Recent advances in multidimensional ultrafast spectroscopy

Abstract

Multidimensional ultrafast spectroscopies are one of the premier tools to investigate condensed phase dynamics of biological, chemical and functional nanomaterial systems. As they reach maturity, the variety of frequency domains that can be explored has vastly increased, with experimental techniques capable of correlating excitation and emission frequencies from the terahertz through to the ultraviolet. Some of the most recent innovations also include extreme cross-peak spectroscopies that directly correlate the dynamics of electronic and vibrational states. This review article summarizes the key technological advances that have permitted these recent advances, and the insights gained from new multidimensional spectroscopic probes.

1. Introduction

Multidimensional optical spectroscopies have unravelled a wealth of structural, energetic and dynamical information about molecular, biological and nanomaterial systems. These studies have been able to probe phenomena spanning: quantum coherence in natural light harvesting, [1–7], exciton dissociation in photovoltaic thin films, [8–11] bound exciton pair correlations in quantum wells and vibrational dynamics in solid-state materials [12–16]. They have been decisive in determining specific molecular motions involved in protein folding [17–19] and structural dynamics [20–23], as well as revealing mechanistic insights into complex non-radiative relaxation [24–27] and chemical reaction or solvation dynamics [24,28–38]. The key advantage that two-dimensional (2D) ultrafast spectroscopies offer over one-dimensional counterparts, such as transient absorption or transient grating, is the correlation between broadband excitation and emission frequencies as a function of system evolution, which enables the resolution of homogeneous (anti-diagonal) and inhomogeneous (diagonal) line shape components. Changes in the 2D line shapes report on the frequency–frequency correlation function (FFCF). The dynamics of the FFCF yield information about the amplitudes and timescales associated with changes in the optical frequencies investigated, caused by changes in molecular structure, or evolution of the surrounding solvent structure or protein [29,31,32,39].

The additional information content available in these multidimensional experiments allows, in most cases, for the simultaneous resolution and detection of overlapping ground state bleach/stimulated emission and excited state absorption features.

Figure 1a shows an example two-dimensional infrared (2DIR) spectrum that illustrates these features. The 2DIR spectrum was acquired for a methyl ammonium (CH₃NH₃⁺) lead iodide perovskite (MAPbI₃) thin film sample. The mid-infrared pump and probe lasers are resonant with the ${\text{NH}}_3^{+}$ symmetric stretching vibration of the $\text{C}{\text{H}}_3{\text{NH}}_3^{+}$ moiety and acquired for waiting time = 250 fs. The 2D correlation spectra (displayed as changes in transmission) contain two features which arise from two distinct third-order nonlinear response pathways; the positive peak corresponds to ground state emission/stimulated emission between the 0–1 vibrational states of the ${\text{NH}}_3^{+}$ symmetric stretching vibration. The negative feature corresponds to an excited state absorption as probed via the 1–2 overtone. In this early waiting time 2DIR spectrum, both features are slightly elongated along the diagonal, as illustrated by fits to the centre line slopes (CLSs, green lines) and nodal line slope (NLS, pink line). The NLS and CLS are incisive probes of changes in the local environment experienced by functional groups in 2DIR, and/or a reflection of any system-bath coupling. For increased values of the waiting time, correlation between initial excitation (ω₁) and eventual emission (ω₃) frequencies is lost, as reflected by the decay in the NLS, figure 1b. The decay in NLS was fit to bi-exponential decay, yielding time constants of 430 fs and 4.6 ps, similar to those previously determined periods for wobbling/tumbling motions of the methyl ammonium cation inside the lead iodide cage from 2DIR anisotropy measurements and molecular dynamics simulations [16]. Such re-orientation means that the ${\text{NH}}_3^{+}$ symmetric stretching mode will experience a variety of slightly different electrostatic potential associated with different faces and/or edges of the PbI₃ lattice. In turn, this leads to slight shifts in the vibrational potential and associated transition frequencies, resulting in the observed spectral diffusion.

Figure 1.

(a) Isotropic absorptive total 2DIR spectrum of methyl ammonium lead iodide perovskite thin film for waiting time 250 fs. The black line indicates the diagonal of the 2D correlation spectrum. The dashed green lines show fits to the centre line slopes (CLS) for the ground and excited state vibrational features. The pink line is a fit to the nodal line slope (NLS). (b) Time-dependent gradient of the NLS extracted from 2DIR data (open circles) and bi-exponential fit to data (red line).

2D ultrafast spectroscopies can also resolve cross-peaks that appear at different absorption and emission wavelengths. The time-dependent amplitudes of cross-peaks can be crucial to determine the associated timescale for chemical exchange, structural changes or anharmonic coupling via 2DIR spectroscopy, or to follow the flow of energy between different excitons in a coupled multi-chromophore system using 2D electronic spectroscopy (2DES). A schematic 2DES spectrum for the latter scenario is illustrated in figure 2 for a system containing three excitons (bound electron-hole pairs), α, β, γ. For the sake of simplicity, peaks are only displayed for ground state bleach pathways. The presence and time-dependence of cross-peaks between the diagonal features reveals physical insights into the nature of energy transfer between the three excitons. For the time zero 2DES spectrum in figure 2a, intense cross-peaks between diagonal features γ and β, at βγ and γβ, reveal that the two excitons are strongly coupled, displaying ‘up-’ and ‘down-’ hill energy transfer pathways. At later waiting times (figure 2b), spectral diffusion results in a loss of elongation along the diagonal for most features, and the intensity of the βγ cross-peak increases relative to that of γβ, as population relaxation starts to dominate over coherent energy transfer. A weak intensity cross-peak, αγ, rises on a far longer timescale and is not accompanied by a corresponding cross-peak at γα, indicating that excitons α and γ are weakly coupled, and that energy transfer occurs via population relaxation, i.e. incoherently. No cross-peaks are present between α and β, informing us that the two states are not dipole coupled.

Figure 2.

Illustrative 2D electronic spectra for a multi-chromophore system, comprised from excitons α, β and γ, for t₂ = (a) 0 ps, and (b) >>0 ps. For simplicity only ground state bleach signals are depicted.

Initial 2D ultrafast spectroscopy experiments were confined to very specific parts of the electromagnetic spectrum, such as the mid-infrared [40–43] and visible [24,44,45]. Historically, this is in part because such pioneering experiments emerged from forerunner narrowband three-pulse photon echo spectroscopies at similar frequencies [46–51], and were driven by the emergence of broadband optical parametric amplifiers (OPA) with commensurate short pulse durations across the visible and in the mid-infrared [52–55]. It was also relatively straightforward to create the necessary phase-locked pulse pairs across these wavelength regions compared with, for example, ultraviolet light.

