IVR Dynamics of Vibrational Levels of the ν1 Mode in (CF3)2C C O

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IVR Dynamics of Vibrational Levels of the ν1 Mode in (CF3)2CCO Molecules Excited by Resonant IR Femtosecond Radiation Vladimir B. Laptev,*,† Victor O. Kompanets,† Sergey V. Pigulsky,† Alexander A. Makarov,†,‡ Gennadii V. Mishakov,§ Dmitry V. Serebryakov,∥ Andrey V. Sharkov,⊥ Sergey V. Chekalin,† and Evgeny A. Ryabov† †

Institute of Spectroscopy, Russian Academy of Sciences, Fizicheskaya street, 5, Troitsk, Moscow 108840, Russia Moscow Institute of Physics and Technology, Institutsky lane, 9, Dolgoprudny, Moscow Region 141700, Russia § Federal Scientific Research Centre “Crystallography and Photonics”, Russian Academy of Sciences, 59 Leninskiy Pr., Moscow 119333, Russia ∥ Institute for Nuclear Research, Russian Academy of Sciences, Fizicheskaya street, 27, Troitsk, Moscow 108840, Russia ⊥ P.N. Lebedev Physical Institute, Russian Academy of Sciences, Leninsky Pr. 53, Moscow 119991, Russia

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‡

ABSTRACT: The intramolecular dynamics of vibrational levels (up to v = 5) of the ν1 mode in the (CF3)2CCO molecule that is induced by a multiphoton selective excitation of this mode by resonant femtosecond IR radiation has been studied. The times of intramolecular vibrational energy redistribution (IVR) from each vibrational level to remaining molecular modes have been determined. In accordance with theoretical predictions, a decrease in the IVR time with increasing quantum number v has been observed for the first time. A sharp decrease in the IVR time (down to 1.5 ps) at a wavelength of 2129 cm−1, corresponding to the v = 3 → v = 4 vibrational transition, is revealed. It has been shown that, with a negative chirp of a femtosecond radiation pulse, the population of high-lying vibrational levels of the ν1 mode increases significantly.

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INTRODUCTION Upon multiphoton excitation of a selected vibrational mode in a molecule by femtosecond resonant infrared radiation, it is possible to initiate photochemical processes that are selective with respect to a bond (or group of bonds). However, this possibility is limited by the effect of intramolecular redistribution of vibrational energy (IVR) from the excited mode to other molecular vibrations.1−7 Nevertheless, upon resonant multiphoton excitation by femtosecond IR laser pulses of vibrations of CNN and CO bonds in molecules of diazomethane and metal carbonyls, it became possible to reveal the nonstatistical character of their dissociation in the gas phase.8,9 It is worth noting that, because of peculiarities of their chemical bonds, these molecules have rather low activation energies, 35−40 kcal/ mol (12000−14000 cm−1), and, furthermore, metal carbonyl molecules are characterized by anomalously long IVR times (∼1 ns).10,11 Attempts to initiate monomolecular decomposition reactions by femtosecond IR irradiation of conventional molecules such as (CF3)2CCO and C4F9COI, the activation energies of covalent bonds of which are higher than 50 kcal/mol (>17500 cm−1), were unsuccessful.12 It is likely that this was related to the fact that, for such molecules, fast (2.4−8 ps) IVR times are observed even at the first level of vibrational excitation.11 According to the predictions of the theory,3 as the excitation level of an isolated vibrational mode in a molecule increases, the IVR times should decrease. This © XXXX American Chemical Society

follows from Fermi’s golden rule for the relaxation rate of vibrational energy (see, e.g., ref 3, page 222) (2πcτIVR)−1 = 2πV̅ 2ρ, where V̅ 2 (in cm−1) is the average nondiagonal element of the anharmonic interaction between the excited state and the close combination of the bath states of the other modes (it is known that Vv , v − 1 ∝ v ), and ρ (in cm) is the density of these states. Therefore, in order to evaluate the feasibility of realizing nonstatistical photochemical reactions for a particular molecule, it is necessary to investigate the IVR process at different vibrational levels of the mode to be excited. Previously, when examining successive vibrational transitions in the ν1 = 2194 cm−1 mode of the (CF3)2CCO molecule with the IR pump−probe method, we failed to register changes in the IVR time with increasing energy of the level to be probed. In our opinion, this was caused by a low intensity of the induced absorption signal from vibrationally excited molecules and, correspondingly, was due to high errors in determining the characteristic damping time of the signal.13 Development of high-sensitivity and low-noise IR detectors based on a CdHgTe linear array opened up new opportunities for measuring the induced optical density with a high accuracy. In the case of selective excitation of the ν1 mode in (CF3)2CCO, Fermi’s golden rule is applicable. Indeed, the Received: November 15, 2018 Revised: December 30, 2018 Published: January 3, 2019 A

