Nonadiabatic interactions that occur between adiabatic potential energy surfaces (PESs) of different electronic states are not only ubiquitous, but also essential in many photochemical and pho-tobiological processes such as photosynthesis, photoisomerization in vision and the photostability of deoxyribonucleic acid (DNA)1. The PES crossing between valence and Rydberg states is one of these most fundamental nonadiabatic interactions. From the physical viewpoint, such a strong nonadiabatic coupling represents an interesting example of a situation in which the Born-Oppenheimer approximation is no more valid for the description of coupling between electronic and nuclear motions.
In a molecule, larger principal quantum number (n) and orbital angular momentum (l) reduce the probability of penetrating a Rydberg electron into the molecular ion core, resulting in a longer lifetime of the Rydberg state. The lifetimes of low (n=3-5) Rydberg states of aromatic molecules are roughly recognized to be slower (i.e., by 1-2 orders of magnitude) than those of the valence electronic excitations in the same energy domain2. The fact that molecular valence and Rydberg states are much more likely to mix in the vacuum-ultraviolet (VUV) than they are in the ultraviolet immediately implies that the lifetimes of low-lying 3s and 3p Rydberg states are remarkably shortened as a result of a larger probability of coupling of a Rydberg electron with valence electrons3, 4. The complicated spectral features and extremely short lifetimes of these mixed valence and Rydberg states pose great challenges in the direct real time observation and characterization of such nonadiabatic couplings between low-lying Rydberg and valence states in polyatomic molecules.
Femtosecond time-resolved photoelectron imaging (TR-PEI) is useful in probing these nonadiabatic interactions on real time in polyatomic molecules. TR-PEI could measure both the kinetic energy and angular distribution of the photoelectrons simultaneously as well as their correlation as a function of time and have been successfully applied in recent years to a variety of molecular systems5, suggestive of an ideal fingerprint sensor for investigating ultrafast nonadiabatic interactions involving changes in electronic characters with nuclear motions in complex molecules.
2-Methyl furan, has served as excellent prototype system for studying nonadiabatic dynamics involving the nature of Rydbergvalence interactions. Compared with the well-documented furan molecule6-9, the prominent differences are that the substitution effect of an H by a methyl group on the neighboring position of oxygen in the furan ring leads to not only a small redshift of the first VUV absorption spectrum but also the presence of several extra Rydberg transitions that are forbidden in furan. The first broad and diffuse VUV absorption band of 2-methyl furan in the energy range 5.00-9.91 eV arises from the mixing of electronic transitions from the ground state S0 to the Rydberg S1[1A′′(π3s)],
1A′(π3px), 1A′′(π3py) and 1A′′(π3pz) states and valence 1A′(ππ*) state. These Rydberg transitions that appear together with valence transitions particularly complicate the vibronic structures in the first VUV absorption spectrum of 2-methyl furan, suggesting that much more complex nonadiabatic interactions might exist in 2-methyl furan. Although extensive experimental10-20 and theoretical12, 14, 20-22 studies have been performed on assignments and characterizations of the first VUV absorption spectrum of 2-methyl furan, ultrafast observables have not yet been explored experimentally.
In the present work, we investigate the nonadiabatic dynamics of 2-methyl furan as an example of a system with strong Rydbergvalence interactions by femtosecond time-resolved photoelectron imaging and femtosecond time-resolved mass spectroscopy. The Rydberg and valence states of 2-methyl furan in the red edge of its first VUV band are optically excited by two-photon absorption at 400 nm, their dynamical evolution is then interrogated by twophoton ionization at 800 nm. The electronic relaxation processes have been directly observed in real-time by the time-dependences of the photoelectron spectra. And the coupled Rydberg and valence components are also successfully extracted and discussed.
