J. Phys. Chem. 1994, 98, 9712-9722
9712
ARTICLES Deuterium Isotope Effects on the Ultrafast Solvent Relaxation of Formamide and NJV-Dimethylformamide Yong Joon Chang* and Edward W. Castner, Jr.* Chemistry Department, Brookhaven National Laboratory, Building 555A, Upton, New York 11973-5000 Received: February 3, 1994; In Final Form: July 26, 1994@
We present the results of our study on the ultrafast solvent dynamics of the amides formamide (FA), N J dimethylformamide (DMF), and their deuterated analogs HCOND2 (&-FA) and DCON(CD3)z (d7-DMF) using femtosecond optical-heterodyne-detected Raman-induced Kerr effect spectroscopy (Om-RIKES). Using nearly transform-limited 50 fs optical pulses and the Fourier-transform relationship, we have studied the liquid dynamics in the frequency range from 0.6 to 400 cm-'. In comparison to the depolarized Rayleigh spectroscopy technique, OHD-RIKES is shown to provide more accurate and detailed information about the low-frequency region that includes the rotational reorientation, librational, and collision-induced dynamics. The effect of deuterium isotope substitution on the inertial as well as diffusive reorientational dynamics of these amide liquids is discussed.
Introduction The study of chemical reaction dynamics in the condensed phase is complicated by the dynamic as well as static influences of the medium surrounding the reactant. Thus, the characterization of neat solvent dynamics is an important step toward understanding how the solvent motions and their interactions with the reacting species affect the overall reaction dynamics. In the past, the experimental studies of dynamic solvent effects on reaction dynamics have emphasized the diffusive part of the solvent dynamical profile. However, recent studies of solvent dynamics using ultrafast four-wave mixing spectroscopy techniques such as the Raman-induced Kerr effectl-10 and impulsive stimulated Raman ~ c a t t e r i n g ~ lhave - ' ~ shown that a substantial part of the overall solvent dynamics originates from the inertially limited or oscillatory intermolecular motions. Also, photon echo,14-17 transient hole and Raman echo21studies have provided important insights into the ultrafast interactions between the solute and solvent molecules and their effect on various dephasing mechanisms in condensed-phase solutions. The consideration of the total dynamical profile of a solvent system is important for those reactions where the reaction coordinate is strongly coupled to the dynamical solvation coordinate. The importance of the inertial part of the solvent dynamics has been demonstrated for the case of dipolar solvation occumng during a charge transfer reaction in both molecular dynamics ~ i m u l a t i o n ~and ~ - ~e ~ p e r i m e n t a l ~studies. .~~.~~ In this report we present the results of our study of the deuterium isotope effect on the ultrafast dynamics of amide liquids: formamide (FA, HCONH2; d2-FA, HCOND2) and N,Ndimethylformamide (DMF, HCON(CH3)z; d7-DMF, DCON(CD3)2). Our motivation for carrying out this study is to characterize the various ultrafast solvent nuclear motions and to obtain a better understanding of the relative contribution of the inertial and diffusive components to the overall solvent dynamics. In this article, we use the term inertial to mean all of the nondiffusive dynamics, Le., all of the dynamics that are @
Abstract published in Advance ACS Abstracts, September 1, 1994.
0022-365419412098-9712$04.50/0
not strongly overdamped. These intrtial motions include inertially limited rotations (where for small angular displacements the molecular rotation frequency approaches the gas-phase free rotor value), translational density fluctuations, molecular collisions, intermolecular vibrations including librations, and of course the intramolecular normal vibrational modes. The broad category of inertial motions defined above will all have a certain degree of memory. For times shorter than the characteristic dephasing time constants of the motion, these inertial dynamics are reversible in time. The strongly overdamped diffusive solvent motions are a result of the same molecular motions mentioned above, but observed on a longer time scale following many molecular collisions and interactions. Thus, the diffusive reorientational dynamics will be observed to have the characteristics of Brownian motions, are not time-reversible, and will obey the Stokes-Einstein-Debye laws of hydrodynamics. The amide liquids studied were chosen because they have large dipole moments [FA (3.37 D) and DMF (3.24 D)] and dielectric constants [FA (109) and DMF (36.7) at 293 and 298 K, respectively] and so are especially relevant for the study of dipolar solvent dynamics. In addition, important comparisons can be made about how the differences in the intermolecular interactions and overall liquid structure found between the protic (FA) and aprotic (DMF) liquids will affect the overall solvent dynamics. The main structural differences arise from the presence and absence of intermolecular hydrogen-bond (H-bond) networks in FA and DMF liquids, respectively. We have shown in our previous work that FA exhibits underdamped oscillations that are assigned to librational motions about the H bond^.^^^^ The librational motions in liquid DMF are observed to be significantly damped. Both amide liquids exhibit polarizability fluctuations on the subpicosecond time scale arising from collision-induced dynamics. The sources of the low-frequency spectral density arising from collision-induced dynamic^^^-^^ have been described by dipole-induced dipole (DID) field interaction^,^^.^' electron density fluctuation^,^^,^^ and molecular frame distortions.4 The dephasing of the coherent librational motions in FA liquid is also measured to occur on a subpico-
