STUDY ON THE VIBRATIONAL DYNAMICS OF PHENOL AND PHENOL-WATER COMPLEX BY PICOSECOND TIME- RESOLVED IR-UV PUMP-PROBE SPECTROSCOPY Yasunori Miyazaki, Yoshiya Inokuchi, Takayuki Ebata Department of Chemistry, Graduate school of Science, Hiroshima University

Vibrational Energy Relaxation Intramolecular Vibrational energy Redistribution (IVR) Fermi’s Golden Rule = anharmonic coupling = density of bath state

Vibrational Energy Relaxation Intramolecular Vibrational energy Redistribution (IVR) Anharmonic coupling (normal mode analysis) Anharmonic term C sij = q s q i q j = anharmonic constant Evaluation of coupling among vibrational modes: s, i, j Fermi’s Golden Rule

IR spectrum of phenol % transmittance in solution Large red-shift Reduced force constant of the OH bond Spectral broadening Vibrational Energy Relaxation Fermi Resonance with overtone and/or combination band Inhomogeneous broadening due to random geometries etc Free OH stretch Hydrogen-bonded OH stretch

IR spectrum of phenol *T. Ebata, et. al., International Journal of Mass Spectrometry, Vol. 159, pp. 111 (1996). in supersonic molecular beam * % transmittance in solution Free OH stretch Hydrogen-bonded OH stretch

Experimental Setup Supersonic Molecular Beam Directional (minimizing the Doppler effect) Population at the lowest vibrational energy level of S 0 Isolated condition Resolution: 14 ps, 5 cm -1

phenol-d 0 transient 1+1 REMPI * Energy diagram Y. Yamada, et. al., J. Chem. Phys., Vol. 120, No. 16, pp (2004). a) OH = cm -1 b) bath = cm -1 ν OH = 3656 cm -1

phenol-d 0 Time Profile a) OH b) bath state Energy diagram ν OH = 3656 cm -1 decay τ = 14 ps rise τ = 14 ps

Summary 1 *Petkovic, M. Journal of Physical Chemistry A, Vol. 116, pp (2012) doorway state γ CH * bath state ν CH *

phenol-d 1 Energy diagram transient 1+1 REMPI a) OD = cm -1 b) doorway = cm -1 ν OD = 2700 cm -1 OD 1 0 6a

phenol-d 1 Time Profile IR O D Energy diagram ν OD = 2700 cm -1

Time evolution of existence probability after time t phenol-d 1 OD: Doorway: Bath:

Fitting parameters * α 1 = β 2 1 = α 2 = β 2 2 = α 3 = β 2 3 = Assignment of the doorway state l a b 1 Summary 2 Energy gap E 13 = cm -1 E 23 = cm -1 E 12 = cm -1 IVR lifetime τ 2 1 = 80 ps τ 2 2 = 90 ps τ 2 3 = 60 ps Y. Yamada, et. al., J. Chem. Phys., Vol. 121, No. 23, pp (2004).

Energy diagram phenol-d 1 ▪ (D 2 O) O D ＩＲ Ｏ D H-bonded ν OD = 2600 cm -1 a) OD = cm -1 b) cm -1 c) cm-1 d) cm -1 transient 1+1 REMPI

Time Profile phenol-d 1 ▪ (D 2 O) O D ＩＲ Ｏ D intramolecularVR τ 1 = 12 ps intermolecularVR τ 2 = 24 ps VP τ 3 = 100 ps Energy diagram H-bonded ν OD = 2600 cm -1

Time Profile phenol-d 0 ▪ (H 2 O) O D ＩＲ Ｏ D * Doi, A.; Mikami, N. J. Chem. Phys. Vol. 129, pp (2008) intramolecularVR τ 1 = 4 ps * intermolecularVR τ 2 = 5 ps VP τ 3 = 25 ps Energy diagram H-bonded ν OH = 3525 cm -1

phenol-water complex RRKM theory Energy scheme phenol-d 1 (D 2 O): phenol-d 0 (H 2 O): 1525

