic Flexibility of Hydrogenase Active Site Models Studied with 2D-IR Spectroscopy.

Hydrogenase enzymes enable organisms to use H2 as an energy source, having evolved extremely efficient biological catalysts for the reversible oxidation of molecular hydrogen. Small-molecule mimics of these enzymes provide both simplified models of the catalysis reactions and potential artificial catalysts that might be used to facilitate a hydrogen economy. We have studied two diiron hydrogenase mimics, µ-pdt-[Fe(CO)3]2 and µ-edt-[Fe(CO)3]2 (pdt = propanedithiolate, edt = ethanedithiolate), in a series of alkane solvents and have observed significant ultrafast spectral dynamics using two-dimensional infrared (2D-IR) spectroscopy. Since solvent fluctuations in nonpolar alkanes do not lead to substantial electrostatic modulations in a solute's vibrational mode frequencies, we attribute the spectral diffusion dynamics to intramolecular flexibility. The intramolecular origin is supported by the absence of any measurable solvent viscosity dependence, indicating that the frequency fluctuations are not coupled to the solvent motional dynamics. Quantum chemical calculations reveal a pronounced coupling between the low-frequency torsional rotation of the carbonyl ligands and the terminal CO stretching vibrations. The flexibility of the CO ligands has been proposed to play a central role in the catalytic reaction mechanism, and our results highlight that the CO ligands are highly flexible on a picosecond time scale.

Oxidation-State-Dependent Vibrational Dynamics Probed with 2D-IR.

In an effort to examine the role of electronic structure and oxidation states in potentially modifying intramolecular vibrational dynamics and intermolecular solvation, we have used 2D-IR to study two distinct oxidation states of an organometallic complex. The complex, [1,1'-bis(diphenylphosphino)ferrocene]tetracarbonyl chromium (DPPFCr), consists of a catalytic diphenylphosphino ferrocene redox-active component as well as a Cr that can be switched from a Cr(0) to a Cr(I) oxidation state using a chemical oxidant in dichloromethane (DCM) solution. The DPPFCr(I) radical cation is sufficiently stable to investigate with 2D-IR spectroscopy, which provides dynamical information such as vibrational relaxation, intramolecular vibrational redistribution, as well as solvation dynamics manifested as spectral diffusion. Our measurements show that the primarily intramolecular dynamical processes-vibrational relaxation and redistribution-differ significantly between the two oxidation states, with faster relaxation in the oxidized DPPFCr(I) radical cation. The primarily intermolecular spectral diffusion dynamics, however, exhibit insignificant oxidation state dependence. We speculate that the low nucleophilicity (i.e., donicity) of the DCM solvent, which is chosen to facilitate the chemical oxidation, masks any potential changes in solvation dynamics accompanying the substantial decrease in the 2.5 D molecular dipole moment of DPPFCr(I) relative to DPPFCr(0) (7.5 D).

Dynamics of rhenium photocatalysts revealed through ultrafast multidimensional spectroscopy.

Rhenium catalysts have shown promise to promote carbon neutrality by reducing a prominent greenhouse gas, CO2, to CO and other starting materials. Much research has focused on identifying intermediates in the photocatalysis mechanism as well as time scales of relevant ultrafast processes. Recent studies have implemented multidimensional spectroscopies to characterize the catalyst's ultrafast dynamics as it undergoes the many steps of its photocycle. Two-dimensional infrared (2D-IR) spectroscopy is a powerful method to obtain molecular structure information while extracting time scales of dynamical processes with ultrafast resolution. Many observables result from 2D-IR experiments including vibrational lifetimes, intramolecular redistribution time scales, and, unique to 2D-IR, spectral diffusion, which is highly sensitive to solute-solvent interactions and motional dynamics. Spectral diffusion, a measure of how long a vibrational mode takes to sample its frequency space due to multiple solvent configurations, has various contributing factors. Properties of the solvent, the solute's structural flexibility, and electronic properties, as well as interactions between the solvent and solute, complicate identifying the origin of the spectral diffusion. With carefully chosen experiments, however, the source of the spectral diffusion can be unveiled. Within the context of a considerable body of previous work, here we discuss the spectral diffusion of several rhenium catalysts at multiple stages in the catalysis. These studies were performed in multiple polar liquids to aid in discovering the contributions of the solvent. We also performed electronic ground state 2D-IR and electronic excited state transient-2D-IR experiments to observe how spectral diffusion changes upon electronic excitation. Our results indicate that with the original Lehn catalyst in THF, relative to the ground state, the spectral diffusion slows by a factor of 3 in the equilibrated triplet metal-to-ligand charge transfer state. We attribute this slowdown to a decrease in dielectric friction as well as an increase in molecular flexibility. It is possible to partially simulate the charge transfer by altering the electron density moderately by adding electron donating or withdrawing substituents symmetrically to the bipyridine ligand. We find that unlike the significant electronic structure change induced by MLCT, such small substituent effects do not influence the spectral diffusion. A solvent study in THF, DMSO, and CH3CN found there to be an explicit solvent dependence that we can correlate to the solvent donicity, which is a measure of its nucleophilicity. Future studies focused on the solvent effects on spectral diffusion in the crucial photoinitiated state can illuminate the role the solvent plays in the catalysis.