The advent of pulse-shaping technology had a significant impact on the multidimensional optical spectroscopy field, in tandem with advances in ultrafast laser technology such as the increased availability of high-power, short-pulse, regenerative amplifiers with repetition rates up to 100 kHz. These developments led to a wider variety of broadband laser sources and the ability to vary time delays between pulses with attosecond precision, or fully compress pulses to the limit of their time-bandwidth product. The consequence for this community is that 2D ultrafast correlation spectroscopies are now routine throughout terahertz (THz), infrared, visible and ultraviolet parts of the electromagnetic spectrum.

Many aspects of 2D optical spectroscopies have been detailed by several comprehensive reviews since their inception [56–69]. In this review, I highlight some of the recent advances in the field such as extreme cross-peak spectroscopies, 2D action spectroscopies such as 2D fluorescence or photocurrent phase modulated spectroscopies and surface-specific 2DIR via sum-frequency generation (SFG) detection. Further, the details of new 2D Raman spectroscopies, as well as 2D spectroscopies that reach into the THz domain exploring low-frequency and phonon modes, or fundamental properties of materials, are discussed. I conclude with some future trajectories for the field.

2. Key technological developments

Several of the advances in multidimensional ultrafast spectroscopies highlighted in this article have only been realized due to the major advances in femtosecond pulse generation and the amplitude and phase control of laser light with pulse shapers such as acousto-optic modulators (AOMs) or spatial light modulators (SLMs). Femtosecond pulse-shaping technology has been widely adapted by the community, making them indispensable pieces of equipment for either dispersion management, phase cycling and/or multiple pulse generation. In this section, I provide a very brief precis of how 2D spectroscopy experimental approaches have evolved since their inception, and the current state of the art.

From the outset, it is important to define nomenclature that will be used throughout this review for the various k-vectors associated with pulses and the inter-pulse time delays. The third-order nonlinear spectroscopic pulse sequence, k-vectors and time delays defined are in figure 3a, and will be described in the context of a mixed time-frequency acquisition scheme which has become the de facto method for 2D ultrafast spectroscopies. For a model three-level system with ground state |g〉, first and second excited states |e〉 and |f〉, an ultrashort broadband laser pulse, k₁ creates coherences between |g〉 and |e〉 states. The system then evolves for a specific coherence time, t₁, before a second pump photon, k₂, converts the system into a population of either |g〉 or |e〉 states. The system is then allowed to evolve on the ground or excited states for a fixed value of the waiting time, t₂, (or pump–probe time delay) before interacting with the probe pulse, k₃. The probe pulse drives the system into a second coherence, either between |g〉 and |e〉 or |e〉 and |f〉 states, before emitting the signal, k_sig, at echo time t₃. Typically, the signal pulse is frequency dispersed onto a multi-element array detector, transforming the time-domain signal into its conjugate, ω₃. This is repeated for many values of t₁ to generate t₁ − ω₃ 2D maps. The t₁ coherence time must be sampled in sufficiently small δt₁ steps to properly sample the Nyquist period of oscillations associated with coherences between |g〉 and |e〉 states. The data are subsequently windowed, apodized and Fourier-transformed along the t₁ axis to generate a 2D ω₁–ω₃ correlation map, for a specific value of the waiting time. Depending on the vertical Franck–Condon factors between the |g〉 and |e〉 states, and the laser bandwidth used, electronic, vibronic or vibrational coherences will be launched and propagated, leading to oscillations in the corresponding 2D spectra as a function of the waiting time [1,3,9,23,70–73].

Figure 3.

(a) Pulse sequence for 2D optical spectroscopies, (b) ‘boxcar’ geometry and (c) pump–probe geometry.

Mixed time-frequency acquisition schemes for 2D spectroscopy, as described above, are now almost universally favoured over wholly frequency domain (e.g. hole-burning) due to the distortions in 2D line shapes the latter scheme can introduce. It also helps to maintain high temporal resolution. For a direct comparison, see [74].

2.1. Beam geometries and pulse shaping

One of the most popular experimental configurations for acquisition of 2DES and 2DIR spectra is in the fully non-collinear ‘boxcar’ geometry (shown in figure 3b), which has distinct advantages over the partially collinear (pump–probe) geometry (figure 3c): (i) the emitted signal field is background free, and heterodyned by a local oscillator (LO) to extract the phase and amplitude information of the third-order nonlinear response. The background-free nature of the measurement is estimated to increase the signal-to-noise ratio compared with a pump–probe geometry by up to a factor of 19.5; [75] (ii) the rephasing and non-rephasing signals are collected separately, but are emitted in the same phase-matched direction [24]. The total 2D frequency-resolved photon echo signal is the sum of these two different measurements; (iii) because the two pump pulses are independent laser beams, the polarization of k₁ and k₂ can be independently controlled and thereby used to implement cross-polarized pump-pair pulse sequences that can greatly enhance the intensities of cross-peaks over diagonal features [76–79].

With these advantages come associated experimental difficulties, such as maintaining phase stability between the pump pulse pair which hampered early 2DES experimental efforts [44]. This problem was initially circumvented using a passive-phase stabilization approach, where k₁ and k₂ are generated using a diffractive optic, and the t₁ time delay controlled by translating wedge pairs [24,80]. Methods in which the t₁ time delay is actively stabilized have also been successfully demonstrated [81–83]. Alternatively, beamsplitters have been used to generate pulse pairs, and the time delay controlled with piezo-electric delay stages with sub-nanometre linear resolution. The latter method has the significant advantage that the time delay is created by using reflective optics, and additional chirp is not introduced to the broadband laser pulses. The principal problem with acquisition in the boxcar geometry is that the signal is emitted non-collinear to the probe beam, and the phase relationship between k₃ and k_sig must be established by additional measurements, such as pump–probe, under the same experimental conditions [24,84]. If the phase relationship is not properly established, the real and imaginary components can mix, leading to dispersive distortions in the absorptive 2D correlation spectra, as highlighted in [85].

The background-free approaches to 2D spectroscopies described thus far, require the physical translation of delay stages to create the t₁ time axes in mixed time-frequency 2D measurements. Several groups have demonstrated an alternative approach, which allows an entire 2D spectrum to be recorded in a single laser shot [86–88]. The 2DES variant, gradient-assisted photon echo spectroscopy (GRAPES), combines the background-free geometry, and inter-pulse time delays are controlled by piezo-electric stages, but pulses are cylindrically focused to a vertical line in the sample. Tilting the pulse front of k₁ relative to k₂ spatially encodes the t₁ time delay in the vertical dimension. The resulting signal is spatially imaged into a spectrograph to record an entire t₁–ω₃ spectrum every shot. This significantly decreases the acquisition time for 2D spectroscopy, making it comparable to pump–probe spectroscopy. There is one pitfall, however; samples must be spatially homogeneous (over a length scale of several millimetres), which partially restricts measurements from investigating dynamics of systems in low-temperature glasses which are generally inhomogeneous.

