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. 2024 Apr 22;15(17):4662–4668. doi: 10.1021/acs.jpclett.4c00646

Generation of High-Lying Vibrational States in Carbon Dioxide through Coherent Ladder Climbing

Ikki Morichika 1, Hiroki Tsusaka 1, Satoshi Ashihara 1,*
PMCID: PMC11073050  PMID: 38647557

Abstract

graphic file with name jz4c00646_0004.jpg

Mid-infrared laser excitation of molecules into high-lying vibrational states offers a novel route to realize controlled ground-state chemistry. Here we successfully demonstrate vibrational ladder climbing in the antisymmetric stretch of CO2 in the condensed phase by using intense down-chirped mid-infrared pulses. Spectrally resolved pump–probe measurements directly observe excited-state absorptions attributed to vibrational populations up to the v = 9 state, whose corresponding energy of 2.5 eV is 46% of the dissociation energy. By the use of global fitting analysis, important spectroscopic parameters in the high-lying vibrational states, such as transition frequencies and relaxation times, are quantitatively characterized. Remarkably, our analysis shows that 40% of the molecules are excited above the typical activation barriers in the metal-catalyzed CO2 conversions. These results not only demonstrate the promising ability of infrared excitation to produce elevated vibrational states but also represent a significant step toward accelerating CO2 conversions and other chemical processes via mode-specific vibrational excitation.

Controlling chemical reactions at the molecular level is one of the ultimate goals of contemporary physical chemistry.1 A promising way toward this goal is mode-specific excitation of the key reagent molecular vibration using mid-infrared (mid-IR) radiation.2−9 In the conventional thermodynamic control such as temperatures and pressures, reactions proceed under thermodynamic equilibrium conditions, where the supplied energy is distributed to all degrees of freedom of motion (namely, translation, vibration, and rotation) and to the entire system (e.g., solutes, solvents, and catalysts). In contrast, mid-IR radiation can selectively excite a specific molecular vibration participating in the reaction coordinate beyond the limit determined by thermodynamic equilibrium. Hence, it is expected to promote chemical reactions in desired directions while minimizing the energy given to the system, offering practical advantages, such as avoiding side reactions, solvent volatilization, and catalyst damage.

Such reaction control via vibrational excitation has been progressing with the development of mid-IR light sources.10 The first demonstration was reported to increase the rate of cis–trans isomerization of HNO2 using an incoherent thermal light source.11−13 Since the advent of mid-IR laser sources, enabling multistep vibrational excitation, or vibrational ladder climbing (VLC), a number of demonstrations were reported such as isotope separation14 and bond dissociation.15−17 Although most previous experiments were conducted in the gas phase, where the vibrational relaxation is relatively slow, the recent availability of high-energy ultrafast mid-IR lasers in a compact setup has opened a new avenue toward reaction control in the condensed phase. Stensitzki et al. demonstrated the acceleration of urethane and polyurethane formation by direct infrared (IR) excitation of the alcohol OH-stretching vibration and the isocyanate NCO-stretching vibration, respectively.18 Delor et al. demonstrated directing electron-transfer processes in donor–acceptor molecules by bond-specific IR excitation.19−21 Recently, we have demonstrated successful driving of ground-state dissociation of W(CO)6 by employing plasmonic near-fields of chirped mid-IR pulses.22−24

One of the important and challenging applications of VLC is controlling the conversion of CO2 into value-added chemicals. To date, a large number of industrial processes, based on thermodynamic control, have not been very effective because CO2 is a highly stable molecule, and most of them are endothermic reactions.25 Thereby, several alternative technologies are being investigated, such as electrochemical,26−28 photochemical,28,29 and plasma chemical30 pathways. In this research trend, several studies have theoretically suggested that vibrational excitation of CO2 can play an important role in the efficient conversion.31−33 However, little study has been done to experimentally investigate the impact of the CO2 vibration on the reaction efficiency due to the difficulty of mode-specific vibrational excitation with current conversion methods. To reveal the vibrational excitation effects, the mode-specific vibrational excitation of CO2 is essential. In this study, we report on successful demonstration of VLC in the antisymmetric stretching mode (ν3) of CO2 in poly(ethylene glycol) (PEG) solution via intense down-chirped mid-IR pulses by use of spectrally resolved mid-IR pump–probe spectroscopy.

