Broadband Transient Absorption and Two-Dimensional Electronic

Article pubs.acs.org/JPCA

Broadband Transient Absorption and Two-Dimensional Electronic Spectroscopy of Methylene Blue Jacob C. Dean,† Shahnawaz Rafiq,† Daniel G. Oblinsky,† Elsa Cassette,† Chanelle C. Jumper,‡ and Gregory D. Scholes*,†,‡ †

Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States Department of Chemistry, University of Toronto, Toronto, ON M5S 3H6, Canada

‡

Downloaded by UNIV OF TEXAS SAN ANTONIO on August 23, 2015 | http://pubs.acs.org Publication Date (Web): August 14, 2015 | doi: 10.1021/acs.jpca.5b06126

S Supporting Information *

ABSTRACT: Broadband transient absorption and two-dimensional electronic spectroscopy (2DES) studies of methylene blue in aqueous solution are reported. By isolating the coherent oscillations of the nonlinear signal amplitude and Fourier transforming with respect to the population time, we analyzed a significant number of coherences in the frequency domain and compared them with predictions of the vibronic spectrum from density function theory (DFT) calculations. We show here that such a comparison enables reliable assignments of vibrational coherences to particular vibrational modes, with their constituent combination bands and overtones also being identified via Franck−Condon analysis aided by DFT. Evaluation of the Fourier transform (FT) spectrum of transient absorption recorded to picosecond population times, in coincidence with 2D oscillation maps that disperse the FT spectrum into the additional excitation axis, is shown to be a complementary approach toward detailed coherence determination. Using the Franck−Condon overlap integrals determined from DFT calculations, we modeled 2D oscillation maps up to two vibrational quanta in the ground and excited state (six-level model), showing agreement with experiment. This semiquantitative analysis is used to interpret the geometry change upon photoexcitation as an expansion of the central sulfur/nitrogen containing ring due to the increased antibonding character in the excited state.

1. INTRODUCTION

Time-resolved coherent spectroscopy yields time-domain information (dynamics) in coincidence with frequency-domain (vibronic) information that is often obscured in steady-state measurements. This is accomplished by using ultrashort, spectrally broadened pulses that excite a coherent superposition of vibronic states in the sample (vibrational wavepackets or coherences), which is subsequently time-resolved to map out its evolution through phase space. The Fourier transform (FT) of these coherent, signal-amplitude modulations yields the relative frequencies of Franck−Condon (FC) active vibrations along with their relative amplitudes which are governed by the displacement between ground and excited-state potential energy surfaces. In this way, coherent spectroscopy yields a probe of the ground and/or excited-state potential energy surfaces, while potentially illuminating real-time chemical dynamics.14−26 High-detail vibronic information can be attained because the frequency resolution of vibronic excitations is only limited by their individual dephasing times, along with the duration of the pump and probe pulses used. It is notable that the vibronic coherences are resolved despite being masked by line

Methylene blue (MB) is a cationic phenothiazinium dye used historically for medical applications ranging from histology, antimalarial, and methemoglobinemia treatment, to more recently photodynamic therapy (PDT).1−3 Its use as an effective PDT agent is a result of its inherent photophysical/ photochemical properties coupled with a high propensity for forming aggregates in solution with molecules and biological interfaces. The absorption of MB monomer is peaked at 664 nm as shown in Figure 1a, placing it well within the range of the “therapeutic window” of the skin (600−950 nm) for PDT treatment,3 and perhaps more importantly MB is an efficient sensitizer of singlet oxygen with quantum yields reported at ΦΔ ∼ 0.5 in solution.4−6 In light of the success of MB as an applicable photosensitizer, characterization of the excited states involved is of fundamental importance to isolating key characteristics or mechanisms responsible for the observed dynamics. For example, significant efforts have been put forth in characterizing MB photochemistry;4,7−13 however, very little is reported on the nature of the involved excited states or its vibronic spectroscopy. Here, we address this directly by employing time-domain coherent spectroscopy to elucidate the underlying vibronic spectroscopy of MB in the condensed phase (aqueous solution). © XXXX American Chemical Society

Received: June 26, 2015 Revised: August 8, 2015

A

DOI: 10.1021/acs.jpca.5b06126 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

