Pyrene, a Test Case for Deep-Ultraviolet Molecular Photophysics.

We determined the complete relaxation dynamics of pyrene in ethanol from the second bright state, employing experimental and theoretical broadband heterodyne detected transient grating and two-dimensional photon echo (2DPE) spectroscopy, using pulses with duration of 6 fs and covering a spectral range spanning from 250 to 300 nm. Multiple lifetimes are assigned to conical intersections through a cascade of electronic states, eventually leading to a rapid population of the lowest long-living excited state and subsequent slow vibrational cooling. The lineshapes in the 2DPE spectra indicate that the efficiency of the population transfer depends on the kinetic energy deposited into modes required to reach a sloped conical intersection, which mediates the decay to the lowest electronic state. The presented experimental-theoretical protocol paves the way for studies on deep-ultraviolet-absorbing biochromophores ubiquitous in genomic and proteic systems.

Insight into photoactivated biological functions requires in-depth knowledge of rapid molecular processes. This can be achieved through dynamically resolved spectroscopies that recently became feasible in the deep ultraviolet (UV) below 300 nm.[1−5] Because of enormous challenges in generating broadband laser pulses, two-dimensional photon echo (2DPE) and conventional transient absorption (TA) and transient grating (TG) experiments in the deep-UV are conducted in a one-color fashion with small bandwidth excitation pulses, limiting temporal resolution and informative value, and consequently the informative value of ultrafast processes on the subpicosecond time scale is limited by the temporal resolution.

Studies that combine state-of-the-art electronic structure computations with nonlinear time-resolved spectroscopy techniques and explicitly incorporate excited state absorption (ESA) features from first-principles have successful simulated broadband-probe spectra in the far-IR to near-UV range.[6−13] Simulations of ESA in the deep-UV are challenging because of the high density of states, making imperative the development of a solid theoretical base on simpler molecules.

The objective of this work is pushing the present spectroscopic experimental and theoretical limits. This is done by applying PE, TA, and TG spectroscopy to pyrene, a widely used molecule owing to its interesting photophysical properties[14−20] with such a remarkably long fluorescence and high fluorescence yields. Its well-separated absorption bands with clear Franck–Condon (FC) progressions in the near-UV (lowest bright state at 320 nm) and in the deep-UV (second bright state at 280 nm) make it an excellent model for assessing spectroscopic techniques. The first two-dimensional (2D) electronic broadband spectroscopy in the near UV was performed on pyrene.[21,22]

Technical challenges have limited the study of the de-excitation dynamics from the second bright state. Our experimental and simulation techniques allow for filling the gap. State-of-the-art electronic structure computations (multiconfiguration second-order perturbation theory based on restricted active space, RASPT2)[23,24] uncover the deactivation involving ultrafast nonadiabatic transitions mediated by conical intersections (CI). The mechanism is scrutinized by high temporal resolution TA and PE conducted between 240 and 300 nm with ultrashort pulses (6 fs fwhm duration)[25] combined with first-principles spectroscopy simulations.

Figure presents the deep UV linear absorption (LA) experimental and simulated spectra of pyrene in ethanol, resolving the absorption band of the second bright state labeled 2B3u (second state in the B3u irreducible representation of D2h symmetry). A well-resolved vibronic progression with peaks at 272 nm (36.7 kcm–1), 262 nm (38.2 kcm–1), and 252 nm (39.7 kcm–1) is observed.[26] Normal mode analysis reveals that the vibronic structure of the S0 → 2B3u transition is attributable mainly to the 1456 cm–1 symmetric carbon–carbon stretching. Low-frequency breathing vibrations at 405 and 592 cm–1 are responsible for the shoulder of the 272 nm band. Other symmetric carbon–carbon stretch vibrations form the Raman-active modes (Table and Figure S7), which agree well with earlier Raman data.[26,27] The solvent has little effect on the ES dynamics, as different solvents and environments—ethanol, polycrystalline powder acetonitrile,[26] benzene[27]—provide similar spectra, in agreement with the gas-phase computations. The theoretical 1336 cm–1 band is the only missing vibration in the experimental Raman spectra; however, depolarization ratios suggest its existence.[26] The 1242 cm–1 band, which is the most intense band in nonresonance Raman, loses intensity in resonance Raman in favor of the 1408 cm–1 band, as well as the low-frequency bands at 408 and 592 cm–1 with an additional band at 574 cm–1 appearing only in resonance Raman. The 1597 cm–1 mode, i.e., the characteristic nonfully symmetric vibration of pyrene observed experimentally, is the only intense mode not appearing in the simulation.[26] However, it loses intensity upon exciting the 2B3u, indicating its smaller importance for dynamics.