0 1994 American Chemical Society
Dynamics of Formamide and N,N-Dimethylformamide second time scale.7 Some major improvements have been made in both the experiment and analysis since our previous report on the ultrafast solvent dynamics of amide^.^ Using 50 fs fwhm laser pulses instead of 90 fs fwhm pulses, we have resolved the liquid dynamics in the frequency range 0.6-400 cm-'. In addition, by using the Fourier-transform deconvolution analysis in the frequency domain, we have been able to study the details of the total intermolecular dynamical spectrum. Here we concentrate on the deuterium substitution effect on the dynamics, whereas the previous work was concerned with concentrationdependent effects of cosolvents on the dynamics. The technique used to measure the ultrafast solvent dynamics is called the optical-heterodyne-detected Raman-induced Kerr effect spectroscopy (OHD-RIKES). This is a polarization spectroscopy technique that provides a signal linear in the thirdorder nonlinear optical response of the liquid sample. We obtain information regarding ultrafast solvent dynamics by measuring the time response of a transient birefringence that is induced in a liquid sample by an intense, highly polarized femtosecond optical pulse. The birefringence of the sample at time zero is generated through electronically nonresonant, impulsive excitation of various nuclear motions that cause fluctuations in the molecular polarizability anisotropy. Because we use nearly transform-limited laser pulses, we are able to use Fouriertransform analysis to study our OHD-RIKES data in both the time and frequency domains. Furthermore, the use of optical heterodyne detection provides a simple linear relationship between the measured transient birefringence signal in the time domain and the third-order nonlinear susceptibility, x(3)(and spontaneous Raman cross section, a,), of the sample in the frequency d ~ m a i n . ~ The , ~ ' low-frequency spectrum obtained in this way from OHD-RIKES data has several distinct advantages over that obtained by other spectroscopic methods: Whereas the spontaneous low-frequency RayleighIRaman spectra suffer from having large Rayleigh line and background scatter intensity, the OHD-RIKES spectrum is free of these interferences and provides more detailed and precise information in the low-frequency region. In addition, the rotational reorientation dynamics can be characterized in detail in the time domain by fitting the OHD-RIKES diffusive response on the long time scale. In short, the OHD-RIKES technique provides comprehensive and detailed information regarding the low-frequency nuclear coordinate dynamics. A potential disadvantage of the OHD-RIKES technique arises from the limitations imposed by the spectral content of the ultrashort optical pulse. In our case, the 50 fs optical pulses provide sufficient spectral coverage to study all of the solvent nuclear motions arising from specific intermolecular interactions and collision-averaged diffusive reorientation. Our results show that both the inertial and the slower diffusive solvent nuclear motions are affected by deuterium isotope substitution. We observe two oscillatory librational motions with approximate frequencies of 100 and 190 cm-' in liquid FA. In liquid DMF, one damped librational motion is observed with a frequency of 66 cm-'. The collision-induced part of the collective polarizability anisotropy is also affected by deuterium substitution. Our observation of multiple exponential rotational diffusion lifetimes is attributed to the fact that FA and DMF molecules are asymmetric rotors with significantly different moments of inertia about the three molecular axes. Recently, Maroncelli et al. have developed a theory to further the understanding of the connection between both inertial and diffusive solvent relaxation to charge solvation dynamics. Specifically, the time correlation function for solvation occurring about an instantaneously created charge is calculated from the
J. Phys. Chem., Vol. 98, No. 39, 1994 9713 solvent dipole autocorrelation function raised to the power of the normalized dipole density (in atomic ~ n i t s ) . Our ~ ~ ,OHD~~ RIKES data include those dynamics that are described by the solvent polarizability autocorrelation function. Despite the fact that the solvent dipole and polarizability autocorrelation functions are very different physical quantities, their dynamics in a given solvent are related!3p44 We have therefore approximated the solvation energy relaxation function, Cy(r),of Maroncelli et al. by substituting the solvent polarizability autocorrelation function from our OHD-RIKES response function for the dipole autocorrelation function.8 In the Gaussian-shaped inertial regime of the calculated Cv(t),the solvation energy relaxation is predicted to occur much faster in FA than in DMF. This is because the inertial solvent motions exhibited by liquid FA contribute more to the initial solvation energy relaxation. In the exponentially-decaying diffusive regime, the relaxation is predicted to occur faster in the aprotic DMF because the rotational diffusion occurs more rapidly than for FA. By using this theoretical anasatz, we are able to make predictions about how the inertial and diffusive solvent dynamics will affect a chemical reaction in solution.
