Multiply Resonant Coherent Multidimensional Spectroscopy

PERSPECTIVE pubs.acs.org/JPCL

Multiply Resonant Coherent Multidimensional Spectroscopy: Implications for Materials Science Andrei V. Pakoulev, Stephen B. Block, Lena A. Yurs, Nathan A. Mathew, Kathryn M. Kornau, and John C. Wright* Department of Chemistry, University of Wisconsin;Madison, Madison, Wisconsin 53706

ABSTRACT Coherent multidimensional spectroscopy (CMDS) has greatly expanded the capabilities of molecular spectroscopy, and it promises to be equally important for materials chemistry. CMDS includes both time domain and multiply resonant frequency domain approaches. Although time domain CMDS has dominated applications, new work shows that multiply resonant CMDS has attractive features for fully coherent spectroscopy of the quantum states that are important for materials spectroscopy. Rather than resolving the temporal oscillations of each coherence, multiply resonant CMDS is an older method that measures the resonance enhancements for different excitation frequencies. It does not require the long-term phase coherence that restricts the coherent pathways and quantum states accessible by time domain methods. This Perspective reviews the multiply resonant CMDS vibrational methods and shows how they can be adapted to the diverse electronic and vibrational states of materials chemistry.

excitation pulses.7 A third interaction involving the last excitation pulse creates a coherence (a quantum mechanical superposition of two quantum states) that emits an output field. Incoherent dynamics can be measured by changing the time allowed for the population to relax. The coherent dynamics can be measured by changing the time allowed for coherences to dephase. Coherences are present between the first and second electric field interactions and after the last interaction. If the output field is heterodyned with a local oscillator, it becomes possible to resolve the phase oscillations of the coherence that appear when changing the time delay between the first two interactions.6,8 In addition, changing the time delay between the last excitation pulse and the local oscillator resolves the phase oscillations of the output coherence. A 2D Fourier transform of the phase oscillations creates a two-dimensional spectrum containing cross-peaks between the coupled quantum states forming the two coherences.9 If the quantum states are not coupled (meaning that excitation of one has no effect on the other), cross-peaks will not appear at the frequencies of the two coherences. Coherent 3D spectroscopy is possible if one uses fully coherent methods. Fully coherent pathways have only coherences and no intermediate population.10 The first two excitation pulses excite different states and create coherences involving either a doubly excited state and the ground state (a double quantum coherence) or two different excited states (a zero quantum coherence). Fourier transformation of the phase oscillations of this intermediate coherence creates the

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ecent developments in ultrafast laser spectroscopy have provided powerful new tools for measuring the coherent and incoherent dynamics of materials.1-4 Historically, methods like pump-probe spectroscopy directly measure the incoherent population dynamics of a state as it relaxes because of interactions with other states or electron transfer between donors and acceptors.5 Newer methods also probe the correlations between quantum states. For example, ultrafast 2D Fourier transform spectroscopy (2DFTS),4 photon echo,3 and transient grating1 methods extend the ultrafast methods to probing couplings between quantum states,4 distinguishing many-body interactions,4 following exciton migration and relaxation dynamics,1 resolving inhomogeneous broadening,2 and observing electronic-vibrational coupling.2 The most recent developments have extended these methods to 3D spectroscopy of the heavy and light hole excitons in GaAs quantum well structures.6

Coherent multidimensional spectroscopy has greatly expanded the capabilities of molecular spectroscopy, and it promises to be equally important for materials chemistry. Partially coherent methods such as pump-probe, stimulated photon echo, transient absorption, and transient grating spectroscopies create excited-state populations by two successive interactions with the electric field of one or two

r 2010 American Chemical Society

Received Date: December 2, 2009 Accepted Date: January 8, 2010 Published on Web Date: February 08, 2010

