J. Phys. Chem. 1996, 100, 11975-11983
11975
Conservation of Vibrational Excitation During Hydrogen-Bonding Reactions† Steven M. Arrivo and Edwin J. Heilweil* Optical Technology DiVision, B208 Building 221, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-0001 ReceiVed: February 19, 1996; In Final Form: April 22, 1996X
We report novel transient infrared “tag and probe” investigations of the equilibrium kinetics and vibrational energy transfer between the free acid Et3SiOH and its 1:1 hydrogen-bonded complex with acetonitrile, Et3SiOH‚‚‚NtCCH3, in dilute (0.1 mol/dm3 acid) CCl4 solutions at 293 K. Picosecond time-resolved infrared double-resonance spectroscopy measures the vibrational population of the OH-stretching mode (via V ) 1 f 2 absorption) after IR excitation of either the free acid or the homogeneously broadened OH(V ) 0 f 1) absorption of the complex. The free acid and 1:1 complex OH(V ) 1) population lifetimes (T1) and equilibrium reaction rate constants affecting hydrogen-bond formation and dissociation are unambiguously determined for this system. Tagged free acid OH(V ) 1) leads to complex formation with OH(V ) 1) excitation, indicating OH(V ) 1) population is maintained during collision and formation of hydrogen bonds. This is the only known example where OH(V ) 1) vibrational population of a polyatomic reactant is prepared and that excitation is followed during a condensed-phase bimolecular reaction which leads to an excited hydrogen-bonded product.
Introduction It is well-established that solutions containing proton donors (acids) and proton acceptors (bases) possess a dynamic equilibrium between the unassociated acid and base and their hydrogen-bonded complexes1
acid (free acid) + base h acid‚‚‚base (complex) Hydrogen bonds formed between the acid and base (e.g., containing nitrogen or oxygen lone pair donators) usually have quite low frequencies (typically 200 K) were unavailable. In this paper we apply picosecond time-resolved IR spectroscopy (psTRIR) to investigate detailed molecular vibrational population and hydrogen-bond formation/dissociation dynamics of acid-base reactions in real time. To more clearly investigate the detailed H-bond vibrational energy and reaction dynamics pertinent to biological systems, we elect to focus on dilute solutions (0.1 mol/dm3 acid, 0.002 mole fraction) of 1:1 acid-base complexes with assignable nonoverlapping IR absorptions. Several groups have utilized time-resolved methods to investigate H-bond and other bimolecular reaction rates and their relationship to molecular structure and solvent properties. For example, a gas-phase bulb experiment studying ethers complexed with hydrogen halides has been performed using tunable nanosecond IR pulses.4 Mataga et al. examined fluorescence † To Professor Robin Hochstrassersa sincerely dedicated scientist, teacher, and mentor. X Abstract published in AdVance ACS Abstracts, June 15, 1996.
quenching of electronically long-lived carbazole charge transfer complexes hydrogen-bonding with pyridine in solution.5 Coherent Raman6 and optical Kerr effect methods7 have also been used to examine solvent rotational effects in hydrogen-bonded solvents. Raftery et al. have used transient infrared spectroscopy to study the vibrational dynamics of product species in condensed-phase bimolecular reactions and found different results than observed for the same system in the gas phase.8 In those studies, a UV pulse photodissociates ICN, producing vibrationally hot CN• (with an unknown distribution of populated vibrational states), which reacts with CHCl3/CDCl3 to form excited HCN/DCN (CN stretch, V ) 0 and V ) 1) at slower than diffusion controlled rates. Graener et al. investigated the dissociation of hydrogen bonds of alcohols and water with psTRIR temperature jump methods.9 The alcohol studies and interpretation of the dynamics were apparently plagued by the presence of unassignable absorbing species (dimers, trimers, and oligomers) formed at high concentration (ca. 3 mol/dm3).9 Molecular dynamics simulations and analytical theories have also been performed to understand mode-specific vibrational relaxation rates of a hydrogen-bonded triatomic in a polar solvent10a and the alcohol oligomer dissociation experiments mentioned above.10b The hydrogen-bond formation process dramatically affects the vibrational spectrum of the high-frequency OH-stretching mode of the proton donor, red-shifting and severely broadening its V ) 0 f 1 and V ) 1 f 2 absorption bands.1,11 For example, the static FTIR spectrum of the equilibrium mixture of Et3SiOH (triethylsilanol ) TES, 0.095 mol/dm3) with the relatively weak base acetonitrile (ACN) in room temperature CCl4 (1.4 mol/ dm3) is shown in Figure 1. Such FTIR spectra taken at many concentrations allows one to conclude that the complex absorption arises from a 1:1 associated species and to extract the equilibrium constant (Keq) from intensities of the absorptions originating from the free acid and complex.1,12 For the TESACN system studied in this paper, Keq ) 0.96 ( 0.05 dm3 mol-1.13 Earlier psTRIR double-resonance experiments performed in this laboratory investigated the effects of hydrogen bonding on vibrational relaxation kinetics in weakly acidic amines (pyrrole NH-stretching mode),12 silanols (TES OH,OD-stretching modes),
S0022-3654(96)00483-2 This article not subject to U.S. Copyright. Published 1996 by the American Chemical Society
11976 J. Phys. Chem., Vol. 100, No. 29, 1996
Figure 1. Static FTIR spectrum of a room temperature (293 K), ternary solution of Et3SiOH-acetonitrile-CCl4 (0.1 mol/dm3 TES, 1.4 mol/ dm3 ACN). The arrows indicate peak absorption frequencies of the OH-stretching (V ) 0 f 1) mode for the free acid (3692 cm-1), 1:1 complex (3550 cm-1), and OH-stretching (V ) 1 f 2) transitions for the free acid (3525 cm-1) and complex (3383 cm-1). The solid line is a Lorentzian fit with 112 cm-1 fwhm. The round data points are transient absorption amplitudes obtained at 3383 cm-1 upon IR excitation at the indicated frequencies. The square data points are normalized (to FTIR absorption maximum) transient bleaching amplitudes obtained at the indicated frequencies with complex excitation at 3550 cm-1. See text and Table 1 for more details.