DOI: 10.1021/acs.jpca.8b11095 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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Figure 1. Spectra of ΔkOD at different values of time delay Δt; the energy fluence is Φpump = 70 mJ/cm2: (a) Survey ΔkOD spectra. The ν1 band is shown by a thick gray line; the spectra in the rectangle are presented in a larger scale in part b. (b) “Tails” of the ΔkOD spectra from part a. The thick gray line is the band of composite vibration ν2 + ν18.

criterion for it is the following equation: 2πV̅ 2ρ ≥ ρ−1. The density of states ρ is unknown and depends on the nature of the bath states. If this is all vibrational states near the energy E̅ vib + ν1 (E̅ vib, the average vibrational thermal energy), then ρ is equal to 106 cm (see our previous paper11). In the case that ρ corresponds to all vibrational−rotational states, then ρvib−rot ≫ ρvib.7 And, last, the bath states may be the combined states of low-order combinations leading to intermode resonances directly responsible for IVR and then ρ ≡ ρres (in our case, ρres ∼ 2 cm11). However, this value can only be used if the bath states are weakly mixed, which is unlikely. The measured value of (2πcτIVR)−1 is approximately 1 cm−1 (∼5 ps13), so the golden rule may be valid even in the third unlikely case. The objective of this work is to study particular features of the dynamics of excited vibrational levels of the mode ν1 = 2194 cm−1 in bis(trifluoromethyl)keten ((CF3)2CCO) molecules that proceeds after its selective excitation by resonant femtosecond IR radiation.

reference beams were focused onto the entrance slit of a monochromator, which had no exit slit. Radiation intensities Iprobe and Iref of the beams emergent from the output grating of the monochromator were measured with two high-sensitivity and low-noise photodetectors cooled by liquid nitrogen. Either photodetector is a linear array composed of 32 epitaxial n-type photoresistors (pixels) on the basis of CdHgTe with a sensitivity of 5 × 105 counts per nanojoule per pixel measured at 4 μm. The measurement was carried out by integrating the charge flowed through the photoresistor by the method of double correlated sampling (CDS), which allows one to appreciably suppress the parasitic illumination and to reduce the noise level. The magnitude of the induced absorption was defined as ij (Iprobe/Iref )pump yz zz Δk OD = log10jjjj z j (Iprobe/Iref )gas zz k {

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(1)

where the subscripts “pump” and “gas” refer to the values of the ratio Iprobe/Iref in the presence and in the absence of the pump, respectively. According to formula 1, the positive value of ΔkOD corresponds to bleaching of the absorption. The amplitude and the spectrum of the ΔkOD signal were measured versus the delay Δt between the pump and probe pulses. The repetition rate of femtosecond pulses was 1 kHz, the energy of the pump pulse at a wavelength of 5 μm was up to 14 μJ, the pulse duration at half-height inside the cell was 120 fs, and the radiation spectral width was 230 cm−1. The temporal and spectral characteristics of the probe radiation were similar. In the majority of experiments, the flux density of the pump energy (energy fluence) inside the cell was Φpump ≈ 70 mJ/ cm2. All measurements were performed in the gas phase at a pressure of (CF3)2CCO of 10 Torr. (CF3)2CCO was purchased from Scientific Industrial Association “P&M-Invest” Ltd. (Russia) and was used without further purification. The content of the basic compound was specified by the manufacturer to be better than 99%, which was confirmed by our IR spectroscopic measurements. The technique that we used is based on the measurement of the IR absorption induced in the probed ν1 mode. As is wellknown, the transition cross section between levels of a harmonic oscillator increases linearly with the level number, which also holds with a good accuracy for an anharmonic oscillator. Since, in this case, the magnitude of the absorption is

EXPERIMENTAL SETUP We used the method of IR pumping and IR probing of molecules in the gas phase accompanied by the spectral analysis of the probe radiation.11 As IR radiation sources, two nonlinear independent converters based on TOPAS-C optical parametric amplifiers (OPAs) with subsequent difference frequency generation in a DFG-1 unit (Light Conversion) were employed. One of these converters was used as a pump source, while the other one, as a probe source. These OPAs were synchronously pumped with a femtosecond Ti:sapphire amplifier (Spectra-Physics) (λ = 800 nm; pulse duration and energy, 50 fs and 1.2 mJ, respectively). The radiation from the second OPA was split by a CaF2 wedge into two beams and was used to form the probe and reference beams. The pump and probe beams were focused by CaF2 lenses and were reunited at an angle of about 9° such that the waist of the probe beam was embedded in the waist of the pump beam. The transverse and longitudinal energy distributions of the pump and probe beams were measured with a Pyrocam III pyroelectric array. The polarizations of the pump and probe pulses were perpendicular to each other. A cell (4.8 mm long, CaF2 windows) with a gaseous (CF3)2CCO was placed in the intersection region of the two waists. The reference beam passed through the cell at a certain distance from the intersection of the waists. After the cell, the probe and B