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DOI: 10.1021/jz9003476 |J. Phys. Chem. Lett. 2010, 1, 822–828


third spectral dimension. It provides additional selectivity for resolving different quantum states. These methods are closely related to multiple quantum coherence NMR methods.11,12 For example, heteronuclear multiple quantum coherence (HMQC) NMR resolves individual residues of proteins containing tens of thousands of spins by exciting four spins on one residue and one on the neighboring residue.13 The structure of a protein can then be determined by systematically performing HMQC NMR on successive residues. Spectra are obtained by Fourier transformation of the temporal phase evolution of the coherences created after each of the excitation pulses. This approach works well for NMR where all of the spins of interest can be excited by the bandwidth of the excitation pulse. The vibrational and electronic states of interest in materials science, however, span a spectral range that exceeds the bandwidth of current excitation pulses. It is possible to use independently tunable excitation sources for time domain CMDS with partially coherent pathways since these pathways have intermediate populations that avoid the need for long-term phase coherence over the entire excitation period. It is currently not possible with fully coherent pathways. Multiply resonant nonlinear spectroscopy is an older approach than coherent multidimensional spectroscopy14-16 that can use partially and fully coherent pathways. Multiple excitation pulses excite multiple quantum states on time scales that are comparable to the states' dephasing times; therefore, multiple quantum coherences are created. Pairs of the states form the output coherences that create directional output beams. Rather than resolving the phase oscillations of the coherences, multiply resonant methods rely on measuring the resonant enhancements that occur as the excitation frequencies scan over the spectral regions of interest. These methods are therefore based in the frequency domain. The advantage for materials spectroscopy is the ability to create multiple quantum coherences with states having diverse energies. Since the phase oscillations of coherences do not need to be resolved, long-term phase coherence of the excitation beams is not required.11,17 The excitation frequencies can therefore be different and can excite any mixture of quantum states, regardless of their energies. It therefore becomes possible to form multiple quantum coherences involving mixtures of electronic and vibrational states. Thus, excitation of electronic donor and acceptor states will isolate the interactions that couple the donor and acceptor. Increasing the number of resonant states provides greater selectivity for the measurement and identifies the states involved in the coupling. If inhomogeneous broadening prevents quantum state resolution, excitation of a subset of states within an inhomogeneous envelop provides an additional resonance enhancement for that subset; therefore, scanning the other resonances can then identify and isolate the spectra of that subset.16 If the excitation pulse widths are chosen to be long enough to spectrally resolve specific states but short enough to resolve the dynamics, it becomes possible to measure both the multidimensional spectra and the coherent and incoherent dynamics of the subset selected by the multiple frequencies.18


The advantage for materials spectroscopy is the ability to create multiple quantum coherences with states having diverse energies.

Figure 1. Logarithm of the intensity (color bar) as a function of ω1 and ω2 when ωm = ω1, τ21 = -5.0 ps, and τ201 = -3.5 ps.

Multiply Resonant CMDS Examples. The applications of multiply resonant CMDS for vibrational spectroscopy have been recently reviewed.17 This Perspective summarizes a subset of the vibrational multiply resonant CMDS methods that have potential applications to materials spectroscopy and then describes the adaptations required to implement the methods. The examples use a model system consisting of the asymmetric (2015 cm-1, labeled ν) and symmetric (2083 cm-1, labeled ν0 ) carbonyl stretch modes of a rhodium dicarbonyl (RDC) chelate. Two tunable optical parametric amplifiers (OPAs) create two beams with frequencies ω1 and ω2. The ω2 beam is split to make a third beam labeled ω20 . The three excitation beams are focused into a sample at angles and create a new beam whose direction is defined by the phase-matching condition kBout = kB1 - kB2 þ kB20 . The output beam intensity is measured as a function of the two frequencies (ω1, ω2) and the two time delays between the three beams (τ21 and τ201). A monochromator isolates the output frequency (ωm = ω1 - ω2 þ ω20 ). Figure 1 shows a 2D spectrum of the output intensity as a function of the two excitation frequencies with the constraint that ωm = ω1.17,19 The color bar is a logarithmic representation of the output beam intensity. Each spectral feature has a wave-mixing energy level (WMEL)15 diagram that visualizes the resonance enhancements associated with the sequence of transitions induced by each excitation pulse for each of the two states forming the particular output coherence. The solid and dotted arrows correspond to the transitions creating the higher- and

