Orientational isomerization of CO

The results obtained with the electrostatic model, presented in the previous section, clearly support the assignment of the two vibrational progressions to a stable blue-shifted C-down isomer and a metastable, red-shifted O-down isomer. In this section, the experimental data and the electrostatic model will be used to extract information on the mechanism for orientational isomerization from C-down to O-down.

It is important to realize that the C- and O-down orientations are separated by a large potential barrier. According to Fig. 5.5b, the barrier height is∼1200 cm⁻¹in the vibrational ground state. Furthermore, the C-down isomer is more stable by around 720 cm⁻¹ (not including zero-point energy (ZPE) corrections). Keep in mind that interactions other than electrostatic interactions are neglected and only orientational DOFs are included. Absolute energies and barriers extracted from the electrostatic model should thus be interpreted with care. Still, the estimated barrier height and energy difference between the two orientations are orders of magnitude larger than the thermal energy available at a surface temperature of 7 K (𝑘

B𝑇/ℎ𝑐≈5 cm⁻¹). Therefore, spontaneous interconversion in the vibrational ground state is not feasible on the timescale of the experiment and the large energy difference would definitely favor population of the C-down isomer. In conclusion, isomerization can only occur for higher vibrational states.

Chapter 5 Laser-induced orientational isomerization in the CO/NaCl(100) monolayer Stabilization of the O-down isomer in high vibrational states

The strong vibrational state dependence of the electrostatic interactions, which is responsible for the fundamental frequency shift, could be relevant to the isomerization dynamics as well. Consider again the interaction of the molecular dipole moment with the surface electric field. As apparent from Table 5.2, the polarity of the dipole moment in the ground state is described by C^𝛿−O^𝛿+polarity (𝜇≈0.125 D), leading to an attractive interaction with the electric field for the C-down orientation. For𝑣 =5, the sign of the dipole moment inverts and the interaction becomes repulsive. In the highest vibrational state observed in the experiments,𝑣 =30, the repulsive dipole-electric field interaction would be more than five times stronger than the interaction in𝑣 =0 (𝜇≈ −0.66 D). [125]

The increasingly repulsive dipole-electric field interaction for high vibrational states should therefore destabilize the C-down orientation. The O-down orientation, on the other hand, would be stabilized, effectively reducing the energy difference between the two isomers.

The electrostatic model presented in Section 5.1.3 can be used to estimate the change in the relative stability of the O-down and the C-down isomer (Δ𝐸(𝑣) =𝐸

O(𝑣) −𝐸

C(𝑣)) in high vibrational states, assuming that the linear dependence of the multipole moments in Table 5.2 still holds. Figure 5.7 compares the calculated PES cuts of𝑣 =0 and𝑣 =30 at 𝜙=90°, along which the C-down and O-down minima are located. In𝑣 =30, the energy difference between the two isomers is significantly reduced fromΔ𝐸(𝑣 =0) ≈720 cm⁻¹ toΔ𝐸(𝑣 =30) ≈100 cm⁻¹, resulting in a change of−620 cm⁻¹. This semi-quantitative trend shows that the vibrational dependence of the electrostatic interactions strongly stabilizes the O-down species relative to the C-down species for high vibrational states of CO. A similar trend is reported in a recent DFT study of the CO/NaCl(100) system, using 𝑝(1×1)and𝑝(2×2)unit cells that contain a single CO molecule. [142]

The change in the relative stability can also be extracted based on the experimental emission spectra, including ZPE contributions. With the fitted spectroscopic constants of the C-down and O-down isomer in the bare monolayer (Table 5.1), it is readily calculated from the corresponding term values𝐺

C(𝑣)and𝐺

O(𝑣)(see Eq. 5.1):

Δ𝐸(𝑣 =30) −Δ𝐸(𝑣 =0) =

𝐺O(𝑣 =30) −𝐺

C(𝑣 =30)

−

𝐺O(𝑣 =0) −𝐺

C(𝑣 =0) . (5.6) The resulting value of −540 cm⁻¹ indicates a significant stabilization of the O-down isomer relative to the C-down isomer in𝑣 =30 compared to𝑣 =0, which is in surprisingly good agreement with the electrostatic model. Unfortunately, only the change in the energy difference can be extracted from the experiment, but not its absolute value.

106

5.1 Results

-180 -120 -60 0 60 120 180

Tilt angle (°) 0

500 1000 1500

Potential energy (cm)

v=0 v=30

Figure 5.7: Comparison of the electrostatic PES cuts (𝜙=90°) obtained from the electrostatic model for different tilt angles of a single CO molecule in𝑣 =0 (black curve) and𝑣 =30 (red curve). As in Fig. 5.5c, both potential curves are referenced to the electrostatic interaction energy for the C-down minimum in𝑣 =0. Note that only the electrostatic interaction energies relative to CO(𝑣) are considered and that the unperturbed𝑣 =30 state actually lies at much higher absolute energies than the𝑣 =0 state.

However, the large stabilization suggests that high vibrational excitation could favor population of the O-down isomer, whereas the C-down isomer is clearly favored in the vibrational ground state.

Kinetic interpretation of the isomerization

Although the presented results are consistent with a stabilization of the O-down species in high vibrational states, the presented vibrationally adiabatic electrostatic model cannot explain why isomerization should occur. Whereas Fig. 5.7 implies that the barrier for interconversion is reduced substantially for 𝑣 = 30, the barrier is still too large to be overcome at cryogenic temperatures.⁴ Potential mechanisms that could explain isomerization despite the large barrier will be discussed in Section 5.2.2, together with recent theoretical work. Nevertheless, some information on the isomerization dynamics can be deduced from the experimental observations, as presented in the following.