DOI: 10.1021/acs.jpca.8b11095 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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in our previous work13 by the point-by-point method. At the same time, the new registration system made it possible to observe the dynamics of the “tail” of the ΔkOD spectrum. An increase in delay time Δt leads to a fast decrease in the intensity of the “tail”. A particularly deep dip in the intensity was observed at a wavenumber of 2129 cm−1, which roughly corresponds to the vibrational transition v = 3 → v = 4. The time evolution of the transient absorbance signal ΔkOD(Δt) was studied by varying the delay time Δt between the pump and probe pulses. Figure 2 presents dependences ΔkOD(Δt) obtained for five probe frequencies, which approximately correspond to the vibrational transitions in (CF3)2CCO from 0−1 to 4−5. The maxima of these transitions were determined by processing the spectral measurements (see below). All of the curves in Figure 2 show an exponential decay of the signal with subsequent reaching of a plateau, which extends up to several hundreds of picoseconds. As the level of vibrational excitation of the resonant mode increased, an exponential decrease in the ΔkOD signal was observed, with the characteristic times varying from τ = 6 ps for the 0−1 and 1−2 transitions to τ = 3.5 ps for the 4−5 transition. This fact contrasts with our previous results,13 when we failed to reveal changes of characteristic times with increasing energy of the level to be probed. We note a sharp (up to 1 ps) decrease in the characteristic time of the signal decay for the 3−4 transition. The spectral measurements of the transient absorbance signal ΔkOD allowed us to obtain quantitative information on the character of the initial vibrational distribution in the ν1 mode.13 For this purpose, it was necessary to know the positions and the intensities of the absorption bands of excited (CF3)2CCO molecules for each vibrational transition of the ν1 mode. In ref 13, the spectral experimental dependence of ΔkOD was fitted by a curve that was obtained as a result of summation of individual model absorption bands of successive vibrational transitions. It was assumed that the absorption bands of the excited states repeat the contour of the ν1 band and are shifted relative to each other by the chosen value of the anharmonic shift 2x11 = 20 cm−1. Simulation of ΔkOD Spectra. In this work, we are going to verify this assumption and to suggest a model that will allow to get parameters needed to reliably calculate the spectrum of the n1 = 1 → n1 = 2 vibrational−rotational band. This model is based on a comparison of the model calculations with the

determined by the difference between the populations for corresponding transitions, then it can be easily verified that the magnitude of the absorption integrated over all levels (and, correspondingly, over the spectrum) does not depend on the energy stored in the mode to be probed. At the same time, the anharmonicity of vibrations leads to a situation that, as the molecule becomes excited, the position (and the shape) of the vibrational spectrum can noticeably change, shifting, as a rule, toward the red range. Precisely these changes of the spectrum, which were taken in a narrow spectral interval, were measured and considered in this work.

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RESULTS Measurements of the Dynamic of ΔkOD Spectra. Figure 1 presents the spectra of transient absorbance signal ΔkOD in the ν1 mode of the (CF3)2CCO molecule upon its multiphoton excitation that were obtained at several values of delay time Δt. The peak with positive ΔkOD corresponds to the bleaching of the vibrational−rotational transition v = 0 → v = 1. Negative values of ΔkOD correspond to the absorption at higher lying vibrational transitions of the ν1 mode. The negative peak in Figure 1a corresponds to the transition v = 1 → v = 2. Its maximum for the delay time Δt = 0.8 ps is redshifted by Δνsh = 25 cm−1. This shift agrees well with the estimate of the anharmonic shift Δνanh = 25.4 cm−1 in the ν1 mode that we obtained from our measurements of the first overtone 2ν1 spectrum (see Table 1). The presented spectra Table 1. Some Characteristics of the Fundamental ν1 Mode of (CF3)2CCO and Its First Two Overtones vibrational band maximum band position (cm−1) full width at half-maximum (cm−1) difference between widths (cm−1) transition frequencies (cm−1) anharmonic shifts (cm−1)

ν1

2ν1

3ν1

2194

4362.6

6510.9

18.1 ± 0.1

24.3 ± 0.3

28.0 ± 0.2

6.2

3.7

1→2 2168.6 25.4

2→3 2148.3 20.3

0→1 2194

show that excited molecules mainly populate the vibrational levels v = 1 and 2. Then, the spectra have rather long “tails”. In total, the spectrum at Δt = 0.8 ps corresponds to that obtained

Figure 2. Dependences of the ΔkOD signal at the ν1 mode on delay time Δt at wavenumbers corresponding to the transitions (a) 0−1, 1−2, and 2− 3 and (b) 3−4 and 4−5. Symbols correspond to experimental values, curves are results of calculations (see below), and black circles for the 3−4 transition present the exponential approximation. The energy fluence is Φpump = 70 mJ/cm2. C