and methanol.14 We found that the vibrational population lifetimes (T1 ) 49 ( 5 and 183 ( 6 ps for dilute pyrrole and Et3SiOH in CCl4, respectively) of these high-frequency vibrational modes are reduced upon H-bond formation.12,13 The “free” proton donor (acid) OH-stretch vibrational relaxation rate can be enhanced by more than an order of magnitude and in proportion to the proton-accepting strength (or basicity) of the base forming the hydrogen-bonded complex. This strong correlation between the decrease of the observed NH- and OHstretching lifetimes and the strength of the hydrogen bond formed was observed with bases such as acetonitrile (ACN), acetone (ACT), tetrahydrofuran (THF), pyridine (PYR), and triethylamine (TEA). Bimolecular encounter experiments were also conducted on dilute ternary solutions of pyrrole with ACN12 and TES (0.1 mol/dm3) with bases (ACN, THF, PYR; 0.1-0.7 mol/ dm3) in CCl4 containing equilibrium mixtures of free acid and complexed acid (OH‚‚‚Base).13 Bimolecular reaction rate constants (kbm) were determined using Stern-Volmer analyses by measuring the T1 vibrational lifetime of the free acid (via V ) 1 f 2 absorption) as a function of base concentration. It was assumed that each encounter of a vibrationally tagged free acid produced an acid-base complex (with unit formation probability) and that the enhanced T1 decay rates did not arise from vibrational deactivation by collisions without H-bond formation. The extracted kbm rate constants for TES and pyrrole agree with estimates for diffusion-limited reaction and were found to be (1.2 ( 0.2) × 1010 and (2.4 ( 0.3) × 1010 dm3 mol-1 s-1, respectively.12,13,15 If microscopic reversibility is applied to H-bonded systems,9d then it is possible to extract the complex dissociation lifetime from the bimolecular association rate according to kdiss ) kbm/Keq. From independently acquired values for kbm and Keq mentioned above, it is found that the spontaneous unimolecular dissociation rate constant for Et3SiOH‚‚‚ACN in room temperature CCl4 solution is approximately 1.3 × 1010 s-1, which is significantly smaller than reported for ethanol multimers 2.0 × 1011 s-1 (ca. 5 ps).9 Our previous experiments which IR-excited the free acid OH stretch and measured its OH(V ) 1) lifetime did not investigate whether new complexes were formed with vibrational excitation
Arrivo and Heilweil
Figure 2. Energy level diagram for the Et3SiOH-acetonitrile-CCl4 system showing OH(V ) 0 f 1) and OH(V ) 1 f 2) transition frequencies for the “free” and acid-base complex species used in the transient ps TRIR experiments.