The experimental setup employed in the present work has been described else where23. The liquid sample of 2-methyl furan (Aladdin, 98%), seeded in helium buffer gas at a background pressure of 2 × 1.01325 × 105 Pa, is expanded through a pulsed valve to generate a pulsed molecular beam. The beam is skimmed and introduced into the ionization chamber where it is intersected perpendicularly with the linear polarized pump and probe laser beams. The generated photoelectrons were extracted and accelerated by the electrostatic immersion lens and then projected onto a two-dimensional (2D) detector. Each image is accumulated over 40000 laser shots. Three-dimensional (3D) distribution reconstructions are performed by the basis-set expansion (BASEX) forward convolution method24. The details of our femtosencond laser system have been described elsewhere25. Briefly, the femtosecond laser seed pulse is generated by a self-mode-lock Ti: sapphire oscillator pumped by a CW second harmonic of an Nd: YVO4 laser, and then amplified by an Nd:YLF pumped regenerative amplifier to generate a 1 kHz pulse train centered at~800 nm of 45 fs pulse width with maximum energy of~1 mJ∙pulse-1. The second harmonic pulse was generated in a 0.5 mm thick BBO (BaB2O4) crystal and the central wavelength was spectroscopically measured to be 400 nm with a bandwidth of~6 nm. In our pumpprobe experiments, the pump pulse (400 nm) energy is attenuated to be less than 1 μJ∙pulse-1 and the optimal probe pulse (800 nm) energy is controlled to be around 30 μJ∙pulse-1. The pump and probe beams are recombined collinearly at a dichroic mirror prior to being softly focused on the molecular beam with a spherical plano-convex lens (focal length (f)=250 mm).
As shown in Fig. 1(a), a typical time of flight (TOF) mass spectrum of 2-methyl furan was recorded with the two-photon 400 nm pump and two-photon 800 nm probe at zero delay time. 2-methyl furan parent ion peak of C5H6O+ is clearly observed, and a minor fragment ion peak of C4H3O+ becomes visible. Normally, the time-resolved photoelectron imaging experiments are required to be conducted with background signals low enough to ensure minimum ionization from either beam operating independently. Where noted, as mentioned above, soft focus is adopted in order to avoid space charge effect and strong field effects. Consequently, nearly no background signals are generated from either beam independently. The area ratio of C5H6O+ to C4H3O+ is 241 : 1 and hence the contribution to the total photoelectron signal from the fragment ion of C4H3O+ could be safely neglected.
In our femtosecond pump-probe scheme, all electronic transitions from the ground electronic state of 2-methyl furan are optically one-photon or two-photon dipole allowed as a result of the reduction of the molecular symetry from C2v in the case of furan6, 7 to Cs in 2-methyl furan. The origins of the singlet S1[1A″(π3s)] and 1A′(ππ*) states have been documented to be at 5.47 and 5.95 eV, respectively19. The low-lying π-3p Rydberg series of 1A′(π3px), 1A″(π3py) and 1A″(π3pz) have been recognised at 5.73, 6.02, 6.06 eV, respectively19. As indicated by the notation, the 1A′(ππ*) state is π-π* valence-type excitation, whereas the S1 state and π-3p Rydberg series are of Rydberg-type characters. For the two-photon excitation scheme used in the present work, the 2-methyl furan molecule is simultaneously pumped into the S1[1A″
(π3s)], 1A′(ππ*) states and the low-lying π-3p Rydberg series from its ground state S0(1A′) by two-photon absorption at 400 nm when taking the broad excitation bandwidth (~6 nm) into account. The virtual states involved in the two-photon transition could be A or A″ states according to the symmetry of the prepared electronic state. As an example, the possible two-photon transition matrix elements for the S1[1A″(π3s)] state could be < A|x|A > < A′|z|A″ > or < A|y|A > < A|z|A″ > with the definition of yz in the plane of the 2-methyl furan molecule if a A′ state acts as a virtual state. In this case, the two-photon transition is induced by two-consecutive dipole transitions with crossed x and z directions or y and z directions. In addition, it is noteworthy that there is no absorbance in the visible region near 400 nm. Thus the one-photon 400 nm excitation process does not occur.