The partially collinear, or pump–probe, geometry (figure 3b) removes the problem of phase matching in experiments where very different pump and probe frequencies are used [89], and greatly reduces the complexity of the alignment procedures and experimental design, as only two beam paths are required. 2D signals in the partially collinear geometry are emitted collinearly with k₃ (k_s = ± k₁ ∓ k₂ + k₃), which acts so as to ‘self-heterodyne’ the signal, with the consequence that the k₃–k_sig phase relationship is known, and 2D spectra are automatically phased [74,90,91]. Consequentially, however, the rephasing (k_s = –k₁ + k₂ + k₃) and non-rephasing (k_s = +k₁ − k₂ + k₃) signals are detected simultaneously and cannot be separated, which may hamper the isolation of specific spectroscopic pathways [92,93]. In the mid-IR, the t₁ delay is often controlled by a Michelson interferometer. The shorter wavelengths associated with visible, and especially ultraviolet, radiation mean that phase-stability issues are more problematic using such an approach. Such problems have been circumvented in the visible domain with wedge-based systems such as translating wedge-based identical pulses encoding system (TWINS) [94,95]. In all cases, to maintain phase relationship between k₁ and k₂ still requires monitoring or post-processing to correct for timing errors, and pump-scatter is a far greater problem in this geometry. Further, the 2D signal of interest is emitted collinearly with the pump–probe signal. The 2D signal oscillates in t₁, whereas the pump–probe signal decays, and thus Fourier-transform along the t₁ axes removes the pump–probe background.

The disadvantages of the partially collinear geometry were surmounted with the introduction of pulse-shaping technology such as AOMs or SLMs [91,96–98] to multidimensional optical spectroscopy. These devices were used to generate phase-locked pulse pairs and control of the relative phases [74,91,96,99]. The groups of Zanni and Olgivie pioneered these approaches for 2DIR and 2DES, respectively, demonstrating that the pump–probe background could be completely removed by ‘phase cycling’ k₁ and k₂ pulses. By changing relative phase between k₁ and k₂ (ϕ₁₂), the phase of the emitted 2D signal is correspondingly altered, but as the pump–probe signal is insensitive to the phase modulation, and through judicious choice of several values of ϕ₁₂ and appropriate summation of the resulting signals, the pump–probe background can be removed. This method can also be used to isolate the rephasing and non-rephasing signals in the partially collinear geometry [91,96,100]. Pulse shapers also offer other significant advantages to physically scanning the t₁ delay: (i) With acousto-optic pulse shapers, the pump pulse pair can be refreshed at the repetition rate of up to several kHz, matching the output of many regenerative amplifiers. (ii) Phase cycling does not reduce the duty cycle of experiments. (iii) A pulse shaper allows 2D spectra to be collected in the fully rotating frame, where ϕ₁₂ is incremented with the t₁ time delay to shift the fundamental frequency to zero. Resultantly the signal will not oscillate as a function t₁, and the envelope of the signal is detected, rather than its fundamental frequency. The rotating frame thus provides a convenient way to under-sample t₁, but in practice, many experiments use a partially rotating frame, where the fundamental frequency is not shifted all the way to zero, but to a frequency with an associated longer Nyquist period. The other significant advantage of using a rotating frame is that pump-scatter can be shifted away from the desired signals [74]. (iv) Compressed sensing is routinely used in 2D NMR spectroscopy, and requires only a fraction of the usual number of measurements to retrieve the same spectrum recorded if t₁ were fully sampled. The same principles apply to 2D ultrafast spectroscopies, the t₁ delay can be randomly sampled with a normal distribution around t₂ = 0 fs, but with uneven δt₁ steps. With no a priori knowledge of the frequencies of interest that should be sampled in t₁, the data can be recovered using complex algorithms. Such schemes are only practical if the t₁ time delay can be changed from shot to shot, and using a partially rotating frame, i.e. with a pulse shaper. A study that applied compressed sensing to 2DIR spectroscopy, reported a 4× speed-up in the acquisition time compared to conventionally sampled 2DIR data [101,102].

As outlined here, there are advantages and disadvantages to the ‘boxcar’ and partially collinear geometries using pulse shapers. Hybrid methods have been used to combine the advantages of the background-free ‘boxcar’ geometry and pulse shapers to generate inter-pulse time delays and ϕ₁₂ [75,103].

2.2. Generation of ultrashort pulses from terahertz to ultraviolet

The rapid commercialization of chirped pulse amplifiers has led to the widescale availability of low-noise high-power laser sources, which in turn has driven further innovations in tunable ultrashort laser sources for 2D spectroscopy, that now span wide portions of the electromagnetic spectrum. There are many approaches to generating these desired sources of light, which are briefly overviewed here. Broadband visible light sources for 2D spectroscopies are generated via two main methods: non-collinear optical parametric amplification (NOPA) [54,55,104], or filamentation of 800 nm in rare gas mixtures (e.g. [105]). The latter has been implemented in conventional ‘boxcar’ or GRAPES background-free configurations of 2DES [106–108]. Recently white light generated from supercontinuum generation in sapphire has been used in combination with a pulse shaper for 2DES measurements of carbon nanotubes [109]. Generation of ultrashort sub-40 fs ultraviolet pulses poses greater challenges. Four-wave mixing in a hollow-core fibre of 800 and 400 nm in rare gases has generated less than 35 fs pulses centred between 266 and 275 nm [110,111], taking advantage of the readily available harmonics of the Ti : sapphire fundamental of the femtosecond amplifiers. More tuneable UV-pulses have been generated by either SFG of broadband NOPA outputs with narrowband higher power 800 nm laser pulses [112], or achromatic doubling using cylindrical focusing to satisfy a broader range of phase matching conditions [113]. Near transform-limited octave-spanning mid-infrared sources have emerged broadly using similar techniques such as filamentation in rare-gas mixtures [114,115], and use deformable mirrors to correct for nonlinearities in the spectral phase. The dawn of sub-picosecond THz pulses with sufficient field intensity to drive nonlinear spectroscopy measurements, meant that multidimensional ultrafast experiments involving THz radiation have finally come of age. THz sources for nonlinear spectroscopic measurements can be generated in several ways; collinear phase matching in nonlinear crystals such as ZnTe with intense 800 nm field; 800 and 400 nm dual pumping of rare gas or air to drive plasma generation or non-collinear phase matching with tilted 800 nm pulse fronts in LiNbO₃ crystals [116,117].

3. Extreme cross-peak multidimensional spectroscopy

Typically 2D ultrafast spectroscopies have probed the same type of transitions (e.g. vibrational or electronic), even if different central pump and probe wavelengths were used [91,118]. This changed with the advent of ‘extreme cross’ peak spectroscopies [119] such as 2D electronic–vibrational (2DEV) [120] and 2D vibrational–electronic (2DVE) [121] spectroscopies. These mixed electronic–vibrational spectroscopies are uniquely placed to investigate how the interplay and coupling between electronic and nuclear degrees of freedom dictates the non-radiative relaxation dynamics of molecules, especially those that involve conical intersections (CIs). Such dynamics underpin the functional dynamics of many systems, for example: (i) the primary steps of vision that involve cis–trans isomerization of rhodopsin [122,123] or (ii) the rapid excited state deactivation of DNA nucleobases [124,125].