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lower-energy states of the output coherence, respectively. In Dirac bra-ket notation, the arrows correspond to the ket and bra side transitions. Time evolves from left to right. As an example, the bottom right cross-peak arises when ω1 is resonant with ν0 and ω2 is resonant with ν. The WMEL diagram shows the three successive resonant interactions that create the sequence of coherences and populations given -2 2 1 by the Liouville pathway gg f gν f gg f ν0 g.15 The two letters label the states involved in forming the output coherence. The first interaction creates a coherence between states g and ν, the second interaction creates a bleach of the ground state with a spatial modulation defined by kB1 - kB2, and the third interaction creates a coherence between states g and ν0 , and that coherence creates the output beam. The example WMEL diagram for the adjacent peak at (ω1, ω2) = (2058, -2 2 1 2015) cm-1describes the Liouville pathway gg f gν f νν f 0 ðν þ ν Þ, ν. The peak is shifted to the left because the anharmonic interaction of state ν with state ν0 changes the fre1 quency of the ν f ν þ ν0 combination-band transition. The oscillating polarizations created by these two pathways are out of phase and would cancel if there were no interaction between ν and ν0 . However, there are anharmonic interac1 tions that change the frequency of the ν f ν þ ν0 relative to 1 0 the g f ν transition, so the destructive interference is incomplete and the cross-peak appears. This sensitivity to coupling is a central characteristic of CMDS methods. It also removes spectral congestion because only transitions that are coupled can appear in the spectra.20 The upper-left cross-peaks at (ω1, ω2) = (2015, 2083) and (1989, 2083) cm-1 are explained the same way, except ω1 and ω2 are resonant with ν and ν0 , respectively. However, there is an additional peak at (ω1, ω2) = (2003, 2083) cm-1 that is caused because a population can relax to another state.21 The example WMEL diagram corresponds to the P:T: -2 2 1 Liouville pathway gg f gν0 f ν0 ν0 w νν f 2ν, ν, which involves an overtone output transition. It is also possible that population relaxation can occur to other states as well (e.g., P:T: -2 2 1 gg f gν0 f ν0 ν0 w xx f ðx þ νÞ, x); therefore, it becomes difficult to definitively identify the states involved in the population relaxation. The diagonal peaks have similar interpretations. Two example WMEL diagrams show pathways that create the -2 2 1 two upper-right diagonal peaks, gg f gν0 f gg f ν0 g and -2 0 2 0 0 1 0 0 gg f gν f ν ν f 2ν , ν at (ω1, ω2) = (2083, 2083) and (2073, 2083) cm-1, respectively. The latter peak is shifted because of the 2ν0 overtone anharmonicity. There is also a third peak at (ω1, ω2) = (2058, 2083) cm-1 arising from population relaxation pathways involving the combination -2 2 P:T: 1 band state such as gg f gν0 f ν0 ν0 w νν f ðν þ ν0 Þ, ν. There may also be contributions from other pathways such as -2 2 P:T: 1 gg f gν0 f ν0 ν0 w xx f ðx þ ν0 Þ, x. The other diagonal and off-diagonal peaks have similar interpretations with ν and ν0 interchanged. There are many more possible pathways for the coherence evolution than are illustrated in Figure 1. The pathways can be separated by tuning the excitation frequencies to particular peaks and scanning the two time delays. For example, Figure 2 shows the temporal dependence on the time delays for the bottom-right cross-peak at (ω1 = ωm, ω2) = (2083,


Figure 2. Logarithm of the output intensity as a function of the two time delays when (ω1 = ωm, ω2) = (2083, 2015) cm-1.

2015) cm-1 in Figure 1.18 The regions are labeled I-VI and correspond to the six possible time orderings of the three excitation pulses. An example WMEL diagram appears for each region. To understand the significance of this figure, consider region III. If τ201 is scanned along the positive x-axis while τ21 is fixed at a negative value, pulse 20 is last and moves further from pulses -2 and 1. It measures the dephasing time of the ν0 ν coherence created by the first two pulses. Fixing τ201 and scanning τ21 measures the dephasing time of the gν coherence. For region V, fixing τ201 and scanning τ21 also measures the dephasing time of the gν coherence. Fixing τ20 2 and scanning τ21 = τ201 measures the population relaxation of the gg - νν population difference. Similar logic applies to the other time-ordered pathways. There is no significant contribution from the pathways in regions II and IV because these involve transitions to the combination band that are not resonant with ω1 or ω2, respectively. If the frequencies are tuned to resonance with the combination band transition and the delay times are again scanned, a different pattern results that allows measurement of the combination band coherence dephasing. Together, these delay time scans allow complete determination of the coupled quantum states' coherent and incoherent dynamics. Figure 2 also illustrates how one can select specific pathways by appropriate choices of ω1, ω2, ωm, τ201, and τ21. Just as the many NMR methods have different capabilities, so also do the different pathways in this figure. Pathways in regions I and III involve zero quantum coherences after the first two excitation pulses, while those in regions II and IV involve double quantum coherences.11 All four time orderings are fully coherent. Pathways in regions V and VI are partially coherent and involve populations. Pathways in regions III and V are rephasing pathways that can narrow correlated inhomogeneously broadened transitions, while those in regions I and VI are nonrephasing pathways. The maximum intensity in regions V and VI appears at the boundary where τ201 = τ21. If inhomogeneous broadening were important in this system,