As the measurement sample, a CO2-dissolved PEG solution is prepared (see the Experimental Methods section for a detailed description of the setup). We choose the PEG solution as a solvent because of its relatively high CO2 solubility34 and no resonant absorptions around the ν3 band. Figure 1 shows the absorption spectrum of the sample measured with an FTIR spectrometer. The intense absorption peak observed at 2337 cm–1 is attributed to the ν3 mode. In addition to the main band, a shoulder on the low-frequency side is present. This is called a hot-band,35−37 arising from a fraction of CO2 molecules thermally excited to the first excited state of the bending mode (ν2), namely |v2, v3⟩ = |1, 0⟩ → |1, 1⟩. By fitting the two peaks with a linear combination of two Lorentz functions, we obtain the center frequencies of 2337.0 and 2324.4 cm–1 and the FWHM line widths of 4.1 and 3.7 cm–1 for the ν3 band and the hot-band, respectively. The frequency shift by 12.6 cm–1 is due to the anharmonic coupling between the ν2 and ν3 modes.35−37

Figure 1.

Figure 1

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Absorption spectrum of CO2 in PEG solutions measured with an FTIR spectrometer. The intense peak centered at 2337 cm–1 is attributed to the ν3 mode, and its shoulder centered at 2324.4 cm–1 is attributed to the hot-band. The blue and orange shaded areas represent each component of the Lorentz function obtained by fitting with a linear combination of two Lorentz functions. The inset shows the spectrum over a broader region around the CO2 stretch absorption.

We performed spectrally resolved mid-IR pump–probe spectroscopy for probing VLC in the ν3 mode (see the Experimental Methods section for a detailed description of the setup). We use nearly Fourier-transform-limited (FTL) pump pulses with a fluence of 170 mJ/cm2, a center frequency of 2285 cm–1, and a FWHM bandwidth of 150 cm–1. The center frequency is deliberately red-shifted with respect to the fundamental frequency of the ν3 mode to spectrally cover the higher transitions of the anharmonic ladder. It is noteworthy that the fluence of the pump pulse is nearly an order of magnitude higher than those used in the previous studies conducting nonlinear-IR spectroscopy for CO2 molecules in the gas phase,38 water,39,40 ionic liquids,36,37,41−43 supported ionic liquid membranes,43,44 ion gels,45 and polymer matrices,46 where the molecules were excited to the vibrational levels of only a few quantum numbers.

In our experiments, the pump and probe pulses are linearly polarized, while the molecules are randomly oriented and rotate in solution. Therefore, both pump and probe efficiencies vary from molecule to molecule depending on the angle between the optical electric field and the molecular transition dipole.47,48 Here we set the probe polarization to the magic angle of 54.7° with respect to the pump polarization to measure population relaxation dynamics excluding rotational relaxation. In this condition, the pump-induced population change, averaged over all possible molecular orientations, is measured (see the Supporting Information for details).

Figures 2a and 2b display the measured transient spectra at varied delay times after excitation with the nearly-FTL pulses. Here, we report on the signal in terms of the absorbance change, ΔA = −log(T/T0), where T and T0 denote the probe transmittance with and without pumping, respectively. After excitation, the CO2 molecules exhibit a negative peak at the fundamental frequency, attributed to the ground-state bleach (v3 = 0 → 1) and stimulated emission (v3 = 1 → 0). In addition, they exhibit positive peaks at the lower frequency range, attributed to the excited-state absorptions: v3 = 1 → 2 at 2314 cm–1, 2 → 3 at 2290 cm–1, 3 → 4 at 2266 cm–1, 4 → 5 at 2241 cm–1, 5 → 6 at 2215 cm–1, 6 → 7 at 2193 cm–1, 7 → 8 at 2167 cm–1, and 8 → 9 at 2142 cm–1. These resonance frequencies, obtained by global fitting analysis (discussed below), agree well with the energy levels expected for a Morse potential:

graphic file with name jz4c00646_m001.jpg 1
graphic file with name jz4c00646_m002.jpg 2