experiment as diagnosed via polarization-gated and transient grating frequency-resolved optical gating (PG-FROG, TGFROG), respectively.44,45 The temporal profile of the pulse was evaluated using the intensity from the FROG map fit to a Gaussian. The TG-FROG map of the pulse used in the 2DES experiments is shown in Figure S1 of the Supporting Information. For the BBTA experiment, the compressed pulses are then split by a wedge into three beams, two of which are less than 1% of the total intensity and used as the reference and probe beams, with the remaining used as the pump pulse. The pulse energy used for the pump was 5 nJ while the probe was kept to less than 200 pJ. The delay stage was scanned in 5 fs steps, and the BBTA shown in Figure 1 is an average of four consecutive scans each averaging 500 pump on/pump off pairs, of which are averages of four pulses. Scatter contributions to the BBTA spectra (seen as fringes on top of each TA spectrum that change in frequency as the pump is scanned) were removed by a filtering algorithm that performs an inverse fast Fourier transform at each population time to bring the transient absorption spectrum into the time domain. A super-Gaussian filter was applied over the probe pulse, which is fixed in the time domain, eliminating scatter from the pump pulse, which is moving away from Δt = 0 in the IFFT. The filtered data are then brought back into the frequency domain by a fast Fourier transform. For 2DES measurements, the compressed NOPA pulse is focused on a 2D diffractive optic generating four phase-stable beams in a box geometry. The four beams are then collimated using a 3 in. spherical mirror, and three beams (with electric fields labeled E1, E2, E3) are passed through pairs of 1° fused silica wedges, each of which incorporates one mounted on a delay stage (Newport VP-25XL). The third beam (E3) is passed through a chopper operating at 50 Hz used for scatter subtraction. The fourth beam acts as the local oscillator for heterodyne detection of the third-order signal, and it is passed through a neutral density filter attenuating it by 104 and imparting a delay such that it arrives ∼250 fs prior to the final pulse. The coherence time, t1, was scanned in 0.2 fs steps from −50 to +50 fs, capturing both nonrephasing and rephasing spectra sequentially at each t2 point. The population time, t2, was scanned to 440 fs with 5 fs step size. The pulse energy of each of the three beams used to generate the nonlinear signal was ∼4 nJ. 2DES spectra were phased according to the projection slice theorem46,47 and by comparison of the projections of the absorptive, rephasing, and nonrephasing spectra along ν1, simultaneously.42 For generation of the 2D oscillation maps, the population dynamics at each point in the 3D data set (ν1, t2, ν3) was removed by fitting a biexponential function along t2, and subsequently removing it. After the purely coherent portion of the 2DES data was obtained, the data were padded to a total of 256 t2 points and Fourier transformed along t2 to obtain the 3D spectral solid (ν1, ν2, ν3). The data presented are the absolute value of the FT amplitude. For comparing individual points in the 2D map at (ν1, ν3), the data were padded to a total of 6000 points following the fitting procedure to ensure that the ν2 resolution was conserved. B. Computational Methods. Density functional theory (DFT) calculations were all performed in the Gaussian09 suite.48 The geometry optimizations and harmonic frequency calculations were done using the M05-2X functional49 with the 6-311++G(d,p) basis set, and the results reported in the

broadening in the absorption spectrum. Related techniques such as femtosecond time-resolved Raman and time-resolved infrared spectroscopy have also proven to be highly sensitive probes of molecular structure during the course of photochemical dynamics.25,27−29 However, we show here that analysis of coherent dynamics in transient absorption (where oscillations can easily be sampled for picoseconds) concurrently with two-dimensional spectroscopic analysis, allows for a more comprehensive assessment of the observed coherences and their spectroscopic assignments. In this report, broadband transient absorption (BBTA) and 2D-electronic spectroscopy (2DES) were used in tandem with density functional theory (DFT) calculations to probe, and subsequently assign, Franck−Condon active vibrations present in MB. Quantum chemical calculations have been shown to aid in the interpretation and modeling of 2DES data by providing predictions of populated conformers, vertical excitation energies, and molecular orbital makeup of electronic transitions, as well as estimated Huang−Rhys factors for simulating 2DES spectra modulated by a single underdamped vibrational mode.30,31 The results presented herein expand upon this combined approach by comparing the frequencies of normal modes and their corresponding Franck−Condon factors calculated by quantum chemical methods to experimental coherent spectra in the frequency domain. We attain unambiguous, semiquantitative vibronic assignments of oscillatory features in time-resolved spectra out to overtones and combination bands. This evaluation provides a benchmark for identifying vibrations giving rise to vibrational quantum coherence, and quantifying the displacement along those coordinates. This concept is vital for elucidating vibronic interactions and ensuing energy transfer dynamics in complex multichromophoric systems, where observed vibrational/ vibronic coherences originate from coordinates that likely play a dominant role in bridging donor/acceptor energy gaps crucial for Förster energy transfer.32−40 Thus, assignment of the coherences present in these systems to particular vibrational coordinates may lend insight toward molecular principles relevant to efficient energy transfer (either coherently or incoherently).

2. EXPERIMENTAL SECTION A. Experimental Methods. The methylene blue (hydrate) sample was purchased from Sigma-Aldrich and was diluted in water to a concentration of ∼2 × 10−5 M to avoid excessive dimer formation, yielding an optical density of 0.14 in a 1 mm cuvette. Absorption measurements were performed on a Cary 6000i UV−vis−NIR spectrometer and fluorescence spectra were collected with a Horiba Fluorolog-3. The reported fluorescence spectrum (uncorrected) was taken with 1 nm excitation and 3 nm emission slit widths, with the excitation wavelength set to the absorption maximum at λmax = 664 nm. The full description of the femtosecond experimental setup can be found elsewhere;21,41,42 however, a brief description is given here. The Ti:sapphire seeded regenerative amplifier (Spectra-Physics, Spitfire) outputs 150 fs pulses at 800 nm at a repetition rate of 5 kHz and is used to pump a home-built noncollinear optical parametric amplifier (NOPA).43 The NOPA pulse spectrum spans ∼90 nm and is shown in Figure 1a. The NOPA pulses are compressed with a folded grating compressor and prism compressor to ∼16 fs full width at halfmaximum (fwhm) in the broadband transient absorption spectrometer and 12 fs in the 2D electronic spectroscopy B