The photoion yields are recorded as a function of the delay time between the pump and probe pulses, and these provide a measure of the lifetime of the excited states. The time-dependent ion signal of C5H6O+ is represented in Fig. 1(b). The signal rapidly decays within the first 200 fs. The decay profile is found to be well reproduced only by a single exponential function convoluted with a Gaussian that describes the instrument response function. In this case, a lifetime of 50 fs is obtained and the fitting error is reasonably within±2 fs. The unsatisfactory fittings with two or even more exponential functions to discern the lifetimes of the prepared excited states are likely due to the extremely short lifetimes of the prepared excited states which are largely restricted by our instrument response function of 160 fs. Thus the lifetime of 50 fs obtained in our experiment is the average lifetime of the S1[1A″(π3s)], 1A′(ππ*) states and the low-lying π-3p Rydberg series.
Fig. 2(a) shows typical photoelectron images measured at various delay time with the two-photon 400 nm pump and twophoton 800 nm probe. Each image corresponds to a slice through the 3D photoelectron scattering distributions observed at the quoted time delay. The linear polarizations of the pump and probe lasers are both vertical in the plane of the figure. The rings (bands) with different radii in the image stand for photoelectrons with different kinetic energy components. In Fig. 2(b), we show the timedependent photoelectron kinetic energy (PKE) distributions (PKEDs) extracted from the corresponding images shown in Fig. 2
(a). The photoelectron spectra have each been normalized to the total photoelectron counts. Each PKED is characterized by several identifiable peaks which are congested in the continuous energy region of 0.05-1.00 eV. Four featured peaks with the central energies of 0.13, 0.49, 0.68 and 0.88 eV are identified in the PKEDs. The adiabatic ionization potential (AIP) of 2-methyl furan is 8.38 eV19, therefore two photons of 800 nm [(AIP-2 × E400)/E800=((8.38-2 × 3.1)/1.55)-2] are required to ionize the excited states. Consequently, the available energy [=hνpump + hνprobe-AIP] in the continuum state can be determined to be 0.92 eV for the twophoton 800 nm ionization to the zero vibrational level of the cationic ground state, and this is also indicated by the arrow as D0 in Fig. 2(a).
According to the previous spectroscopic studies10-22, the four featured peaks with the central energies of 0.13, 0.49, 0.68 and 0.88 eV are respectively assigned to be ionized from the S1[1A″(π3s)], 1A′(π3px), 1A″(π3py) and 1A″(π3pz) Rydberg states. More interestingly, ionization from the 1A′(ππ*) state is also expected to yield a photoelectron band with the energy around 0.67 eV, which overlaps with the above featured peaks. As an added support for our assignments, the energies and quantum defects of Rydberg states can be obtained by26
where T(Rydberg) and hνpr is the energy of the Rydberg states and the probe photon, respectively, IP is the ionization potential, n is the principal quantum number, δ is the quantum defect, and R is the Rydberg constant, 13.606 eV. Hence, the quantum defect values for the delay times of 0 fs are respectively calculated to be 0.86, 0.72, 0.63 and 0.52 for the four featured peaks with the central energies of 0.13, 0.49, 0.68 and 0.88 eV with the assumption of principal quantum numbers n=3. The quantum defect is a constant that depends on the symmetry and types of the Rydberg orbital. For molecules composed of second-row atoms, typical δ values are 0.9-1.2 for s orbital, while the δ values of p orbital are about 0.3-0.5, and δ values of p orbital are about 0 27. Giuliani et al.19 obtained the quantum defect values of 0.84, 0.73, 0.60 and 0.58 for the S1[1A″ (π3s)], 1A′ (π3px), 1A″ (π3py) and 1A″(π3pz) Rydberg states, respectively, and found that the quantum defect values for 3p Rydberg orbitals seemed to be a little bit high and explained this could be due to the Rydberg-valence interaction. This interaction could be more important in this molecule than in furan since the 3p state is now much closer in energy with the valence 1A(ππ*). Therefore, quantum defect values further suggest that the assignments of the four featured peaks seem consistent with the previous work.19
Inspection of the PKEDs of 2-methyl furan in Fig. 2(b), the intensities of the PKEDs rapidly decrease with increasing delay time, which is coincident with the short lifetime of 50 fs for the parent ions. Upon a more detailed inspection of the time-dependent behavior between 0 and 39 fs, the intensities of the featured peaks in each PKED monotonously decay in a similar manner. The energy positions of these featured peaks do not change with the delay time, however, the relative changes in the peak intensities among these featured peaks are not apparent. By analogy to the case of furan, similar decay channels could be correlated to these featured states in 2-methyl furan. As discussed above, the S1[1A″(π3s)], 1A′(ππ*) states and the low-lying π-3p Rydberg series of 1A′(π3px), 1A″(π3py) and 1A″(π3pz) states could be simultaneously excited from its ground state S0(1A′) by two-photon absorption at 400 nm. Hence, internal conversions among these featured states are likely to occur.