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transitions |n1 = 0⟩ → |ni > 0⟩ (without changes in the remaining vibrational quantum numbers)]: • The histogram of transitions for an ensemble of vibrational states at any given energy Evib, where the number of close states is ≫1 (for the (CF3)2CCO molecule, this requirement is fulfilled with a window of 1 cm−1 starting immediately from 500 cm−1, whereas the average energy at room temperature is about 1500 cm−1 and the population of the ground state is ≤1%), can be well approximated by the Gaussian ÑÉ ÅÄÅ GE Å (ω − ω̃ )2 ÑÑÑ ÑÑ G (ν ) = expÅÅÅÅ− ÑÑ ÅÅÇ σ π σ2 (4) ÑÖ where ν1 is the fundamental frequency. • The three parameters of Gaussian (4)integral GE, position of the maximum ω̃ , and the half-width at the e−1 levelcoincide with the calculated average intensity, average frequency, and standard deviation. • The parameter GE coincides with the total population of levels at Evib, and the parameters ω̃ and σ are well described by linear dependences on Evib. We will use these summarized properties and simulate contributions of all populated vibrational states, attributing the two parameters

experimentally measured spectra of the fundamental n1 = 0 → n1 = 1 band and the first overtone n1 = 0 → n1 = 2 band. To obtain data necessary for calculations, using the IFS125HR Fourier spectrometer (Bruker), we measured the spectra of the first and second overtones of the ν1 mode at room temperature with a resolution of 0.1 cm−1. The measurement results are given in Table 1. We note that the width of the first overtone of the ν1 mode, 2ν1, is greater than the width of the fundamental tone by 6.2 cm−1, whereas the width of the second overtone of the ν1 mode, 3ν1, is greater than the width of the second overtone by 3.7 cm−1; i.e., the bands of the ν1 mode and its first two overtones broaden in decreasing order. The anharmonic shifts for these bands also differ noticeably. First of all, we will calculate the spectra of the n1 = 0 → n1 = 1 and n1 = 0 → n1 = 2 bands at room temperature including all vibrational−rotational transitions. For the rotational constants, we will use the following values: A0 = 0.046 cm−1, B0 = 0.035 cm−1, and C0 = 0.025 cm−1, as was defined in ref 14. To simulate these spectra, we should also know the rotational constants for the states |n1 = 1⟩ and |n1 = 2⟩. Since the ν1 vibration occurs on the axis with the medium value of the moment of inertia, we neglect changes in constant B. As for changes in the other two constants, we will treat them as unknown parameters of the model, which are introduced by the relations (for our purposes, it is more convenient to use these relations instead of the commonly used spectroscopic constants aA = A1 − A0 and aC = C1 − C0) A 0 − A n1

= aAn1 − bAn1(n1 − 1), A0 C0 − Cn1 = aC n1 − bC n1(n1 − 1) C0

ω̃0 → n1(Evib) = ν0 → n1 − a ω̃ [n1 − βn1(n1 − 1)]Evib

(5)

σ0 → n1(Evib) = aσ [n1 − βn1(n1 − 1)]Evib

(6)

to their ensemble at a given energy Evib. Here, as in eq 2, a similar, close to linear, dependence on n1 is introduced, with the same small parameter β, as was introduced by eq 3. Thus, we have the following seven parameters of the model:

(2)

aA , bA , aC , bC , a ω̃ , aσ , and β

where the nonlinear terms are assumed to be small; i.e., bA/aA ≪ 1 and bC/aC ≪ 1. The calculated spectra of the vibrational−rotational transitions serve as basic ones for further simulations that involve all populated vibrational states. Each such state |Φ⟩ is represented by a set of vibrational quantum numbers {ni}. Therefore, it contributes to the resulting spectra by anharmonic shifts Δν(Φ) 0→n1 of the |0⟩ → |dn1⟩ transition. These shifts depend on {ni} as

(7)

Our goal is to fit the results of model calculations to experimentally measured spectra of the fundamental 0 → 1 and first overtone 0 → 2 bands. To simplify the problem, we will reduce list (7) to four unknowns assuming that aC = aA and bA/ aA = bC/aC = β. Clearly, this assumption seems to be arbitrary, but it proved to be adequate to fit model calculations to experiment. The remaining four parameters that correspond to the best fit are presented in the first four columns of Table 2.

s Φ) Δν0(→ n1 = [n1 − βn1(n1 − 1)]∑ nixi1 i=2

Table 2. Parameters of the Model Corresponding to the Best Fit and Homogeneous Width due to IVR

(3)

where s = 27 is the number of vibrational degrees of freedom of our molecule, {ni} is the occupation number of mode νi, xi1 is the intermode spectroscopic anharmonicity constant due to anharmonic terms in the vibrational Hamiltonian, which couple mode ν1 with mode νi, and a small term, nonlinear in n1, is added for generality. If all xi1 and β are known, we can calculate the resulting spectra quite easily. As for the small value of β, it can be considered as an unknown parameter of the model, similarly to a and b in eq 2. However, the values of xi1 are not known in our case, and it is practically impossible to consider them similarly. Therefore, some other approach should be used. Fortunately, an approach to the description of an ensemble of anharmonic shifts based on statistical considerations has been developed in ref 15. Numerical experiments performed in this work led to the following basic conclusions [here, the conclusions are adapted to the case of

β

aA,C

aω̃ a

aσa

ϒIVRb (cm−1)

0.083

0.010

0.0019

0.0046

0.88

a

This parameter enters eqs 5 and 6 as a coefficient in front of energy Evib expressed in wavenumbers. bFor the transitions 0 → 2, the doubled value was used, in accordance with the IVR time of 3 ps.