of the OH stretch or if formation of the hydrogen bond deactivated the OH-stretching vibration. Observing vibrationally excited complexes after IR excitation of the free acid OH-stretch mode directly affords the formation rate of the hydrogen bond. Such measurements would lend credence to the proposed “box” model kinetic scheme (see below) for these systems,5,9d,13 by confirming the earlier assumption that each encounter leads to complexation, and directly extract the reaction and vibrational decay rates. As discussed below, we demonstrate that vibrational excitation of the free acid is preserved with high efficiency as OH(V ) 1) population in the complex formed in the H-bonding reaction. We are unaware of any analogous gas- or condensedphase studies which directly probed vibrational excitation conservation in such large molecular systems during a bondforming chemical reaction. Experimental Section Experiments reported here use IR excitation (V ) 0 f 1 pumping) to “tag” a free or complexed acid (minimally perturbing the system and pKa) and the kinetics of the complex OH stretch are monitored with V ) 1 f 2 IR transient absorption methodology (see energy level diagram in Figure 2). This scheme ensures that only complexes with OH-stretch vibrational excitation are detected, allowing direct investigation of the equilibrium kinetics between free and complexed acid species in solution. The experimental apparatus used to perform these studies has been previously described in detail,12 and the technique is briefly explained. By using three amplified (20 Hz), tunable, synchronously-pumped (via grating compressed CW Nd+3:YAG SHG) dye lasers, two independently tunable IR pulses are generated by down conversion of two dye laser pulses in LiIO3 crystals. Pump pulses have nominally 2 ps full width at half-maximum (fwhm) duration, 8 cm-1 fwhm bandwidth, and 5-7 µJ energy at the sample. These pulses were used to IR-excite samples from 3695 to 3450 cm-1. Probe pulses have 1.5 ps fwhm duration, 8 cm-1 fwhm bandwidth, and ca. 50 nJ energy. These probe pulses are split into two beams before the sample; one passes through the flowing liquid cell (CaF2 windows, 0.82 mm path length) overlapped with the pump pulse (signal channel), while the other passes through a static 1 mm reference cell (reference channel). Each probe beam is focused onto a liquid nitrogen cooled single element InSb detector, read with a boxcar integrator and digitally collected on each laser shot by a microcomputer. The energy of the probe beam overlapped with the pump beam is alternately ratioed against the reference beam with (T) and without (T0) the pump beam present. Signal/
Vibrational Excitation During H-Bonding Reactions reference normalization is computed on each laser shot, and the transient transmission at each pump-probe time delay (td) is computed from an average of 400 total laser shots. Kinetic traces are collected by moving retro mirrors in the probe beam path by a computer-controlled translation stage ((1 µm position accuracy) and repeating the process until the transient kinetics are mapped. Time delays nominally range from -35 to +100 ps with time steps of 1.33 to 6.67 ps, depending on the nature of the kinetics and the desired accuracy. Transient absorption differences are presented as the natural logarithm of the transmitted beam divided by the reference beam [-ln(T/T0)]. This quantity is directly proportional to the instantaneous population (via an optical density change) of the mode being probed. T1 lifetimes were obtained by averaging all negative-time transmission data to obtain a normalized base line value of 1.0, obtaining a semilogarithmic plot of td versus ln(-ln(T/T0)) and fitting the resultant data to a line using a linear least squares routine. The combined standard uncertainty in T1 is reported as the square root of the sum of the squares of the uncertainties ((1σ) obtained by analyzing single kinetic traces. Typical relative errors in T/T0 for a single kinetic trace were (0.3% and as low as (0.1% for multiply-averaged data. The instrument response function (IRF) and td ) 0 (maximum pump-probe temporal overlap) were determined from pumpprobe IR second harmonic cross-correlations using a 1 mm thick LiIO3 crystal with time steps of 0.33 ps. Independently tunable IR pump and probe pulses allow kinetic experiments to be performed over a wide range of frequencies. Most of the experiments performed here use IR pump pulses tuned to either the absorption peak of the free acid (3692 cm-1) or the complex (3550 cm-1). An OH-stretch V ) 1 f 2 absorption excitation spectrum was also obtained by tuning the pump pulse from 3692 to 3450 cm-1 in 25 cm-1 steps with a fixed probe frequency of 3383 cm-1 (see Figure 1). To monitor vibrational relaxation or H-bond formation kinetics of the complex, IR probe pulses were tuned to the peak of the complex V ) 1 f 2 absorption (determined from the OH(V ) 0 f 2) FTIR overtone spectrum to be at 3383 cm-1 and bandwidth of ca. 260 cm-1 fwhm), while other transient spectra were obtained using probe pulses tuned over the range of 3283-3692 cm-1. All double-resonance IR experiments were collected using relative pump-probe polarizations at the magic angle (54.7°) to eliminate transient contributions from molecular reorientation.12 Commercially available Et3SiOH and spectroscopic grade CCl4 were used as received, while acetonitrile was dried over molecular sieves prior to use. Typical absorption spectra for samples used in the psTRIR experiments displayed peak absorption optical densities similar to that shown in Figure 1 (OD e 0.5) with TES and ACN concentrations in CCl4 of 0.1 and 1.4 mol/dm3, respectively. Results Vibrational Relaxation Lifetimes and Energy Transfer Experiments. Figure 3 depicts representative kinetic transients obtained by using the IR double-resonance technique with ca. 5 µJ, 2 ps pump pulses. Kinetic trace 3a shows the transient behavior of the 1:1 complex OH-stretch V ) 1 f 2 absorption (3383 cm-1) after direct V ) 1 excitation of the complex OHstretching mode at 3550 cm-1. Note that the absoprtion increase exhibits an instrument-limited rising edge followed by a single exponential decay (T1 ) 25 ( 5 ps) arising from complex OH(V ) 1) population relaxation. This lifetime was determined by averaging twenty T1 values obtained from individual decay scans acquired over several days. The data shown in Figure 3a are the average of six of these individual kinetic traces. The
J. Phys. Chem., Vol. 100, No. 29, 1996 11977
Figure 3. Transient OH-stretch kinetics collected with the IR doubleresonance technique on an equilibrated Et3SiOH-acetonitrile-CCl4 sample (0.1 mol/dm3 TES, 1.4 mol/dm3 ACN). The three traces were obtained with (a) pump ) 3550 cm-1 (complex V ) 0 f 1), probe ) 3383 cm-1 (complex V ) 1 f 2 absorption), (b) pump ) 3692 cm-1 (free acid V ) 0 f 1 absorption), probe ) 3383 cm-1 (complex V ) 1 f 2 absorption with amplitude × 2.0), and (c) pump ) 3692 cm-1 (free acid V ) 0 f 1 absorption), probe ) 3560 cm-1 (complex V ) 0 f 1 bleach). The solid lines are amplitude-normalized results from kinetic simulations of the data using independently determined experimental parameters (see text).