Figure 1

Experimental (blue line) and simulated (red line and stick spectrum) absorption spectra of pyrene, overlapped with the experimental laser spectrum (green dashed line).

Table 1

Frequencies (ω, cm–1) and Huang–Rhys (HR) Factors of the Fundamental Raman Modes in Our Simulated Gradient Projection (grad. proj.) Approach and Adiabatic Molecular Dynamicsa

	simulation				experiment
	grad. proj.		mol. dynamics		HTG		Raman		res. Raman
	ω	HR	ω	HR	ω	int	ω	int	ω	int	type
v1	405	0.15	425	0.19	390		407	0.33	408	0.40	breathing
v2	592	0.26	546/607	0.240/0.157	597	0.28	592	0.26	574/592	0.50	breathing
v3					888
v4	1079	0.12	1093	0.06	1073		1066	0.18	1067	0.10	C–C stretch
v5	1271	0.10	1275	0.10	1238	0.52	1241	1.00	1242	0.45	C–C stretch
v6	1347	0.03	1335	0.07							C–C stretch
v7	1456	0.16	1457	0.20	1413	1.00	1406	0.86	1408	1.00	C–C stretch
v8	1574	0.06	1578	0.06			1550	0.09	1553	0.10	C–C stretch
v9					1592		1594	0.64	1597	0.30
v10	1668	0.05	1639	0.03	1626		1628	0.27	1632	0.30	C–C stretch
v11					2942	0.29					C–H stretch

See section 3.2.1 in the Supporting Information. Frequencies (ω, cm–1) and intensity (int) of the vibrational modes obtained in ethanol by heterodyne transient grating (HTG, this work), from crystalline powder by Raman spectroscopy,[27] and in acetonitrile by resonance Raman.[26]

The 2B3u absorption band is similar to that of the lowest bright state which absorbs around 320 nm, labeled 1B2u.[26] Resonance Raman spectroscopy of the 1B2u,[26] as well as previously reported vibrationally resolved LA simulations,[28] reveal that the same high-frequency (1456 cm–1) and low-frequency (405 cm–1) modes are responsible for the 1B2u band vibrational progression and broadening.

Figure shows TA spectra up to 200 ps. Because of the extremely strong contribution of the nonlinear solvent response around zero delay and undesirable scattering effects of the solvent in the UV,[29] the early time dynamics cannot be resolved. We observe an intense positive band at 272 nm associated with the bleach of the fundamental, together with two negative ESA signatures at 255 and 265 nm. A weak bleaching at 261 nm matching the first overtone of the 2B3u state in the LA spectrum is also present in the experimental TA spectrum, although very faintly because of overlap with the ESA.

Figure 2

Experimental TA kinetics of pyrene up to 200 ps (a, 500 fs step) and first 2.5 ps of a fine-resolution measurement (b, 20 fs step) measured in ethanol. (c) Simulated TA spectrum up to 1 ps. Colors are in differential transmission dT (counts/a.u.).

