# Femtosecond Time-Resolved Observation of Relaxation and Wave Packet Dynamics of the S1 State in Electronically Excited o-Fluoroaniline

^{1}

^{2}

^{3}

^{4}

^{*}

^{†}

## Abstract

**:**

_{1}state, intramolecular vibrational redistribution first occurs on the time scale τ

_{1}= 349 fs, and then the transition to the triplet state occurs through the intersystem crossing on the time scale τ

_{2}= 583 ps, and finally, the triplet state occurs decays slowly through the time scale τ

_{3}= 2074 ps. We find the intramolecular vibrational redistribution is caused by the 0

^{0}, 10b

^{1}and 16a

^{1}vibrational modes of the S

_{l}state origin. That is, the 288.3 nm femtosecond laser excites the molecule to the S

_{1}state, and the continuous flow of the vibrational wave packet prepares a coherent superposition state of three vibrational modes. Through extracting the oscillation of different peak intensities in the photoelectron spectrum, we observe reversible changes caused by mutual interference of the S

_{1}0

^{0}, S

_{1}10b

^{1}and S

_{1}16a

^{1}states when the wave packets flow. When the pump pulse is 280 nm, the beat frequency disappears completely. This is explained in terms of increases in the vibrational field density and characteristic period of oscillation, and statistical averaging makes the quantum effect smooth and indistinguishable. In addition, the Rydberg component of the S

_{1}state is more clearly resolved by combining experiment and theory.

## 1. Introduction

^{−15}s; ultrafast) timescale, so conventional experimental methods do not yield ideal results. To study the wave packet dynamic of molecule, researchers have developed a series of femtosecond time-resolved (pump-probe) experimental methods such as femtosecond time-resolved photoelectron spectroscopy [1,2], femtosecond time-resolved photoelectron image (TRPEI) [3], and femtosecond time-resolved negative-ion velocity image [4,5]. When the bandwidth of the pump pulse contains multiple transition frequencies, the molecule is not excited to a quantum state corresponding to a single frequency but to a quantum state that is a superposition of such states. In a coherent superposition state, a wave packet is generated in which the position of the constructive interference changes over time, and its probe reveals an exponential decay in the intensity of the ionized signal with damped cosine oscillations with time [6,7]. This peculiar phenomenon of repeated oscillation is called quantum beat frequency and has attracted the attention of researchers in recent years [8,9,10].

^{−1}(7.89 eV). Waware’s team [12] synthesized polyaniline-o-fluoroaniline by in-situ copolymerization of aniline and o-fluoroaniline through oxidation and found that the alternating current (AC) conductivity of the copolymer was greatly improved. Many studies have also been done on quantum beat frequency. Fengzi Ling’s team used femtosecond TRPEI to study the quantum beats of 2,4-difluorophenol [13], o-fluorophenol [14], and 2,4-difluoroaniline [9]. This research showed that beat frequency was caused by a change in molecular conformation. Shuai Li’s team used femtosecond TRPEI to study the wave packet evolution of pyrimidine [15], showing that beat frequency was caused by transitions between different vibrational energy levels of the ion state. The group of Junggil Kim studied the wave packet dynamic of 2-fluorothioanisole [16] via the femtosecond time-resolved pump-probe method and showed that there were two minimal energies when the molecule was in the S

_{1}state. At these minima, the angles between the methyl group and the benzene ring were 0° and 51°, and the swinging motion of the methyl group made the molecule exhibit a beat frequency.

- (1)
- Can quantum beat frequency be explained by the ionization cross-section?
- (2)
- Do in-phase signals appear in quantum beat phenomena?

^{0}vibrational mode of o-fluoroaniline has a higher ionization probability, while the 10b

^{1}and 16a

^{1}vibrational modes are inverse. When the molecule is pumped to the excited state, it may oscillate due to different ionization probabilities. The bandwidth of a femtosecond laser is so wide that it can perfectly include those vibration modes near the S

_{1}state origin, forming a vibrational wave packet. In addition, the femtosecond laser reacts rapidly and can detect the evolution information of wave packets. On this basis, we use o-fluoroaniline as a model, conduct femtosecond TRPEI, and perform theoretical calculations to describe the relaxation dynamics of the molecular S

_{1}state in detail.