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manuscript are for gas-phase MB. However, the results for polarizable continuum model (PCM) calculations using water can be found in the Supporting Information. Franck−Condon simulations were performed in Gaussian09 using the geometries and frequencies from the S0 and S1 structures, and the displacements, Δd, were manually calculated by an external fitting to the simulation results by use of the recursion relations given in Henderson et al.50

3. RESULTS AND DISCUSSION A. Steady-State and Broadband Transient Absorption (BBTA) Spectroscopy. The absorption spectrum of MB is peaked at 15060 cm−1 (664 nm) with a vibronic subband and residual dimer absorption to the blue at 16340 cm−1 (612 nm). The fluorescence spectrum (red trace, Figure 1a) shows a Stokes shift of 570 cm−1 with the emission maximum at 14490 cm−1. The parallel-polarized BBTA spectrum is displayed in Figure 1b. At early times the positive signal (red) is strongest at 14940 cm−1, suggesting contributions from both S0−S1 groundstate bleaching (GSB) and S1−S0 stimulated emission (SE) signals. At higher wavenumber, the signal direction is reversed (blue) and the S1 → Sn excited-state absorption (ESA) signal spans from ∼17000 to 18000 cm−1, consistent with prior studies.4 The GSB/SE signal is clearly modulated by coherent oscillations that persist for the entirety of the 2 ps time window shown. The purely coherent BBTA spectrum is shown in Figure 1c and was obtained by fitting the population dynamics with a biexponential function at each emission wavenumber point and subtracting that fit from the total signal.21,51 In this spectrum, the oscillating portion of the BBTA signal is highly evident with a peak of ΔI/I ∼ 0.01, approximately 20% of the GSB/SE magnitude. Comparing with the BBTA signal, the coherence amplitude is peaked primarily at the red edge of the signal, and a node is observed separating the signal with opposite phase (red/blue). In fact, the node illuminates the dynamic Stokes shift to ∼14780 cm−1 within 2 ps. One-dimensional traces from this spectrum and their FTs are shown in Figure 2a,b, respectively, and the oscillations are clearly multicomponent. Fourier transforming the coherent spectrum yields a map of the FT amplitude (Figure 1d), with rich structure out to ∼1700 cm−1 in FT wavenumber. The largest amplitude is found at 450 and 500 cm−1, giving rise to beating in the time domain at a period of ∼640 fs (Tbeat = 1/(cΔν)) clearly evident in the coherent time-domain traces. Peaks at lower FT wavenumber are also observed around 120 and 250 cm−1, and several smaller bands to higher frequency are labeled in Figure 2b. Figure 2b clearly displays the large number of frequencies present in the time-domain data, with FT peaks showing line widths of ∼25 cm−1 fwhm. The persistence of FT amplitude at the wings of the 450 and 500 cm−1 peaks is likely due to a combination of interference effects from their proximity in frequency,18 and Δv = 1 excitations between neighboring levels at higher quanta which exhibit some anharmonicity (i.e., v = 1 ↔ v = 2). Comparing the amplitude of these features along the emission axis, we find the node observed in the time domain is present in the FT and nearly matches the frequency of the absorption maximum (dashed white line). This is suggestive of predominantly ground-state vibrational coherence activated through an impulsive Raman process.16,18,19,21,51 Interestingly, another node can clearly be found between the two segments of 250 cm−1 amplitude near 17000 cm−1 in emission wavenumber. Because the node is positioned near the onset of the ESA

Figure 1. (a) Absorption (black) and fluorescence (red) spectra of methylene blue, and laser pulse spectrum (NOPA) used in BBTA and 2DES. (b) Parallel-polarized BBTA spectrum of MB. (c) Coherent BBTA spectrum and (d) its Fourier transform spectrum. Dashed lines are maxima in the absorption (white) and fluorescence (red) spectra.

signal, it can be inferred that this frequency is the S1−Sn absorption maximum on similar grounds as for ground-state bleaching. This is not obvious by inspection of the BBTA spectrum in Figure 1b, likely due to overlap of the ESA signal in this region with residual GSB. C


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Figure 2. (a) Traces of coherent BBTA and (b) their respective FT spectra at the fluorescence maximum (14490 cm−1), absorption maximum (15060 cm−1), vibronic subband (16340 cm−1), and ESA region (17400 cm−1).

