Supporting Materials

Transcription

1 Supporting Materials Figure S1 Experimental Setup Page Figure S (a) (b) (c) Feynman Diagrams Page 3-6 Figure S3 D IR Spectra Page 7 Figure S4 Kinetic Model Page 8 Figure S5 Van t Hoff Plots Page 9 1

2 k 1 k k 3 k k 3 k 1 Sample End View k e = k +k 3 -k Vib. Echo 1 Beam Combiner Local Oscillator MCT Array Monochromator k e k k 3 k 1 vibrational echo emission Sample τ 1 T w 3 τ figure S1 Figure S1. Experimental setup for performing the ultrafast D IR vibrational echo spectroscopy. The three input pulses have wave vectors k 1, k, and k 3. The vibrational echo pulse generated in the sample has wave vector k e = k + k 3 k 1. The vibrational echo signal is combined with the local oscillator pulse to heterodyne detect the signal. This provides full phase information. The heterodyned signal is dispersed by a monochromator and detected using a 3 element MCT array. The pulse sequence is shown at the bottom of the figure. At each T w, τ is scanned to produce an interferogram at each wavelength. The Fourier transform of the interferogram provides the ω τ axis spectrum. The Fourier transform taken experimentally when the monochromator disperses the heterodyned signal provides the ω m axis spectrum (see Figs. 3 and 4).

3 Figure S. (a): D IR spectrum at T w = 14 ps (see Fig. 3b). The peaks are labeled to indicate whether they are diagonal or off-diagonal and whether they involve the 0-1 transition region or the 1- transition region of the spectrum. (b) and (c): Double sided Feynman diagrams contributing to all peaks in the D IR spectrum. The spectra are purely absorptive, which comes from the sum of two experimental τ scans, that is, scanning pulse 1 from 0 to τ and then pulse from 0 to τ. The two scans, which correspond to the diagrams with wave vectors k 1 + k + k3 (rephasing) and k 1 k + k3 (non-rephasing), where ki is the wave vector of the input pulses. The sum of the data taken in these two scans yields a purely absorptive D vibrational echo spectrum.(1) ke is the vibration echo wave vector. The vibrational echo emissions follow the wave vector matched conditions, given above, for both sets of diagrams. ω c is the 0-1 transition frequency (631 cm -1 ) of the complexed phenol, ω f is the 0-1 transition frequency (665 cm -1 ) of the free phenol, ω ' c is the 1- transition frequency (538 cm -1 ) of the complexed phenol, ω ' f is the 1- transition frequency (575 cm -1 ) of the free phenol, and the dashed vertical arrows between pulse and pulse 3 represent exchange. (b): Diagrams for the 0-1 region of the spectrum (red peaks in Fig. 3). For either set of the diagrams, each peak comes from two equal contributions: the excited state path and the ground state path. Exchange is taken to occur only during the T w period for the off-diagonal peaks (CF and FC, see text). (c): Diagrams for the 1- portion of the spectrum (blue peaks, see Fig. 3). For either set of diagrams, each peak comes from only one contribution, the excited state path. Exchange is taken to occur only during the T w period for the off-diagonal peaks (CF 1 and FC 1, see text). Because of the difference in the origins of the blue and red peaks, the experiments can determine whether the vibrational excitation changes the system. In particular, it is possible to determine whether vibrational excitation modifies the exchange rates and even if it does, the combined analysis of the data from the 0-1 and 1- portions of the spectra permit the ground state thermal equilibrium dynamics to be obtained. 1. M. Khalil, N. Demirdoven, A. Tokmakoff, Phys. Rev. Lett. 90, 0474(4) (3). 3

4 (a) T w = 14 ps CF FF ω m (cm -1 ) CC FC CF 1 FF 1 CC ω τ (cm -1 ) FC 1 figure Sa 4

5 Rephasing Nonrephasing (b) excited state path ground state path excited state path ground state path Peak CC Peak FF Peak CF P e a k C F Peak FC figure Sb 5