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Figure 3. Logarithm of the output intensity as a function of the two time delays when (ω1, ω2, ωm) = (2083, 2015, 2015) cm-1.

Figure 4. (a) Logarithm of the intensity (color bar) as a function of ω1 and ω2 when ωm = ω1 and τ21 = τ201 = -2.0 ps. (b,c) Example WMEL diagrams for the peaks at (ω1, ω2) = (1967, 2081) and (1974, 2081) cm-1, respectively.

the maximum intensity would shift toward region V because of the rephasing with this time ordering. This shift is the 3 pulse echo peak shift (3PEPS) that in quantum confined materials defines the spectral density associated with dephasing from surface ligands and the surrounding environment.22 The presence of inhomogeneous broadening would also appear as a narrowing along the diagonal of 2D frequency spectra if a rephasing pathway were chosen by the time ordering.15 The discussion thus far has assumed that the output coherence frequency is defined by a driven process during the excitation pulses. However, in these mixed frequency/ time domain experiments, the output frequency also contains a component from the free induction decay of coherences following the excitation pulses. Coherence transfer, however, can cause a large shift in the output frequency when one of the two states in the coherence evolves to a different state.23-25 An 0 example coherence transfer pathway is C:T: -2 2 1 gg f gν w gν0 f νν0 f νg.17 The output now has a frequency of νg output coherence rather than the expected ν0 g output coherence. Coherence transfer is a signature of coherent electron transfer in photosynthetic complexes.26 For example, Fleming's group observed that the excitation of a zero quantum coherence involving two excitonic states undergoes coherence transfer where one of the two states C:T: evolves to different excitonic states (e0 e w e00 e) to create zero quantum coherences with different frequencies. Figure 3 shows the effects of coherence transfer on the dynamics. It has the same excitation frequencies and scans the same time delays as Figure 2, but the monochromator is now tuned to the νg output coherence frequency.23 The dependence is similar, but it is now modulated along the τ21 axis at the frequency difference between the νg and ν'g coherences resulting from the feeding and receiving coherences getting in- and out-of-phase with each other. The modulation is a signature of coherence transfer. Theoretical simulation of the modulation requires consideration of

interference effects between the different coherence pathways that result from transfer occurring at different times in the sequence of interactions. These pathways interfere to create the observed modulations.23 The coherence transfer peaks are weaker than the directly excited peaks. If the phase matching is changed to kBout = -kB1 þ kB2 þ kB20 , the directly excited cross-peaks will be forbidden, and the coherence transfer peaks will now dompathway for a directly excited inate.24 An example Liouville 2 20 -1 cross-peak is gg f νg f 2ν, g f 2ν, ν0. The 2ν,ν0 output coherence requires a three-quantum change so its transition moment is negligible. However, coherence transfer results C:T: 2 20 -1 in a pathway like gg f νg w ν0 g f ðν þ ν0 Þ, g f ðν þ ν0 Þ, ν0, which has an allowed output transition. These pathways also have the signature modulations of coherence transfer. Although these experiments used two-color excitation, it is also possible to perform coherence transfer spectroscopy with a single color.25 These approaches offer a different strategy for coherent multidimensional spectroscopy that isolates coherence transfer processes. Higher-order multiple quantum coherences can be created by increasing the excitation intensity so that the Rabi frequency of the transitions becomes comparable to the dephasing rate.27 A specific phase-matching condition can define the minimum number of interactions in a multiple wave-mixing process, but at high Rabi frequencies, higher-order processes will become important as well. For a four-wave-mixing phasematching geometry, all multiply enhanced even-order wavemixing (MEOW) processes will contribute at high Rabi frequencies. These MEOW processes create a series of new spectral features that probe the higher parts of the potential energy surface using both partially and fully coherent pathways.19 Figure 4 shows the cross-peak and diagonal peak at the top of Figure 1 for intensities where higher-order processes are important and ωm= ω1 and τ21= τ201 = -2.0.19 Examples of the Liouville pathways with the lowest order of interactions