By fitting the resonance frequencies using eq 2, we obtain the anharmonicity of χe = 0.52% and the corresponding anharmonic shift of 2χeω0 = 24.6 cm–1, which is consistent with those reported in the previous studies.36,38−40,45,49 From these results, we can conclude that the CO2 molecules are vibrationally excited up to the v3 = 8 state. Note that the small peaks observed between the |0, v3⟩ → |0, v3 + 1⟩ transitions can originate from the ladder transitions of the hot-band (|1, v3⟩ → |1, v3 + 1⟩).

Figure 2.

Figure 2

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Transient absorbance change spectra for varied delay times after excitation with (a, b) nearly-FTL and (c, d) down-chirped pulses. The insets in (a, c) are enlarged views of the spectra at around 0 ps delay time. The blue and red lines in (b, d) represent linear combinations of multiple Lorentz functions fitted to the measured spectra.

For further excitation, we employ temporal pulse shaping. A simple and effective way is to add a linear chirp to the pump pulse. Since the transition frequencies decrease while climbing the ladder, the climbing efficiency can be substantially enhanced by using a down-chirped pulse that maintains the instantaneous frequency resonant to the subsequent steps of the ladder.16,22,47,50 Here, we perform the pump–probe experiments using down-chirped pump pulses with the group-delay dispersion of −15000 fs2. For comparison, the fluence is adjusted to the same value as that of the nearly-FTL pulses used in the previous measurement.

Figures 2c and 2d represent the measured transient spectra after excitation with the down-chirped pulses. In addition to the peaks observed in the previous case, a new peak of the v3 = 9 → 10 transition is observed at 2118 cm–1, indicating the generation of vibrational populations up to the v3 = 9 state. Remarkably, negative peaks are clearly observed at the v3 = 4 → 5 and 5 → 6 transitions at early delay time. This suggests that the stimulated emission overcomes the excited-state absorption, demonstrating population inversions are formed: the population in the upper state is larger than that in the lower state.47 These results indicate that the down-chirping contributes to raising the vibrational population to higher-lying states.

Interestingly, the spectral features within the pump pulse duration are clearly different between the two cases, as shown in the insets of Figures 2a and 2c. A strong oscillatory structure is observed for the nearly-FTL pulse excitation, whereas positive absorbance changes shifting from the high-frequency side to the low-frequency side are observed for the down-chirped pulse excitation. The former is also observed for the sample cell without the solution, indicating that the origin is cross-phase modulation in the CaF2 window.51 In contrast, the latter is not observed for the PEG solution without dissolved CO2, suggesting that the observed signal certainly originates from the CO2 molecules. The transient spectra theoretically simulated based on the Liouville–von Neumann equation show a good agreement with the experimental data, leading us to presume that the observed feature reflects the dynamics of the sequential climbing following the chirp rate of the pump pulses (see the Supporting Information for details). Here the suppression of the cross-phase modulation signal should be due to the lower peak intensity of the down-chirped pulses. Note that weak oscillatory structures decaying toward negative delay times observed in both cases can originate from the perturbed free induction decay: the coherent polarization excited by the probe pulse is perturbed by the pump pulses.52,53

For further quantitative discussion, we perform global fitting analysis for the measured transient spectra at delay times of T ≥ 1 ps with a linear combination of Lorentz functions given by

graphic file with name jz4c00646_m003.jpg 3

where ωv,v+1 is the transition frequency, Av,v+1(T) is the amplitude, and Bv,v+1 is the FWHM line width of each transition line. Considering the transition frequency and the line width should not change with delay time, the corresponding fitting parameters (ωv,v+1 and Bv,v+1) are constrained to be equal for all spectra. The resulting fitting curves, represented by solid lines in Figures 2b and 2d, agree well with the measured data.

