Two-dimensional spectroscopy at infrared and optical frequencies

High-Frequency Multidimensional Spectroscopy

The experimental and theoretical basis for extending the experiments like NMR correlation spectroscopy to the much higher IR and optical frequencies comes from a generation of research on nonlinear molecular spectroscopy, which has been concerned with understanding the responses of molecular materials to successive interactions with light fields (8). The literature of this field is necessarily intimately associated with formal quantum dynamics theory, but the intent of this Perspective is to provide some physical insights, free from mathematical equations.

The most common practical nonlinear optical processes that lead to structural inferences involve interactions with relatively few fields, such as three or five, and the nonlinear processes are visualized by identifying the various superpositions, or mixtures of states that the system achieves at successive stages in its interaction with these fields. In such pictures, the linear or first-order spectroscopies involve the emission of a superposition of ground and excited states created by one field, whereas third-order spectroscopies involve detecting a mixed quantum state created by three fields, and so on. The various 2D and 3D spectroscopic methods surveyed in this Perspective are third-order, like many of the most widely applied forms of nonlinear spectroscopy. In this sequential picture of nonlinear processes, the system remains close to equilibrium during its interactions with the fields. On the contrary, NMR experiments commonly involve more than just a tickling by the incident fields and so are not described by low-order interactions (9).

The three electromagnetic fields of the third-order nonlinear interaction needed for multidimensional spectroscopy act on the sample at three separate instants of time as represented pictorially in Fig. 1. Furthermore, the intervals between these interactions are experimentally controllable if the sources are chosen as extremely short, femtosecond timescale pulses. During the first interval, usually referred to as the “coherence evolution period” (τ), the system is in a coherent nonequilibrium state like the one that radiates to create linear spectra. In the second interval, or “mixing period” (T), the next two pulses cooperate to create the superposition, or mixed state, that radiates the signal oscillating at optical or IR frequencies. The signal is detected at each interval (t) after the third pulse. The techniques for manipulating the pulses used in these experiments, choosing the phases by beam directions or by pulse shaping, and detecting the signal fields have arisen from applications to solution and solid-state dynamics of the enormous arsenal of methods of ultrafast spectroscopy and nonlinear optics.

Challenging directions for these multidimensional spectroscopies involve the creation of fast, efficient, and accurate methods of controlling the frequency and phases of the electric field oscillations of the IR and optical waves that are used and generated in the 2D experiments. The electromagnetic waves for mid-IR light that excites amide modes of peptides have periods in the range of 20 fs, whereas those of optical waves are 10 times shorter than this, so both are much faster than the response times of IR or optical detectors, which therefore cannot be used to directly measure the oscillations of the generated fields: instead, these detectors generate a current that depends on the mean square of the field. One trick learned from radio receiver technology that has been used in high-frequency spectroscopy is heterodyning, in which the field to be measured is combined with another field (the local oscillator) (Fig. 1) whose envelope, frequency, and phase are known. The detector signal that arises from the interference of these two fields is usually what is processed to obtain the required signal field (10). The multidimensional experiments are being greatly improved in speed and accuracy by development of new IR materials and devices (11, 12) for coherent optical manipulation. The paper by Zanni and coworkers (13) in this special feature presents results on automation and phase control of IR pulses in 2D IR spectroscopy. Another significant technical challenge is the miniaturization and automation of the femtosecond lasers that are needed to generate the pulse sequences. With foreseeable improvements in IR laser technology and pulse shaping, one can imagine that these multiple-pulse 2D IR and visible spectroscopies could become quite compact, low-power, commercially available devices.

In broad terms, the 2D spectra have diagonal- and cross-peak regions just as in NMR, but their detailed interpretations are totally different. For both electronic and vibrational 2D spectra, the diagonal peaks correspond to the transitions that would be seen in conventional spectroscopic experiments but with several important modifications. We now know that the elongation of the peaks along the diagonal displays the instantaneous distribution of frequencies in the transition, whereas the minor axes of the elliptically shaped diagonal peaks, illustrated in Fig. 2, are measures of the homogeneous contributions to the vibrational spectrum. Usually these two dynamic processes are not seen separately, so this property of 2D spectroscopy is already a very useful result. The presence of cross-peaks, displayed pictorially in Fig. 2, implies that the transitions represented on the diagonal are sensing one another. Many different phenomena such as mode coupling, energy transport, internal energy reorganization, and other relaxation properties of the distributions of states can influence in understandable ways the detailed shapes of the diagonal and cross-peaks and the mixing time dependence of the 2D spectra.