## 2. Results and Discussion

#### 2.1. Ground State Geometry of o-Fluoroaniline

_{1}state is 4.25 eV, which is caused by the transition of orbital 29 → 30, with the transition wavelength center at 291.88 nm. And the vertical excitation energy of the S

_{2}state is 5.09 eV, which is caused by the transition of orbital 29 to orbital 32, and the overall transition wavelength is 243.54 nm. Similarly, the vertical excitation energy of the T

_{1}state is 3.45 eV, which is caused by the transition of orbital 30 to orbital 32, and the overall transition wavelength is 359.37 nm. We can find that the energy of the S

_{1}state and the T

_{1}state is relatively close, and the intersystem crossing (ISC) process may occur between them. Figure 2 shows the transition-related orbital shape. It should be noted that the conformations of the ground state, S

_{1}state and T

_{1}state calculated later have no imaginary frequency, indicating that our theoretical calculation is reasonable, as shown in Figure A1 in the Appendix A. Figure A2 in the Appendix A shows the molecular structure and Cartesian coordinate system of the ground state, S

_{1}state, and T

_{1}state.

#### 2.2. Relaxation Kinetics of o-Fluoroaniline

_{1}= 349 ± 17.43 fs, τ

_{2}= 583 ± 29.16 ps, and τ

_{3}= 2074 ± 103.69 ps. It is worth noting that τ

_{3}decay for a long time, well above the upper limit of our delay platform, and therefore cannot be measured accurately. When the pump pulse is changed to 280 nm, the time decay curves of the parent ions are obviously different, as shown in Figure 3b. The Gaussian cross-correlation function and convolution of three exponential decay functions are also used to fit the data. The time scales of the three decay components are significantly different from the data of 288.3 nm, and their lifetimes are τ

_{1}= 274 ± 13.71 fs, τ

_{2}= 480 ± 24.00 ps, and τ

_{3}= 3230 ± 161.48 ps. The τ

_{1}and τ

_{2}components at the pump pulse of 280 nm become faster, which is also found in previous work [9]. This is attributed to the differences in internal energy and vibrational density.

_{1}is on the sub-picosecond scale, which is similar to the values for phenol [23] and derivatives [13,14,24,25,26,27], aniline [28] and derivatives [29,30], chlorobenzene [31]. There are also similarities in the structure between them, and predecessors attributed the sub-picosecond time scale to the process of intramolecular vibrational redistribution (IVR); therefore, we also attribute this to IVR. The theoretical data of Table 1 shows that the vertical excitation energy of the S

_{1}state is 4.25 eV. The photon energy of 280 nm is 4.43 eV, and the 288.3 nm photon energy is 4.30 eV, which can only excite the S

_{1}state of the molecule. Therefore, the τ

_{1}component can be more precisely linked to the IVR of the wave packet from the vertical Franck-Condon (FC) region to the S

_{1}origin of the lowest energy. There are two possible mechanisms for the τ

_{2}component: one is an internal conversion to the S

_{0}state. Given the very poor FC factor between the S

_{0}state with high vibrational energy and the cationic state, it is difficult to ionize the thermal ground state molecules efficiently, which contradicts the existence of the τ

_{2}component. The second possibility is ISC. It is worth noting that previously studied benzene [32], aniline [33], 2,4-difluoroaniline [29], and 2,5-difluoroaniline [27] and the time scale of 100 picoseconds was also obtained. Since the o-fluoroanilines that we studied are similar to their structures, and the time scale of hundred picoseconds is also obtained, we tend to the same attribution, ISC. The long life of the τ

_{3}component is a direct consequence of the slow deactivation of the triplet state.

_{1}state. Moving on to the third peak, the energy remains basically unchanged, which is explained by the fact that energy from the triplet state flows into this peak. So, the third peak may be related to both the S

_{1}state and the triplet state. The characteristics of these peaks also indicate that it is reasonable to attribute the τ

_{2}component to ISC.

_{800 nm}= 1.55 eV. The molecule can absorb two photons without being ionized; that is, m can be 2. For the first to fourth peaks, the suitable value of n is 3, and the calculated δ values are 0.84, 0.63, 0.47 and 0.36, respectively. About the sixth and eighth peaks, it is reasonable that the principal quantum number is only 4, that is n = 4, with resulting δ values of 0.91 and 0.29. In general, δ for second-group elements is 0.9~1.2 for s orbital, 0.3~0.5 for p orbital, and approximately 0 for d orbital [34]. Here, it is worth noting that the s, p, and d orbitals correspond to the principal quantum numbers of 1, 2, and 3, and the molecular orbitals are spherical, spindle-shaped, and plum-shaped. Therefore, the first to the fourth, sixth, and eighth peaks are identified as 3s, 3p

_{1}, 3p

_{2}, 3p

_{3}, 4s, and 4p, respectively. We also calculate the excitation energies of these peaks via:

_{Rydberg}is the excitation energy of the Rydberg state, and those are 4.97, 5.46, 5.77, 5.93, 6.46 and 6.90 eV, respectively.

_{y}, 3p

_{x}, 4s, and 4p

_{y}. Therefore, the second peak is only 3p

_{z}, and the seventh peak is 3s.