By using the parameters obtained from the global fitting, we extract vibrational populations at each delay time. As described in the Supporting Information, the band area of each absorbance change is given by

graphic file with name jz4c00646_m004.jpg 4

where C is a constant, μv,v+1 is the transition dipole moment, and N is the number density of molecules. ⟨ΔPv⟩ ≡ ⟨Pv⟩ – ⟨P0v⟩ is the difference in the vibrational population, averaged over all possible molecular orientations, with (⟨Pv⟩) and without (⟨P0v⟩) pumping. In our case, the molecules rarely exist in the excited states without pumping (⟨P0v=0⟩ = 1, and ⟨P0v ≥1⟩ = 0). Since the observed transitions are up to v3 = 8 → 9 for the nearly-FTL pulse excitation and up to v3 = 9 → 10 for the down-chirped pulse excitation, ⟨Pv≥9⟩ = 0 and ⟨Pv≥10⟩ = 0 are reasonably assumed for each case. Considering the small anharmonic constant of χe = 0.52%, we can assume that the transition dipole moments follow the harmonic oscillator formula: Inline graphic. By solving eq 4 with N and ΔSv,v+1, extracted from the linear and transient spectra, respectively, we can estimate excitation efficiency or vibrational populations of each state, averaged over all possible molecular orientations.

Figure 3a shows the estimated population distributions at a 1 ps delay time after nearly-FTL (blue) and down-chirped (orange) pulse excitation. In both cases, more than half of the CO2 molecules are shown to be vibrationally excited. Focusing on the distribution, it can be clearly seen that the population is distributed to higher-lying states for down-chirped pulse excitation, which is due to the efficient sequential climbing of the ladder. In particular, it has a maximum value in the v3 = 6 state, forming population inversion among the v3 = 4, 5, 6 states, which can be because the center frequency of the pump pulse is located around the v3 = 3 → 4 transition (see gray shaded areas in Figures 3b and 3d). In terms of the total energy given to the ν3 mode, the expected values of vibrational energy given by ∑v⟨Pv⟩Ev are estimated to be 3500 cm–1 (0.43 eV) for nearly-FTL excitation and 6000 cm–1 (0.74 eV) for down-chirped excitation, demonstrating simple down-chirping increases the excitation efficiency by 1.7 times.

Figure 3.

Figure 3

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(a) Vibrational population distributions at a 1 ps delay time after nearly-FTL (blue) and down-chirped (red) pump excitation. (b, c) Delay-time dependence of vibrational population of each state for (b) nearly-FTL and (c) down-chirped pulse excitation. Dashed lines represent fitting curves for each population relaxation. (d) Population relaxation constants for each vibrational level deduced from the transient spectra using nearly-FTL (blue marker) and down-chirped (red marker) pump pulses. The black dashed curve is an eye guide inversely proportional to the vibrational quantum number.

In the present experiment, the highest vibrational level to be populated is v3 = 9, whose corresponding energy of 20000 cm–1 (2.5 eV) is as high as 46% of the first bond dissociation energy (5.45 eV).54 While it may be difficult to dissociate CO2 directly, the use of a catalyst can open up the possibility of accelerating the conversion through vibrational excitation. For example, typical activation barriers for the metal-catalyzed CO2 conversions are less than 1.0 eV,32,55,56 corresponding to the vibrational energy of the v3 = 3 state. Our analysis shows that 40% of the CO2 molecules are excited into the v3 ≥ 3 states, indicating the potential for accelerating the reaction via vibrational excitation.