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Together, they define the potential energy surface of RDC along diagonal and off-diagonal coordinates up to 12300 cm-1.19 The weak peak in the lower-left part of Figure 5 falls at the frequency of the νg transition. It would not normally be expected because the ω1 value is resonant with the g f ν0 transition. It arises from the coherence transfer that was described earlier. The examples given so far have used triply vibrationally enhanced (TRIVE) CMDS.11,18 The output frequencies occur close to or at the excitation frequencies and are therefore subject to scattering interferences. Doubly vibrationally enhanced (DOVE) CMDS is a complementary fully coherent four-wavemixing method that uses three different frequencies.20,28,29 DOVE CMDS uses a double quantum transition that becomes allowed because of coupling and an excited state Raman transition to create an output frequency that is shifted from the excitation frequencies. Furthermore, the output frequency is in the UV/visible part of the spectrum where there are more sensitive detectors that allow observation of weaker transitions and lower concentrations. The capabilities of fully coherent pathways such as those in DOVE were recently demonstrated by Klug's research group. By measuring the relative concentrations of the amino acids in proteins, they showed that DOVE CMDS can uniquely identify specific proteins.30 In addition, they have demonstrated that multiply resonant CMDS is also welladapted to multidimensional imaging. The greater selectivity associated with MQCs provides increased contrast for label-free imaging of specific moieties within complex structures. The feasibility of multiply resonant CMDS imaging has been demonstrated using kidney cells.30 Since these experiments are fully coherent, they probe the direct couplings between quantum states and avoid population relaxation effects that create new spectral features involving indirect couplings. These capabilities will also be useful for extensions to materials science.

Figure 5. Logarithm of the intensity as a function of ωm and ω2 when τ21 = 1.5 ps, τ201 = 0 ps, and ω1 = 2078 cm-1.

responsible for the features at (ω1, ω2) = (1967, 2081)0 and 2 -2 2 -2 (1974, 2081) cm-1 are gg f gν0 f g, 2ν0 f ν0 , 2ν00 f 2ν0 , -2 0 1 0 0 0 -2 0 2 0 0 2 2ν f ðν þ 2ν Þ, 2ν and gg f gν f g, 2ν f ν , 2ν f 2ν0 , 2ν0 P:T: -1 w ðν þ ν0Þ,ðν þ ν0 Þ f ð2ν þ ν0Þ,ðν þ ν0Þ,respectively. Figure 4b,c show the corresponding WMEL diagrams. Both are partially coherent pathways with intermediate populations, and both obey the kBout = kB1 - kB2 þ kB20 phase-matching condition. The second pathway also involves a population relaxation. There are many other equivalent pathways with different odd numbers of interactions with the excitation beams that interfere and must be considered in describing the peaks. Clearly, a nonperturbative approach is required at these intensities where the Rabi frequencies are high enough to allow higher-order processes. This experiment demonstrates that the multiple quantum coherences in MEOW can probe the potential energy surface along both diagonal and offdiagonal coordinates. In addition, it demonstrates the feasibility for MEOW to form higher-order coherences from different states in ways that promise to expand the selectivity of CMDS methods, much as HMQC has done for NMR methods. Population relaxation in partially coherent pathways creates cross-peaks in multidimensional spectra between quantum states that are not directly coupled but do receive population from an initially populated state. These pathways allow one to follow the complete incoherent dynamics, but they often hide the directly coupled features. Fully coherent multiple quantum coherence pathways provide a method to measure quantum-stateresolved dynamics of directly coupled states.12,17 Figure 5 shows an example of a MEOW-MQC spectrum for the diagonal and cross-peaks on the right side of Figure 1 when the Rabi frequencies are comparable to the dephasing rates, ω1 = 2078 cm-1, τ201=0, and τ201=1.5 ps. The ω1 value enhances only the peaks on the right side of Figure 1, and there are now a wide variety of peaks that probe the potential energy surface along both the symmetric and asymmetric CO stretch coordinates. Examples of Liouville pathways with the lowest order of interactions responsible for the features at (ωm, ω2)=(2038, 2058) and (2072, -1 20 -20 1 0 1 1970) cm-1 are gg f ν g f 2ν0 , g f 2ν0 , ν0 f 3ν0 , ν0 f 3ν0 , 0 2 2 -2 -2 1 2ν0 f 4ν0 , 2ν0 f 5ν0 , 2ν0 f 5ν0 , 3ν0 f 5ν0 , 4ν0 and gg f ν0 g 0 1 -1 2 -2 f 2ν0 , g f 2ν0 , ν0 f ðν þ 2ν0 Þ, ν0 f 2ν0 , ν0 , respectively. The other 16 features are all assigned to similar pathways.12