Also, the fifth column was added to Table 2, which contains the value of the homogeneous width due to IVR. This value corresponds to the IVR time of 6 ps, and it was included in our calculation by convolution of the Lorentzian γIVR L(ω) = ÄÅ ÉÑ 1 2π ÅÅÅÅ(ω − ω̃ )2 + 4 γIVR 2 ÑÑÑÑ (8) Ç Ö with the inhomogeneously broadened spectra of the 0 → 1 vibrational−rotational transitions. Final results of calculations D

DOI: 10.1021/acs.jpca.8b11095 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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Figure 3. Experimental (symbols) and calculated (lines) spectra of (CF3)2CCO: (a) the ν1 band and (b) its first overtone 2ν1.

for the ν1 and 2ν1 vibrations are shown in Figure 3 together with experimental data. We can see good agreement between the model and experiment. The parameters presented in Table 2 were used to reproduce the spectra of the successive transitions n1 = 1 → n1 = 2, n1 = 2 → n1 = 3, and n1 = 3 → n1 = 4. Here, it should be noted that these spectra were calculated under the assumption that there are no changes in the distribution in modes other than ν1. Similar n1-dependences of all of the parameters were examined, i.e., almost linear but with a small nonlinearity introduced by parameter β. The parameter values for all three transitions are presented in Table 3.

The calculated spectra of the 0−1, 1−2, 2−3, and 3−4 individual vibrational transitions are presented in Figure 4a. The anharmonic shift between each pair of the spectra of individual transitions was chosen to be 22 ± 1 cm−1. After fitting of amplitudes, these spectra were used to obtain the theoretical summarized spectral dependence of ΔkOD. This dependence is shown in Figure 4b along with the experimental spectrum of ΔkOD obtained for unchirped, femtosecond pulses. The value of the anharmonic shift 22 ± 1 cm−1 ensured the best fit for the most intense experimental peaks corresponding to the 0−1 and 1−2 transitions. The theoretical spectrum was calculated assuming that the time delay between pump and probe pulses is “zero” (it is minimal), which can be estimated to be ∼120 fs. However, the experimental spectrum of ΔkOD was obtained at the minimum delay time of Δt = 0.8 ps. Unfortunately, we were unable to make the time delay shorter than 0.8 ps due to some technical problems. The spectrum of the 4−5 transition has also not been calculated because we failed to measure the experimental spectrum of the third overtone of (CF3)2CCO. Therefore, the theoretical dependence does not completely describe the “tail” of the experimental spectrum of ΔkOD. Nevertheless, we can indicate the main difference between the calculated and experimental spectra. The theoretical curve clearly shows the ΔkOD spectra of individual absorption bands. This is not surprising, since the values of the anharmonic shifts measured for (CF3)2CCO (25.4 and 20.3 cm−1) exceed the half-widths of these spectra (about 18 cm−1). At the same time, the experimental spectrum of ΔkOD does not have such features and is much more smooth (see Figure 1).

Table 3. Parameters of the Model Corresponding to the Best Fit and Homogeneous Width due to IVR on the Successive Vibrational Transitions transition

aA,C

aω̃ a

aσa

ϒIVR (cm−1)

1→2 2→3 3→4

0.0083 0.0067 0.0050

0.0016 0.0013 0.0010

0.0038 0.0031 0.0023

2.49 3.81 4.84

a This parameter enters eqs 5 and 6 as a coefficient in front of energy Evib expressed in wavenumbers.

Note that the parameters a for the rotational constants and those that describe the anharmonicity effects are equal to differences between their values for the upper and lower vibrational states; at the same time, ϒIVR for Lorentzian (8) are now sums of the IVR rates of the lower and upper levels.