complex OH-stretch lifetime did not exhibit a dependence on base concentration (with implications discussed below) which was studied over the range 0.64-9.3 mol/dm3 ACN in CCl4 and in neat ACN. Figure 3b was obtained by similarly probing the complex OH(V ) 1 f 2) absorption (3383 cm-1) after direct IR excitation of the free acid OH(V ) 0 f 1) transition (at 3692 cm-1). The observed kinetics for the complex OH(V ) 1) population absorption obtained after IR excitation of the complex (Figure 3a) and free acid (Figure 3b) are distinctly different. The transient absorption kinetics observed when pumping at 3692 cm-1 exhibit a slow rising edge, maximum absorption increase (-ln(T/T0) ≈ 0.03) at 15-20 ps, and a single exponential decay with the time constant 70 ( 15 ps. The marked differences in these kinetic results, obtained from multiple experiments, strongly suggest that the observed transients originate from different energy transfer processes, and experiments discussed below substantiate this conclusion. Transient bleaching kinetics, shown in Figure 3c, were obtained by probing the hydrogen-bonded complex OH(V ) 0 f 1) transition (3560 cm-1) after IR excitation of the free acid OH stretch (3692 cm-1). Compared to the TES-ACN OH(V ) 1 f 2) transient absorption data shown in Figure 3b, this trace also has a delayed maximum and exponential recovery with a lifetime of ca. 70 ps. Transient decay amplitudes and vibrational lifetimes extracted from the data depicted in Figure 3 are summarized in Table 1. The solid lines in Figure 3 are amplitude-normalized results from a computer model simulation (using four coupled firstorder differential rate equations) of a four state kinetic scheme exhibiting equilibrium between free acid and acid‚‚‚ base complexes in both their ground (V ) 0) and excited (V ) 1) vibrational states (see Discussion).9d The four linear differential equations for this model were solved using a fourth-order variable step size Runge-Kutta ordinary differential equation (ODE) solver. Independently determined vibrational T1 lifetimes, dissolved species concentrations, equilibrium constants (Keq), and bimolecular rate constants (kbm) were used (see Discussion) to calculate the OH-stretch V ) 0 and V ) 1 populations of free acid and complexed acid after direct
11978 J. Phys. Chem., Vol. 100, No. 29, 1996
Arrivo and Heilweil
Figure 4. Early time transient IR kinetics collected with the IR doubleresonance technique using the same conditions as in Figure 3a,b (complex OH(V ) 1 f 2) absorption with 2.0 × amplitude) and (c) instrument response function determined by non-collinear second harmonic IR cross-correlation.
TABLE 1: Results of IR Double-Resonance Experiments on the Et3SiOH-Acetonitrile-CCl4 Hydrogen-Bonded System at 293 K υpump (cm-1)
υprobe (cm-1)
3692 3674 3650 3625 3600 3550 3500 3450
3383 3383 3383 3383 3383 3383 3383 3283
V ) 1 f 2 complex V ) 1 f 2 complex V ) 1 f 2 complex V ) 1 f 2 complex V ) 1 f 2 complex V ) 1 f 2 complex V ) 1 f 2 complex V ) 1 f 2 complex
3692 3692 3692 3692
3600 3560 3545 3525
3692
3510
3692
3500
3550 3550 3550 3550 3550 3550 3550
3692 3650 3600 3550 3525 3510 3450
probe OH-stretch transition
ln(T/To)max
T1 or decay (ps)
0.033 0.026 0.018 0.025 0.038 0.075 0.038 0.025
70 ( 15 70 ( 20 25 ( 7 25 ( 7 25 ( 7 25 ( 5 25 ( 7 25 ( 7
V ) 0 f 1 complex V ) 0 f 1 complex V ) 0 f 1 complex V ) 1 f 2 free & V ) 0 f 1 complex V ) 1 f 2 free & V ) 0 f 1 complex V ) 1 f free & V ) 0 f 1 complex
-0.045 -0.080 -0.075 0.050
70 ( 20 70 ( 20 70 ( 20 17 ( 8
0.070
50 ( 10
0.025
IRF
V ) 0 f 1 free V ) 0 f 1 complex V ) 0 f 1 complex V ) 0 f 1 complex V ) 0 f 1 complex V ) 0 f 1 complex V ) 0 f 1 complex V ) 1 f 2 complex
-0.040 -0.03 -0.077 -0.18 -0.165 -0.080 -0.01
70 ( 20 30 ( 7 30 ( 7 30 ( 7 30 ( 7 30 ( 7
excitation (instantaneous population) of either the free acid or complex V ) 1 levels. Comparison of simulated IR transient signals (proportional to ∆(population) ≡ lower - upper) to the experimental IR data provides support of the kinetic mechanism which describes the vibrational and reaction dynamics of the system under study. Note again that the close model and experimental data fit is achieved without any adjustable parameters except a single amplitude scaling factor. Results from an examination of the early-time kinetics of the transient OH(V ) 1 f 2) absorption of the complex with IR excitation of either the free acid or complex OH(V ) 0 f 1) transitions (3692 or 3550 cm-1, respectively) are shown in Figure 4. We also show in Figure 4 the IR pump-probe second harmonic cross-correlation (IRF) measurement obtained under identical experimental conditions as the kinetic data. From this measurement one finds an instrumental time resolution of 1.5 ps. It is more evident in this figure that direct OH-stretch excitation of the complex (OH(V ) 0 f 1) pumping at 3550
