Testing for memory-free spectroscopic coordinates by 3D IR exchange spectroscopy

Abstract

Using 3D infrared (IR) exchange spectroscopy, the ultrafast hydrogen-bond forming and breaking (i.e., complexation) kinetics of phenol to benzene in a benzene/CCl4 mixture is investigated. By introducing a third time point at which the hydrogen-bonding state of phenol is measured (in comparison with 2D IR exchange spectroscopy), the spectroscopic method can serve as a critical test of whether the spectroscopic coordinate used to observe the exchange process is a memory-free, or Markovian, coordinate. For the system under investigation, the 3D IR results suggest that this is not the case. This conclusion is reconfirmed by accompanying molecular dynamics simulations, which furthermore reveal that the non-Markovian kinetics is caused by the heterogeneous structure of the mixed solvent.

Keywords: 3D IR spectroscopy; solvent dynamics; ultrafast dynamics.

Fig. 1.

Sketch of (A) diagonal- and cross-peaks in a 2D IR exchange experiment. At short waiting time t, only diagonal peaks (CC and FF) are present. Upon increasing t, cross-peaks CF and FC emerge. (B) Diagonal- and cross-peaks in a 3D IR exchange experiment. At short t₁ and t₂ population times only two diagonal peaks corresponding to unchanged species C and F are present (CCC and FFF). Upon increasing t₁ and/or t₂, cross-peaks emerge (CCF, FFC, FCC, CFF, CFC, and FCF). The dotted lines show the projections of the 3D IR peaks onto the ω₁₂, ω₁₃, and ω₂₃ planes.

Fig. 2.

Absorption spectrum of deuterated phenol in a mixed benzene–CCl₄ solvent with two peaks: the OD-stretch vibration of a phenol-OD–benzene complex at 2,631 cm⁻¹ (ω_C) and that of free phenol-OD at 2,666 cm⁻¹ (ω_F).

Fig. 3.

3D IR spectra of phenol–benzene complexation at various population times (t₁, t₂). The (0.1, 0.1)-ps spectrum is shown fully in 3D, the other spectra only as projections onto the ω₁₂, ω₂₃, and ω₁₃ planes. Experimental data are shown in red, fits to the data in black. Emerging cross-peaks are assigned.

Fig. 4.

Correlation function as defined in Eq. 4 (black squares), together with an exponential (blue line) and a stretched exponential fit (red line).

Fig. 5.

Three-time-point joint probability functions p_CCC, p_FCC, and p_CCF deduced from (A) the MD simulation and (B) the two-state model which uses parameters deduced from 2D IR spectroscopy (11). Contour lines are in steps of 5% of the peak signal of p_CCC.

Fig. 6.

Ratios p_CCF/p_CCC and p_FCC/p_CCC for (A) experimental 3D IR data, (B) MD simulation, and (C) two-state model. Contour lines are in steps of 0.05 and are the same for all three plots. The dots in A (Insets) mark the positions where 3D IR spectra have been taken. Ratios p_FCC/p_CCC and p_CCF/p_CCC along t₂ and t₁, respectively, with the corresponding other time coordinate fixed to 3.0 ps.