Figure 4. (a) Calculated spectra of individual vibrational transitions at “zero” time delay (see text). (b) Experimental (symbols) and calculated (thick black line) ΔkOD spectra; individual ΔkOD spectra are shown by thin black lines; the experimental time delay is Δt = 0.8 ps. E

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The Journal of Physical Chemistry A The Effects of the Fluence, the Intensity, and the Chirp of Laser Radiation on the ΔkOD Spectra. The fluence and the IR intensity of femtosecond radiation, which is proportional to it, affect the induced absorption signal magnitude ΔkOD as follows. An increase in the radiation fluence by a factor of ∼2.5 (from 70 to 170 mJ/cm2) causes a nearly proportional increase in the ΔkOD signal from the 0−1 and 1−2 transitions and practically does not affect the amplitude of the ΔkOD signal from higher-lying transitions. For a few decades, the various methods of quantum control were employed to manipulate the course of physical and chemical processes (see the review in ref 16). The different tailored or combined IR laser pulses have been used (in experiment or by simulations) for optimization of multiphoton excitation of a selected vibrational mode in molecules.17−19 In particularly, a negative chirping of a femtosecond pulse arranges its frequencies such that they decrease from the beginning of the pulse to its end (from blue to red). Therefore, the frequency of the pulse is tuned to the frequencies of successive vibrational transitions in the molecule, which decrease due to anharmonicity. This allows optimization of vibrational ladder climbing of molecules and leads, e.g., to an increase in the dissociation yield.20 To negatively chirp a laser pulse in our experiments, a laser beam was passed through a LiF crystal with a thickness of 25 mm. In this case, the pulse duration increased from 120 to 800 fs. The result of this experiment is shown in Figure 5.

array allowed us to reliably determine the shape of the spectral distribution and its dynamics. The resonant multiphoton excitation of the ν1 mode in the (CF3)2CCO molecule by femtosecond IR radiation results in a selective excitation of rather high levelsup to v = 5 or maybe even higher (see Figure 1b). The spectral distribution has a rather peculiar shape: excited molecules are mainly located at the lowest levels v = 1 and v = 2, and only a small fraction of molecules are excited to higher states. Our experiments on the excitation of (CF3)2CCO molecules by negatively chirped pulses showed that the population of high-lying vibrational states can be substantially increased (see Figure 5), but the shape of the distribution as a whole is retained. The characteristic decay times of the ΔkOD signal that we measured in this work and the IVR times for the 0−1 and 1−2 vibrational transitions, τ = 6 ps, which are related to them, are well consistent with the same times, τ = 5 ± 0.3 ps, that were measured in ref 13. However, the dynamics that we observed in this work for high-lying vibrational transitions was much richer. First, we revealed that, as the level of the vibrational excitation increases, the characteristic decay times of the ΔkOD signal decrease from 6 to 3.5 ps (for the 4−5 transition), which was not measured in ref 13 (for more details, see below). Second, we revealed a fast dynamics of the ΔkOD spectrum near the frequency 2129 cm−1, which approximately corresponds to the position of the 3−4 transition (see Figure 1b). The characteristic decay time of the amplitude of ΔkOD at a frequency of 2129 cm−1 sharply decreases to τ = 1 ps compared to other transitions (see Figure 2b). In the same frequency range, the band of composite vibration ν2 + ν18 of (CF3)2CCO is situated, which is centered at 2138 cm−1. Apparently, this coincidence is not accidental, and we can assume that the resonance of excited vibrational transition 3−4 with composite vibration ν2 + ν18 contributes to the acceleration of the IVR and fast energy outgoing from the excited ν1 mode of (CF3)2CCO to the remaining vibrational modes of the molecule. In this case, composite vibration ν2 + ν18 may be considered as a so-called “doorway state”.6 As is mentioned above, the mostly expected dependence of the IVR rate on the vibrational quantum number v for (CF3)2CCO is linear due to Vv , v − 1 ∝ v (see above). However, in principle, it may be irregular, if the picture of intermode resonances changes with v.21 The hierarchy of vibrational couplings exists in this case that leads to multiple time scales of IVR dynamics.22,11 Also, in one case, the quadratic dependence of the Lorentzian contribution to the overtone spectra on v was observed.23,24 However, the quadratic law can hardly be explained as the IVR into the bath but can be naturally explained in terms of the dephasing due to the dynamics in the bath itself (see chapter 3 in refs 3 and 7). In our case, we observed, namely, such breaking of regularity due to accidental intermode resonance. As was already noted above, the calculated and experimental spectra of ΔkOD differ from each other rather noticeably. On the theoretical curve, individual absorption bands can be clearly seen, while the experimental spectrum is smoother. To clarify the reason for this, we approximated the experimental spectrum of ΔkOD by a sum of absorption bands, each of which had its own amplitude and repeated not the spectrum of individual transitions v = n → v = n + 1 but rather the spectrum of overtones of (CF3)2CCO. For the 1−2 and 2−3 transitions, the experimental spectra of the first and second overtones were taken. For the 3−4 and 4−5 transitions, model bands were used, the shape of which repeated the shape of the

Figure 5. ΔkOD spectra for nonchirped (1) and negative chirped (2) laser femtosecond pulses; the time delay is Δt = 0.8 ps, and the energy fluence is Φpump = 170 mJ/cm2.