_{3}components at the pump pulses of 266 nm, 260 nm, 250 nm, and 240 nm are not much different from the previously measured pulses of 280 nm and 288.3 nm and are long-lived. While τ

_{1}and τ

_{2}are in the range of hundreds of picoseconds and a few seconds, they are gradually decreased by about the order of hundreds of femtoseconds. However, the S

_{1}state is still excited. This is probably because the pump pulse is gradually shortened, thereby increasing the energy, so the molecular vibration energy increases and the decay time shorten. In addition, the τ

_{1}component is getting shorter and shorter, which also shows that attributing τ

_{1}to IVR is reasonable. Because a higher vibration will promote the occurrence of IVR, IVR will be faster.

#### 2.3. Quantum Beat of the S_{1} State of o-Fluoroaniline

_{1}component to an IVR, and now we analyze this ultrafast formation in detail. We measure the photoelectron image at different time delays and extract the corresponding photoelectron energy spectrum, as shown in Figure 6a. This fig is integrated to obtain the signal intensity of the six peaks varying with delay time. After fitting with the cross-correlation function and the convolution of the three exponential decay functions (The three decay functions correspond to 349 fs, 583 ps, and 2074 ps), the decay components are subtracted to obtain the residual and the beat signals. In order to describe the beat phenomenon in detail, a fast Fourier transform (FFT) is performed on the extracted beat signal about all peaks (time domain signal is converted into frequency domain signal), as shown in Figure 6b. It is determined the frequency of the oscillating component in the frequency domain, and there are some frequencies that are 21, 52, 84, 105, and 126 cm

^{−1}, as shown in Table 3. Figure 6c is the result of five cosine function convolution cross-correlation functions, and the formula is given below:

^{−1}, which is compared with the MATI of the o-fluoroaniline [37]. The frequency observed is very close to the energy level difference (ΔE = 103 cm

^{−1}) between 0

^{0}and 10b

^{1}of the S

_{l}state origin. About other frequencies, the group of Suzuki [38] studied the wavepacket dynamics of

^{1}B

_{2}(

^{1}Σ

_{u}

^{+}) of CS

_{2}by sub-20 fs photoelectron imaging, also got some extra frequencies, they explained these by difference frequency and overtone frequency. The frequency of the 0

^{0}vibration mode is 0, ν

_{1}represents the 10b

^{1}vibration mode, and the vibration frequency is 103 cm

^{−1}; ν

_{2}represents the 16a

^{1}vibration mode with a frequency of 246 cm

^{−1}. On the basis of this, we explain that 21, 52, 85, and 126 are $\frac{1}{2}$ × ν

_{2}− ν

_{1}, $\frac{1}{2}$ × ν

_{1}, 2 × ν

_{1}− $\frac{1}{2}$ × ν

_{2}and $\frac{1}{2}$ × ν

_{2}, respectively. It should be noted that the true frequencies of 0

^{0}, 10b

^{1}, and 16a

^{1}are 34,583, 34,686, and 34,829 cm

^{−1}in the MATI spectrum, corresponding with energies of 4.29, 4.30, and 4.32 eV. Because the bandwidth of the femtosecond laser is relatively wide, when the pump pulse is 288.3 nm, 10b

^{1}and 16a

^{1}may be excited simultaneously. It can be seen that these frequencies are related to 10b

^{1}and 16a

^{1,}and our attribution of frequencies is reasonable. This indicates that the beat signal originates from the evolution of coherent vibrational wave packets by simultaneous excited the S

_{l}0

^{0}, S

_{l}10b

^{1}and S

_{l}16a

^{1}vibration modes.

_{1}state, first, it is in the FC region with a high vibrational state and relaxes to the more stable S

_{1}state of the lowest energy. We also see that all the photoelectron peaks almost reach the maximum or minimum at the same time, which means that the beat signals of the peaks are in the same direction basically. A careful review of the MATI of the o-fluoroaniline cation [37] shows that the intensity of the S

_{l}0

^{0}state is maximal, and the vibrational peaks of the S

_{l}10b

^{1}and S

_{l}16a

^{1}states are almost invisible in the spectrum. Therefore, the transition probability of the S

_{l}0

^{0}state is much higher than that of the S

_{l}10b

^{1}and S

_{l}16a

^{1}states in o-fluoroaniline ionization, or the FC factor of the S

_{l}0

^{0}state is larger [15], making the S

_{l}0

^{0}state easier to ionize, and the S

_{l}10b

^{1}and S

_{l}16a

^{1}states are much less likely to ionize. When the wave packet is constantly flowing, there are two scenarios with delay: (1) when the energy in the wave packet is mainly concentrated near the S

_{l}0

^{0}vibration mode, it can ionize the S

_{l}0

^{0}vibration mode but cannot ionize the S

_{l}10b

^{1}and S

_{l}16a

^{1}modes, so the signal is at maximum, and (2) when the energy in the wave packet is mainly concentrated near the S

_{l}10b

^{1}and S

_{l}16a

^{1}vibration modes, the signal is at a minimum because neither of the three vibration modes can be ionized. The photoelectron signal continuously oscillates as the vibrational wave packets continuously flow. It is noted that the process is reversible because the wave packets are constantly flowing.