Diagonal Peaks Probe the Environments of Chemical Bonds

Molecular spectra in solutions and solids are shaped by lifetime broadening, which is caused by the finite survival time of the populations of states that are formed by the light pulses, and by the distribution of transition frequencies arising from the range of the local environments experienced by the molecules in a disordered sample. The latter may often be the dominant contribution and a significant challenge is to learn how to map this frequency distribution onto the underlying structure distributions. For any particular molecule, its transition frequency, its atomic scale structure, and its charge distribution are naturally time dependent because of changing interactions with neighboring molecules, and so a time dependence is introduced into all of the relaxation parameters. This implies that the dynamics of the environments that are sensed by a molecule or by some chemical bonds that are part of a structure can be tracked over a broad range of timescales through the time evolution, or homogenization of the electronic and vibrational frequency distributions. Although all of this information is stored in the spectral shapes and their time evolutions, the quantitative inversion of the data to structure has not yet become straightforward. This is one of the reasons why the combination of experiment and quantum statistical theory is so essential in realizing the full power of high-frequency multidimensional spectroscopies. The optical 2D spectra provide a deeper vision of the underlying structure of complex molecular electronic transitions (14). A recent example of the use of the diagonal-peak shapes in 2D IR is found in the studies of transmembrane peptides for which the relaxations were dissected on a residue-by-residue basis across a lipid bilayer (15), implicating the presence of water molecules in the membrane.

The diagonal regions of these 2D spectra exhibit additional peaks having opposite signs to the main peaks. In the optical spectra, these peaks correspond to absorption by the excited molecular electronic states or electron hole-pair excitations that are created by the first two pulses (Fig. 3 Left). These new transitions provide information on both one and two quantum excited states whose characterization for complex biological cofactors presents challenges for computational chemistry and energy transfer theory. In the IR, they correspond to absorption of a second vibrational quantum with the diagonal transitions corresponding to the 0→1 and the IR excited state absorptions to the 1→2 transitions, which are shifted along the detection frequency axis by the vibrational anharmonicity. For moderate-sized molecules, such as peptides, the establishment of quantitative relationships between anharmonicity and extended structure presents significant challenges for modern computational methods (16–18).

Cross-Peaks Expose Time Dependence of Couplings and Angular Distributions

The 2D spectra present many opportunities to characterize the interactions between molecules and between specific pieces of molecules through the cross-peaks. But at that point the discussions of optical and IR multidimensional methods diverge because they teach us about very different properties of molecules. The optical 2D spectra of molecular assemblies reveal energy transport and coherent phenomena associated with electronic excitations (19), whereas optical 2D Fourier transform spectra of semiconductors teach us about new properties of many body interactions (20). The remainder of this Perspective will deal mainly with 2D IR, which uses vibrations to signal molecular processes.

The recognition of multidimensional spectral patterns and their relationship to structure and dynamics in complex systems is one of the biggest challenges of this field. Naturally, the information displayed by 2D spectra greatly exceeds that found in conventional spectroscopies. The two frequency dimensions ω_τ and ω_t of the 2D correlation spectra S(ω_τ,ω_t;T) correspond to the double Fourier transforms of the time traces of the signal S(τ,t;T) along the evolution and detection intervals. The relationships between these observables and traditional nonlinear optical experiments such as transient gratings, pump-probe spectra, photon echoes of various types, and hole burning are sketched in Fig. 4. A great power of the multidimensional methods is that all of the possible nonlinear responses for a given phase choice are incorporated into one single measurement of either of the two interferograms depicted in the top line of Fig. 4.