At higher emission wavenumber, the FT changes with the dominant 450/500 cm−1 peaks being reduced, thereby uncovering buried structure nearby at 590 and 670 cm−1. The ESA region shows the same frequencies as the GSB/SE with different relative amplitudes. The high-frequency components are more evident in the time-domain trace shown for this region in Figure 2a (bottom). Given that the probe intensity approaches zero here, however, this region is not considered in detail in the discussion that follows.16 B. Franck−Condon Analysis of Vibrational Coherences. To assign the various vibrational coherences present in MB, DFT/TDDFT geometry optimizations and harmonic frequency calculations were performed. MB is heavy-atom planar and classified in the C2v point group with a total of 108 normal modes. As shown in the FT spectra, however, only those modes that are Franck−Condon active will give rise to wavepacket motion and consequently FT amplitude. Therefore, a FC simulation was carried out using the calculated S0 and S1 structures, and the result is shown in Figure 3a compared with the FT spectrum integrated over the GSB/SE region. The simulated intensities are shown as the relative absorption coefficients for all vibronic transitions calculated for MB, i.e., a linear vibronic absorption spectrum. Because each FC factor represents the modulus squared of the transition dipole moment for a single vibronic transition (when excitation is to a single electronic state with no borrowed intensity from additional electronic states), the intensities plotted are simply the FC factors weighted by the corresponding absorption frequency. However, because the window of active vibrational coherences is within ∼1600 cm−1 (small relative to S0−S1 energy), very little difference is found between the relative vibronic absorption coefficients and FC factors when normalized to the 0−0 origin transition of the simulation. As such, the individual FC factors and vibrational overlap integrals for each vibronic excitation are used directly for comparison with the experimental coherences for simplicity. Immediately obvious is that the simulation captures most of the active vibrational coherences present, and the relative FC factors (or intensities) reasonably agree with the FT amplitude observed in the experiment. The relative intensities are much larger for the lower frequency modes and inverted for the 450/ 500 cm−1 pair in the simulation, but relative to the 450/500 cm−1 peaks, the intensity pattern is quite close at higher wavenumber. Subtle differences may be related to slight interferences by coherences with similar frequencies, or effects

Figure 3. (a) Franck−Condon simulation with Δν = 30 cm−1 fwhm (top) and experimental FT spectrum integrated over the bleach region (bottom). (b) Franck−Condon active vibrational modes assigned in the FT spectrum.

from residual pulse chirp.18,52 The comparably lower amplitude of the lowest frequency coherence (120 cm−1) is likely due to a combination of broadening in the frequency domain due to the finite sampling period of 2 ps (capturing approximately six vibrational periods), along with an overestimation of the simulated intensity of this low-frequency mode in the gas-phase simulation (see Figure S5 for comparison with PCM results). Regardless, the result can be utilized to assign normal modes to the vibrational coherences present. The vibrational modes are labeled using the Mulliken scheme,53 and their vibronic assignments are given in Figure 3a; the active modes in the spectrum are summarized in Table 1, and those prominent in Table 1. Relevant Vibrational Modes of Methylene Blue with Calculated and Experimental Frequencies, Symmetry, Displacement, and Assignments

a

mode no.a

νcalc (cm−1)b

35 34 32 30 27 16 8

109 244 450 510 794 1465 1717

νexp(cm−1)

sym

Δd

mode

120 250 450 500 770

a1 a1 a1 a1 a1 a1 a1

0.53 0.21 0.60 0.50 0.26 0.23 0.16

CN(CH3)2 sci C−N(CH3)2 str CSC/CNC b CSC/CNC b CNC b/CC str C−N str/CH3 umb CC str

Mulliken scheme53 bDFT//M05-2X/6-311++G(d,p).

the spectrum are shown in Figure 3b. Most of the transitions labeled in the figure are fundamentals, the largest of which are ν32 and ν30 described by CSC/CNC bending of the central MB ring, assigned to the 450 and 500 cm−1 peaks. Notably, several combination bands are assignable and the overtone of ν32 is confidently assigned in the FT spectrum demonstrating the resolving power of the present analysis. D


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excited-state fundamentals in the stimulated emission signal was found to be very close to GSB and can also be found in the Supporting Information. C. 2D Electronic Spectroscopy and 2D Oscillation Maps. 2DES is an effective method of dispersing the BBTA signal into two dimensions by addition of the excitation axis, ν1, and by separating the constituent rephasing and nonrephasing nonlinear signals captured simultaneously in pump−probe measurements.41,54−56 In a molecule with many coherences such as MB, it serves to better isolate the oscillating signals/ pathways that can aid in assigning coherences to ground or excited-state vibrations, or differentiating between vibrational and electronic coherence signatures. Several absorptive 2DES spectra of MB taken at different population times, t2 (Δt in BBTA), are shown in Figure 4a with colored boxes labeling (ν1,