Experimentally, the positive signal at 272 nm loses intensity, while the negative band at 255 nm gains in intensity. The decay associated spectra (DAS) were extracted by means of a global analysis, obtaining four lifetimes: 0.75 ps, 8 ps, 24 ps, and an infinitely long lifetime (Figure ).

Figure 3

Decay associated spectra from a short time range TA spectrum (top, fitting the TA spectrum from Figure b) and a long time range TA spectrum where the longest time constant was fixed to infinity (bottom, fitting the TA spectrum from Figure a). Vertical axes are in differential transmission dT (counts/a.u.).

The 0.75 ps lifetime is associated with the initial increase of the ESA band intensity, and it is accompanied by the decrease of the positive 272 nm signal, followed by vibrational cooling with an 8 ps lifetime which blue-shifts the maxima of the contributions. The decreasing ESA intensity at later times can be fitted with another exponential curve of 24 ps. The infinitely long lifetime can be representative of either ESA decay or ground-state bleaching (GSB) recovery, a S1 bottleneck trap, or the sum of multiple phenomena.

The high temporal resolution of our experiments allows the observation of intensity beating in the TA and in the HTG spectra (Figure S20). The Fourier transform of the residuals provides the frequencies responsible for the oscillatory features (Figures S21 and S22; the most intense contributions are provided in Table ). The extracted frequencies match those from the normal-mode analysis of the 2B3u state.[26,27] Because of the overlap of bleach and photoinduced absorption in the probed window, the assignment of the Raman modes is not unambiguous and we do not exclude the possibility of resolving vibrational coherences in the ground state. However, we note that the 2942 and 888 cm–1 modes are absent in Raman experiments, the former being associated only with the 255 nm ESA.

The deactivation mechanism was followed through energy minimization techniques (Figure ). The FC point exhibits two dark electronic states near the bright 2B3u state, denoted as 1B1g and 2B1g (Table S4). The near degeneracy allows ultrafast nonadiabatic population transfer to 1B1g. Because of missing stimulated emission (SE) signatures in the TA spectrum, we assume that 2B3u decays to 1B1g before probing is initiated (i.e., before 200 fs). This assumption has been recently confirmed experimentally in a two-color (deep-UV pump visible-probe) TA experiment.[22]

Figure 4

Top: schematic representation of the main decay paths after excitation into the bright 2B3u state. Energies are in electronvolts with respect to the ground state. Orange, green, and red indicate the potential energy surfaces of states 2B3u, 1B1g, and 1B3u, respectively. Bottom: characteristic bond lengths (shown in Å) along the nonadiabatic deactivation path to the lowest dark state 1B3u. Shown are only symmetry-nonequivalent atoms. Inset: mirror planes and rotation axes of pyrene in D2 symmetry.

According to our computations, the lowest bright state 1B2u is not involved in the immediate relaxation after 2B3u excitation. A nearly constant 0.5 eV 2B3u/1B2u gap is observed in both static and dynamic calculations on the 2B3u state, rationalized by the identical vibrational modes (1456 and 405 cm–1) characterizing both states (sec. 3.2.3 of the Supporting Information).

The 1B1g state exhibits a considerable energetic stabilization with a minimum 0.4 eV below the 2B3u minimum. Molecular orbital analysis at the 1B1g minimum demonstrates that geometrical deformations leading toward a CI with the state 1B2u destabilize more substantially the dark state 1B3u, so that CI optimization encounters a three-state CI(1B1g/1B3u/1B2u) about 0.08 eV above the 1B1g minimum. D2h symmetry is reduced at the CI to C2v. This is realized along with a 350 cm–1 in-plane bending mode of 1B2u symmetry, which creates a coupling between the 1B1g and 1B3u states. In fact, while the gradient difference vector at the CI is of Ag symmetry (having large overlap with the 1668 cm–1 mode), the derivative coupling vector exhibits a large overlap with the 350 cm–1 mode of 1B2u symmetry. These observations indicate that at the three-state CI the wave packet populates the 1B3u state. The nonadiabatic transfer is facilitated by the same set of 12 modes of B2u symmetry, enabling the 2B3u →1B1g decay. We assign the 0.75 ps lifetime to the decay through the CI. The relatively long excited-state lifetime with respect to the sub-100 fs lifetimes of the bright states 1B2u and 2B3u[30,31] could be rationalized by the time required to distribute energy in the decay-determining 1668 cm–1 mode, which has a small Huang–Rhys factor of 0.05 in the 2B3u state, as required in order to overcome the 0.1 eV barrier to reach the CI. Static fluorescence spectra collected after 260 nm excitation (Figure ) show a small shoulder between 350 and 368 nm associated with 1B2u emission.[32] Nevertheless, the short lifetime of the 1B2u state strongly suggests that no significant population could accumulate that could be the source of a measurable spectroscopic signal from 1B2u.[30,31]