6 (c) Rephasing excited state path Nonrephasing excited state path k e (ω c ) k e (ω c ) Peak CC 1 k 3 (ω c ) 1 k 3 (ω c ) 1 k e (ω f ) k e (ω f ) Peak FF 1 k 3 (ω f ) 1 k 3 (ω f ) 1 Peak CF 1 k e (ω f ) k 3 (ω f ) 1 k e (ω f ) k 3 (ω f ) 1 k e (ω c ) k e (ω c ) figure Sc Peak FC 1 k 3 (ω c ) 1 k 3 (ω c ) 1 6

7 fs ps 3ps 5ps 7ps 8ps ps 1ps 14ps Figure S3. The time dependence of the D IR vibrational echo spectra in the 0-1 transition region showing the growth of the off-diagonal peaks with increasing T w (the number shown next to each spectrum). Each spectrum has been normalized to its largest peak. figure S3 7

8 CF FF CC FC Kinetic Model D C k CF CC CF k C exchange k FC k F vibrational relaxation Cause signal to decay D F orientational relaxation d ([ CC ( t )] f C ( t, θ )) dt d ([ CF ( t )] f F ( t, θ )) dt = ( k C + k CF + D C I ) ([ CC ( t )] f C ( t, θ )) + k FC ([ CF ( t )] f F ( t, θ )) = ( k F + k FC + D F I ) ([ CF ( t )] f F ( t, θ )) + k CF ([ CC ( t )] f C ( t, θ )) equations describing time-dependence of peaks [ CC ( t)] Cos ( θ, t) 4 ( kc + kcf + 6 DC), kfc [ CC(0)] = exp t [ CF( t)] Cos( θ,) t 15 kcf, ( kf + kfc + 6 DF ) [ CF(0)] 1 ( k C + kcf), kfc [ CC(0)] + exp t 3 k CF, ( k F + k FC ) [ CF (0)] Solutions figure S4 Figure S4. Kinetic model and its mathematical solution. The material describes only the portion of the model for the peaks CC and CF. The treatment is identical for the two other peaks in the 0-1 portion of the spectrum and for all of the peaks in the 1- portion of the spectrum. In this model, orientational relaxation is taken to be diffusive. The exchange, vibrational relaxation, and rotational relaxation affect the two species at the same time. Exchange causes cross peaks to grow and the diagonal peaks to diminish. Vibrational relaxation and rotational relaxation cause all peaks to decay. In the model the vibrational relaxation rate constants and the orientational relaxation rate constants for the two species are independent. In the equations, [xx(t)] is the time dependent concentration, f i ( t, θ ) is the angular distribution function, I is the spherical harmonic operator, D i is the rotation diffusion coefficient, k i is the vibrational decay constant, and k ij is the exchange rate constant (C for complexed phenol and F for free phenol). [ XX( t)] Cos ( θ, t) in the solution represents the vibrational echo signal for each peak generated from parallel polarized input pulses. More mathematical details of the treatment of the orientational relaxation under exchange have been presented (). The data points in fig. 5B and 6D are obtained by scaling ((divided by) scaling factor: free peaks, 1; complex peaks,.3 ; exchange peaks,.3) the volume of each peak with the transition dipole moment 8

9 difference ((µ complex : µ free ) = ε complex : ε free =.3) measured from FTIR, according to the fourwave mixing theory (3). The fitting curves are obtained by employing the parameters (only the exchange rate is adjustable, the others are measured) listed in text into the solution of the kinetic model. () Dynamics in Complex Liquids, Hu Cang, PhD thesis, Stanford University, pages 9-3 (4). (3) S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford University Press, New York, 1995). 9

10 0 Phenol in Benzene-CCl 4 Phenol in P-xylene-CCl 4 Phenol in Bromobenzene-CCl 4 R(lnK) /T figure S5 Figure S5. Van t Hoff Plots for the three phenol complexes used to determine complex formation enthalpies, H 0. R is the gas constant. K is the equilibrium constant for the standard state (see text). The data were obtained by measuring the temperature dependence of the IR absorption spectrum. The areas of the peak for the complex and the peak for the free phenol were determined at each temperature and used to obtain K. At room temperature, the enthalpies are 1.1, 1.67, and.3 kcal/mol for phenol-bromeobenzene, phenol-benzene, and phenol-pxylene, respectively.