The modes assigned to the vibrational coherences present in the time-resolved spectrum of MB are predominantly associated with motion of the central CSC/CNC ring and peripheral CN(CH3)2 groups as displayed in Figure 3b. In particular, stretching of the CN(CH3)2 groups and bending motion of the CSC and CNC groups in the chromophore backbone dominate the vibronic activity. On that basis, we can infer that the relative bond order is changing throughout MB in going from S0 to S1, with the electron density of the heavy atoms playing a key role. In addition, all of the assigned vibrations are totally symmetric (a1), retaining motion in the molecular plane. The excitation of nontotally symmetric vibrations requires even overtones on the basis of Franck− Condon considerations, and indeed is generally much smaller when present. However, given their complete absence in the spectrum, the computational prediction that MB retains its C2v symmetry after photoexcitation is validated, with no spectral signatures of change in any out-of-plane coordinates. It is noted that the FC simulation is a model of vibronic transitions in the linear regime, whereas the BBTA is a probe of the third-order polarization integrating over all possible rephasing and nonrephasing Feynman pathways at each emission wavenumber. The agreement of the simulation with the integrated FT spectrum is a remarkable result as the amplitude of each coherent pathway in the third-order signal is determined by a product of the four transition dipole terms affiliated with each vibronic interaction undergone in the fourwave mixing process, i.e., μ(1)μ(2)μ(3)μ(4). However, the agreement between the DFT prediction and experimental FT spectrum in Figure 3a suggests that summing over all coherent pathways leads to a somewhat unbiased scaling of the represented transition dipole moment terms, yielding qualitative agreement with a linear vibronic model such as this. To further investigate this comparison, the summed amplitudes of all relevant pathways contributing to the observed coherences in the integrated BBTA spectrum were calculated by approximating each transition dipole term as the vibrational overlap integral extracted from the vibronic analysis presented here, i.e., μv′v″ = ⟨χv′|χv″⟩ = √FCFv′v″, with v′ and v″ labeling the upper (lower) and lower (upper) vibrational levels participating in the transition. The sum of the dominant transition dipole moment products then gives an estimate on the integrated FT amplitude for each fundamental, AFund, or overtone coherence, AOvertone. Assuming that the magnitudes of μ are identical in excitation and de-excitation (i.e., μ10 = μ01) and that the frequencies of each vibration are identical in the ground and excited state, the integrated amplitudes in the ground state (GSB) are given as GSB AFund =

Figure 4. (a) 2DES spectra of MB taken at various t2 times. Colored squares denote ν1/ν3 positions where one-dimensional traces are shown in (b). (b) t2 residual traces after population dynamics were removed from rephasing (blue), nonrephasing (red), and absorptive (black) spectra with the corresponding Fourier transforms (c).

ν3) points traced in Figure 4b. The signal forms a box matching the absorption spectrum of MB with cross peaks arising between the primary band and vibronic subband. More interesting, however, is the evolution of the 2DES spectrum. The spectrum at t2 = 40 fs shows a diagonally elongated diagonal peak with signal quickly decaying to the red in both dimensions. At 85 fs, the spectrum becomes dispersed significantly along the emission axis extending well past the fluorescence maximum. By t2 = 120 fs, the spectrum returns to a similar shape as before, with some amplitude left dispersed following the round-trip of the wavepacket. This evolution of the 2DES line shape is consistent with the experimental and theoretical results of Nemeth et al.31 and Mančal et al.,57 respectively, where modulations of the 2DES line shape and amplitude due to vibrational wavepackets were unambiguously demonstrated. The rephasing (blue), nonrephasing (red), and absorptive (black) traces in Figure 4b and their FTs yield features similar to those of BBTA (at the expense of ν2 resolution due to the limited population time range of the 2DES setup), but the oscillations are clearly separated. Crosspeaks at higher ν1 display higher frequency coherences and the inverse at lower ν1. A larger set of 2DES spectra can be found in the Supporting Information.

∑ (μv(1) μ(2) μ(3) μ(4) ) ′v″ v′v″ v′v″ v′v″ n n

= 2μ10 2 (μ00 2 + μ112 + 2μ00 μ11) GSB A Overtone = 2μ10 μ21(2μ00 μ20 + 2μ20 μ22 + μ10 μ21)

(1) (2)

Only the dominant contributions to the oscillations in the ground state were included in eqs 1 and 2 (Figure S3 and Figure 5a), and the factor of 2 at the front of each expression is due to the rephasing and nonrephasing signals contributing equivalent transition dipole moment products. Indeed, close correspondence with the linear model is found, and the results are plotted in Figure S4 in the Supporting Information along with further calculation details. The calculated amplitude for E


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Figure 5. (a) Diagrams of rephasing 2D oscillation maps for fundamental coherences (left) and overtone coherences (right) with the respective energy level diagrams to right. Red boxes are associated with ground-state coherences generated in ground-state bleach signals, and blue circles denote excited-state coherences seen as stimulated emission; dashed boxes and circles designate those pathways that are expected to have significantly smaller amplitude. (b) Experimental 2D oscillation maps of rephasing signal after removal of population dynamics. (c) Simulated oscillation maps of fundamentals (440, 550, 780 cm−1) and overtone coherences (890 cm−1).

amplitude during t2. Given this, the corresponding coherence/ oscillation maps (Fourier transformed 2DES along t2) yield amplitude at distinct (ν1, ν3) positions defined by those “coherent” Feynman pathways, and at ν2 frequencies that match vibrational coherences active in the sample. All coherent Feynman pathways contributing to the oscillation maps can be described by their corresponding double-sided Feynman diagrams, which are shown in Figure S3 in the Supporting Information. Figure 5b shows 2D oscillation maps of the rephasing signal at several ν2 frequencies that were tentatively assigned in the FC analysis. It is noted that slight ν2 differences exist between the BBTA FT and the 2D maps, which is a result of the added ν2 uncertainty in the 2DES experiment (t2max = 440 fs).