3.1. Two-dimensional electronic–vibrational spectroscopy

2DEV spectroscopy can be viewed as the extreme cross-peaks between 2DES and 2DIR. To date, 2DEV spectroscopy has been used to investigate a range of photochemical dynamics of molecular systems such as the strength of solute–solvent coupling for specific high-frequency vibrations of dye molecules [126,127], and coupled electronic–nuclear motion through CIs [128]. Further, 2DEV spectroscopy has been used to investigate the time-dependent site populations of light-harvesting complex II (LHCII) [129,130].

2DEV is part of the third-order nonlinear spectroscopy family of photon echo spectroscopies. The 2DEV pulse sequence is the same as the generic sequence described in figure 2; however, the pump and probe pulses are non-degenerate: electronic transitions are interrogated in the t₁ coherence, and vibrations in the t₃ period. The 2DEV pulse sequence is given in figure 4a. Figure 4b displays the energy structure for a model system containing two electronic states (g, e), each with a nestled manifold of vibrational states (0, 1, 2) as indicated by the subscripts. Figure 4c,d shows the associated double-sided Feynman diagrams that define the rephasing and non-rephasing Liouville pathways, for dynamics that propagate during the waiting time on the excited or ground electronic states, respectively. All 2D spectra shown in this review article are displayed as change in transmission (ΔT), and thus signals that arise from the Liouville pathways shown in figure 4c will be negative, whereas those from figure 4d are positively signed.

Figure 4.

(a) 2DEV pulse sequence, (b) model system containing two electronic states with an associated vibrational manifold. Double-sided Feynman diagrams for the rephasing and non-rephasing 2DEV pathways associated with evolution during t₂ on the (c) excited and (d) ground electronic states.

The signal pathways displayed in figure 4 neglect the possibility of directly exciting |e₁〉 due to limited bandwidth of pump pulses. As recent theoretical simulations demonstrate, this introduces additional pathways and associated spectral features [131]. One of the notable advantages of 2DEV spectroscopy over 2DES is the limited number of Liouville pathways, meaning the assignment and interpretation of data is far less ambiguous when compared to 2DES [132,133]. In all implementations to date [120,134], 2DEV spectroscopy has been performed in the partially collinear geometry (figure 3c) with a pulse shaper, meaning the 2DEV spectra are automatically phased, as the mid-IR probe pulse (k₃) self-heterodynes the signal (k_s), with phase cycling of k₁ and k₂ used to remove the pump–probe background, and isolate the rephasing and non-rephasing signals if desired.

The successful implementation of 2DEV spectroscopy was first demonstrated for a model push–pull emitter dye, 4-(dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran (DCM) in dimethyl sulfoxide solution [120]. The 2DEV spectra of DCM revealed correlated electronic–vibrational shifts for one high-frequency vibrational mode. These observations were understood by recognizing the significant differences in geometry associated with the ground and first excited electronic state of DCM. Franck–Condon excitation places the molecules out of equilibrium on the excited state, and to reach the electronically excited state minimum, changes in the molecular geometry driven by vibrational cooling induced via solute–solvent coupling is required. To account for the shift in the observed infrared frequency, part of this reorganization must therefore involve changes in the bond lengths associated with the probed C=C/C–C backbone mode.

Theoretical response functions were derived to model the dynamical correlations observed between electronic and vibrational transition frequencies in 2DEV spectra for model monomeric molecules [126,127]. These studies used the energy structure shown in figure 4b. Independent baths were used for the electronic and vibrational degrees of freedom, given that electronic transitions will experience more rapid and intense fluctuations which are quickly damped, whereas the vibrational coordinate is fairly rigid and slowly damped. This is further justified in terms of the magnitude of the dipole moments and the respective bath spectral densities. Using Kubo line shapes and in the approximation of the impulsive limit, numerical simulations revealed that the NLS that exists between interfering positive and negative features in the total absorptive 2DEV spectra (see schematic 2DEV spectra in figure 5) decays on the same timescale as a fluctuation correlation time chosen for the probed high-frequency vibrational mode [127].

Figure 5.

Schematic 2DEV spectrum for (a) early waiting times and (b) long waiting times. Overlaid dashed lines depict the two different CLS.

For degenerate multidimensional spectroscopic measurements, such as 2DES or 2DIR, the accumulated phase in the t₁ coherence can, in principle, be removed in the t₃ period via the rephasing pathway. In 2DEV spectroscopy, however, as noted above, two different types of transitions are propagated in the t₁ and t₃ coherences, which means that the phase accumulated in t₁ cannot be entirely removed in t₃.

Owing to the non-degenerate nature of 2DEV spectroscopy the diagonal and anti-diagonal CLS (as indicated in figure 5) for vibrational features on the ground or excited state (as denoted by subscript g or e) have different gradients, i.e. dω₁/dω₃ (k_g or k_e) is inequivalent to dω₃/dω₁ (k_g′ or k_e′). This also means the limiting values for the CLS in 2DEV spectra will not be ±1, as per 2DES or 2DIR spectroscopy.

Analytical expressions for the dynamics associated with the two 2DEV CLS were directly compared with experimental data for 3,3′-diethylthiatricarbocyanine iodide (DTTCI) in deuterated chloroform [126]. Using the short-time approximation, i.e. electronic or vibrational dephasing in t₁ and t₃, respectively, are far shorter than the lifetime of the electronically excited state, analytical forms for the two different CLS were derived. The analytical functions showed that the 2DEV CLS are sensitive to correlated electronic–vibrational bath fluctuations, and any static inhomogeneous distribution in transition frequencies. The decay in correlation of either centre line slope for a predominantly homogeneously broadened system, such as a dye molecule in solution, was found to be dependent on the vibrational dephasing time.

The derived analytical expressions showed that the ratio of decay rates for the diagonal and anti-diagonal CLSs of a specific vibrational feature, could be used to extract the relative solute–solvent coupling strength for a vibration on the ground and excited electronic states. Thus, providing a direct probe of the specific spectral density associated with high-frequency vibrational modes. The only other way to extract this information using ultrafast spectroscopic investigations would be to perform 2DIR and corresponding transient-2DIR experiments.

Specifically, the decay rates for the k_g and k_g′ CLS of the C=C backbone vibration of DTTCI dissolved in deuterated chloroform, revealed the coupling of a vibrational mode to the solvent bath for the 0–1 vibrational transition is stronger in the electronically excited state by a factor of 1.5 compared to the ground state. This is not surprising given that the electronically excited state has a larger permanent dipole moment compared to the ground electronic state, meaning it has a far greater polarizability and solute–solvent interactions are expected to be stronger. If vibrations that evolved in |e₁〉 during t₂ were observed, and the ratio of decay rates for k_e and k_e′ measured, the relative coupling of |e₀〉 and |e₁〉 levels to the solvent bath could also be determined.