Since isomerization probably occurs in the highest vibrational states, lower vibrational states of the O-down isomer can only be populated by vibrational relaxation. However, emission from the O-down isomer is observed for all vibrational states down to𝑣 =4 within the first 200µs after laser excitation (see Fig. 5.1)—despite the fact that the effective

4Note that the cuts through the PES do not resemble the minimum energy path.

Chapter 5 Laser-induced orientational isomerization in the CO/NaCl(100) monolayer lifetimes for vibrational relaxation are much longer. Relaxation starting from the highest vibrational states of the O-down isomer would require several milliseconds to populate 𝑣 =4 (compare with Fig. 4.10). Therefore, the emission from low vibrational states of the O-down isomer indicates that the lifetime for back-conversion to the C-down isomer is longer than the time between two laser pulses (100 ms).⁵ In this case, population in the O-down isomer survives relaxation to the vibrational ground state on the millisecond timescale and can participate in the VEP process following the next excitation laser pulse. Eventually, the competition between back-conversion to the C-down isomer and population of the O-down isomer due to laser excitation will lead to a steady-state concentration of the O-down isomer.

Further evidence for a steady-state concentration is given by the temporal behavior of selected vibrational states, which is shown for a low vibrational state (𝑣 =7) and a high vibrational state (𝑣 =22) in Fig. 5.8. Without a steady-state concentration, the𝑣 =7 state of the O-down species could not be populated within the first microseconds after laser excitation. In addition, the shapes of the C-down and O-down time profiles barely differ for identical vibrational states during the first 300µs after laser excitation, where VEP dominates the vibrational dynamics. Only after 300µs, the time profile of the O-down isomer in𝑣 =22 deviates from the time profile of the C-down isomer in𝑣 =22.

This observation indicates that the VEP dynamics of the two isomers are comparable, which is also reflected in the similar intensity patterns observed in the experimental emission spectrum (Fig. 5.1). The finding that the VEP dynamics are similar is not entirely surprising, given that the difference in the harmonic frequencies of the two isomers (Δ𝜔

𝑒 ≈ −17 cm⁻¹) is even smaller than two times the anharmonic constant of the two species (2𝜔

𝑒𝑥

𝑒≈24 cm⁻¹).⁶

Alternatively, identical time profiles could indicate rapid interconversion between the O-down and the C-down species in the same vibrational state. In this case, the time profiles should also be correlated at late times and decay with the same relaxation rate, which is clearly not observed. More rapid decay of the O-down species is observed instead. Interestingly, the effective lifetimes of the O-down species are about 2 times shorter than those of the C-down species, for both𝑣 =7 and 22.⁷ The differences in the

5Recall that the lifetime for vibrational relaxation of the O-down molecule and the lifetime for back-conversion to the C-down isomer are two different quantities, both of which depend on𝑣.

6Recall that the excess energy, which determines the rate constant of a CO(n) + CO(m)→CO(n+1) + CO(m– 1) energy transfer process, is given byΔ𝐸

𝑛𝑚≈Δ𝜔

is similar for both species.

7Note that the effective lifetimes observed for the C-down isomer are in excellent agreement with those in Fig. 4.10.

108

5.1 Results observed lifetimes are so small that they can probably be explained by slightly different VEP and relaxation dynamics rather than isomerization dynamics. Unfortunately, a direct comparison of the temporal profiles of C-down and O-down states above𝑣 =22, where isomerization dynamics could probably be observed, is not possible because the corresponding emission lines overlap significantly.

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0

Figure 5.8: (a) Time profiles of the C-down (black squares) and O-down (red dots) isomer in 𝑣 =7 with a bin time of 2.56µs. (b) Time profiles of the C-down (black squares) and O-down (red dots) isomer in𝑣 =22 with a bin time of 2.56µs. (c) Rebinned time profiles for𝑣 =7 with a bin time of 40.96µs. (d) Rebinned time profiles for𝑣 =22 with a bin time of 20.48µs. Straight lines in panels (c) and (d) indicate exponential fits to the asymptotic decays for both isomers. The corresponding effective lifetimes are also noted. For all panels, a logarithmic y-axis is chosen to emphasize the similarities of the curve shapes and to highlight the exponential decay at long times. Also note that the absolute number of counts differs between the left and right panels due to rebinning.

Back-conversion of the O-down isomer to the C-down isomer was directly observed for the buried monolayer. The lifetime of the buried¹³C¹⁸O monolayer is indefinitely long at 7 K, as no change in the O-down absorption peak is detected over the course of

Chapter 5 Laser-induced orientational isomerization in the CO/NaCl(100) monolayer several hours. On the other hand, back-conversion at 22 K occured within about 20 min (see also Section 5.1.2). Recent experiments by Arnab Choudhury, using time-resolved FTIR measurements to probe the rate constants for the back-conversion in𝑣 =0, reveal a large activation energy of about 500 cm⁻¹, [143] which is consistent with the indefinitely long lifetime at 7 K.

Unfortunately, the absorption peak of the O-down isomer in the bare monolayer has not been detected with FTIR or LIF spectroscopy so far. Those spectra require several minutes to be acquired, which gives an upper limit to the time for back-conversion of the O-down isomer to the C-down isomer. In addition, the lifetime must be longer than the time between two laser pulses (100 ms). Therefore, the lifetime for back-conversion of the O-down isomer in the bare monolayer at 7 K can be estimated between approx. 0.1 and 100 s.

5.2 Discussion