It can be seen that the absorption caused by the 1−2 vibrational transition noticeably decreases, while the absorption of (CF3)2CCO molecules filling the higher vibrational transitions sharply increases. For the chirped pulse, the ΔkOD signal of the tail shows a maximum at a frequency of 2054 cm−1, the magnitude of which is 10 times higher than the ΔkOD signal for the pulse without chirp. Therefore, this experiment showed that the optimization of the frequency composition of a femtosecond pulse affects the degree of vibrational excitation of the ν1 resonance mode of (CF3)2CCO much stronger than the mere increase of the radiation fluence/ intensity.

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DISCUSSION An “instantaneous” registration of the spectra of induced absorption ΔkOD with IR detectors based on a CdHgTe linear F

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Figure 6. Experimental (symbols) and fitted (thick black line) ΔkOD spectrum at time delay Δt = 0.8 ps; individual ΔkOD bands are shown by thin black lines: (a) Survey ΔkOD spectrum; the spectrum in the rectangle is presented in a larger scale in part b. (b) “Tail” of the ΔkOD spectrum in part a.

beams was geometrically modeled. The final value l = 0.046 cm was selected after the calibration of ΔkOD 0,1 by directly measuring the absorption due to transition 0−1 in the spectrum of the transmitted pump radiation. Using experimental values of ΔkOD at the frequency of corresponding transitions, setting z8 = 0, and using σ0,1 = 4.1 × 10−18 cm2, which was determined from the IR absorption peak of the ν1 mode, we can calculate the distribution of molecules over levels of the resonant ν1 mode. This distribution obtained for Φpump = 70 mJ/cm2 is shown in Figure 7. Under these

experimental absorption bands of the first and second overtones, and the half-width of each next model band was increased by 5 cm−1 compared to the second overtone band and the preceding model band. The value of the broadening by 5 cm−1 was chosen as an average of the broadening of 2ν1 compared to ν1 and of 3ν1 compared to 2ν1 (see Table 1). The anharmonic shift between each pair of individual bands of ΔkOD, as before, was chosen to be 22 ± 1 cm−1. The result of this approximation is shown in Figure 6. We can see that this approximation describes much better the experimental spectrum of ΔkOD. In our opinion, the reason for this is as follows. The minimum delay time between the pump and probe pulses is 0.8 ps. This time is small compared to the relaxation time of 6 ps of the population of the first vibrational level. However, according to the predictions of the theory, even for the second vibrational level, this time is 3 ps (see below), and for the next levels, it should decrease inversely proportionally to v3. Therefore, the IVR rate for excited vibrational levels will increase, which will result in a decrease in the amplitudes of the absorption bands for individual transitions during the 0.8 ps delay and in their additional broadening. It seems that the approximation of individual bands by the spectra of overtones that broaden with increasing overtone number makes it possible to take into account the partial intramolecular relaxation of excited levels and, thereby, to better describe the experimental ΔkOD spectrum of the (CF3)2CCO molecule. As was already said above, quantitative information on the character of the initial vibrational distribution in the ν1 mode can be obtained from amplitudes of individual bands of the ΔkOD signal.13 From relation (1), the following system of equations for the relative population of levels zn can be obtained:

Figure 7. Reconstruction of the vibrational distribution in the ν1 mode at Δt = 0.8 ps and Φpump = 70 mJ/cm2 (dark bars). For comparison, the Boltzmann distribution for Tvib = 2353 K (gray bars) and the Poisson distribution for the average level of vibrational excitation of 0.31 quanta per molecule (white bars) are shown.

conditions, 26% of molecules are excited. The above-described procedure disregards the transverse and longitudinal inhomogeneities of the laser intensity distribution. We also neglected the contribution of homogeneous broadening because its width (∼1 cm−1) corresponding to the measured IVR time (see below) is much lower than the width (18 cm−1) of the ν1 absorption band. Nevertheless, the data of Figure 7 rather adequately represent the qualitative shape of this distribution. For comparison, this figure also presents the Boltzmann and Poisson distributions. The former describes the distribution of (CF3)2CCO molecules upon their heating under equilibrium conditions, while the latter distribution describes their multiphoton excitation with respect to a selected mode, in our case, ν1 (see, e.g., ref 25). To calculate these distributions, the equilibrium temperature (Boltzmann) or the average

Δk OD0,1 = −(lge) ·p0 lσ0,1(z1 − z 0 + 1), for transition 0−1 (9)

Δk OD v , v + 1 = −(v + 1)lge ·p0 lσ0,1(zv + 1 − zv), for remaining transitions

(10)

Here, p0 is the concentration of molecules, l is the intersection length of the pump and probe beams in the cell, and σ0,1 is the absorption cross section for transition 0−1. To determine the value of l, the intensity distributions of the laser radiation were measured in the transverse and longitudinal directions and the intersection region of the pump and probe G