The 2DEV spectroscopy was also used to investigate the role of CIs in the ultrafast non-radiative relaxation dynamics of a model carbonyl containing carotenoid in solution [128]. Carotenoids play a dual role in photosynthesis, acting as light-harvesting elements in parts of the solar spectrum where chlorophyll does not absorb, and as photo-regulatory elements that can help dissipate excess energy in plants under high-light intensities [135,136]. A schematic potential energy structure showing the canonical three-state model of the β-apo-carotenal (bapo) is given in figure 6a. The visible absorption spectrum is dominated by a strong absorption at approximately 500 nm arising from vibronic transitions to the S₂ electronic state (¹B_u⁺). CIs are thought to play an important mechanistic role in the non-radiative relaxation from the S₂ state, and underpin the associated short excited state lifetime (approx. 200–300 fs) [128,137,138]. CIs are formed when two (or more) potential energy surfaces intersect, and in their simplest form comprise two key dimensions: the tuning and coupling coordinates [139,140]. Motion along the tuning coordinate first brings the states into degeneracy at the point of intersection. Continued movement in this degree of freedom subsequently breaks the degeneracy. The coupling modes are formed by nuclear motions that break the degeneracy of the two states at every point along the intersection, and provide the off-diagonal coupling matrix elements to mediate surface crossing. CIs are regions of the potential energy surface where the Born–Oppenheimer approximation can break down, and electronic and nuclear motion can no longer be decoupled. In carotenoids, CIs are thought to provide a route for ultrafast deactivation to lower-lying excited states such as the $2^1{A}_{\mathrm{g}}^{-}({\text{S}}_1)$ state, which has eluded direct spectroscopic investigations as it is formally forbidden to one photon absorption. 2DES spectroscopy has been used to interrogate these phenomena for β-carotene [27,141] and the orange carotenoid protein [142], revealing correlations in the decay of the S₂ → S_n stimulated emission features with the onset of absorptions for S_n ← S₁ excited state absorptions. These studies, while informative, did not provide direct information relating to the specific nuclear motions that mediate the coupling between potential energy surfaces and drive passage through the conical intersection, whereas 2DEV is uniquely placed to interrogate these phenomena.

Figure 6.

(a) Schematic non-radiative pathways for β-apo-carotenal in solution. (b–d) 2DEV spectra of C=C antisymmetric stretch feature of bapo in acetonitrile-d₃. Adapted with permission from Oliver & Fleming [128] (Copyright © 2015 American Chemical Society).

There has been some controversy surrounding the assignment of the excited state vibrational modes of bapo [143], due to lack of reliable ab initio calculations and an abnormally large Duschinsky rotation associated with changes in bond lengths associated with polyene backbone [128,143–145]. Fortunately, the relative orientation between the electronic and vibrational transition dipole moments (TDMs) can be deduced from analysis of centre line slope in 2DEV spectra [128]. In degenerate 2D optical spectroscopies, it is highly unusual to observe anti-correlated spectral features, as pump and probe pulses generally interrogate transition dipoles with the same, or very similar, vectors [146]. In 2DEV spectroscopy, correlations are made between electronic and vibrational TDMs, meaning the correlations in the 2DEV spectra should be sensitive to the relative orientation of the two TDMs. The positive or negative gradient of the CLSs in 2DEV spectra is dictated by whether the solvent environments are polarized along parallel or orthogonal vectors by the two different TDMs. With knowledge of the S₂ ← S₀ electronic TDM, which can be reliably predicted from time-dependent density functional calculations, the vectors associated with each normal mode, in tandem with the sign of the CLS in 2DEV spectra, allowed for the relative orientation of the two TDMs to be deduced, and make definitive assignments for some of excited state vibrational modes of bapo.

The C=C excited state feature at ω₃ approximately 1590 cm⁻¹ in the 2DEV spectra of β-apo-carotenal displayed in figure 6b–d is assigned to the C=C antisymmetric stretch on the photoexcited states. This feature blue-shifts and narrows along the ω₁ axis as a function of increasing t₂ time delay, and simultaneously the central infrared frequency also shifts to higher wavenumbers along ω₃. The latter observation is associated with the changes in the force-constant associated with the vibrational mode, as molecules are transferred from the S₂ surface to the S₁ state, in line with ab initio calculations for shorter polyenes [147]. The bandwidth employed in this study (approx. 2000 cm⁻¹ FWHM) is sufficient to excite one quanta of the high-frequency mid-IR probed after photoexcitation to the S₂ state, and therefore the blue-shifting and narrowing along ω₁ is interpreted as vibrational cooling of this mode in very anharmonic potential after ultrafast transfer to the S₁ state. While no explicit modelling supports these specific observations, static 2DEV line shape calculations performed after the initial study support these hypotheses [131].

The most striking result from the 2DEV study of bapo was the long-lived correlation between electronic and vibrational line shape components for the C=C antisymmetric stretching mode, as probed via the k_e CLS, plotted in figure 6b–d. The decay of the k_e was fitted to an exponential decay with a 750 fs time constant, which is more than three times longer than the S₂ lifetime. This is particularly surprising given the large reorganization on the S₁ potential energy surface (λ approx. 8000 cm⁻¹) that must occur after passage through the S₂/S₁ CI, which normally would be expected to quickly destroy any correlations. This means the solvent bath must remain frozen in the wake of change in electronic state and nuclear motions associated with this normal mode. Consequentially, the S₂–S₁ crossing must be ballistic and driven by a conical intersection close to the Franck–Condon region. The enhanced vibrational activity of this specific mode, and slow decay of the CLS relative to the S₂ lifetime provide evidence to support the hypothesis that the antisymmetric C=C stretch of bapo is one of the tuning modes at the S₂/S₁ CI.

In dipole-coupled J-aggregates, such as light-harvesting antenna of plants, the excited electronic states are not localized to individual chromophores, but through dipole–dipole coupling delocalized across multiple pigments [148]. Figure 7a,b depicts the differences between the site (diabatic) and exciton (adiabatic) bases used to describe the energy structure of J-aggregates. The flow of energy between the different excitons has been revealed using 2DES for a large number of light-harvesting antenna [1,150–153]. However, establishing a link between exciton and site energies, and extraction of the intermolecular dipole coupling constants (J) has remained problematic without use of prior theoretical Hamiltonians or accompanying complex genetic mutant studies and polarization-dependent 2DES that help constrain the model [79,153].

Figure 7.

(a) Site basis of system containing five chromophores, labelled A through E, with each chromophore represented by an orb, (b) shaded boxes (1–3) depict the spatial delocalization for each exciton in the same system, (c) crystal structure of LHCII (PDB code 2BHW from Standfuss et al. [149]), where the protein is shown as a blue ribbon, and the skeletal structure of Chl-a, Chl-b and carotenoids are shown in red, green and black, respectively.

Molecular vibrations are typically localized to specific physical chromophores, and therefore can act as a specific marker, or tag, for the exciton population on specific sites. This is illustrated in figure 7a,b, where individual chromophores are labelled with upper case letters and represented by orbs, vibrations localized to each chromophore are labelled in lower case letters, where v_a ≠ v_b, etc. If the vibrational response could be correlated with broadband electronic excitation of all the associated exciton states, the time-dependent flow of energy between the various chromophores could in principle be followed.