By removing the population dynamics from the 2DES data and Fourier transforming along t2, we can map the amplitude of coherences out in two dimensions. This has recently been shown to greatly aid in the assignment of coherences, particularly by mapping out each set of Feynman pathways giving rise to the oscillating signals.20,36,38,40,41,58−61 Each Feynman pathway represents a potential signal in the 2D map, with a spectral position (ν1, ν3) defined by the resonant frequency of the first light-matter interaction (that initiates the optical coherence between ground and excited states) and by the final frequency of the emitted signal, respectively. All of the possible pathways that fall within the bandwidth of the pulses employed contribute to the 2D spectrum; however, only those pathways that generate a coherence (or superposition of states) during the population time will give rise to oscillatory signal F


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and that the frequencies of each vibration are identical in the ground and excited state (or nearly so within the resolution of 2DES). This is validated by DFT harmonic frequency calculations and greatly simplifies predictability in (ν1, ν3). Lastly, the spectral bandwidth of the laser pulse is not taken into account here and the individual features are represented by two-dimensional Gaussians with a line width of ∼700 cm−1. Further simulation details and all of the double-sided Feynman diagrams used in the simulation are given in the Supporting Information. The results for several simulated rephasing maps are shown in Figure 5c. For the primary fundamentals present in the experiment, ν2 = 440 and 550 cm−1, the ground-state bleach simulation generally captures the location of the coherence amplitude. The simulation shows the peak of the amplitude shifted closer toward ν1 = 15060 cm−1, which might suggest a small fraction of SE (excited state) amplitude present in the experimental spectrum to shift the maximum to higher wavenumber. Out of the nine Feynman pathways simulated (black squares or dots), only the four that do not incorporate transitions with v = 2 (or g2/e2) give significant amplitude. This result indicates that only the first vibrational level is necessary to evaluate the position of coherences in 2D maps where the nuclear displacements are modest, as in the case of MB (Table 1). The positions of the low-amplitude pathways are represented in Figure 5a by dashed squares/circles. The map for ν2 = 780 cm−1 shows resolution of the individual peaks at higher ν2; however, this is not observed in the experimental spectrum where only a single, broad feature is resolved. This is tentatively attributed to the contribution of a combination band, which occurs at all (ν1, ν3) points split by the frequencies of all combination members and their sum. The predicted wavenumber positions for overtone coherences contrasts fundamentals in that occurrences at 1/2ν2 are present. This provides a signature for overtones in that they diverge from the pattern of increasing splittings as ν2 is increased. In addition, the pattern on the 2D map differs from fundamentals in that all nine contributions from GSB occur below the diagonal and at the absorption maximum, and the six for SE are distributed uniquely from fundamentals and its GSB counterpart. The latter difference is due to the two pump interactions generated by E1 and E2. For GSB, coherence between g0 and any excited-state vibrational level (e0, e1, en) can be initiated with E1 so long as it is within the same coordinate or they are coupled through a combination band. After this excitation, E2 then initiates the ground-state overtone coherence. For SE, however, the pump interactions are limited to only e0 and e2 to engage the excited-state coherence directly. The result is that no amplitude is generated in ν1 for the vibrational states between the two in the coherence, and this limits the total number of Feynman pathways possible. The amplitude of the 890 cm−1 overtone is much larger in the GSB map compared with that for SE, and the amplitude is maximum at the center of the nine points. The central contribution is the only one that does not incorporate μ2−0, the direct transition between the zero-point level and overtone that has a small FC factor. The remaining amplitude is evenly distributed by those peaks sharing an edge (Figure 5a, right), with the corners of the box effectively scaling to zero due to the μ2−02 term involved (see Figure S3 in the Supporting Information). Overall, the simulated map agrees well with the experimental oscillation map, confirming the assignment of this coherence to the first overtone of ν32.