Histidine Orientation Modulates the Structure and Dynamics of a de Novo Metalloenzyme Active Site.

The ultrafast dynamics of a de novo metalloenzyme active site is monitored using two-dimensional infrared spectroscopy. The homotrimer of parallel, coiled coil α-helices contains a His3-Cu(I) metal site where CO is bound and serves as a vibrational probe of the hydrophobic interior of the self-assembled complex. The ultrafast spectral dynamics of Cu-CO reveals unprecedented ultrafast (2 ps) nonequilibrium structural rearrangements launched by vibrational excitation of CO. This initial rapid phase is followed by much slower ∼40 ps vibrational relaxation typical of metal-CO vibrations in natural proteins. To identify the hidden coupled coordinate, small molecule analogues and the full peptide were studied by QM and QM/MM calculations, respectively. The calculations show that variation of the histidines' dihedral angles in coordinating Cu controls the coupling between the CO stretch and the Cu-C-O bending coordinates. Analysis of different optimized structures with significantly different electrostatic field magnitudes at the CO ligand site indicates that the origin of the stretch-bend coupling is not directly due to through-space electrostatics. Instead, the large, ∼3.6 D dipole moments of the histidine side chains effectively transduce the electrostatic environment to the local metal coordination orientation. The sensitivity of the first coordination sphere to the protein electrostatics and its role in altering the potential energy surface of the bound ligands suggests that long-range electrostatics can be leveraged to fine-tune function through enzyme design.

Solvent-dependent dynamics of a series of rhenium photoactivated catalysts measured with ultrafast 2DIR.

The spectral dynamics of a series of rhenium photocatalysts, fac-Re(4,4'-R2-bpy)(CO)3Cl, where R = H, methyl, t-butyl, and carboxylic acid, as well as Re(1,10-phenanthroline)(CO)3Cl were observed in multiple aprotic solvents using two-dimensional infrared spectroscopy (2DIR). The carbonyl vibrational stretching frequencies showed slight variations due to the electron-donating or -withdrawing nature of the substituents on the bipyridine. The different substituents had minimal to no influence on the spectral diffusion time scales of the compounds within a particular solvent, but among the three different solvents investigated (DMSO, THF, and CH3CN), we find the spectral diffusion times to correlate with the solvent's donor number (DN). Because the donicity is a measure the Lewis basicity of the solvent, these findings may help establish a more complete dynamical picture of the photocatalysis, where the first chemical step following optical excitation is electron transfer from a sacrificial donor to the rhenium complex.

Crowding induced collective hydration of biological macromolecules over extended distances.

Ultrafast two-dimensional infrared (2D-IR) spectroscopy reveals picosecond protein and hydration dynamics of crowded hen egg white lysozyme (HEWL) labeled with a metal-carbonyl vibrational probe covalently attached to a solvent accessible His residue. HEWL is systematically crowded alternatively with polyethylene glycol (PEG) or excess lysozyme in order to distinguish the chemically inert polymer from the complex electrostatic profile of the protein crowder. The results are threefold: (1) A sharp dynamical jamming-like transition is observed in the picosecond protein and hydration dynamics that is attributed to an independent-to-collective hydration transition induced by macromolecular crowding that slows the hydration dynamics up to an order of magnitude relative to bulk water. (2) The interprotein distance at which the transition occurs suggests collective hydration of proteins over distances of 30-40 Å. (3) Comparing the crowding effects of PEG400 to our previously reported experiments using glycerol exposes fundamental differences between small and macromolecular crowding agents.