The VLC progression is currently limited by the available bandwidth of the laser spectrum: the spectral intensity at the v3 = 9 → 10 transition frequency is as low as 3% of that at the peak (see Figures 2b and 2d). To achieve VLC in the higher vibrational states, mid-IR pulses with a broader bandwidth are needed. For example, to address the vibrational states corresponding to the first bond dissociation energy, more than 500 cm–1 of the bandwidth is necessary. A possible solution is to broaden the bandwidth of the excitation pulses via self-phase modulation in a nonlinear crystal.57 Moreover, the excitation efficiency can be improved by employing more sophisticated waveform shaping beyond the down-chirping.58

Figures 3b and 3c show the estimated vibrational populations for each state as a function of delay time for nearly-FTL and down-chirped pulse excitation, respectively. For several middle states, the populations are found to first grow and then decay. This behavior can result from the combination of the population increase associated with relaxation from the upper state and the population decrease associated with relaxation into the lower state. To extract population relaxation rates (Γv) for each vibrational state, we model the population flow as following rate equations:

graphic file with name jz4c00646_m006.jpg 5

The analytical solution of eq 5 is given by

graphic file with name jz4c00646_m007.jpg 6

where vh is the quantum number of the highest vibrational state and cv’s are integration constants. By using eq 6, we fit the population dynamics in order from the upper vibrational level. The resulting fitting curves are shown by solid lines in Figures 3b and 3c, which are in line with the experimental data.

Figure 3d shows the obtained population relaxation time constants (τv = 1/Γv) for each vibrational level. The τ1 values are longer than those for CO2 in water (∼10 ps)39,40 and slightly shorter than those for CO2 in ionic liquids (∼60 ps).36,37,41,42 Considering that vibrational relaxation results from the energy flow into a combination of lower frequency modes, the difference in the lifetimes should be caused by differences in the local environments: different distributions and couplings of the bath modes.

As for the higher vibrational states, the relaxation times up to the third (fifth) level for the nearly-FTL (down-chirped) pulse excitation are found to almost inversely scale with the quantum number (black dashed line in Figure 3d), which is similar to that reported by Strasfeld et al. in W(CO)6.58 This tendency can be explained by a harmonic oscillator model linearly coupled to a thermal bath59 in consistent with the low anharmonic constant of the ν3 mode.

On the other hand, above the third (fifth) level for the nearly-FTL (down-chirped) pulse excitation, the tendency for the relaxation times to decrease according to the inverse square law becomes less pronounced. One possible reason for this discrepancy is intramolecular vibrational relaxation between the stretching and other vibrational modes, which is not considered in our rate equation model used for the numerical fitting. Previously, Giammanco et al. performed two-dimensional IR spectroscopy for CO2 in an ionic liquid and reported the presence of population transfer due to the anharmonic coupling between the stretching and bending vibrations.37 Similar anharmonic couplings can exist in higher vibrational states. Indeed, the sum of the estimated vibrational population slightly deviates from unity at early delay times (Figure S3), implying the existence of the anharmonic couplings. Additional experiments and analyses, such as detailed spectroscopic analysis and comprehensive fitting incorporating hot-bands, might be required to elucidate the intramolecular relaxation dynamics at higher vibrational levels. This represents the potential future directions for the presented work.

In conclusion, we successfully demonstrate VLC in the ν3 mode of CO2 in PEG solutions by using intense down-chirped mid-IR pulses. Spectrally resolved pump–probe measurements directly observe the induced absorption and emission lines up to the v3 = 9 → 10 transition. The observed transition lines are observed to be equidistant, in agreement with the energy levels expected for the Morse potential. The down-chirping contributes to raising vibrational populations to higher-lying states, resulting in population inversion at some of the ladder transitions. We also observe the sequential VLC dynamics following the chirp rate of the pump pulses revealed by suppression of the cross-phase modulation. By use of global fitting analysis, we quantitatively extract the time evolution of the population distributions from the measured transient spectra. The total vibrational energy given to the ν3 mode is estimated to be enhanced by 1.7 times by simple down-chirping. Remarkably, our analysis shows that 40% of the CO2 molecules are excited above the typical activation barriers in the metal-catalyzed CO2 conversions, indicating the potential for accelerating the reaction via vibrational excitation. Finally, the population relaxation dynamics are reasonably characterized by the analytical solution of the rate equations. Although the obtained relaxation constants for lower vibrational levels are found to inversely scale with the quantum number, which is expected for a harmonic oscillator linearly coupled to a thermal bath, those for higher vibrational levels are found to deviate from the inverse scaling law, implying the existence of anharmonic coupling with the other modes. Together with the further development of mid-IR laser technologies and optimal control theories, this study can not only demonstrate the promising ability of IR excitation to produce the elevated vibrational states but also represent a significant step toward vibrational control of the CO2 conversions and other chemical processes.