_{1}0

^{0}, S

_{1}10b

^{1}and S

_{l}16a

^{1}states.

## 3. Experimental and Theoretical Methods

#### 3.1. Experimental Parameters

^{−6}Pa. When the pulse valve is opened to inject the sample, the vacuum level of the beam source chamber is between 1.0 × 10

^{−3}Pa, and the ionization chamber is 1.0 × 10

^{−5}Pa. The ionization chamber is shielded with a μ-metal (iron-nickel alloy) layer to protect the electrons from external electromagnetic fields.

_{1}state origin of the o-fluoroaniline molecule (34,583 cm

^{−1}). The other beam of the fundamental laser generated a probe pulse with a center wavelength of 800 nm. According to experience, the 800 nm probe pulse can cause some accidental resonances in the molecule. The polarization direction of the pump pulse and probe pulse was adjusted to be parallel to the probe pulse using a variable-wave plate and a half-wave plate, respectively. The photoelectron image was collected under different pump-probe time delays, and then each three-dimensional image was reconstructed with a basis set expansion (BASEX) transformation [40]. The typical cross-correlation is measured to be 152 ± 25 fs obtained by non-resonant ionization of Xe.

_{G}= 0 V, V

_{E}= −2758 V, and V

_{R}= −4000 V. The photoelectron image was collected by a CCD camera mounted on the back of the probe, and a photomultiplier tube was also used to collect photoelectron/ion mass spectrometry signals. The sequence of the whole system was controlled by a DG535 controller.

#### 3.2. Theoretical Calculation

_{1}and S

_{2}states based on TD-DFT and CAM-B3LYP/6-311G+(d,p) basis set. To determine the molecular p and d orbital information, we optimize and calculate the excitation energy of the Rydberg state based on the founding structure and DFT CAM-B3LYP/aug-cc-pvtz basis set. The wave function information of the molecules of the Rydberg state is imported into the Multiwfn 3.7 [35,46] program package, and these orbitals are analyzed and plotted.

## 4. Conclusions

_{1}state, IVR first occurs on the timescale of 349 fs, after which it transits to the triplet state through ISC on the timescale of 583 ps, and the triplet decays slowly through a timescale of 2074 ps. The IVR is caused by the 0

^{0}, 10b

^{1}and 16a

^{1}vibrational states of the S

_{l}state origin; that is, the 288.3 nm femtosecond laser excites the molecule to the S

_{1}state and prepares a coherent superposition state. Reversible changes are observed through the oscillation of different photoelectron peaks in the photoelectron energy spectrum. When the pump pulse is 280 nm, the 0

^{0}, 10b

^{1}, and 16a

^{1}vibrational modes are ionized, and the beat frequency completely disappears. In this experiment, we found the wave packet dynamics process formed by three vibration modes different from the previous ones. And experiment and theory are combined for the first time to more clearly resolve some Rydberg states of the S

_{1}state. This work provides an important reference for interpreting the excited-state dynamic of other fluorine-containing aniline molecules and resolving the Rydberg state.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Sample Availability

## Appendix A

**Figure A1.**The infrared spectrum of the ground state, S

_{1}state, and T

_{1}state of the molecule shows no imaginary frequency. For the S

_{0}state, calculation method and basis set: DFT and CAM-B3LYP/6-311+G(d,p). For S

_{1}and T

_{1}states, calculation method and basis set: TD-DFT and CAM-B3LYP/6-311+G(d,p).

**Figure A2.**Molecular structure and Cartesian coordinate system of the ground state, S

_{1}state and T

_{1}state, and the Z axis is perpendicular to the paper surface. For the S

_{0}state, calculation method and basis set: DFT and CAM-B3LYP/6-311+G(d,p). For S

_{1}and T

_{1}states, calculation method and basis set: TD-DFT and CAM-B3LYP/6-311+G(d,p).