cm-1) produces an instrument-limited rising (integrated IRF) absorption edge which decays with the aforementioned 25 ( 5 ps time constant. Pumping the free acid produces a delayed absorption onset with a noticeable rise time (maximum at 1520 ps) and substantially longer decay (lifetime ≈ 70 ps). Comparison of the IRF with both transient absorptions clearly shows that the delayed rise time is not a consequence of the experimental time resolution but is attributable to a delay in accumulation of transferred population in the complex OHstretch V ) 1 state. The small bleach feature observed in Figure 4b near td ) 0 likely arises from coherent interference of the pump and probe pulses16 and is not due to depletion of the complex OH(V ) 1) vibrational level at td ) 0. Infrared Excitation Spectrum and Broadening of the Complex Absorption Band. Because of the partial spectral overlap of the free acid absorption with the high-frequency tail of the complex OH-stretch absorption (see Figure 1), it was necessary to determine whether any contribution to the complex V ) 1 f 2 absorption kinetics (Figures 3 and 4) resulted from direct complex excitation when pumping at 3692 cm-1. A twocolor IR excitation profile was obtained by tuning the pump pulse across the V ) 0 f 1 absorptions of the free acid and complex while monitoring the complex V ) 1 f 2 absorption at 3383 cm-1. Results from these experiments are presented in Figure 1 and summarized in Table 1. The filled circles are the maximum transient absorption excitation amplitudes (which are time-dependent) of the probe tuned to 3383 cm-1 (at the peak of the complex V ) 1 f 2 absorption) with IR-excitation of the sample at the frequencies indicated. The observed maximum amplitudes of the complex OH(V ) 1 f 2) absorption closely resemble the complex (V ) 0 f 1) absorption profile. T1 lifetimes obtained when pumping the complex OH(V ) 0 f 1) absorption band at the frequencies depicted in Figure 1 (3450-3625 cm-1) were found to be the same to within experimental uncertainty (25 ( 5 ps). The solid line in Figure 1 is a Lorentzian fit to the hydrogen-bonded complex OH(V ) 0 f 1) absorption profile having a bandwidth of 112 cm-1 fwhm. Population bleaching experiments were performed on the complex V ) 0 f 1 absorption band by pumping at 3550 cm-1 and tuning the probe pulse across the band. The bleaching amplitudes obtained are shown as squares in Figure 1. These amplitudes follow the absorption profile, and the T1 lifetime remains constant across the band suggesting the complex V ) 0 f 1 absorption is homogeneously broadened. To eliminate interference from monomer absorption, population bleaching experiments were also performed on 0.1 mol/dm3 TES in neat acetonitrile. These bleaching amplitudes are shown in Figure 5, along with a normalized Lorentzian fit to the complex V ) 0 f 1 absorption band. The amplitudes again closely follow the absorption profile with constant (ca. 20 ps) recovery, suggesting further that the complex V ) 0 f 1 absorption band is homogeneously broadened. Data points were not obtained below 3500 cm-1 because of spectral overlap with the complex OH(V ) 1 f 2) absorption. Discussion The overall goal of this study is to directly obtain hydrogenbonding association (and dissociation) reaction rate constants by monitoring “tagged” vibrational energy in a dilute free proton donor while its 1:1 hydrogen-bonded complex is formed in room temperature solution. In this discussion, we review a kinetic scheme appropriate for H-bond reactions and provide evidence
Vibrational Excitation During H-Bonding Reactions
Figure 5. Static FTIR solvent-subtracted spectrum (broken line) of a room temperature (293 K) solution of Et3SiOH in neat acetonitrile (0.05 mol/dm3 TES). The arrow indicates the pump frequency used to obtain probe bleaching intensities across the band (filled diamonds) to determine band homogenity. The solid line is a Lorentzian profile with 120 cm-1 fwhm. All bleach amplitudes are normalized to the absorption peak at 3530 cm-1 and the recovery lifetimes were constant (20 ( 5 ps).