Molecular vibrations are anharmonic, so when a pulsed IR field excites one mode the effect of the excitation is sensed by other modes: fundamentally, this picture arises because the eigenmodes of the complete system are not equally spaced. The coupling between modes is often maximized when the two groups of moving atoms are not too far apart or when they have atoms in common. Under these conditions, manifestation of the anharmonicity can become most pronounced when the two modes have similar frequencies such as for the amide modes of polypeptides deriving from the four central CONH atoms of each amide unit. In particular, the amide-I mode of a polypeptide, which is largely a carbonyl motion, can be visualized as a vibrational excitation that is delocalized along the peptide backbone. The energy spread of amide-I modes of polypeptides is caused mainly by the electrostatic interactions between the modes. This is the essential reason why the global characteristics of amide-I spectra of proteins signal important information about the secondary structure (21). These unique spectral signatures are created in large measure by the sensitivity of coupling to the distances and geometric relationships of the different amide units in the backbone.

In the simple example where there are two modes, such as in a dipeptide, it is easy to see that the excitation of one of them influences the frequency of the other when there is an electrostatic coupling. In an experiment, this coupling is manifested through the energies of the vibrational eigenstates of the combined two mode oscillator. The existence of this intermode anharmonicity gives rise to a cross-peak in the 2D IR. The cross-peak therefore signals that the two modes are close enough to interact, and a quantitative analysis of the coupling can place strict limits on their spatial separation. Furthermore, models that are used to interpret linear spectra, such as an exciton description of mode interactions, can be directly evaluated through the 2D IR. The methods also permit the characterization of complex structures through the coupling between modes such as in the recent example of 3₁₀-helices (22). The transient detection of such structures is important because of their possible role as folding intermediates.

The cross-peaks are also invaluable as indicators of energy transport. Although it is true that the existence of the electrostatic coupling mentioned above implies that there is some delocalization of the excitation, the probability that the excitation survives at a particular site in such delocalized states is oscillatory: the oscillation frequency of this coherent energy transfer is approximately β/h. If the electrostatic coupling β is proportional to 1/R ³ as would be the case for a dipole–dipole interaction between two modes, then the coherent energy transfer rate has the same intermode distance dependence. However, because the frequencies and interactions are fluctuating in response to the solvent motions, there is also irreversible decay of the survival probability which occurs at a rate proportional to β², which has a 1/R ⁶ dependence. This incoherent transport is seen in 2D IR experiments by the steady growth of the relative strength of the cross-peak during the mixing time. Such behavior allows the immediate visualization of which chemical groups are spatially close enough to be linked by the cross-peak, so that information about their proximity is obtained even for otherwise very complex structures.

In addition to the direct flow of energy from one mode to the other, there are many other possible pathways of energy transfer that present experimental and theoretical challenges to multidimensional spectroscopy. For example, the transfer could be indirect, involving intermediate states that are coupled both to the initial and final states associated with the cross-peak (23). Another common reason for cross-peaks in the 2D IR spectra can be the Fermi resonances, which often involve the coupling of overtone or combinations of vibrations with spectrally intense fundamentals (24). The existence of such mode coupling is exactly what is required for the occurrence of cross-peaks in 2D IR spectra. Cross-peaks also expose the differences in the dynamics of the various modes that are accessed in the pulse sequences. The decays of the crosscorrelations associated with each of these coupling mechanisms present challenges for condensed phase dynamics theory concerned with the solventinduced coupling of different nuclear motions.

The cross-peaks are usually very sensitive to the relative polarization of the IR pulses in the sequence because the probability of exciting a particular mode depends on the projection of its transition dipole moment onto the electric vector of the exciting field. If two modes are excited in a pulse sequence, which is the requirement for a cross-peak, the outcome depends on the angle between the transition dipoles involved in the two steps. When combined with the knowledge of how the two transition dipoles are oriented in a coordinate system fixed in the molecular system, this angular measurement can yield important structural knowledge that is invaluable in applications to peptide structure determination (25, 26). The transition moment directions are often quite well defined relative to the structure, such as for the NH or CD modes where the dipole is close to the bond axis. For modes involving a number of atoms that are not related by symmetry, such as in the amide-I mode of peptides, the determination of the direction of the transition dipole in the molecular framework is not known a priori so that significant experimental and theoretical study (27) is needed to determine it. It turns out that the amide-I dipole is directed rather close to the carbonyl bond axis. Recent theoretical predictions of very informative chiral effects on the 2D IR cross-peaks (28) should be challenging experimentalists to extend the polarization flexibility of the multidimensional measurement into the regimen where magnetic dipole and electric quadrupole effects are isolated.