A theoretical formalism for a coupled heterodimer system, using similar dipole coupling strengths, site reorganization energies and fluctuation correlation timescales to those previously derived for photosynthetic proteins, confirmed that 2DEV spectroscopy could be used to extract the uncoupled site energies and dipole coupling constants [129]. The key caveats are that vibrational frequencies associated with the two monomers must be distinct and so long as the excitonic splitting is resolvable in the inhomogeneous limit. The model requires that electronic coupling between the two moieties should not be strong enough to induce vibronic mixing in the vibrational Hamiltonian. This requirement is plausible for chlorophyll containing J-aggregates given the dipole coupling constants are modest, and the mid-IR active modes of chlorophyll (Chl) that can be investigated with 2DEV spectroscopy have very low associated Huang–Rhys factors [154,155]. Further the exciton energy splitting and vibrational modes probed must be very different. Again, for chlorophyll containing light-harvesting proteins this is reasonable as most of the exction energy gaps are an order of magnitude smaller than the mid-infrared active modes of Chl-a/b [156–160].

Simulated 2DEV spectra using Redfield theory in the secular approximation [161] showed that ground or excited state features could be used to extract the electronic site populations. The amplitude of each feature is proportional to the exciton population localized on each monomer, and thus the time-dependent site populations. This only requires the 2DEV spectral amplitudes and the ratios of the vibrational TDMs on the ground or electronically excited states. The former is the easiest to obtain from the linear absorption spectrum, whereas vibrational TDMs on electronically excited states require significant computational effort for multi-chromophore proteins such as light-harvesting complexes.

This theoretical work paved the way for 2DEV studies of LHCII [130]. LHCII is the most abundant pigment-protein complex on the planet, containing 14 chlorophyll molecules (eight Chl-a, six Chl-b) and four carotenoid moieties per monomer, and naturally forms a trimer (figure 7c). To date, no technique has been able to disentangle the site energies of pigments and the inter-pigment J-coupling constants, as prior 2DES measurements interrogate the adiabatic exciton structure [2,150,151]. As per the aforementioned theoretical study, the experimental approach is to use the high-frequency vibrational modes localized on Chl-a or Chl-b moieties as a proxy for spatial position inside the protein. The binding pockets for each chlorophyll molecule are inhomogeneous throughout the protein, which has two main effects: the electrostatic protein pockets shift the individual site energies of each chlorophyll moiety, which also modulates the inter-pigment J-coupling constants. Further, depending on the strength of the binding interactions and orientation of chlorophyll to proximal ligands, shifts in the mid-infrared vibrational frequencies can be induced.

The downside is that assignment of each LHCII vibrational feature is very difficult, as the protein-induced shifts are often very small, and LHCII contains 14 chlorophyll moieties per monomer. At present several features in the mid-infrared are readily assignable based on 2DEV studies of the individual Chl-a and Chl-b pigments in low-temperature glasses [162], and prior FTIR measurements [163]. Whereas assignments of many other features remain tentative and rely on previous LHCII Hamiltonians, which are based on fits to linear absorption, linear dichroism, circular dichroism, fluorescence spectra and transient absorption measurements [164].

The LHCII electronic linear absorption spectrum has previously been assigned to dominantly Chl-a (675 nm) and Chl-b (650 nm) excitons. For t₂ > 50 ps, excited state energy transfer between the excitonic states is considered complete, and only a ‘thermal’ distribution of the lowest energy exciton states will be populated. The best theoretical Hamiltonians available predict that these excitons will be dominantly localized to Chl-a chromophores [164]. The 2DEV spectra reveal that this is not the case and that the lowest energy exciton states of LHCII have a significant population localized on Chl-b moieties via the presence of a peak that on the ω₁ axes lies at 675 nm, but on the ω₃ probe axes associated with Chl-b C=O stretching vibrations. The 2DEV study of LHCII has inspired further 2DES experiments and a re-evaluation and modifications to the LHCII Hamiltonian [165].

The most recent 2DEV spectroscopic studies [134] have used broadband octave-spanning mid-infrared probes (1600 cm⁻¹ FWHM bandwidth) [115], which have the significant advantage of affording far more spectral bandwidth and far shorter pulse durations (21 fs) compared with OPA-generated mid-infrared pulses [53]. This means that the instrument response associated with 2DEV experiments is greatly reduced, enabling the technique to reach further back into the earliest time epoch of the excited state photochemical dynamics.

3.2. Two-dimensional vibrational–electronic spectroscopy

In tandem with the development of 2DEV spectroscopy, came the inception of a 2DVE spectroscopy, which interrogates the complementary extreme cross-peak between 2DIR and 2DES [121,166]. In this technique, mid-infrared laser pump (k₁ and k₂) prepares a population of a high-frequency vibration in either |g₀〉 or |g₁〉 states (figure 4a) that evolves in the t₂ waiting time. The electronic probe pulse, k₃, creates vibrational coherences between ground and excited electronic states, prior to emission and detection of the optical echo. 2DVE has offered insights into the nuclear-electronic dynamics between high-frequency ground state and electronic/vibronic Franck–Condon excitations. Courtney et al. used this spectroscopic technique to investigate vibronic coupling metal–metal charge transfer (MMCT) or ligand–metal charge transfer (LMCT) states of iron–ruthenium and iron-containing complexes [121,166]. The 2DVE spectra reveal signatures of features assigned to combination bands of C–N stretching modes coupled to low-frequency modes, which are strongly coupled to the MMCT and LMCT electronic transitions.

4. Two-dimensional fluorescence and photocurrent detected action spectroscopies

The 2D optical spectroscopies discussed thus far in this article employ three excitation pulses to induce the coherent nonlinear four-wave mixing (FWM) signals. Alternatively, instead of measuring the coherent signal, the third-order spectroscopic response of a system can be encoded in incoherent fields such as spontaneous fluorescence or photocurrents [98,167,168]. The same pulse sequence given in figure 2a is used; however, a fourth pulse, (k₄) is used to convert the second coherence into a population state, which is amenable to detection via spontaneous fluorescence or photocurrent detection. The 2D optical correlation spectra can be encoded in the fluorescence or photocurrent by phase modulation of the four laser pulses, to retrieve the third-order nonlinear response of interest. Further, because the signal is detected purely in the time domain, both t₁ and t₃ delays must be scanned to construct the ω₁–ω₃ correlation maps. Despite the necessity to scan two time axes, 2D fluorescence spectroscopy (2DFS) can be implemented with rapid data acquisition using pulse shapers that change the pulse sequence at the repetition rate of the laser. The most recent studies report a root mean square error of less than 0.05 for 1 min of data acquisition and averaging for a single 2D spectrum [168].