that vibrational excitation is conserved in the OH stretch during reaction. We further argue that, in the TES-ACN liquid-phase system, there are sufficient degrees of freedom present to allow OH(V ) 1) excitation to migrate to other internal complex vibrational modes (intramolecular vibrational redistribution ) IVR) rather than populating several quanta of the hydrogenbond stretching mode before thermal dissociation occurs. Kinetic Model for Hydrogen-Bonding Reaction Rates and Population Transfer. The following kinetic scheme, including vibrationally unexcited OH(V ) 0) and excited OH(V ) 1) free acid and 1:1 acid-base complexes, was proposed to better understand the acid-base equilibrium rate constants, effects on the measured OH(V ) 1) T1 lifetime of complexes, and the “deactivation” of vibrationally excited free acid OH-stretch in the presence of base:13 kbm
} [(Et)3SiOH‚‚‚Base]V)1 [(Et)3SiOH]V)1 + [Base] {\ kdiss Vk1 Vk2 kbm
[(Et)3SiOH]V)0 + [Base] {\ } [(Et)3SiOH‚‚‚Base]V)0 k diss
The value used in this model for 1/k1 (the relaxation lifetime of the free TES OH(V ) 1) level) of 183 ( 6 ps was obtained from a single exponential fit of several measurements of T1 for dilute Et3SiOH in CCl4.13 Experiments performed to obtain k2 (the OH(V ) 1) relaxation rate of the complexed acid) were performed at several ACN concentrations (up to 50% by volume or 9.3 mol/dm3 and in neat ACN with all TES complexed). Barring deactivation processes such as vibrational energy transfer to modes of ACN,17 the observed OH(V ) 1 f 2) transient absorption decay should yield the value for k2 in the limit that all acid molecules are complexed. A lack of a strong concentration dependence on k2 is also expected since the dissociation reaction is unimolecular. Measurements of the OH(V ) 1) T1 lifetime of the complex at various concentrations showed that T1 slightly decreases with increasing base concentration for the Et3SiOH-ACN system. From the lowconcentration experiments, we determined the value T1 ) 25 ( 5 ps and in neat ACN, T1 ) 16 ( 4 ps (which may include a 10-20% reduction from OH to CH-stretch energy transfer). From these measurements, the value 1/k2 ) 16 ( 4 ps is used in the model. The model predicts minor variations in the transient absorption amplitude with concentration, but these changes occur after three 1/e times from the transient absorption
J. Phys. Chem., Vol. 100, No. 29, 1996 11979 maximum. Our experimental signal to noise ratio is not sufficient to observe such effects. The hydrogen-bond formation rate, assumed to be the free acid-base encounter rate, is described by the bimolecular rate constant (kbm) multiplied by the base concentration. The value used in the model was previously determined to be kbm ) (1.2 ( 0.2) × 1010 dm3/(mol‚s).13 Taking the predetermined value of 0.96 for the equilibrium constant, Keq ≡ kbm/kdiss, the spontaneous unimolecular dissociation rate for TES-ACN complexes, kdiss ) 1.3 × 1010 s-1.13 We assume that Keq is the same for species in OH(V ) 1) or the ground (V ) 0) state. This assumption is likely to be valid for the small dipole changes induced in the acid by vibrational excitation. However, it should be pointed out that different equilibrium constants have been measured for electronically tagged charge transfer species with large excited state dipole moments.5 The time-dependent kinetics for this model, shown in Figure 3, predict that a maximum transient population of 25% (occurring near 30 ps) of the vibrationally tagged free acid OH(V ) 1) species become hydrogen-bonded complexes in OH(V ) 1). Since the complex OH(V ) 1) state is produced by bimolecular association of long-lived free acid OH(V ) 1) species with base, the resulting complex OH(V ) 1) population decays on a longer (70 ps) timescale. These features are in contrast to the observed and model kinetics resulting from direct IR excitation of the complex OH stretch (having pulse-width limited rise and ≈25 ps decay). Additionally, the model predicts removal (bleaching) of ground state complexes in response to the excitation of free acid ground state population to OH(V ) 1) (tagging). As seen in Figure 3, the experimental results agree very well with these model predictions. A more complete model should contain additional crossrelaxation pathways describing the dynamics of hydrogenbonded systems. For example, a free acid with OH(V ) 1) excitation could form a complex and instantaneously lose its OH-stretch vibrational quantum to produce the OH(V ) 0) ground state complex. Similarly, as mentioned above, an excited OH(V ) 1) complex could dissociate to form free acid in its OH(V ) 0) state. Direct collisional vibrational energy transfer from excited free acids to already associated complexes could also occur. In the following sections, we show that these energy transfer channels contribute negligibly to our observations and the rates associated with these processes are slower than the tagged OH(V ) 1) excitation or other relaxation processes during H-bond association and dissociation in this system. Conservation of Vibrational Excitation During the Hydrogen Bond Reaction. From results of the above kinetic modeling, and since we vibrationally tag long-lived free acid OH(V ) 1) species and probe reasonably long-lived OH(V ) 1) complexes, a potentially dominant pathway for energy deposition would be that tagged OH(V ) 1) free acid produces vibrationally excited complexes after diffusion and hydrogen bonding to a base molecule. Therefore, the measured slow transient absorption rise time could originate from the bimolecular formation of hydrogen-bonded species while preserving the vibrational excitation. The complex OH(V ) 1) transient decay shown in Figures 3b and 4b would arise from transfer of the long-lived OH(V ) 1) source (reactant) population of the free acid to newly formed acid-base (product) complexes. The kinetic model discussed above predicts that the decay of the complex OH(V ) 1) state formed from excited free acid will be single exponential, and the experimental data support an OH(V ) 1) complex transient decay time of 70 ( 15 ps. Examination of Figure 1 reveals that absorption from the free