Peptide and Protein Structural Dynamics Challenge 2D IR Experiments

The cartoon in Fig. 5 recalls some of the issues that 2D IR experiments on peptides are poised to address. The structural preferences of the backbone structure of the peptide can be characterized by the distance and angular constraints from 2D IR of the amide-I, amide-II, and NH mode spectra by invoking the known planarity of the amide unit (29). Furthermore, the experimental proximities and correlations between, for example, CO, CN, and NH groups are accessible by 2D IR experiments. It remains a major theoretical and experimental challenge to characterize quantitatively the structural basis of the mode coupling effects in peptides as discussed earlier. Isotope replacement of carbon and oxygen atoms on the backbone can permit a wide range of 2D IR experiments that can characterize the interactions between specific pieces of the structure. Very nice examples now exist for α-helices (30) where coupling constants between amides of different residues, such as 2–3, 1–3, and 1–4 represented in Fig. 5, were found to be determined by electrostatic interactions. The proximities of the various pieces of the backbone structure are manifested also in the energy transfer between units, which again can be selected by isotope substitution. The making and breaking of hydrogen bonds (H-bonds) within the backbone and those with the surrounding water cause fluctuations in the amide vibrational frequencies that contribute to the shapes of the 2D IR spectra. The spectral shapes and frequencies that each individual residue contributes to the overall IR spectrum appear to be largely determined by the fluctuating electrostatic fields at the mode from the moving charges in the peptide and the surrounding solvent. The development of sound, predictive theories of peptide 1D and 2D vibrational spectra of peptides in water remains as a major challenge that is being met by a variety of approaches (31–34).

An important consequence of the sensitivity of these spectra to electrostatic coupling is that there is no requirement for the coupled modes to be part of the same molecule or be connected by conventional chemical bonds. For example, the cross-peaks that were observed between the amide modes associated with the different helices of a transmembrane dimer, like the one depicted in Fig. 5 Right, illustrates that the vibrational interactions can be used to study tertiary structures (35). Of course, these experiments on complex systems must be strongly connected to computational studies so there are significant challenges for theory to predict the spectral character of highly nonlinear responses. This special feature contains an example of the theory and computation of 2D IR spectra in the important area of amyloid fibrils, which has already been extensively explored by NMR (36), where the effects of isotope replacent are computed in efforts to highlight the essential vibrational features of the aggregates that might lead to structural inferences (37).

Dual-Frequency 2D IR Provides Additional Constraints

Another major technical challenge concerns the generation of IR pulses that are short enough that their bandwidth incorporates a substantial fraction of the vibrational IR spectrum. This would allow characterization of complex structures through almost instantaneously generated 2D maps of the couplings between vibrational modes. Such maps would square the amount of structural knowledge compared with conventional (1D) spectroscopy. At present, pulses having different center frequencies have to be incorporated into the pulse sequences in order that correlations between vibrations having different frequencies can be accessed. This need has given rise to the techniques known as dual-frequency 2D IR (38–40) that employ pulses having different center frequencies such as depicted by the red and blue pulses of Fig. 1 Upper. Each “color” intercepts a different vibrational mode. It is expected that such methods will prove extremely useful in biology where already experiments have been carried out that involve the coupling and identification of the correlation of the frequencies of amide vibrations and modes separated by H-bonds.

The dual-frequency experiments introduce the possibilities of obtaining a larger set of structural constraints as implied in the cartoons of Fig. 5. One significant technical challenge will be to extend these types of multiple-frequency experiments to include more fields, such as in the fifth order (41, 42), where at least six structural constraints could be obtained from each cross-peak.

Equilibrium Chemical Kinetics Is Sensed by 2D IR

The multidimensional methods hold promise for exposing fast chemical processes. The exchange between chemically distinct species at equilibrium is readily measured in 2D IR, because it introduces cross-peaks on the timescales of the equilibrium chemical dynamics. The cross-peaks arise because a particular molecule having a vibration of type A (Fig. 6) might chemically react to produce one of type B during the sequence of pulses. The temperature dependence of these 2D IR experiments opens up possibilities to obtain properties of the free energy surfaces in different vibrational quantum states. Only a small number of experiments using these IR photon echo approaches have so far been reported, and these have mainly implicated equilibrium H-bond exchange (43, 44). A major challenge is to capitalize on the power of the 2D methods by investigating more complex kinetic networks as illustrated in Fig. 6 Lower Left. An important example of a complex network would be the H-bond structure distributions associated with spatially separated pieces of a peptide backbone or of different groups of water molecules that are making and breaking H-bonds near the surfaces of proteins or at protein–protein interfaces (45). The paper by Fayer and coworkers (46) in this special feature discusses 2D IR experiments on chemical exchange at equilibrium as a means of revealing solvent–solute interactions. Chemical exchange by 2D IR, and the related ultrafast IR pump-probe methods (65), exposes kinetics on the picosecond timescale, which is many orders of magnitude faster than for the analogous experiment in NMR.