According to the nodal pattern observed in BBTA results (Figure 1c,d), we expect that most of the coherences are occurring on the ground state. By comparing (rephasing) coherent Feynman pathways shown in Figure 5a, we expect ground-state coherences to predominantly occur in a “box” below the diagonal represented as solid red boxes in the diagram. Excited-state coherences yield some amplitude above the diagonal, giving way to a marked signature of excited-state contributions.59 Furthermore, at each ν2 the splitting between each pair of points along ν1/ν3 is expected to be the respective ν2 frequency (for fundamentals), as represented in the model diagrams. The energy levels represented in the six-level model shown in Figure 5a are labeled gv and ev, for v = 0, 1, 2 in the ground and excited electronic states, respectively, keeping with the notation given by Turner et al.61 Inspection of the top three maps in Figure 5b corroborates the assignment of these peaks to fundamentals observed on the ground state, as the FT amplitude is peaked below the diagonal at the center of the four oscillatory contributions. Homogeneous line broadening prevents observation of each individual contribution, (ν1, ν3) = (νabs, νabs), (νabs, νabs − ν2), (νabs + ν2, νabs), (νabs + ν2, νabs − ν2), but instead an average is observed at the center of the “box”, displaced symmetrically from the diagonal maximum at (15060, 15060 cm−1). The oscillation map at 650 cm−1 shows amplitude resolved in ν2, unlike the ν1-integrated BBTA. This frequency was assigned to the ν30ν35 combination band in the FC analysis. The 780 cm−1 map is close to the DFT predicted fundamental of ν27; however, the amplitude is asymmetrically distributed from the diagonal maximum and is likely a composite with the ν30ν34 combination band. It should be noted that combination bands incorporate a vast number of Feynman pathways because two coordinates are implicitly connected (16 contributions from ground-state coherence alone) as further discussed in the Supporting Information. The ν2 = 890 cm−1 coherence, however, was confidently assigned to the 2ν32 overtone coherence in BBTA, and its assignment is verified here with the amplitude peaking at Δν1 ∼ +1/2(ν2), and nearly the same in Δν3. Indeed, nine Feynman pathways for ground-state overtone coherence are predicted with the center being split from the diagonal maximum by (1/2ν2, −1/2ν2). This is illustrated in the overtone diagram in Figure 5a (right). It is expected toward higher ν2 frequency that pulse discrimination becomes a factor at very low ν3 values, as the pulse abruptly decays below the fluorescence maximum (Figure 1a). This effect likely accounts for the slight offset in the observed ν3 position; nevertheless the peak position closely matches that predicted. By using the predicted peak positions from each Feynman pathway contributing to the oscillation map (Figure 5a), in accordance with the Franck−Condon factors calculated from the one-dimensional analysis in section 3B, we can model the oscillation maps by using the vibrational overlap integrals for the various vibronic transitions present. This model is an extension of the framework presented by Egorova,59 with several assumptions made to retain simplicity in the modeling of the MB oscillation maps. The first of which is that the magnitude of the individual transition dipole moments can be approximated by only the time-independent vibrational overlap integrals as was done for calculating the integrated amplitudes in section 3B. This is valid in the absence of vibronic coupling or nearby excited states. Again, it is assumed that the magnitudes of μ are identical in excitation and de-excitation G


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The Journal of Physical Chemistry A The nonrephasing oscillation maps are less readily assignable, showing amplitude shifted to higher wavenumber than is expected on the basis of Feynman pathways; this disagreement is currently still under investigation. However, the oscillation maps of the total data set recover the node near the absorption maximum in ν3 as observed in BBTA. This occurs despite the amplitude being nonzero in rephasing and nonrephasing signals separately, which are shown in Figure 6a,b for comparison. The


Figure 7. (a) Frontier orbitals for the S0−S1 transition in MB with the transition dipole moment (TDM) direction denoted. (b) Bond lengths (angstroms) of central ring in S0 and S1 structures optimized at the (TD)DFT//M05-2X/6-311++G(d,p) level of theory.

FC simulation is not unexpected but demonstrates the level of molecular detail available through the identification of vibrational coherences.24,62−64 Realization of the geometry change at this detail presents a valid starting point for modeling photochemical and energy transfer dynamics driven predominantly by intramolecular processes (presuming dynamics are not occurring within the dephasing time of the vibration). It is noted, however, that reaction coordinates may preclude this level of analysis, appearing in the time domain as a vibration with large displacement, or not observable at all due to fast dephasing driven by solvation dynamics or rapid displacement out of the FC region.65 Yet, in that case the transient behavior of spectroscopic signals complements a purely spectroscopic approach, highlighting the versatility of analysis in both the time and frequency domains.15,24,26 This type of negative result can also be used in comparisons with computational predictions, perhaps to identify those coordinates involved in fast photochemical processes or those coupled strongly to the solvation coordinate by solute−solvent interactions.