Figure 5

Static fluorescence emission spectrum of pyrene in ethanol. Excitation wavelength, 260 nm; excitation slid, 20 mm; emission slid, 1.5 mm. Average time of acquisition for each wavelength is 5 s.

Upon transfer to the 1B3u state, pyrene encounters a steep potential toward equilibrium. A weak feature between 300 and 350 nm in the static fluorescence spectrum is tentatively assigned to the vibrational dynamics in the hot 1B3u state. According to simulations, half of the potential energy is stored in two modes: the 350 cm–1 in-plane bending (B2u symmetry) and a 1668 cm–1 carbon–carbon stretching (Ag symmetry, Figure S8). In support of our mechanism, we draw the reader’s attention to a recently reported two-color (deep-UV pump visible-probe) TA experiment by Borrego-Varillas et al. Therein, the authors report a quantum beat with a frequency of 390 cm–1 shown unambiguously to arise from the wavepacket on S1 after pumping the 2B3u state at 270 nm.[22] The quantum beat can be attributed to dynamics along a symmetric mode (a 410 cm–1 mode has been observed in Raman experiments, see Table ), which unexpectedly gains in intensity after decay to S1 in contrast to other Raman modes (e.g., 590 cm–1, not observed by Borrego-Varillas et al.). We note however that the frequency of 390 cm–1 matches closely that of the 350 cm–1 in-plane bending mode, predicted by our calculations to dominate the vibrational dynamics on the S1 state after passage through the three-state CI. The temporal resolution of the experiment of Borrego-Varillas et al. (∼16 fs) does not allow the detection of the other dominant mode (1668 cm–1) predicted by our model. Studies on azobenzene and rhodopsin have shown that large amounts of energy into a few modes could induce intensity beats in the TA lasting for picoseconds.[8,12] Thus, the 8 and 24 ps lifetimes can be associated with vibrational cooling of photoactive vibrational modes.

Following the proposed mechanism, we simulated the TA spectrum up to 1 ps. After the pump pulse, we observe SE out of 2B3u, which enhances the signal intensity in the GSB region (270–275 nm) and reaches down to 290 nm. The 2B3u state shows a weak ESA band around 250–260 nm which partially cancels the second vibronic band at 262 nm. Our calculations predict further characteristic fingerprints around 360 and 540 nm, observed recently experimentally.[22] The 2B3u fingerprint signals decay on a 100 fs time scale. (A phenomenological 100 fs lifetime was adopted for the 2B3u→ 1B1g population transfer in agreement with recent findings by Borrego-Varillas et al.[22]) At later times new signatures appear: a strong ESA between 250 and 260 nm (labeled PA1) and a weaker ESA around 280 nm (labeled PA2). Both peaks are fingerprints of the 1B3u state populated with the 0.75 ps lifetime. The 1B3u state exhibits further characteristic ESA in the near-UV at 370 nm and in the visible at 475 nm,[9,21,22] potentially accessible through a two-color pump–probe setup. PA2 overlaps strongly with the GSB and is responsible for the intensity beat pattern in the 270 nm region. Simulated TA shows intensity beating due to the vibrational dynamics in the pair of 1B3u-specific modes 350 and 1668 cm–1. The experimental TA also shows an intensity beat pattern, with weak contributions from the pair of 1B3u-specific modes. However, the 1413, 1238, and 597 cm–1 modes dominate the modulation of the ESA signatures, previously assigned to the 2B3u state. A progression of 1450 cm–1 is visible at 300–350 nm in the static fluorescence spectrum, indicating memory conservation upon departure from the 2B3u state, a mechanism not implemented in our simulations, leading to overemphasizing 1B3u-specific modes. The 1B1g state intermediately populated in the relaxation has no characteristic ESA in the probed spectral window, but our calculations show that it exhibits absorption features in the visible which could be addressed to scrutinize the proposed model. Two close-lying states absorbing 3.6–3.8 eV above the S3 equilibrium would lead to an intense signal in the transient spectra around 330 nm. Thus, we propose a two-color, deep-UV pump near-UV probe, experiment with pulses centered at 290 and 330 nm, respectively, for validating the 1B1g involvement.