These experiments probe the direct couplings between quantum states and avoid population relaxation effects that create new spectral features involving indirect couplings, capabilities that will also be useful for extensions to materials science. Potential Extensions of Multiply Resonant CMDS to Materials Science. Although these examples were based on multiple resonances with vibrational states, electronic resonances and a mixture of electronic and vibrational resonances serve equally well. For example, the first fully resonant and fully coherent CMDS methods used the vibrational and electronic states of pentacene.16 Since multiply resonant CMDS methods do not require long-term phase coherence between the excitation pulses, MQCs may be formed between any states. As an example of the correspondence between molecular and materials spectroscopy,

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excitons in quantum dots (e.g., 1Se, 1Sh) correspond to vibrations in our examples, multiexcitons (e.g., n(1Se, 1Sh)) correspond to overtones, and mixed-state multiexcitons (e.g., m(1Se, 1Sh) þ n(1Pe, 1Ph)) correspond to combination bands.5 Peaks will only appear if there is coupling between states. For example, Coulombic interactions are required to change the frequencies or dynamics of -2 1 20 the gg f g, ð1Se ,1Sh Þ f ð1Pe ,1Ph Þ, ð1Se , 1Sh Þ fð1P0 e ,1Ph Þ, 1 2 -2 g and gg f g, ð1Se , 1Sh Þ f ð1Pe , 1Ph Þ, ð1Se , 1Sh Þ f ½ð1Pe , 1Ph Þ þ ð1Se , 1Sh Þ, ð1Se , 1Sh Þ pathways so that they do not destructively interfere. Spectra would show two peaks that would be analogous to the two peaks at the lower right in Figure 1. Their separation would reflect the frequency shift caused by Coulombic coupling in the mixed (1Pe, 1Ph) þ (1Se, 1Sh) biexciton. An exciting application is measuring the coherent and incoherent dynamics associated with electron transfer. Electron transfer will result in coupling of electronic and vibrational states because of changes in the Coulombic coupling along the electron-transfer pathway. Excitation of quantum states on the donor and acceptor would provide a way to directly probe the coupling responsible for the electron transfer. The states that are directly coupled would appear as cross-peaks in fully coherent pathways. Coherence transfer spectroscopy would detect coherent relaxation and coherent coupling as the wavepacket associated with electron transfer evolved while propagating through a donor-acceptor heterostructure. The dynamics in the fully coherent pathways would define the dephasing rates associated with the different coupled states. The states that are indirectly coupled by population transfer would form pathways that create new spectral features in partially coherent experiments. The dynamics of the partially coherent pathways would define the population transfer rates. The use of rephasing pathways would allow line narrowing of inhomogeneously broadened transitions and provide quantum state resolution. Increasing the number of states contained in MQCs would increase the selectivity required to resolve the presence of particular sites and components in a complex material. The narrow line widths of vibrational state transitions would be particularly valuable for providing selectivity. The combination of vibrational states with electronic states in a MQC would provide the selectivity required to resolve the electronic states associated with the vibrational states from other electronic states that normally hide the states of interest. Although these examples are speculative, the use of multiply resonant coherent multidimensional spectroscopy still shows great promise for providing the new tools required to guide the discovery of the materials required for our technological future.