## References

- Kuthirummal, N.; Weber, P.M. Rydberg states: Sensitive probes of molecular structure. Chem. Phys. Lett.
**2003**, 378, 647–653. [Google Scholar] [CrossRef] - Cheng, X.X.; Zhang, Y.; Deb, S.; Minitti, M.P.; Gao, Y.; Jónssonad, H.P.; Weber, M. Ultrafast structural dynamics in Rydberg excited N,N,N′,N′-tetramethylethylenediamine: Conformation dependent electron lone pair interaction and charge delocalization. Chem. Sci.
**2014**, 5, 4394–4403. [Google Scholar] [CrossRef] - Cheng, X.X.; Zhang, Y.; Gao, Y.; Jónsson, H.; Weber, P.M. Ultrafast structural pathway of charge transfer in N,N,N’,N’-tetramethylethylenediamine. J. Phys. Chem. A
**2015**, 199, 2813–2818. [Google Scholar] [CrossRef] - Minitti, M.P.; Weber, P.M. Time-Resolved Conformational Dynamics in Hydrocarbon Chains. Phys. Rev. Lett.
**2007**, 98, 253004. [Google Scholar] [CrossRef] - Deb, S.; Minitti, M.P.; Weber, P.M. Structural dynamics and energy flow in Rydberg-excited clusters of N,N-dimethylisopropylamine. J. Chem. Phys.
**2011**, 135, 044319. [Google Scholar] [CrossRef] [Green Version] - Zewail, A.H. Femtochemistry: Atomic-scale dynamics of the chemical bond using ultrafast lasers (Nobel Lecture). Angew. Chem. Int. Edit.
**2000**, 39, 2586–2631. [Google Scholar] [CrossRef] - Kobayashi, T.; Kida, Y. Ultrafast spectroscopy with sub-10 fs deep-ultraviolet pulses. Phys. Chem. Chem. Phys.
**2012**, 14, 6200–6210. [Google Scholar] - Pruna, F.R.; Springate, E.; Offerhaus, H.L.; Krishnamurthy, M.; Farid, N.; Nicole, C.; Vrakking, M.J.J. Spatial alignment of diatomic molecules in intense laser fields: I. Experimental results. J. Phys. B At. Mol. Opt. Phys.
**2001**, 34, 4919–4938. [Google Scholar] [CrossRef] - Baumert, T.; Gerber, G. Fundamental Interactions of Molecules (Na
_{2}, Na_{3}) with Intense Femtosecond Laser Pulses. Isr. J. Chem.**1994**, 34, 103–114. [Google Scholar] [CrossRef] - Ling, F.Z.; Wang, Y.M.; Li, S.; Wei, J.; Tang, Y.; Zhang, B. Imaging Reversible and Irreversible Structural Evolution in Photoexcited 2,4-Difluoroaniline. J. Phys. Chem. Lett.
**2018**, 9, 5468–5473. [Google Scholar] [CrossRef] - Ling, F.Z.; Li, S.; Song, X.L.; Tang, Y.; Wang, Y.M.; Zhang, B. Visualization of coherent nuclear motion between different geometries in photoexcited 2,4-difluorophenol. Phys. Rev. A
**2017**, 95, 043421. [Google Scholar] [CrossRef] - Lin, J.L.; Tzeng, W.B. Ionization energy of o-fluoroaniline and vibrational levels of o-fluoroaniline cation determined by mass-analyzed threshold ionization spectroscopy. Phys. Chem. Chem. Phys.
**2000**, 2, 3759–3763. [Google Scholar] [CrossRef] - Waware, U.S.; Rashid, M.; Hamouda, A.M.S. Highly improved AC conductivity of poly (aniline-o-fluoroaniline). Ionics
**2019**, 25, 1057–1065. [Google Scholar] [CrossRef] - Ling, F.Z.; Li, S.; Song, X.L.; Wang, Y.M.; Long, J.Y.; Zhang, B. Femtosecond time-resolved observation of butterfly vibration in electronically excited o-fluorophenol. Sci. Rep.
**2017**, 7, 15362. [Google Scholar] [CrossRef] [Green Version] - Li, S.; Long, J.Y.; Ling, F.Z.; Wang, Y.M.; Song, X.l.; Zhang, S.; Zhang, B. Real-time visualization of the vibrational wavepacket dynamics in electronically excited pyrimidine via femtosecond time-resolved photoelectron imaging. J. Chem. Phys.
**2017**, 147, 044309. [Google Scholar] [CrossRef] - Kim, J.; Woo, K.C.; Kim, S.K. Femtosecond Wavepacket Dynamics Reveals the Molecular Structures in the Excited (S
_{1}) and Cationic (D_{0}) States. J. Phys. Chem. A**2021**, 125, 6629–6635. [Google Scholar] [CrossRef] - Stolow, A.; Bragg, A.E.; Neumark, D.M. Femtosecond time-resolved photoelectron spectroscopy. Chem. Rev.
**2004**, 104, 1719–1758. [Google Scholar] [CrossRef] [Green Version] - Neumark, D.M. Time-resolved photoelectron spectroscopy of molecules and clusters. Annu. Rev. Phys. Chem.
**2001**, 52, 255–277. [Google Scholar] [CrossRef] [Green Version] - Reid, K.L. Photoelectron Angular Distributions. Annu. Rev. Phys. Chem.
**2003**, 54, 397–424. [Google Scholar] [CrossRef] - Suzuki, T. Femtosecond time-resolved photoelectron imaging. Annu. Rev. Phys. Chem.
**2006**, 57, 555–592. [Google Scholar] [CrossRef] - Stavros, V.G.; Verlet, J.R.R. Gas-phase femtosecond particle spectroscopy: A bottom-up approach to nucleotide dynamics. Annu. Rev. Phys. Chem.
**2016**, 67, 211–232. [Google Scholar] [CrossRef] - Carley, R.E.; Heesel, E.; Fielding, H.H. Femtosecond lasers in gas phase chemistry. Chem. Soc. Rev.
**2005**, 11, 949–969. [Google Scholar] - Roberts, G.M.; Chatterley, A.S.; Young, J.D.; Stavros, V.G. Direct Observation of Hydrogen Tunneling Dynamics in Photoexcited Phenol. J. Phys. Chem. Lett.
**2012**, 3, 348–352. [Google Scholar] [CrossRef] - Livingstone, R.A.; Thompson, J.O.F.; Iljina, M.; Donaldson, R.J.; Sussman, B.J.; Paterson, M.J.; Townsend, D. Time-resolved photoelectron imaging of excited state relaxation dynamics in phenol, catechol, resorcinol, and hydroquinone. J. Chem. Phys.
**2012**, 137, 184304. [Google Scholar] [CrossRef] [Green Version] - Remmers, K.; Meerts, W.L.; Rentien, A.Z.; Barbu, K.L.; Lahmani, F. Structural information on the S
_{0}and S_{1}state of o-fluorophenol by hole burning and high resolution ultraviolet spectroscopy. J. Chem. Phys.**2000**, 112, 6237–6244. [Google Scholar] [CrossRef] - Karsili, T.N.; Wenge, A.M.; Marchetti, B.; Ashfold, M.N. Symmetry matters: Photodissociation dynamics of symmetrically versus asymmetrically substituted phenols. Phys. Chem. Chem. Phys.