For a further analysis of the PKEDs associated with the correlated relaxation dynamics of the S1[1A″(π3s)], 1A′(ππ*) states and the low-lying π-3p Rydberg series, we expect to extract the spectral components that independently arise from the ionization of the corresponding S1[1A″(π3s)], 1A′(ππ*) states and the low-lying π-3p Rydberg series. Generally the Levenberg-Marquardt method28 is mostly used to perform non-linear least squares fitting of the PKEDs. The measured PKED at each delay time is fitted by the sum of five Voigt functions and a polynomial. The Voigt function profile (i.e., a convolution of Gaussian and Lorentzian functions) is preferentially selected to reproduce the S1[1A″ (π3s)],
1A′(ππ*), 1A′(π3px), 1A″(π3py) and 1A″(π3pz) component spectra by assuming the component peak centers to be fixed at 0.13, 0.67, 0.49, 0.68 and 0.88 eV, corresponding to the ionization channels from the S1[1A″(π3s)], 1A′(ππ*), 1A′(π3px), 1A″(π3py) and 1A″(π3pz) states. In addition, a polynomial is unavoidably added to match the residual background. As an example, Fig. 3 shows the fitting of PKED at the delay time of 0 fs, and the fitting residue is also given in the bottom panel of Fig. 3. The open circles represent the experimental PKED, and the blue solid line shows the sum of the fitting components which nearly reproduce the experimental PKED. Thus the time-dependent intensities of the five components are easily obtained by integrating the area of each component at different delay time and are shown in Fig. 4. Note that the timedependent intensities of the 3s, 3py and 3pz components are respectively multiplied by a factor of 3, 5 and 2.5 to make them more visibly comparable with those of the 1A′ (ππ*) and 3px components in the same plotting.
As seen in Fig. 3 and Fig. 4, the five components appear simultaneously at the delay time of 0 fs, and the 1A′(ππ*) and 3px components carry much more intensities than those of the other three components, suggesting that the optical transition strengths for the 1A′(ππ*) and 1A′(π3px) states are much larger than those for the S1[1A″(π3s)], 1A″(π3py) and 1A″(π3pz) states. The intensity profiles for the five components indicate that the S1[1A″(π3s)], 1A′(ππ*), 1A′(π3px), 1A″(π3py) and 1A″(π3pz) states decay rapidly within 50 fs upon their excitations, in fair agreement with the lifetime of 50 fs measured for the parent ions. However, each of the intensity profiles could not be well reproduced by only a single exponential decay function. The 3s component seems to decay with two different rates, i.e., a slower rate before 10 fs and a faster rate after 10 fs. This implies that population transfers from other initially excited states to the S1[1A″(π3s)] state might occur within the first 10 fs. A similar situation accounts for the 3px component, decaying with a faster rate before 25 fs and a slower rate after 25 fs. In the case of 3py and 3pz components, it is interesting that the intensity profiles seem to behave inversely. The population transfer between the 1A″(π3py) and 1A″(π3pz) states is likely to occur due to their overlap in energy. More interestingly, the intensity profile for the 1A′ (ππ*) component exhibits more complex decay features. The 1A′(ππ*) component carries the most intensity than those of the other components, and exhibits multiple decay rates. Thus we speculate that the 1A′(ππ*) state might playa key role during the deactivation dynamics and act as the bridge to connect with the neighboring excited states although it could not be clearly visualized as a sharp peak in the PKED. In addition, the 1A′(ππ*) component exhibits a broad distribution, in support of the nature of a valence state. In consideration of the complex decay dynamics among the five components and the insufficient data points, we could not further extract the decay time constants for the five components by fitting each of the intensity profiles with multiple exponential decay and rise functions. Thus, note that discussions of decay time constants in Fig. 4 are qualitative rather than quantitative.