Figure shows experimental and simulated 2DPE spectra at a 1000 fs waiting time. Spectra at further waiting times are provided in section 4.1 (simulation) and section 11 (experiment) of the Supporting Information. A checkerboard pattern of positive and negative contributions along two stripes at ωτ = 36.7 kcm–1 and ωτ = 38.2 kcm–1 corresponding respectively to the fundamental and the first overtone of the 2B3u band is shown. Diagonal bleach contributions (positive, red color) are detected at (36.7, 36.6) kcm–1 and (38.0, 38.2) kcm–1 in the experiment, while off-diagonal bleach contributions are encountered at (38.0, 36.7) kcm–1 (intense, above diagonal) and at (37.0, 38.2) kcm–1 (weak, below diagonal). The pattern arises from strong coupling of the electronic transition to the high-frequency carbon–carbon stretching. The signals are characterized by an oscillatory intensity. Theoretical simulations reproduce the experimental bleach pattern and its dynamics, allowing for the separation of individual contributions to the PE. The intensity oscillations (period of approximately 22 fs) are associated with the dynamics of an interstate coherence created by the pump–pulse pair between the fundamental and first overtone in the potential of the carbon–carbon stretch. At early times (first 100 fs), for which only simulations are available, the spectra resolve additional peaks below 36.0 kcm–1 resulting from the strong SE out of the 2B3u state (sec. 4.2 in the Supporting Information). Their absence in the experimental PE spectra supports that 2B3u decays on a sub-200 fs time scale. There are several 2B3u fingerprints contributing to the ESA at early times, but their transition dipole moments are orthogonal to the dipole moment of the GS-2B3u transition, consequently appearing weak when all pulses have identical polarizations (Figure S11). Instead, a cross-polarized pump–probe pair of pulses would enhance the intensity ESA signatures (Figure S12).

Figure 6

Experimental (a) and simulated (b) 2D maps of pyrene at waiting time of 1000 fs. Experimental (c) and simulated (d) intensity fluctuations of selected peaks in the 2DPE. Photoinduced absorption signal PA1, which gives rise to peak 2 in panel a appears red-shifted below the diagonal bleach signal in the simulated spectrum (b). A Fourier transform of the oscillations in panel c is shown in the Supporting Information (Figure S27).

The bleach pattern is typical for vibrational coherences in a coupled two-level system.[33] Further negative contributions appear in the PE spectrum at approximately ωt = 36.0 kcm–1, ωt = 37.5 kcm–1, and ωt = 39 kcm–1, associated with the mentioned ESA signatures PA1 and PA2 observed also in the TA spectrum. PA1 spreads from ωt = 35.5 to ωt = 37.5 kcm–1 and falls under the bleach of the fundamental. PA2 exhibits a vibrational progression from ωt = 37.0 kcm–1 to ωt = 40.0 kcm–1 with absorptive and dispersive features associated with the dynamics in the 1660 cm–1 mode connecting the CI with the 1B3u minimum. It covers completely the bleach of the second overtone. Both PA1 and PA2 lead to the ESA feature at ωt = 37.5 kcm–1 which interferes with the bleach of the first overtone (see sec. 4.3 in the Supporting Information). The bleach–ESA interference, although complicating the analysis of the spectral dynamics, is essential for interpreting the spectra.