**2014**, 16, 588–598. [Google Scholar] [CrossRef] [Green Version] - Wei, J.; Cao, L.; Song, X.L.; Wang, Y.M.; Zhang, S.; Zhang, B. Wavepacket dynamics of the excited (S
_{1}) state of 2,5-difluoroaniline by accidental resonance with the Rydberg states. J. Chem. Phys.**2022**, 157, 204302. [Google Scholar] [CrossRef] - Thompson, J.O.F.; Livingstone, R.A.; Townsend, D. Following the relaxation dynamics of photoexcited aniline in the 273-266 nm region using time-resolved photoelectron imaging. J. Chem. Phys.
**2013**, 139, 034316. [Google Scholar] [CrossRef] - Ling, F.Z.; Li, S.; Wei, J.; Liu, K.; Wang, Y.M.; Zhang, B. Unraveling the electronic relaxation dynamics in photoexcited 2,4-difluoroaniline via femtosecond time-resolved photoelectron imaging. J. Chem. Phys.
**2018**, 148, 144311. [Google Scholar] [CrossRef] - Kirkby, O.M.; Sala, M.; Balerdi, G.; Nalda, R.D.; Bañares, L.; Guérin, S.; Fielding, H.H. Comparing the electronic relaxation dynamics of aniline and d
_{7}-aniline following excitation at 272–238 nm. Phys. Chem. Chem. Phys.**2015**, 17, 16270–16276. [Google Scholar] [CrossRef] [Green Version] - Liu, Y.Z.; Qin, C.C.; Zhang, S.; Wang, Y.M.; Zhang, B. Ultrafast Dynamics of the First Excited State of Chlorobenzene. Acta Phys.-Chim. Sin.
**2011**, 27, 965–970. [Google Scholar] - Parker, D.S.N.; Minns, R.S.; Penfold, T.J.; Worth, G.A.; Fielding, H.H. Ultrafast dynamics of the S
_{1}excited state of benzene. Chem. Phys. Lett.**2009**, 469, 43–47. [Google Scholar] [CrossRef] - Scheps, R.; Florida, D.; Rice, S.A. Influence of large amplitude vibrational motion on the rate of intersystem crossing: A study of single vibronic level fluorescence from aniline- h
_{7}, aniline N, N-d_{2}, aniline- d_{5}, and aniline- d_{7}. J. Chem. Phys.**1974**, 61, 1730–1747. [Google Scholar] [CrossRef] - Robin, M.B. Higher Excited States of Polyatomic Molecules; Academic Press: New York, NY, USA, 1974; Volume 1. [Google Scholar]
- Lu, T.; Chen, F.W. Multiwfn: A multifunctional wavefunction analyzer. J. Comput. Chem.
**2012**, 33, 580–592. [Google Scholar] [CrossRef] - Davidson, E.R. Comment on Dunning’s correlation-consistent basis sets. Chem. Phys. Lett.
**1996**, 260, 514. [Google Scholar] [CrossRef] - Yang, S.C.; Tzeng, W.B. Mass-analyzed threshold ionization spectroscopy of deuterium-substituted isotopomers of o-fluoroaniline and m-fluoroaniline cations. J. Mol. Spectrosc.
**2011**, 269, 49–55. [Google Scholar] [CrossRef] - Spesyvtsev, R.; Horio, T.; Suzuki, Y.I.; Suzuki, T. Observation of the wavepacket dynamics on the
^{1}B_{2}(^{1}Σ_{u}^{+}) state of CS_{2}by sub-20 fs photoelectron imaging using 159 nm probe pulses. J. Chem. Phys.**2015**, 142, 074308. [Google Scholar] [CrossRef] - Hao, Q.L.; Long, J.Y.; Deng, X.L.; Tang, Y.; Abulimiti, B.; Zhang, B. Superexcited State Dynamics of OCS: An Experimental Identification of Three Competing Decay-Channels Among Autoionization, Internal Conversion and Neutral Predissociation. J. Phys. Chem. A
**2017**, 121, 3858–3863. [Google Scholar] [CrossRef] - Dribinski, V.; Ossadtchi, A.; Mandelshtam, V.A.; Reisler, H. Reconstruction of Abel-transformable images: The Gaussian basis-set expansion Abel transform method. Rev. Sci. Instrum.
**2002**, 73, 2634–2642. [Google Scholar] [CrossRef] [Green Version] - Frisch, M.J.; Trucks, G.W.; Schlegel, H.B.; Scuseria, G.E.; Robb, M.A.; Cheeseman, J.R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G.A.; et al. Gaussian09 Revision D. 01; Gaussian, Inc.: Wallingford, UK, 2010. [Google Scholar]
- Lu, T. Molclus Program, Version 1.9.9.7. Available online: http://www.keinsci.com/research/molclus.html (accessed on 16 December 2021).
- Stephens, P.J.; Devlin, F.J.; Chabalowski, C.F.; Frisch, M.J. Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields. J. Phys. Chem.
**1994**, 98, 247–257. [Google Scholar] [CrossRef] - McLean, A.D.; Chandler, G.S. Contracted Gaussian-basis sets for molecular calculations. 1. 2nd row atoms, Z = 11–18. J. Chem. Phys.
**1980**, 72, 5639. [Google Scholar] [CrossRef] - Raghavachari, K.; Binkley, J.S.; Seeger, R.; Pople, J.A. Self-Consistent Molecular Orbital Methods. 20. Basis set for correlated wave-functions. J. Chem. Phys.
**1980**, 72, 650. [Google Scholar] - Liu, Z.Y.; Lu, T.; Chen, Q.X. An sp-hybridized all-carboatomic ring, cyclo 18 carbon: Electronic structure, electronic spectrum, and optical nonlinearity. Carbon
**2020**, 165, 461–467. [Google Scholar] [CrossRef]