11980 J. Phys. Chem., Vol. 100, No. 29, 1996 acid and complex acid ground vibrational states overlap at 3692 cm-1. Therefore, observation of complex V ) 1 f 2 transient absorption upon IR excitation at 3692 cm-1 could arise from two sources: (1) direct IR excitation of the complex or (2) formation of a hydrogen bond while the free acid is in OH(V ) 1). At the ACN concentrations typically used for this study (ca. 1.4 mol/dm3), the underlying high-frequency complex absorption tail at 3692 cm-1 is ≈15% of the complex peak absorption at 3550 cm-1. Consequently, if the transient measured at 3383 cm-1 (OH(V ) 1 f 2 of the complex) was solely due to direct complex excitation, the ratio of intensities is expected to be ca. 1:8 compared to equivalent experiments which directly IR pump the complex absorption band at 3550 cm-1 (assuming the band is homogeneous; see below) and the rise would be instantaneous. As shown in Figure 1, the IRIR excitation spectrum clearly does not follow the complex absorption profile alone. The observed intensity ratio for pumping at the free acid absorption to the peak of the complex absorption is approximately 1:2.3, suggesting that the transient signal cannot be entirely due to direct complex V ) 0 f 1 pumping. Also, as the pump pulse was tuned to lower energy (from 3692 cm-1 in 25 cm-1 steps), the transient absorption peak amplitude drops by a factor of 2 and the transient absorption kinetics change from having a delayed rise and long (≈70 ps) decay to an instrument-limited rise and a short (25 ( 5 ps) decay lifetime (at 3650 cm-1 and lower energy; see Figures 1, 3, and 4). We estimate from kinetic fits and the above arguments that at most 10-15% of the transient absorption amplitude shown in Figure 3b (maximum ln(T/T0) of ca. 0.0035) could arise from spectral overlap of the free acid absorption with the 1:1 complex absorption band. This contribution is comparable to the noise level of our double-resonance measurements and would produce only a minor contribution to the transient signal during the first 10 ps or so. These conclusions strongly suggest that the main contribution to the observed transient when pumping at 3692 cm-1 (free OH(V ) 1)) originates from OH(V ) 1) free acid forming a hydrogen bond and preserVing Vibrational excitation in the complex. Given the above discussion, it is interesting to compare the model transient absorption amplitudes to our experimental results. Using the fixed model rate parameters discussed above, the expected maximum transient population of the acid-base complex OH(V ) 1) species is 25% of the initially excited free acid OH(V ) 1) population (see Figure 4). We also found from the determination of Keq (concentration studies of FTIR absorption spectra)13 that the peak frequency extinctions for both the free acid and TES-ACN OH(V ) 0 f 1) absorptions are nearly the same ( ≈ 110 dm3/(mol‚cm)). Assuming the peak absorption for the complex OH(V ) 1 f 2) transition (at 3383 cm-1) is comparable to that of the free acid OH(V ) 1 f 2) transition strength (at 3525 cm-1), we can compare the amplitudes of transient complex absorption signals to the OH(V ) 1 f 2) absorption of the dilute free acid. We typically measured free acid (no base, sample OD ≈ 0.5) transient absorption maximum signals of approximately ln(T/T0) ) 0.12 using similar pumping pulse conditions (≈5 µJ) as those monitoring the transfer dynamics. Using the model prediction, one would expect to observe a peak transient absorption of the complexed OH(V ) 1) species after free acid excitation to be on the order of ln(T/T0) ) 0.03. This prediction is indeed quite close to the typical experimentally found value of 0.035 (see Figures 3 and 4), indicating that the majority of free acid OH(V ) 1) species react to form complexes in OH(V ) 1). It is also interesting to note that the ratio of transient absorption amplitudes (3383 cm-1 probe) produced by pumping
Arrivo and Heilweil at the peak absorptions of the free acid and complex, respectively (see Figure 1), is ca. 1:3.3 (30%). This value was extracted by subtracting the Lorentzian tail of the complex absorption (from direct complex excitation) from the absorption maximum at 3692 cm-1. The similarity in amplitudes predicted by the model and this experiment further supports the claim that most of the initially prepared free acid excitation transfers to the newly formed complex and is retained as OH(V ) 1) population. Two concurrent processes may be responsible for observing the bleaching signal (decrease of the OH(V ) 0)-OH(V ) 1) population; see Figure 3c) at the complex OH(V ) 0 f 1) transition frequency (3560 cm-1) after IR excitation of the free acid: (1) transient accumulation of population in OH(V ) 1) of the complex (which is directly observed via V ) 1 f 2 absorption at 3383 cm-1 after IR excitation at 3692 cm-1; see Figure 3b) and (2) complexes in OH(V ) 0) spontaneously dissociate, forming new free acid in the ground state OH(V ) 0) level. The kinetic model incorporates these two processes for populating OH(V ) 1) complexes and removing ground state OH(V ) 0) complexes after free acid IR excitation. Since we assume the equilibrium constant for association and dissociation is the same for vibrational ground and excited states, both processes occur simultaneously and with the same rates (a consequence of Keq ≈ 1). In this case, the population difference between V ) 0 and V ) 1 of the complex is twice that of the V ) 1 population. Under these circumstances the bleach signal maximum would be twice that of the V ) 1 f 2 transient absorption if the transition intensities