The experimental 2D spectrum shows a very intense ESA contribution along the trace of the overtone at (ωτ, ωt) = (38.2 kcm–1, 39.0 kcm–1) in disagreement with theory. This feature is observable only with broad-band UV-ES 2D spectroscopy. Tentatively, this pronounced ESA intensity could be assigned to the weak bleach contribution at the “overtone” pump frequency (whereas it is stronger at the “fundamental” pump frequency, canceling the ESA more effectively). This interpretation does not hold for long delay times when the system has relaxed in the lowest S1 vibrational level and the probe signal is no longer correlated with the pump frequency. Consequently, at longer delay times, the signal at a certain probe frequency ωt should be understood as a convolution of the electronic probe spectrum of the lowest vibrational level with the pump (i.e., linear absorption) spectrum. The most intense band in the LA spectrum is that of the “fundamental” frequency and so should be signals along the “fundamental” pump frequency in the 2DES spectrum at longer delay times. However, the intense ESA along the “overtone” pump frequency survives for tens of ps. A more plausible interpretation of this long-lasting feature is that the population transfer to 1B3u is more efficient when the overtone of the 2B3u band is excited, because of additional kinetic energy in the carbon–carbon stretch at disposal for reaching the sloped CI(1B1g/1B3u/1B2u), whereas part of the population excited in the fundamental remains trapped in the 1B1g state.

A combination of experimental and theoretical advances has been applied for the first time to record and interpret the pyrene time-resolved broadband spectroscopy in the deep-UV (250–300 nm). On the basis of TA, HTG, and 2D PE experiments and state-of-the-art electronic-structure computations, we propose a model for the deactivation following excitation of the second bright 2B3u state. Computations reveal an ultrafast sub-200 fs depopulation of the bright state into a dark state 1B1g, which has neither emissive nor absorptive features in the probed spectral region. The emergence of a prominent ESA band at 250 nm in the TA and HTG spectra with a build-up time of 0.75 ps is shown to match the population time of the lowest dark state 1B3u that acts as a bottleneck and is accessed via a sloped three-state conical intersection. The process exhibits characteristic ESA signatures, reproduced in the simulations.

While the first bright 1B2u state decays within ∼100 fs,[30,31] the second bright state 2B3u lives 1 order of magnitude longer in the higher-lying ES manifold. Long-lasting intensity oscillations with a dampening time of tens of picoseconds indicate weak coupling with the environment, in agreement with the picosecond-lasting lifetimes, and associated with vibrational cooling on the lowest trapping 1B3u state.

The unprecedented high temporal resolution of our setup allowed for the identification of high-frequency carbon–carbon stretch vibrations as the modes responsible for the vibrational progression in the LA, the intensity beats in the TA, and the checkerboard pattern of the 2DPE spectra. Bleach–ESA signal interference leads to coherent oscillations with a complex pattern, making simulations essential to disentangle individual contributions. A prominent feature present in the 2DPE spectra is an intense ESA contribution along the trace of the 2B3u overtone. This suggests that the efficiency of the population transfer to the 1B3u state is enhanced when more kinetic energy is deposited into the driving modes in agreement with the sloped nature of the conical intersection found along the decay path.

Experiments to further scrutinize the proposed mechanism have been proposed. The joint experimental–theoretical protocol developed and applied here sets the stage for similar studies on the deep-UV-absorbing biorelevant chromophores found in DNA and proteins.