Summary 3 *Petkovic, M. Journal of Physical Chemistry A, Vol. 116, pp (2012) dominant Intermolecular vibrational mode for dissociation *

Future Works  Obtain more data about IVR process of phenol-derivatives after the OH stretching vibration  Measure the predissociation lifetime of various H-bonded phenol-d 1 ▪(X) complexes where X = (π-type) acetylene, ethylene, benzene, (σ-type) dimethyl ether, etc Effect of intramolecular hydrogen-bonding? Coupling of non-CH related vibrational modes and its IVR rate? Comparison to the dissociation lifetime of phenol-d 0 (X) complex

Introduction Molecular Vibration = periodical oscillation of atoms in a molecule ● Harmonic “ball and spring” model ● Anharmonic (Morse) -dissociation energy -overtone and coupling among vibrations →realistic picture of bond a diatomic molecular system

Introduction Vibrational Energy Relaxation (VER) in solution 1. Excitation OH vibrational mode of the target molecule 2. Irreversible energy redistribution via anharmonic couplings with other internal vibrational mode(s) within molecule (IVR) 3. Energy transfer from the system to solvent molecules via anharmonically coupled degrees of freedom between them (VET) 4. Thermal equilibrium in the solution (VC)

Introduction Vibrational Energy Relaxation (VER) in jet Energy dissipation process from an activated vibrational mode to another that returns equilibrium on picosecond/femtosecond time scale ● monomer ● 1:1 complex

Time-resolved IR-UV pump-probe spectroscopy ● VER of monomer (IVR) ● Dissociation of H-bonded complex

2-fluorophenol ● only cis-form exists in jet intramolecular H-bonded OH stretching = 3639 cm -1 (17 cm -1 red-shift compared to bare phenol) Fitting of Time Profile time constant = 12 ps (IVR rate is accelerated by intramolecular H-bonding with F) 12 ps

phenol-d 0 Time evolution of each state population Fitting of Time Profile decaytime constant of OH 1 0 band = 1/k 1 = 14 ps riseassuming k2 >> k1, “OH stretch doorway state” energy flow is the rate- determining step of IVR from the OH stretching vibration

Time evolution of each state population ● quasi-stationary state: →Each n th state contains lOD>, ll 1 > and ll 2 > component ● coherently-excited quasi-stationary state: where, including the decay rate constant phenol-d 1

evaluation of weight of each constant C n at t = 0, only vibrationally excited lOD> state is created due to allowed transition and ● coherently-excited quasi-stationary state: Time evolution of existence probability of lOD> after time t, where phenol-d 1

Time evolution of existence probability of ll 1 > after time t, where Quantum Beats decay with phase shifts whose freq is determined by the energy gap between two states, excited within the laser pulse width phenol-d 1

Let eignestate |n> and its eigenvalue En At t = 0, eigenstate |k> By solving the time-dependent Schrodinger equation  is wavefunction and its time evolution is expressed Intramolecular Vibrational Energy Redistribution (IVR)

● Superposition state |s> =  cn|n> ● Self-interaction function Intramolecular Vibrational Energy Redistribution (IVR)

● Squaring the self-interaction function indicates the probability of occupying the initial state at time t Intramolecular Vibrational Energy Redistribution (IVR)

● Quantum Beats = radiationless decay with phase shifts ● For simplicity, two energetically closed-lying eigenstates, a and b, that strongly couple to a bath are considered for the derivation of quantum beats. Quantum Beats

● If the energy spacing between |a> and |b> is shorter than a laser pulse, |a> and |b> are “coherently” excited. ● These coherently excited |a> and |b> states couple to a bath with the decay rate constant ka and kb, respectively. ● Superposition of two stationary states Quantum Beats

● Superposition of two non-stationary states (or quasi-stationary state) Adding an exponential decay factor: k = k a ≈ k b Quantum Beats

self-interaction function Quantum Beats

● Squaring the self-interaction function indicates the probability of occupying the initial state at time t Quantum Beats

● Taking only the real parts of the product (any observable physical quantity must be real.) ● Quantum beats are oscillations whose frequency corresponds to the energy difference between the two coherently excited states Quantum Beats

phenol-d 5