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To solve this system for different v, the value of τIVR1 was taken to be 6 ps. This value was chosen because signals ΔkOD 0,1 and ΔkOD 1,2 decay with this characteristic time (see Figure 2a). This is not surprising because the relaxation of the population difference upon the 0−1 transition is directly related to the IVR at the first excited level v = 1. On the basis of this value, the IVR times at the next vibrational levels should be equal to τIVR2 = 3 ps, τIVR3 = 2 ps, τIVR4 = 1.5 ps, and τIVR5 = 1.2 ps. The lines in Figure 2 show the results of calculation of the system of eq 12 with these times. It can be seen that, even in terms of a simple model, the calculation makes it possible to determine the characteristic decay times of ΔkOD and to well describe the experimental curves. The only exception is the dependence ΔkOD 3,4(Δt) for transition 3−4, in which the calculation does not take into account an anomalously rapid relaxation of the signal, the possible reason for which we discussed above. Nevertheless, if we assume that τIVR3 is decreased to 1.5 ps, then the experimental dependence ΔkOD 3,4(Δt) can be satisfactorily approximated without worsening the agreement between calculation and experiment for the remaining transitions. Therefore, the processing of the experimental kinetic curves of ΔkOD(Δt) for different vibrational transitions that we performed on the basis of a simple model convincingly confirmed theoretical predictions that the IVR time decreases inversely proportionally to the number of the vibrational level.3

excitation level (Poisson) was chosen such that the fraction of excited molecules was 26%, as in the case of excitation by the femtosecond radiation. The average excitation level of (CF3)2CCO molecules was measured experimentally, and its value was equal to 0.34 ± 0.04 quanta per molecule, which agrees well with the value of 0.31 quanta per molecule that was used in calculations of the Poisson distribution. We can see that the character of the distribution differs substantially both from the Boltzmann distribution and from the Poisson distribution, and this difference increases with increasing quantum number v. The main distinctive feature of the distribution that was formed in the ν1 mode upon excitation of (CF3)2CCO molecules by the femtosecond radiation is the occurrence of an extended tail. One possible reason for this shape of the observed distribution may be that the femtosecond pulse that we used was partly negatively chirped (from blue to red). If the characteristic decay times of the ΔkOD signal at frequencies corresponding to the absorption bands of each particular vibrational level are measured and the relative populations of these levels are known, then it becomes possible to retrieve true IVR times. To do this, we will use the simplest phenomenological model, the scheme of which is shown in Figure 8. Let the characteristic IVR time for the first excited

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CONCLUSION In this work, we presented the results of experiments on the study of the resonant selective excitation of the ν1 mode in the (CF3)2CCO molecule by femtosecond IR radiation. We applied the IR pump−probe technique to investigate the dynamics of the induced absorption spectra of ΔkOD and IVR for different vibrational levels of this mode. We were the first, to our knowledge to determine the characteristic IVR times for each vibrational level of the ν1 mode and confirmed predictions of the theory that the rate of IVR is proportional to the vibrational quantum number v. We revealed that the ΔkOD signal of the 3−4 transition sharply decreases, which can be attributed to a nonproportional decrease in the IVR time at the vibrational level v = 3 because of its resonance with the composite vibration ν2 + ν18 = 2138 cm−1. From the comparison of the theoretical and experimental ΔkOD spectra, we inferred that it is necessary to take into account the broadening of absorption bands of high-lying vibrational transitions that is caused by a finite delay time between the pump and probe pulses. We showed that the optimization of the frequency composition of a femtosecond pulse due to its negative chirping has a much stronger effect on the level of vibrational excitation of the resonant ν1 mode of (CF3)2CCO than the increase in the radiation fluence/intensity.

Figure 8. Scheme of IVR for excited vibrational levels of the ν1 mode of the (CF3)2CCO molecule.

vibrational level with v = 1 be τIVR1. Then, according to ref 3, this time for the vth level will be given by τIVRv = τIVR1/v and its population nv will decrease exponentially with time t as follows:7 nv(t ) = n0, v exp( −tv /τIVR1)

(11)

where n0,v is the initial population of the vth level after its excitation by pumping pulse. In this model, we neglect all other physical processes leading to a change in the population of level v. Then, for experimental amplitudes ΔkOD v,v+1 for each transition v → v +1, we can write the following general equation Δk OD v , v + 1 = bv[nv(t ) − nv + 1(t )] + sv , v + 1

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AUTHOR INFORMATION

Corresponding Author

(12)

*E-mail: [email protected].

where sv,v+1 is the dilution factor.7 Similarly to (10), bv = av(v + 1)(lge)·p0lσ0 but with the difference that the adjustable parameter av = 1−1.8 appears, which is needed for quantitative fitting of the kinetics ΔkOD(Δt) due to the presence of factor sv,v+1 in (12).

ORCID

Vladimir B. Laptev: 0000-0001-8952-8212 Notes

The authors declare no competing financial interest. H

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ACKNOWLEDGMENTS We are grateful to S. A. Klimin (Institute of Spectroscopy, RAS) for the measurements of the IR transmittance spectra of overtones of the ν1 mode of the (CF3)2CCO molecule. This work was supported by means of the governmental budgetary financing of the Institute of Spectroscopy.

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REFERENCES

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