There are several advantages of 2D action-based spectroscopies over conventional experiments that emit a coherent four-wave mixing signal: (i) Fluorescence is detected background free, and does not require heterodyne detection to retrieve the phase and amplitude information. Further, fluorescence detection is far more sensitive, as detectors capable of counting single photon emission events, such as photomultipliers or avalanche photodiodes, can be used with lock-in amplifiers. (ii) For molecules where photo-bleaching is an issue, such as DNA nucleobases, pump fluences required to generate the 2D signal can be greatly reduced by orders of magnitude. (iii) Fluorescence detection is insensitive to background noise generated from solvent scatter, which is especially a problem with ultraviolet pulses. (iv) There are no constraints on the geometry of the experiment and it can be performed in the fully collinear geometry. Such approaches could be used to report the 2D optical spectrum of sub-ensemble molecules, or even facilitate 2D spectra of single molecules. The recent fluorescence-encoded IR spectroscopy technique could also be applied to achieve these ambitions, where IR pump–probe measurements are encoded and read out by linear 2-photon fluorescence [169].

The Marcus group used 2DFS to determine the conformations of porphyrin dimers in phospholipid membranes [170,171], and a π-stacked dinucleotide [172]. Comparisons between 2DFS and 2DES spectra show the information content is very similar, but intensities for stimulated emission or excited state absorption features vary. Through a combination of simulations and experiments, it was shown that 2DFS and 2DES spectra are only identical if the final population state has a fluorescence quantum yield of 1. Self-quenching or fast non-radiative relaxation processes are the main causes for differences between the two sets of spectra, and can be exploited to deduce conformational structures [170,171].

While 2D action spectroscopies offer some practical advantages over coherently detected counterparts, they can also be used to extract the influence of photoexcitation on macroscopic properties, such as photocurrents, a key parameter used to determine the viability of photovoltaic cell efficiencies. The same pulse sequences used for 2DFS can also be used to detect photocurrent signals induced by four ultrafast laser pulses (2D photocurrent spectroscopy (2DPS)), and has recently been applied to semiconducting nanostructures, organic photovoltaic and PbS quantum dot containing photocells [173–175]. In the case of PbS quantum dots, 2DPS spectra contained very different spectral signatures to 2DFS data acquired under the same experimental conditions, for two different excitation wavelengths. 2DPS revealed signatures for multiple exciton generation via increasingly dispersive line shapes in the 2D correlation spectrum, whereas 2DFS spectra appeared insensitive to these processes [175].

5. Surface-specific two-dimensional infrared spectroscopy

As already discussed in this article, 2DIR spectroscopy is an incisive probe of vibrational coupling, macromolecular structure and protein folding of bulk structures. SFG is an even-order spectroscopic technique that is insensitive to centrosymmetric centres, such as bulk liquids, and sensitive to non-centrosymmetric centres such as surfaces interfaces. The Zanni group combined the surface-sensitivity of SFG spectroscopy with 2DIR spectroscopy to create a heterodyne detected 2D SFG technique, (HD) 2DSFG, and generate 2DIR correlation spectra of vibrations very near to, or at surface interfaces [176–178]. The pulse sequence is the same as shown in figure 3a, generated with a mid-infrared pulse shaper, but uses an additional narrowband visible pulse to up-convert the non-centrosymmetric infrared echo into the visible. The (HD) 2D SFG technique was used to investigate the conformation of a monolayer of AHP peptides on a gold surface [179]. 2D SFG was able, where linear SFG could not, to determine that the peptide adhered to the Au surface are α-helical and lie perpendicular to the plane of the gold surface, via the different anharmonic shifts extracted from 2D SFG and 2DIR spectra. In α-helical structures, normal modes are delocalized over multiple residues, and the associated amide-I vibrational potential is only slightly anharmonic. In randomly structured coils, the vibrational modes are far more localized and have larger associated anharmonic potentials. Thus, the greater anharmonic shifts observed in the 2DIR spectra, compared with (HD) 2D SFG measurements, demonstrated that AHP protein on the gold surface forms α-helical structures. Random coil residues are also detected via cross-peaks in the (HD) 2D SFG spectra via vibrational energy transfer between ordered and random coils, as the corresponding direct interrogation of these vibrations that would appear on the diagonal of the spectrum are forbidden.

6. Two-dimensional Raman and terahertz spectroscopies

Initial experiments by the Fleming and Miller groups to record two-dimensional Raman spectroscopy (2DRS) of liquids such as CS₂ using non-resonant Raman pulses in six-wave mixing schemes were plagued by cascaded signals from sequential four-wave mixing processes [180–183]. Cascaded processes in these experiments originate from the third-order signal emission from one molecule, combining with incident laser beams, to induce a third-order emission from a second molecule. Most problematically, these signals emit in the same phase-matched direction as the desired fifth-order response 2D Raman signal.

Recently, the groups of Moran and Harel have implemented different excitation schemes to measure 2D Raman correlation spectra, with the majority of Raman interactions resonant with electronic states, and have demonstrated that such approaches ensure that the fifth-order 2D Raman response is dominant over sequential third-order cascaded processes [184–189].

Moran's group have used two different implementations of 2DRS, one where 2D correlation spectra are acquired exclusively in the time domain, and a second which involves a femtosecond-stimulated Raman scattering probe step which is amenable to mixed time-frequency detection [189]. The particular variant is chosen depending on the Raman frequencies of interest. 2DRS investigations have shown that wavepackets created in photoexcitation of ${\text{I}}_3^{-}$ in aqueous solution map into the ${\text{I}}_2^{-}$ photofragment product upon I–I bond cleavage [190]. Molesky et al. used 2DRS to reveal inhomogeneously broadened vibrations proximal to propionic acid side chains of water-ligated myoglobin, indicating that the side chains are conformationally flexible, with changes in structure driven by thermal fluctuations [186].

An alternative approach by the Harel group, takes advantage of the single shot 2DES method GRAPES, called gradient-assisted multidimensional electronic-Raman spectroscopy (GAMERS) [187,188]. A non-resonant Raman impulsive scattering pump that generates vibrational coherences on the ground electronic state, at time t₀, is then proceeded via a typical 2DES pulse sequence. Data acquisition for a single t₂ delay in GAMERS requires the t₀ delay to be scanned, as the t₁ delay is spatially encoded in the sample. The vast data content allows for frequency correlations to be made, via the appropriate Fourier-transform, between the ω₀, ω₁, ω₂ and ω₃ dimensions. Correlation maps between ω₀ and ω₃ for a dye molecule, IR 140 in solution reveal Raman active modes on ground or electronically excited states depending on which quadrature of the 2D electronic-Raman spectrum they appear in. Beating maps for specific Raman modes were constructed and overlaid with the ω₁–ω₃ 2DES correlation plots, revealing the parts of the electronic absorption spectrum associated with each Raman active vibration. The GAMERS spectroscopic technique is likely to prove decisive if applied to light-harvesting pigment-protein complexes, where arguments still persist whether observed oscillatory components of 2DES spectra arise from ground state or excited state vibrational wavepackets [132,191,192].