**Figure 1.**o-Fluoroaniline energy varies with angle, and the five structures of the molecule are given. Calculation method and basis set: DFT and CAM-B3LYP/6-311+G(d,p).

**Figure 2.**MO29, MO30, MO32 orbitals of o-fluoroaniline S

_{1}state. Calculation method and basis set: TD-DFT and CAM-B3LYP/6-311+G(d,p).

**Figure 3.**Time decay curves of the parent ion measured with (

**a**) a 288.3 nm pump pulse and 800 nm probe pulse, (

**b**) a 280 nm pump pulse and 800 nm probe pulse. The circles are experimental data, and the solid lines are fitted data. Both curves are fitted using a Gaussian cross-correlation function and a convolution of three exponential decay functions, resulting in different decay times.

**Figure 4.**Photoelectron spectra at delay times of (

**a**) Δt = 0.027 ps and (

**b**) Δt = 1.429 ps. The ordinates of the two plots are normalized, and (

**b**) is normalized with the maximum value of (

**a**) as a reference. The insets are the corresponding optoelectronic images (the original image on the left and BASEX transformed image on the right).

**Figure 5.**Time decay curves of the parent ion measured with (

**a**) 266 nm pump pulse and 800 nm probe pulse, (

**b**) 260 nm pump pulse and 800 nm probe pulse, (

**c**) 250 nm pump pulse and 800 nm probe pulse, and (

**d**) 240 nm pump pulse and 800 nm probe pulse. The circles are experimental data, and the solid lines are fitted data. All curves are fitted using a Gaussian cross-correlation function and a convolution of three exponential decay functions to obtain different decay times.

