Erratum: “Ultrafast vibrational spectroscopy (2D-IR) of CO₂ in ionic liquids: Carbon capture from carbon dioxide’s point of view” [J. Chem. Phys. 142, 212425 (2015)]

We previously investigated two-dimensional infrared (2D-IR) spectroscopy of $CO2$ in alkylimidazolium ionic liquids.¹ Peak 1c (Fig. 5 in the original paper) was not assigned in the original paper. Pump power-dependence, frequencies, and sign show that it is a fifth-order signal, as are several other features. The correct assignments of the $ν3$ 2D-IR spectrum of carbon dioxide in 1-butyl-3-methylimidazolium trifluoroacetate $[C4C1Im][TFA]$ are given in Fig. 1 and Table I.

The magnitude of a third-order signal is linear in pump light intensity since there are two pump electric field interactions, while that of a fifth-order signal (with four electric field interactions) is quadratic. We assessed the magnitude of each peak when the pump power was changed by a factor of two (Table I). There is a clear distinction between the pump power dependence of the third order signals (1a, 1b, 2a, 2b, and their population exchange cross-peaks) and the fifth order signal (1c, 3a, 3b, and 31a). The reported intensity ratio is the ratio of volumes of a single peak when the pump power doubles. Thus, for the main “red” peak (1b: $ν3$ excited state absorption with ground state $ν2$⁠), peak volume goes up by a factor of $2.2±0.1$ when pump power doubles. Peak 1c’s volume, however, increases by a factor of $3.3±0.2$⁠.

The fifth-order perturbative pathways have previously been described by Garrett-Roe and Hamm for 3D-IR (five IR pulses) spectroscopy.² The assignment of a “name” for each fifth-order pathway (Table I and Fig. 2) follows the scheme used by Garrett-Roe and Hamm, where pathways are described by listing the vibrational quantum numbers of the three coherent states that contribute to them. Non-rephasing diagrams are shown for all pathways.

Since a 2D-IR experiment only has two coherence times (which give two frequency axes), we can only resolve two of the three coherences in the fifth-order pathway. When up-pumping occurs during the first two (“pump”) pulses, either t₁ or t₃ will be unresolved. Thus, each pathway can give two spectral peaks on a 2D-IR spectrum if the coherent frequencies in t₁ and t₃ differ. For fifth-order pathways in Table I, the coherence noted in parentheses does not contribute to the observed peak since oscillation of the first coherence will not be observed when there are multiple electric field interactions during a single 100 fs pulse. That is, the pathway $10|21|32$ contributes to peaks 1c and 1f. Peak 1f results from up-pumping during the first pump pulse, $10|21|32$⁠, and thus only the $|21|$ and $|32|$ coherences are observed. Peak 1c results from up-pumping during the second pulse, $10|21|32$⁠, and thus only the $|10|$ and $|32|$ coherences are observed. The center frequency and sign of the peak amplitude for each observed fifth order peak match those predicted by the corresponding fifth-order pathway (Table I).

The peaks 1c, 3a, 3b, and 3-1a are fifth-order signals, not cascading third-order signals. Two of the peaks, 1c and 3b, cannot be generated by a cascade because they involve walking up the vibrational ladder to a $|32|$ coherence. Given the presence of these unambiguously direct fifth-order signals, we would expect to find spectral contributions from other fifth-order pathways. Peaks 3a and 3-1a are located where we would predict an additional fifth-order signal. The correspondence of the sign of the signal to those predicted by a direct fifth-order pathway is also important because the relative signs of cascading third-order signals and fifth-order signals are opposite (due to the difference of i² in the pre-factor in the infrared). Furthermore, the relative magnitudes follow the predictions based on the various pathways through population states and harmonic transition dipole moment scaling.² Finally, the relative peak intensities, including those of direct third-order signals, do not substantially vary with the concentration of the chromophore (data not shown). Cascaded signals scale proportionally to c², and thus would not scale with the other peaks on the spectrum.

A corrected version of Fig. 5, which contains the peak labels and energy level diagram, from the original paper is included (Fig. 1).

The microscopic rate constant (k_up) for $CO2$ bending mode fluctuations in $[C4C1im][TfO]$⁠, from the Monte Carlo simulations, was not given. It is estimated to be $kup=2.5±1ns−1$⁠. The corresponding down rate, which is analogous to the vibrational relaxation rate in off-equilibrium pump-probe experiments, is estimated to be $kdown=30±12ns−1$⁠. The kinetic Monte Carlo simulations include the non-equilibrium pumping that was explained by Fayer et al.³ Their pump-probe measurements showed an increase in the ground state bleach band due to differences in the transition dipole moment between the ground state $|000$ and the “hot” band $|0110$ transition dipole moments. The 2D measurement resolves the excitation frequency, so those dynamics are visible as separate cross-peaks, where the pump-probe measurement observes the sum of the two peaks (the projection of the spectrum onto the $ω3$-axis). The main ground state bleach decays with bending mode exchange, and the cross-peak grows. If the dipoles of the two states are the same, these two terms cancel in the pump-probe measurement; however, the differences in dipole lead to effective rises in the pump-probe ground state bleach signal.

The conclusions of the original paper are unchanged.

The authors acknowledge the financial support from the National Science Foundation (No. CHE-1454105) and acknowledgment is made to the Donors of the American Chemical Society Petroleum Research Fund (No. PRF# 53936-DNI6) for partial support of this research.