Quantum chemical calculations of the excited states in 2-methyl furan, especially concerning with the conical intersections among the excited states, or dynamics simulations of the excited states, have not been performed yet. By analogy to the case of furan7-9, similar internal conversions among the S1[1A″(π3s)], 1A′(ππ*) states and the low-lying π-3p Rydberg series of 1A′ (π3px), 1A″ (π3py) and 1A″(π3pz) states are likely to dominate in 2-methyl furan. Upon the two-photon excitation at 400 nm, 2-methyl furan molecules are simultaneously pumped from its ground state S0(1A′) to the S1[1A″(π3s)], 1A′(ππ*) states and the low-lying π-3p Rydberg series of 1A′(π3px), 1A″(π3py) and 1A″(π3pz) states. The vibrational energies deposited for the S1[1A″(π3s)], 1A′(ππ*), 1A′(π3px), 1A″(π3py) and 1A″ (π3pz) states are 0.73, 0.25, 0.47, 0.18 and 0.14 eV, respectively. The fact that the valence state (1A′(ππ*)) and the Rydberg states (S1[1A″(π3s)], 1A′(π3px), 1A″(π3py) and 1A″(π3pz)) are very close in energy and overlap with each other is supportive of the speculation for the high complexity of the potential energy surfaces. Therefore, numerous potential energy surface crossings, i.e., conical intersections, probably exist among these excited states. Furthermore, the ultrashort decay time (less than 50 fs) for these excited states implies that conical intersections are more likely to locate in the Franck-Condon region and act as the driving force to accomplish such ultrafast deactivations of these excted states. As discussed above, the 1A′(ππ*) state might play a key role during the deactivation dynamics and intersect with the neighboring excited states. Thus, as shown in Fig. 5, the deactivations of the five excited states might initially continue on their own potential energy surface, and then rapidly internally converts to the neighboring excited states through conical intersections, and finally return to the hot ground state.
A comparison with the nonadiabatic dynamics of furan7-9 and 2-methyl furan shows many similarities. In both molecules, internal conversion takes place on an ultrafast time scale as the main deactivation mechanism. The appearance of conical intersections among the potential energy surfaces effectuates such ultrafast internal conversion processes. On the other hand, due to the strong coupling of the Rydberg states with valence states, the lifetimes of n=3 Rydberg states are considerably shortened to be on the order of tens of femtoseconds. Of particular interest is the difference with regard to the nonadiabatic interactions in furan and 2-methyl furan. In the case of 2-methyl furan, the couplings of the n=3 Rydberg states with the 1A′(ππ*) valence state are much stronger than that of the S1[1A2(π3s)] Rydberg state with the S2[1B2(ππ*)] valence state in the furan case. The n=3 Rydberg transitions that appear together with valence transition in 2-methyl furan particularly complicate and dominate the nonradiative relaxation pathways from the Franck-Condon region along the multidimensional reaction coordinate back to the ground state. It is noted that no intersystem crossing process with triplet states are observed in the current measurements. In most cases, the triplet states also play significant contributions to photochemistry processes29, especially when the energy level of the involved singlet and triplet states are very close30, 31. However, the triplet states differ in energy as the prepared singlet state in 2-methyl furan. Moreover, there are no molecular features which would drive an ultrafast intersystem crossing in the observed time window, neither by an El Sayed mechanism as well as by a heavy-atom effect.
We have used femtosecond time-resolved photoelectron imaging coupled with time-resolved mass spectroscopy to observe the nonadiabatic dynamics in electronically excited 2-methyl furan. The n=3 Rydberg states (i.e., S1[1A″(π3s)],
1A′(π3px), 1A″(π3py) and 1A″(π3pz)) and the valence state (1A′(ππ*)) are simultaneously excited from the ground state and the average lifetime of these states is measured to be on the time scale of 50 fs. Ultrafast internal conversions among these states are observed and dominated as the nonradiative relaxation mechanism.