**Figure 6.**(

**a**) Time-resolved photoelectron spectrum obtained with a 288.3 nm pump pulse and 800 nm probe pulse. (

**b**) The spectrum obtained by Fourier transform of the residual data at the fourth peak. (

**c**) Signal intensities of the six peaks as functions of delay time. Experimental data are given as open circles, while solid lines are fitted results.

**Figure 7.**(

**a**) Time-resolved photoelectron spectrum obtained with 280 nm pump pulse and 800 nm probe pulse. (

**b**) Signal intensities of the six peaks as functions of delay time. Experimental data are given as open circles, while solid lines are fitted results.

**Table 1.**Wavelength, vertical excitation energy (E), oscillator strength (f) and transition orbital of S

_{1}, S

_{2}and T

_{1}states of o-fluoroaniline molecules. Calculation method and basis set: TD-DFT and CAM-B3LYP/6-311+G(d,p).

State | Transition | Wavelength/nm | E/eV | f |
---|---|---|---|---|

S_{1} | 29 → 30 | 291.88 | 4.25 | 0.0600 |

S_{2} | 29 → 32 | 243.54 | 5.09 | 0.0107 |

T_{1} | 30 → 32 | 359.37 | 3.45 | 0.0023 |

**Table 2.**Theoretically calculated molecular hole delocalization index (HDI), electron delocalization index (EDI), and Rydberg energy (E), and experimentally obtained Rydberg excitation energy (T). The E represents the theory calculated value, and T is the Rydberg excitation energy calculated according to Equation (3) for the experimental data. The theoretical method is used the basis set DFT and CAM-B3LYP/aug-cc-pvtz.

Theoretical Value | Experimental Value | |||||||
---|---|---|---|---|---|---|---|---|

Peaks | PKE (eV) | HDI | EDI | E (eV) | n | δ | T (eV) | States |

1st | 0.18 | 11.31 | 2.72 | 5.11 | 3 | 0.84 | 4.97 | 3s |

2nd | 0.67 | 3 | 0.63 | 5.46 | 3p_{z} | |||

3rd | 0.98 | 9.64 | 3.84 | 5.70 | 3 | 0.47 | 5.77 | 3p_{y} |

4th | 1.14 | 10.31 | 1.79 | 5.88 | 3 | 0.36 | 5.93 | 3p_{x} |

6th | 1.67 | 8.20 | 1.61 | 6.44 | 4 | 0.91 | 6.46 | 4s |

7th | 1.77 | 11.31 | 2.72 | 5.11 | 3 | 0.83 | 5.01 | 3s |

8th | 2.11 | 8.72 | 2.99 | 6.67 | 4 | 0.29 | 6.90 | 4p_{y} |

**Table 3.**The frequency of FFT and their allocation. ν

_{1}represents 10b

^{1}vibration mode, and the vibration frequency is 103 cm

^{−1}; ν

_{2}represents the 16a

^{1}vibration mode with a vibration frequency of 246 cm

^{−1}.

Vibrational State | $\frac{1}{2}\times {v}_{2}-{v}_{1}$ | $\frac{1}{2}\times {v}_{1}$ | $2\times {v}_{1}-\frac{1}{2}\times {v}_{2}$ | v_{1} | $\frac{1}{2}\times {v}_{2}$ |
---|---|---|---|---|---|

Frequency (cm^{−1}) | 21 | 52 | 84 | 105 | 126 |

Periodicity (fs) | 1588 | 642 | 397 | 318 | 265 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Abulimiti, B.; An, H.; Gu, Z.; Deng, X.; Zhang, B.; Xiang, M.; Wei, J.
Femtosecond Time-Resolved Observation of Relaxation and Wave Packet Dynamics of the S1 State in Electronically Excited *o*-Fluoroaniline. *Molecules* **2023**, *28*, 1999.
https://doi.org/10.3390/molecules28041999

**AMA Style**

Abulimiti B, An H, Gu Z, Deng X, Zhang B, Xiang M, Wei J.
Femtosecond Time-Resolved Observation of Relaxation and Wave Packet Dynamics of the S1 State in Electronically Excited *o*-Fluoroaniline. *Molecules*. 2023; 28(4):1999.
https://doi.org/10.3390/molecules28041999

**Chicago/Turabian Style**

Abulimiti, Bumaliya, Huan An, Zhenfei Gu, Xulan Deng, Bing Zhang, Mei Xiang, and Jie Wei.
2023. "Femtosecond Time-Resolved Observation of Relaxation and Wave Packet Dynamics of the S1 State in Electronically Excited *o*-Fluoroaniline" *Molecules* 28, no. 4: 1999.
https://doi.org/10.3390/molecules28041999