Figure 6. Oscillation maps at 440, 550, and 780 cm−1 for (a) rephasing, (b) nonrephasing, and (c) absorptive 2DES signals.

absorptive spectra clearly display the lower and upper “lobes” characterized predominantly by rephasing and nonrephasing spectra respectively, with maxima at ν1 ∼ 15060 cm−1 + ν2. Inspection of the trace of the diagonal peak at ν1 = ν3 = 15060 cm−1 shown in Figure 4b (top) demonstrates that the nodal structure is largely induced by phase cancellation when the rephasing and nonrephasing signals are added. This observation has been briefly highlighted in earlier experimental and theoretical 2DES work,31,57 but here the oscillation maps clearly display the appearance of the node in the full twodimensional map. D. Geometry Change of Methylene Blue. These precise vibronic assignments now enable us to evaluate the geometry change of MB initiated by photoexcitation. The largest amplitude coherences were affiliated with distortion of the central sulfur/nitrogen containing ring, suggesting that the largest displacement between potential energy surfaces is along those coordinates. DFT calculations predict the S 0 −S 1 transition to be nearly exclusively HOMO → LUMO, and the molecular orbitals are shown in Figure 7 along with the bond lengths of the optimized S0 and S1 geometries. The molecular orbitals indeed show that the largest change in electron density occurs at the central ring, with increased antibonding character in the excited state along the CS and CN bonds, resulting in an increase of bond lengths of the central ring in S1. This ring expansion is enhanced in PCM calculations perhaps due to the larger dipole moment induced by the solvent field (Supporting Information). The correspondence of the vibrational coherences with the DFT predictions of the geometry change and corresponding

4. CONCLUSIONS The excited-state geometry and Franck−Condon active vibrations of methylene blue (MB) in solution were determined with accuracy by use of coherent spectroscopy in tandem with quantum chemical calculations. Analysis of the 2D oscillation maps in coincidence with Franck−Condon simulations allowed for the assignment of combination bands and overtones in addition to their larger fundamentals, leaving little ambiguity in the nature of the coherences observed for MB. In the broadband transient absorption (BBTA) and 2DES experiments reported here for MB in solution, most of the vibrational coherences are observed on the ground electronic state similarly to resonance Raman experiments in the frequency domain. The Fourier transform spectra of the oscillations sampled in BBTA allowed for a direct comparison with the expectedly active vibrations, their relative Franck−Condon factors, and nuclear displacements. Remarkably, the integrated FT spectrum of MB matched well with the DFT FC simulation based on direct vibronic transitions. This was further validated by calculation of the integrated, oscillatory nonlinear signals using only the vibrational overlap integrals. This agreement permitted accurate vibronic assignments to the vibrational coherences activated in the time-domain experiment. All of the active vibrational modes were found to be a1 symmetry, and the dominant contributions to the FT spectra were isolated to five vibrational modes. All of those active modes involve motion of the central sulfur/nitrogen containing ring with some H



The Journal of Physical Chemistry A incorporating CN(CH3)2 motion, immediately yielding insight as to the expected change in geometry in S1. Indeed, DFT geometry optimizations verify this geometry change, with the S1 state showing increased C−S and C−N bond lengths due to increased antibonding character largely localized on the central ring. 2DES and 2D oscillation maps provided a second probe of the coherences present in MB, permitting an avenue by which to spread out the various Feynman pathways presumed to be active for detailed evaluation. By immediate inspection of the oscillation maps, it was found that the fundamental coherences were primarily occurring on the ground state, and the 2D signature of the overtone coherence was found to be distinctly different from that expected for fundamentals. The qualitative agreement between DFT predictions and the integrated FT spectrum of MB promoted the use of the generated FC factors in modeling the amplitude of individual coherent Feynman pathways present in 2DES spectra. By employing a timeindependent model based solely on vibronic overlap integrals, we modeled the oscillation maps, and reasonable agreement was found with experiment. In particular, such an approach is useful in determining where the largest amplitude contributions are expected in different regimes of nuclear displacement, and for higher coherent excitations (combination bands, overtones, etc.). It is surmised that a model incorporating pulse effects, such as bandwidth considerations, would capture some subtleties apparent in the experimental spectra that were not captured by the current model. Vibrational coherence is a highly useful probe in multichromophoric systems such as photosynthetic complexes, where the vast degrees of freedom are reduced to the few FC-active coordinates affected by excitation. Proper characterization of these active vibrations and pigment geometry changes is necessary to connect vibronic coupling mechanisms responsible for long-lived electronic coherence signatures to structural models of the protein. Such insights are vital to lightharvesting design principles, and it is possible that the form of the vibration is equally as important as the frequency/ resonance criterion between donor and acceptor. This idea begs the question of “built-in” vibronic interactions and/or energy level matching mechanisms imprinted on the pigment geometry change itself to promote efficient, and perhaps directed energy transfer.40 The analysis given here provides a benchmark for beginning to explore such vibronic interactions in these complex systems, and what effects these interactions have on energy transfer dynamics.

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ACKNOWLEDGMENTS

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REFERENCES

The authors acknowledge support for this work by the Natural Sciences and Engineering Research Council of Canada John C. Polanyi Award, the Air Force Office of Scientific Research (FA9550-13-1-0005), and Princeton University. D.G.O. and C.C.J. acknowledge support from the Natural Sciences and Engineering Research Council of Canada. J.C.D. thanks R. D. Pensack and Y. Song for many insightful discussions.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b06126. The TG-FROG map of the NOPA pulse, an extended set of 2DES spectra for MB, double-sided Feynman diagrams for fundamentals, combination bands, and overtone coherences, details on calculations of integrated BBTA FT amplitudes, and polarizable continuum model (PCM) computational results (PDF)

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest. I


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