Mixed Raman-THz 2D spectroscopy experiments have been used to investigate the collective structural dynamics and intermolecular modes of water at ambient temperatures [193,194]. These studies highlight the appearance of an echo in the 2D Raman-THz spectra of liquid water that hints towards an inhomogeneous distribution of intermolecular hydrogen-bonding modes lives for up to 200 fs. This is significantly shorter than the lifetime of a single hydrogen bond (1 ps) and implies that extended water structures are not persistent at room temperature, bringing into question the conclusions drawn from prior X-ray scattering experiments. Recent 2D Raman-THz spectroscopic investigations of salt solutions revealed the correlation between bulk viscosities, where order in the water–hydrogen bonding network is far longer lived than in pure water, and that the cations can have a significant influence on the water network structure and associated reorganization timescales [195]. 2D THz-Raman experiments were also used to elucidate the off-diagonal anharmonic coupling between low-frequency Raman modes of halogenated liquids [196].

The wider availability of THz pulses, and free-space electro-optic sampling which fully characterizes the absolute phase and amplitude of THz pulses has allowed nonlinear ultrafast 2D THz spectroscopies to explore a variety of material properties. 2D THz spectroscopy has been used to investigate intersubband transitions in double quantum well systems, where a 2π Rabi flop is observed from coupling of the large dipole moment of the intersubband transition to the THz radiation [117,197]. For graphene, it was demonstrated that even at small THz driving fields, the nonlinear response is outside of the non-perturbative limit, and that coupling of carriers to the electromagnetic field dominated over any other scattering process [198]. Very recently, 2D THz spectroscopy has been used to reveal the nonlinear response of magnons, collective spin waves, in anti-ferromagnetic crystals. This work paves the way to investigate spin interactions between anti-ferromagnetic and ferromagnetic order switching [199]. Investigations of pure liquids or molecular-based systems with 2D THz spectroscopy have yet to be realized, because of the far lower nonlinearities associated with these molecular systems compared with solid-state materials, and insufficient THz pulse energies [117]. Hopefully, future developments of higher power plasma THz sources will provide sufficient pulse energies for 2D THz investigations of low-frequency intermolecular phonon modes of pure liquids and solute molecules.

7. Future research directions

Multidimensional optical spectroscopies now represent some of the premier tools for studying condensed phase dynamics of chemical, biological and nanomaterial systems. Since their first inception [40,44], they have rapidly evolved from original infrared and optical domains, spawning three-dimensional counterparts, [37,200] and can interrogate ultrafast dynamics throughout the entire electromagnetic spectrum. Theoretical calculations by Mukamel predict that future 2D spectroscopies using X-ray pulses could directly probe non-Born–Oppenheimer dynamics involving CIs [201–203].

7.1. Two-dimensional electronic–vibrational spectroscopy with ultraviolet excitation

Coupling broadband ultraviolet light with vibrational probes is one logical extension of 2DEV for the study of non-adiabatic dynamics in ultraviolet chromophores such as nucleobases, cytochromes, photoswitches and smaller polyenes that are more amenable to ab initio studies. In the majority of these systems, CIs near to the vertical Franck–Condon region are far more commonplace than in visible chromophores and almost always inevitably lead to strongly coupled electronic–nuclear motion that 2DEV spectroscopy is well placed to interrogate [128,139,204,205]. The necessary technological components already exist: ultrashort broadband UV sources are readily available [184,206], 2DES has been performed with ultraviolet laser pulses and thus the significant technological challenge of creating phase-locked UV pulse pairs has been surmounted [95,207–211].

Photoexcitation of UV chromophores is normally associated with large nuclear displacements, which in particular cases may drive wavepacket dynamics associated with the high-frequency vibrational modes. If the same frequencies can be probed with mid-infrared pulses, this will inevitably lead to an increased number of 2DEV spectroscopic pathways than depicted in figure 4, as probed via 1 → 0 or 2 ← 1 vibrational transitions on the excited state. Depending on the coherences generated, some of these pathways may very well oscillate in the waiting time.

7.2. Spatially resolved two-dimensional electronic spectroscopy

The work of Baiz and Tokmakoff demonstrated that a fully collinear 2DIR pulse train could be successfully combined with confocal microscopy, to realize 2DIR with micrometre spatial resolution [212]. Such experiments were quickly followed by wide-field 2DIR imaging by the Zanni group [213,214]. Such spectroscopies, even with spatial resolution above the diffraction limit, provide opportunities to explore the infrared signatures of heterogeneous biological samples such as tissues in vivo. Furthermore, the reduced spot size means samples experience far higher peak powers, which generates larger nonlinear signals which may afford reduced acquisition times. While many forays have been made to perform visible pump–probe microscopy experiments [215–218], which with near-field delivery of pulses to samples can attain spatial resolutions below the diffraction limit [219], to date no experiment has reported spatially resolved 2DES measurements. If applied to photovoltaic materials, one imagines that spatially resolved 2DES could reveal additional key information about the influence of spatial morphology on energy transfer or charge-separation dynamics. Visible pulses are potentially more damaging to samples than mid-infrared, and can induce photo-bleaching, as already demonstrated for confocal transient absorption measurements. This will be more problematic for confocal 2DES because of the increased acquisition times due to the requirement that t₁ must be scanned (cf. just t₂ in pump–probe). But with the proven success of compressed sensing to 2D correlation spectroscopies and rapid phase cycling, it is foreseeable that these problems can be surmounted in the near future. An alternative approach would be to employ 2D action spectroscopies such as 2DFS, where far lower pump intensities can be used [168].

7.3. Fully chiral two-dimensional electronic spectroscopy

The interpretation of oscillatory signals observed in 2DES data for photosynthetic light-harvesting proteins have attracted a lot of controversy [1,3,4,72,132,191,220,221]. The ongoing debate revolves around whether these signals originate from purely electronic, vibrational or mixed vibronic effects. To date, experiments have yet to be able to definitively differentiate between signals arising from these processes. Recently, theoretical calculations from the Collini and Olaya-Castro groups have shown that fully chiral 2DES experiments could be used to differentiate between purely electronic, vibronic and vibrational coherences [222,223]. To date, only experiments using either pump or probe pulses that are elliptically polarized have been demonstrated for 2DES [224,225]. If experimentally realized, fully chiral 2DES could answer this almost 10-year-old debate. Such a technique would also be incredibly sensitive, as all chiral-specific spectroscopies are, to changes in conformational structure involving chiral centres induced by excited state dynamics.

Data accessibility

Isotropic 2DIR data for MAPbI₃ are available for download from the University of Bristol's Research Data Storage Facility: https://doi.org/10.5523/bris.1qlc372dvn9in2gtnb7vpxfait.

Competing interests

I have no competing financial or non-financial interests.

Funding

The author acknowledges funding from the Royal Society via a University Research Fellowship (UF140231), Research Grant (RG160046) and the Engineering and Physical Sciences Research Council (EP/P010253/1).