Experimental Methods

Sample Preparation

The sample solution is prepared by passing gaseous CO2 (99.9% purity) through 40 mL of poly(ethylene glycol) 300 (Wako Chemicals) for 1 h at a flow rate of 1 L/min under normal temperature and pressure conditions. The solution is held between two CaF2 windows (35 × 35 × 3 mm3) separated by 25 μm with a Teflon spacer.

FTIR Measurement

The linear absorption spectrum of the sample is measured with an FTIR spectrometer (FT/IR-4000, JASCO) under nitrogen purge. A total of 64 scans each with a resolution of 0.5 cm–1 are collected. During the experiments, the setup is continuously purged with dry nitrogen to suppress atmospheric background signals.

Pump–Probe Measurement

Femtosecond mid-IR pump–probe spectroscopy is performed with the following system. An integrated Ti:sapphire regenerative amplifier (Solstice Ace, Spectra-Physics) generating 90 fs, 7 mJ, 800 nm pulses at a 1 kHz repetition rate is used to pump an optical parametric amplifier followed by difference frequency generation (TOPAS, Light Conversion). The generated mid-IR pulses are 100 μJ in energy and centered at 2285 cm–1 with a FWHM bandwidth of 150 cm–1. A small fraction (4%) of the mid-IR pulses is split off with a wedged BaF2 window to obtain probe and reference pulses, and the remainder is used for the pump. Down-chirped pump pulses are generated by propagation through a 40 mm thick CaF2 crystal. The pump energy is adjusted with a pair of wire-grid BaF2 polarizers (WP25H-B, Thorlabs). The polarization of the probe pulse is set to the magic angle of 54.7° with respect to the pump pulse by placement of a pair of wire-grid ZnSe polarizers (WP25H-Z, Thorlabs). The pump and probe pulses are focused and spatially overlapped in the sample by an off-axis parabolic mirror with an effective focal length of 3 in. The fluences of the pump pulses are estimated to be 170 mJ/cm2 from the pulse energy of 30 μJ and the spot diameter of 150 μm at the sample position. To avoid window degradation, the sample is raster scanned vertically and horizontally during the measurement. The transmitted probe and reference pulses are dispersed by a 320 mm monochromator (iHR320, Horiba) with a 120 lines/mm grating and detected on liquid nitrogen cooled, 2 × 32 pixel HgCdTe detector arrays (Infrared Systems Development). To measure the population relaxation dynamics excluding the rotational relaxation, the polarization of the probe pulse is set to the magic angle of 54.7° with respect to the pump pulse by placement of a pair of wire-grid ZnSe polarizers (WP25H-Z, Thorlabs) before and after the sample. During the experiments, the setup is continuously purged with dry nitrogen to suppress atmospheric background signals.

Acknowledgments

This work was supported by JSPS KAKENHI Grants 20K20556 to S.A., 20K22518 to I.M., and 21K14584 to I.M. and by JST CREST Grant JP20348765 to S.A.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpclett.4c00646.

  • Description of pump–probe signals for vibrational ladder climbing in randomly oriented and rotating molecules, numerical simulations of excitation dynamics, and dynamics of total vibrational population (PDF)

The authors declare no competing financial interest.

Supplementary Material

jz4c00646_si_001.pdf (1.7MB, pdf)

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