Equilibrium excited state dynamics of a photoactivated catalyst measured with ultrafast transient 2DIR.

A detailed understanding of photocatalyzed reaction dynamics requires a sensitive means of investigating the transient catalytically active species. Ideally, the method should be able to compare the electronically excited photocatalyst directly to the ground state species. We use equilibrium and transient two-dimensional infrared (2DIR and t-2DIR) spectroscopy to study the ground and excited state spectral dynamics of [Re(CO)3(bpy)Cl] in tetrahydrofuran (THF). We leverage the long-lived triplet excited state of the molecule to re-establish an equilibrated state relative to intersystem crossing dynamics and external solvent fluctuations, allowing access to the dynamics experienced by the excited state photocatalyst. The decay of frequency correlations within the excited triplet state species differs significantly from the ground state (slower by a factor of 3), indicating that the electronic excitation and subsequent metal-to-ligand charge transfer and associated structural changes are sufficient to perturb the spectral dynamics as sensed by the carbonyl ligands. In addition, we observe a 2-fold slowdown in ground state spectral dynamics around the in-phase symmetric vibrational mode compared to the two lower frequency, out-of-phase symmetric and asymmetric modes. Following electronic absorption and metal-to-ligand charge transfer the symmetry of the vibrational modes are disrupted, and all vibrational modes experience inhomogeneous broadening and spectral diffusion. The qualitative change in broadening mechanisms arises from the charge redistribution, indicating that direct comparisons of vibrational spectral dynamics on different electronic states-reported here for the first time-can be highly sensitive indicators of changes in electronic structure and in the concomitant solvation dynamics that underlie the microscopic details of charge transfer reactions.

Monitoring equilibrium reaction dynamics of a nearly barrierless molecular rotor using ultrafast vibrational echoes.

Using rapidly acquired spectral diffusion, a recently developed variation of heterodyne detected infrared photon echo spectroscopy, we observe ∼3 ps solvent independent spectral diffusion of benzene chromium tricarbonyl (C6H6Cr(CO)3, BCT) in a series of nonpolar linear alkane solvents. The spectral dynamics is attributed to low-barrier internal torsional motion. This tripod complex has two stable minima corresponding to staggered and eclipsed conformations, which differ in energy by roughly half of kBT. The solvent independence is due to the relative size of the rotor compared with the solvent molecules, which create a solvent cage in which torsional motion occurs largely free from solvent damping. Since the one-dimensional transition state is computed to be only 0.03 kBT above the higher energy eclipsed conformation, this model system offers an unusual, nearly barrierless reaction, which nevertheless is characterized by torsional coordinate dependent vibrational frequencies. Hence, by studying the spectral diffusion of the tripod carbonyls, it is possible to gain insight into the fundamental dynamics of internal rotational motion, and we find some evidence for the importance of non-diffusive ballistic motion even in the room-temperature liquid environment. Using several different approaches to describe equilibrium kinetics, as well as the influence of reactive dynamics on spectroscopic observables, we provide evidence that the low-barrier torsional motion of BCT provides an excellent test case for detailed studies of the links between chemical exchange and linear and nonlinear vibrational spectroscopy.

Rapid and accurate measurement of the frequency-frequency correlation function.

Using an implementation of heterodyne-detected vibrational echo spectroscopy, we show that equilibrium spectral diffusion caused by solvation dynamics can be measured in a fraction of the time required using traditional two-dimensional infrared spectroscopy. Spectrally resolved, heterodyne-detected rephasing and nonrephasing signals, recorded at a single delay between the first two pulses in a photon echo sequence, can be used to measure the full waiting time dependent spectral dynamics that are typically extracted from a series of 2D-IR spectra. Hence, data acquisition is accelerated by more than 1 order of magnitude, while permitting extremely fine sampling of the spectral dynamics during the waiting time between the second and third pulses. Using cymantrene (cyclopentadienyl manganese tricarbonyl, CpMn(CO)3) in alcohol solutions, we compare this novel approach--denoted rapidly acquired spectral diffusion (RASD)--with a traditional method using full 2D-IR spectra, finding excellent agreement. Though this approach is largely limited to isolated vibrational bands, we also show how to remove interference from cross-peaks that can produce characteristic modulations of the spectral dynamics through vibrational quantum beats.