at the probe frequencies used are fortuitously equal. This conclusion seems plausible and may be supported by the experiment because the bleach signal intensity is about a factor of 2 larger than for the OH(V ) 1 f 2) absorption of the complex under identical free acid pumping conditions. Unfortunately, we cannot unambiguously distinguish between contributions from these two population transfer processes with psTRIR spectroscopy because they both produce the same kinetic response and the actual absorption intensities for the V ) 0 f 1 and V ) 1 f 2 complex transitions at the probe frequencies used are unknown. Another complication which can contribute to the bleach intensity is overlap of the broad V ) 1 f 2 absorption which we know occurs but with unknown magnitude. The same logic can be applied to experiments (see Table 1) which pumped the complex OH(V ) 0 f 1) absorption at 3560 cm-1 and probed the OH(V ) 0 f 1) transition of the free acid at 3692 cm-1. Again, for this case, a slowly rising (ca 20 ps) bleach signal was observed with a long (≈70 ps) recovery time. The model also predicts ground state population depletion analogous to the experiments discussed in the previous paragraphs and shown in Figure 3. This recovery, we believe, reflects the hydrogen-bond thermal dissociation lifetime at room temperature and is likely to be much faster than IR pumpinduced dissociation of complexes (see below). Energy Transfer Mechanisms through Other Relaxation or Reaction Channels. We conclude that conservation of OH(V ) 1) excitation occurs with high quantum transfer efficiency during hydrogen-bond association and dissociation in this system, but now explore other transfer mechanisms which may participate during these thermal reactions. A vibrational energy transfer mechanism which would exhibit similar behavior to that found in Figures 3 and 4 has free acid OH(V ) 1) species undergoing collisional transfer of excitation to already associated complexes. This intermolecular transfer process has been analyzed using the box model by substituting the concentration of complexes for the base concentration. In this case, we know from Figure 1 and Keq that the concentration
Vibrational Excitation During H-Bonding Reactions of complexes in OH(V ) 0) present at the base concentration used in the experiments is half the acid concentration (0.05 mol/ dm3). The model produces a transient response similar in character to Figure 3b but with a slightly longer rise time and nearly 50 times smaller peak transient complex OH(V ) 1) population. We conclude that while this process is potentially involved in the dynamics, we would be unable to observe the extremely small number of OH(V ) 1) complexes produced in this way. Instantaneous deactivation of OH(V ) 1) free acid species via collisions which produce ground state complexes or complexes with excitation in other vibrational modes is an expected pathway. At this point we are confident that such processes do not dominate our observations. For one reason, the hydrogen-bond association reaction is ca. 1000 cm-1 (3 kcal/ mol) exothermic and need not cause any observable change in the high-frequency OH-stretch population. While some of the reaction exothermicity may end up in the neighboring hydrogenbond H‚‚‚N stretch mode, we cannot determine how this would effect our current measurements. Recall that the kinetic model predicts that the maximum transient population of vibrationally excited complexes is 25% of the tagged free acid population. Since we detect most of the expected hydrogen-bonded species containing OH(V ) 1) excitation after reaction (see above), our results indicate that deactivation to form complex OH(V ) 0) during H-bond formation is a minor pathway. Kinetic modeling employing relaxation from free acid OH(V ) 1) to complex OH(V ) 0) using the same value for kbm predicts a factor of 2 smaller transient maximum signal for the complex OH(V ) 1). Since our experimental results closely match the predicted amplitudes without this pathway, we believe that this is a slow process which does not significantly participate in the kinetics. It is also interesting to note that the simple box model accurately represents earlier bimolecular encounter experiments performed in this laboratory.13 Using the experimentally varied base concentrations, fixed Keq and k2 complex vibrational decay rates for TES with ACN, PYR, and THF bases, the observed free acid OH(V ) 1) T1 decay as a function of concentration is accurately predicted with values for kbm of (1.3-1.6) × 1010 dm3/(mol‚s). Incorporating the cross-relaxation pathway required a value of kbm on the order of 0.6 × 1010 (dm3/mol‚s) to match the observed decays. This value is significantly far from the experimentally determined value of (1.2 ( 0.2) × 1010 (dm3/ (mol‚s). Is There Direct Hydrogen-Bond Dissociation After OH(W ) 1) Excitation? Another key process of interest is the direct production of ground OH(V ) 0) state free acid species after OH(V ) 1) excitation of acid-base complexes. However, we have studied and discussed the excited state OH(V ) 1) bimolecular reaction and vibrational energy transfer process in the proceeding paragraphs and concluded that these mechanisms occur rapidly (in 1) with nonoverlapping IR absorption bands. At ambient temperature, the TES-ACN thermal dissociation reaction occurs with a lifetime of about 80 ps. There is presently no spectroscopic evidence that complexes dissociate from direct OH(V ) 1) excitation on this time scale. As discussed for ether-HX gas-phase bulb systems, dissociation occurs in these and related systems because HX-stretch excitation eventually populates multiple H-bond stretch overtones to exceed the dissociation barrier. This process may take many nanoseconds to occur in TES-ACN and would therefore be a small contribution to the detected signals during our observation time (
