Research
Three molecular vibrational modes and schematic representation of all intramolecular and molecule-cavity resonances.
Average (over 2 ps) survival probability of initial ZOS |3,0,0,0> with cavity mode frequency.
Distribution of inverse participation ratio (IPR) of different cavity mode frequencies.
We show that tuning the cavity frequency to a key reactant stretching mode results in a strong perturbation of the cavity-free IVR pathways. The resonance condition corresponds to the situation when the cavity mode is tuned to the NCO stretch mode of frequency 2260 cm-1. At the “on-resonance” condition, we observe a significant suppression of the average survival probability - which indirectly correlates with the observed[1] suppression of rate constant when cavity mode is tuned to the NCO stretch mode because it is a key vibrational mode involved in the transition state (TS) of the alcoholysis reaction. To analyze the nature of eigenstates under cavity coupling, we compute the inverse participation ratio (IPR). Which accounts for the total number of zeroth-order basis states participating in making up an eigenstate. we show the distribution of the participation ratio of all eigenstates of the coupled system belonging to a “superpolyad” 15 to clearly understand the localization and delocalization effect of the cavity mode. We observe that when the cavity mode is far “off-resonant”, the distribution is narrow with a peak at a low value of participation ratio which suggests that in this scenario, almost all the eigenstates are localized in the QNS. However, when the cavity mode is “on-resonance” condition, specifically in the range of ωc ≈ 2100- 2500 cm−1, we see a broad distribution with a peak at high values of participation ratio. This indicates that there is a high degree of delocalization of eigenstates happening in the QNS. At the resonance condition, eigenstates are highly delocalized over many zeroth-order states which explain facile IVR and fast decays of survival probability. Furthermore, the behavior of “localization-delocalization-localization” of eigenstates while tuning the ωc from low to high values, is qualitatively, similar to the observed[1] trend in the variation of the reaction rate constant with ωc.
Polariton Chemistry
Cavity Mediated Modulation of Vibrational Energy Flow Pathways
Recent experiments in polariton chemistry indicate that reaction rates can be significantly enhanced or suppressed inside an optical cavity. One possible explanation for the rate modulation involves the cavity mode altering the intramolecular vibrational energy redistribution (IVR) pathways by coupling to specific molecular vibrations in the vibrational strong coupling (VSC) regime. However, the mechanism for such cavity-mediated modulation of IVR is yet to be understood. In a recent study, Ahn et. al.[1] observed that the rate of alcoholysis of phenyl isocyanate (PHI) is resonantly suppressed when the cavity mode is tuned to be resonant with specific reactant and product vibrational modes. In particular, the role of the NCO-stretching mode of PHI was highlighted. Here we analyze the quantum and classical IVR dynamics of a model effective Hamiltonian for PHI molecule which consists of the high-frequency NCOstretch mode (ν6 = 2260 cm−1 ) and two key low-frequency phenyl ring modes (ν14 = 1175 cm−1 and ν16 = 1105 cm−1 ). We compute various indicators of the extent of IVR in the cavity-molecule system.
The cavity mode, particularly in the “on-resonance” condition, significantly perturbs the dynamics of IVR of the “off-coupling” case. Our primary focus is to highlight the subtle aspects of the competition between quantum and classical IVR dynamics. For the “off-coupling” limit, in the quantum (upper panel) case, more than 75% of the initial |3, 0, 0, 0⟩ population decays at around 250 fs. However, classically (lower panel), the decay of the population is even more - almost 90% of the initial excitation decays down at around a similar (≈ 250 fs) time scale. Vibrational quanta flow out of the initial |3, 0, 0, 0⟩ state to other ZOSs via series intramolecular resonances. In the “on-resonance” condition, Almost 100% of the initial population gets transferred to other ZOSs at around 100 fs time. Thus a properly tuned cavity mode actively participates in redistributing vibrational energy into different molecular modes. We also observe a very good classical-quantum correspondence.
Quantum (upper panel; a,b,c,d) and classical (lower panel; e,f,g,h) survival probabilities (black) of initial ZOS |3,0,0,0>. Cross-survival probabilities with other ZOSs (color-coded with legends), for which probability > 0.15 at any instant, are also shown. The first column is for without coupling case and the rest are for the scenario when the molecule is coupled to the cavity of various frequencies. ωc = 2260 cm−1 represents the “on-resonance” condition.
To summarize our findings:
We show that tuning the cavity frequency to a key reactant stretching mode results in a strong perturbation of the cavity-free IVR pathways.
We find that for ωc ≈ ωNCO an ultrafast and coherent energy exchange occurs between the NCO-stretch and the cavity mode. Subsequently, the IVR dynamics leads to extensive energy flow into the various molecular states.
However, the extent of IVR is strongly mode-specific and depends upon the cavity frequency as well as the nature of the molecular anharmonic resonances.
In the VSC regime, the cavity mode efficiently scrambles the initial zero-photon state over the molecular quantum number space, as indicated by the behavior of the Shannon entropy (not shown here) and participation ratio distributions.
We observe an excellent agreement between classical and quantum dynamics. Our dynamical studies also allow for the identification of purely quantum effects that may be relevant for polariton chemistry. Back
Some Relevant References:
Ahn et. al., Science, 380, 1165-1168 (2023).
S. Mondal, S. Keshavamurthy, Cavity Mediated Modulation of Vibrational Energy Pathways in a Molecule, 2024. (To be submitted)