2D IR Exposes the Structural Fluctuations in Liquids at Equilibrium

The 2D IR concepts that have been described with reference to peptides or proteins extend to molecular liquids, so it is natural that the method has been widely applied to the study of the structure and dynamics of water (47–50) and other H-bonded liquids (51). The basic notions behind the interpretative method for liquids are conceptually similar to those for molecular complexes, which on short timescales manifest a distribution of well defined structures, characterized by diagonal- and cross-peak signatures in the 2D spectra, which then evolve spectrally on a range of timescales. To use 2D IR experiments to make quantitative advances in understanding the properties of liquids, particularly water, a strong theoretical component is necessary (52–54). Recent advances in the theory of the vibrational spectra of water are described in the special feature article by Skinner and coworkers (54).

Nonequilibrium Dynamics Can Be Revealed by 2D IR

The notion that structures of complex systems, particularly chemical reactions and biologically interesting processes, could be followed in real-time experiments was always the principal motivation for the development of 2D IR spectroscopy (55). Because the experiments involve femtosecond laser pulses, it is natural to combine the 2D IR measurement with a trigger pulse of light that photoinitiates a process of interest. A challenging area for 2D IR is protein folding or other conformational dynamics where one goal might be to follow specific structural features as selected conformation distributions evolve toward equilibrium. Many exciting experiments on the folding of basic secondary structure motifs and of small proteins already have been accomplished by means of a wide variety of spectral probe techniques (56). The temperature jump method, which is often used to trigger the interchange of equilibrium distributions of states, has been used recently also in conjunction with 2D IR to examine the transition states of ubiquitin folding (57).

Surely, the most promising and also the most challenging task for 2D IR is to address questions that reach beyond those that are accessible by the existing kinetic probe techniques, by obtaining structural parameters and their distributions at high time resolution. In an ideal nonequilibrium experiment, a narrow structure distribution is initially prepared, and then a chemical or conformational change is photoinitiated. Significant new information can be obtained by using 2D IR during the period that some spatial coherence is maintained. This type of experiment presents major challenges for the synthesis, mechanistic study, and simulations (58) of photochemically triggerable structures. Some ultrafast triggering processes have already been explored such as disulfide bond breaking (59) and photoisomerism (60), and 2D IR was recently used to visualize the local structure dynamics of the opening of a peptide β-turn by triggering disulfide bonds (61). However, this remarkable field is in its infancy, and the opportunities seem unlimited to find quantitative explanations for the basic structural fluctuations that determine protein dynamics. Nature often takes advantage of the optical triggering of ultrafast dynamics such as in the visual process (62), and in light harvesting and electron transfer in plants and bacteria (63). In every case, rapid photoinduced electronic processes trigger conformational changes for which the multidimensional spectroscopic methods should provide new insight. The photodissociation of ligands from hemoproteins has been a key starting point in studies of protein dynamics using many forms of time-resolved spectroscopy. In this special feature, a paper by Hamm and coworkers (64) uses 2D IR to follow the relaxation of myoglobin substates after photolysis.

Conclusion

Although this field has not yet been in place for 10 years, we have already seen applications of the 2D IR methods to peptides, aqueous ions, secondary structures such as sheets and helices, transmembrane proteins, oligonucleotides, and H-bonded liquids. Both equilibrium and nonequilibrium dynamics have been exposed by the new techniques. Given the increased knowledge obtained by multidimensional spectroscopies, the analytical and imaging spectroscopies of the future may ultimately be replaced by 2D methods, just as has happened with NMR. Much more subtle aspects of extended structure and the associated molecular motions will then become part of the arsenal of sample characterization and visualization.