Ultrafast 2DIR probe of a host-guest inclusion complex: structural and dynamical constraints of nanoconfinement.

Two-dimensional infrared (2DIR) spectroscopy is used to study the influence of nanoconfinement on the spectral diffusion dynamics of cyclopentadienyl manganese tricarbonyl (CpMn(CO)3, CMT) free in solution and confined in the cavity of ß-cyclodextrin. Contrary to the reorientation correlation function of the solvent molecules, determined through molecular dynamics simulations, measurements in three different solvents indicate that CMT confined in ß-cyclodextrin undergoes spectral diffusion that is faster than free CMT. To account for this discrepancy, we propose that spectral diffusion time scales contain a dynamical contribution that is dependent on the effective size of the conformational space presented by the solvation environment. This solvation state space size is related to the number of participating solvent molecules, which in turn is proportional to the solvent accessible surface area (SASA). We test the role of the number of participating solvent molecules using a simple Gaussian-Markov simulation and find that an increase in the number of participating solvent molecules indeed slows the time required to search the available conformational space. Finally, we test this dependence by comparing the spectral diffusion of a previously studied manganese carbonyl, dimanganese decacarbonyl (Mn2(CO)10, DMDC), to CMT and find that DMDC, which has a larger SASA, exhibits slower spectral diffusion. The experimental observations and the supporting simplistic solvation model suggest that vibrational probe molecules, such as CMT, might be able to function as sensors of conformational entropy.

Reply to "Comment on: 'Isolating Vibrational Polariton 2D-IR Transmission Spectra'".

In a Comment on our recent Letter, the authors take issue with our method of refining 2D-IR transmission spectra to remove a background contribution that arises from nonpolaritonic molecules in the cavity. In our response to their Comment, we describe how our approach was motivated by the previous work of the authors, and we present a spatially dependent molecule-cavity Tavis-Cummings model that can account for the significant response from localized molecules with nonzero oscillator strengths. The telltale signature of the localized molecule response is the spectral diffusion dynamics of the bare W(CO)6 molecules in the polar butyl acetate solvent. Inhomogeneous broadening is absent from polaritonic states due to the extreme degree of exchange narrowing in coupling very large numbers of molecules to a cavity mode.

Site-specific coupling of hydration water and protein flexibility studied in solution with ultrafast 2D-IR spectroscopy.

There is considerable evidence for the slaving of biomolecular dynamics to the motions of the surrounding solvent environment, but to date there have been few direct experimental measurements capable of site-selectively probing both the dynamics of the water and the protein with ultrafast time resolution. Here, two-dimensional infrared spectroscopy (2D-IR) is used to study the ultrafast hydration and protein dynamics sensed by a metal carbonyl vibrational probe covalently attached to the surface of hen egg white lysozyme dissolved in D(2)O/glycerol solutions. Surface labeling provides direct access to the dynamics at the protein-water interface, where both the hydration and the protein dynamics can be observed simultaneously through the vibrational probe's frequency-frequency correlation function. In pure D(2)O, the correlation function shows a fast initial 3 ps decay corresponding to fluctuations of the hydration water, followed by a significant static offset attributed to fluctuations of the protein that are not sampled within the <20 ps experimental window. Adding glycerol increases the bulk solvent viscosity while leaving the protein structurally intact and hydrated. The hydration dynamics exhibit a greater than 3-fold slowdown between 0 and 80% glycerol (v/v), and the contribution from the protein's dynamics is found to slow in a nearly identical fashion. In addition, the magnitude of the dynamic slowdown associated with hydrophobic hydration is directly measured and shows quantitative agreement with predictions from molecular dynamics simulations.

Ultrafast α-like relaxation of a fragile glass-forming liquid measured using two-dimensional infrared spectroscopy.

Ultrafast two-dimensional infrared (2D-IR) spectroscopy is used to study the picosecond dynamics of a vibrational probe molecule dissolved in a fragile glass former. The spectral dynamics are observed as the system is cooled to within a few degrees of the glass transition temperature (T(g)). We observe nonexponential relaxation of the frequency-frequency correlation function, similar to what has been reported for other dynamical correlation functions. In addition, we see evidence for α-like relaxation, typically associated with long-time, cooperative molecular motion, on the ultrafast time scale. The data suggests that the spectral dynamics are sensitive to cooperative motion occurring on time scales that are necessarily longer than the observation time.