AUTHOR INFORMATION Corresponding Author: *To whom correspondence should be addressed.

ACKNOWLEDGMENT This work was supported by the National Science Foundation under Grant DMR-0906525.

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The use of multiply resonant coherent multidimensional spectroscopy still shows great promise for providing the new tools required to guide the discovery of the materials required for our technological future.


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Pakoulev, A. V.; Rickard, M. A.; Kornau, K. M.; Mathew, N. A.; Yurs, L. A.; Block, S. B.; Wright, J. C. Mixed Frequency-/TimeDomain Coherent Multidimensional Spectroscopy: Research Tool or Potential Analytical Method?. Acc. Chem. Res. 2009, 42, 1310. Meyer, K. A.; Thompson, D. E.; Wright, J. C. Frequency and Time-Resolved Triply Vibrationally Enhanced Four Wave Mixing Spectroscopy. J. Phys. Chem. A 2004, 108, 11485. Mathew, N. A.; Yurs, L. A.; Block, S. B.; Pakoulev, A. V.; Kornau, K. M.; Wright, J. C. Fully Coherent and Partially Coherent Pathways in Multiply Enhanced Odd-Order Wave-Mixing Spectroscopy.J. Phys. Chem. A 2009, DOI: 10.1021/ jp9088063. Zhao, W.; Wright, J. C. Spectral Simplification in Vibrational Spectroscopy Using Doubly Resonant Infrared Four Wave Mixing. J. Am. Chem. Soc. 1999, 121, 10994. Kurochkin, D. V.; Naraharisetty, S. R. G.; Rubtsov, I. V. A Relaxation-Assisted 2D IR Spectroscopy Method. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 14209. Joo, T.; Jia, Y.; Yu, J. Y.; Lang, M. J.; Fleming, G. R. Third-Order Nonlinear Time Domain Probes of Solvation Dynamics. J. Chem. Phys. 1996, 104, 6089. Rickard, M. A.; Pakoulev, A. V.; Kornau, K.; Mathew, N. A.; Wright, J. C. Interferometric Coherence Transfer Modulations in Triply Vibrationally Enhanced Four-Wave Mixing. J. Phys. Chem. A 2006, 110, 11384. Rickard, M. A.; Pakoulev, A. V.; Mathew, N. A.; Kornau, K. M.; Wright, J. C. Frequency- and Time-Resolved Coherence Transfer Spectroscopy. J. Phys. Chem. A 2007, 111, 1163. Pakoulev, A. V.; Rickard, M. A.; Mathew, N. A.; Kornau, K. M.; Wright, J. C. Frequency-Domain Time-Resolved Four Wave Mixing Spectroscopy of Vibrational Coherence Transfer with Single-Color Excitation. J. Phys. Chem. A 2008, 112, 6320. Engel, G. S.; Calhoun, T. R.; Read, E. L.; Ahn, T. K.; Mancal, T.; Cheng, Y. C.; Blankenship, R. E.; Fleming, G. R. Evidence for Wavelike Energy Transfer through Quantum Coherence in Photosynthetic Systems. Nature 2007, 446, 782. Mathew, N. A.; Block, S. B.; Yurs, L. A.; Kornau, K. M.; Pakoulev, A. V.; Wright, J. C. Multiply Enhanced Odd-Order Wave Mixing Spectroscopy. J. Phys. Chem. A 2009, 113, 13562. Zhao, W.; Wright, J. C. Measurement of χ(3) for Doubly Vibrationally Enhanced Four Wave Mixing Spectroscopy. Phys. Rev. Lett. 1999, 83, 1950. Zhao, W.; Wright, J. C. Doubly Vibrationally Enhanced Four Wave Mixing Spectroscopy;The Optical Analogue to 2D NMR. Phys. Rev. Lett. 2000, 84, 1411. Fournier, F.; Guo, R.; Gardner, E. M.; Donaldson, P. M.; Loeffeld, C.; Gould, I. R.; Willison, K. R.; Klug, D. R. Biological and Biomedical Applications of Two-Dimensional Vibrational Spectroscopy: Proteomics, Imaging, and Structural Analysis. Acc. Chem. Res. 2009, 42, 1322.


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Multiply Resonant Coherent Multidimensional Spectroscopy

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