Experimental Section FA and DMF were purchased from Aldrich in spectrophotometric grade and were further purified by fractional vacuum distillation immediately prior to the experiment. HCOND;! (4FA) (98%, MSD Isotopes) and &-DMF (99.5%, CIL) were used as received. Sample cells were 1 mm path fused silica from NSG Precision Cells. The OHD-RIKES technique has been described in detail by McMorrow and Lotshaw.'S2 Our particular experimental setup has also been previously described in detaiL8s9
Data Analysis The numerical methods for deconvolution of the effective instrument (laser cross-correlation) response and frequencydomain representation of the time-domain OHD-RIKES data were presented by McMorrow and L o t s h a ~ . More ~ , ~ ~recently, the relationship between the material response from OHDRIKES and that from spontaneous and coherent Raman scattering has been presented by Cho et The discussion in this section concentrates on making the connection between the RDRS(W) representation, commonly used to analyze depolarized Rayleigh/Raman scattering (DRS) data,43*46-52 and the spectral representation provided by analysis of the OHD-RIKES data. Fourier-transform deconvolution of the measured OHDRIKES data, T(t),by the laser cross-correlation, GO),provides the frequency domain spectrum R R I K E S ( W ) , ~ ~ ~ ~
The imaginary part of RNKES(O)contains information on only the nuclear coordinate motions and is related to the susceptibility tensor, xyzyz(w), by6
The depolarized Raman spectrum, SDRS(W), is related to the same susceptibility tensor by
Therefore,
Chang and Castner
9714 J. Phys. Chem., Vol. 98, No. 39, 1994 The subscripts y and z refer to the polarization axes in the laboratory frame with the pump polarization aligned along the z axis and the probe polarization aligned 45' with respect to the two axes. The RDRS((O) representation that enables the analysis of the low-frequency wing feature in the spontaneous DRS spectrum is related to the total scatter intensity, SDRS(W),by the equation43,49
Thus, the OHD-RIKES generated spectrum, I~[RMKEs(w)], is related to the RDRS(W) representation of the DRS spectrum by lm[R,,S(w)l
OC
RDP,S(o)/o
(6)
This relationship between I~[RMKEs(o)Iand RDRS(O)is presented because of our interest in comparing the information provided by the OHD-RIKES and DRS techniques. Also, the RDRS(W) representation has been used in the past for spectral moment calculations to determine the relative contribution of reorientational versus collision-induced dynamics to the Rayleigh wing i n t e n ~ i t y . ~ ~The . ~ ~spectral - ~ ~ moment analysis developed by Gordon57 is a method to separate an intensity profile, for example, RDRS(O), into even and odd parts that relate to the real and imaginary parts of a time correlation function, respectively. Recently, Rodriguez and McHaleS2have obtained the RDRS(O)representation for DMF and d7-DMF liquids and studied the depolarized wing feature using the spectral moment analysis. We have generated the RDRS(W)spectra from our OHD-RIKES data for DMF and d7-DMF using eq 6. We have also calculated the spectral moments and compared them with the results of Rodriguez and McHale. The diffusive rotational reorientation responses have been analyzed by nonlinear least-squares fitting. We have tried the single, double, triple, and stretched (Kohlrausch-WilliamsWatt) exponential decay functions as models. Prior to the fitting, the base line before zero time delay was averaged and then subtracted from the data. The account for the inertial dynamics, the starting point for the fits ranged from ca. 0.5 to 2 ps. In no case were we able to obtain a reasonable fit to the data using a single or stretched exponential decay function. The triple-exponential decay function gave the best fit to the data when the starting point for the fit was 0.5 ps. Both doubleand triple-exponential decay functions gave fits with nearly identical x2 and residuals when the starting point for the fit was 2 ps. Because the shortest time constant obtained from the triple-exponential decay function was always subpicosecond and thus overlapped with the inertial response, we chose instead the double-exponential decay function (with a fit starting point of 1 ps) as a model to describe the observed diffusive reorientational response. The analysis of the band pofiles in the Im[Rm&o)] spectrum is carried out by fitting the spectra to a number of different line shapes. Normal, skewed, and antisymmetrized versions of Lorentzian and Gaussian functions were fit to the observed librational bands, and for the lowest-frequency inertial bands, a smooth asymmetric function given by eq 7 was used. Equation 7 has been used by Cho et al.536 to fit the lowestfrequency inertial bands in several molecular liquids.
ZBL(w)FZ wa exp(-w/w,)
(7)
The combination that always gave the best overall fit was a sum of antisymmetrized Gaussian functions for the librational bands plus eq 7 for the lowest-frequency bands, including the
(B)
- DMF
P
d,-DMF
--
E
Electronic Response
z
0
2
1
3
Time (ps)
Figure 1. Raw OHD-RIKES data for FA, dz-FA, DMF, and d7-DMF at room temperature. The instantaneous electronic hyperpolarizability contribution to the total response is shown represented by the pumpprobe cross-correlation. (A) FA and d2-FA. (B) DMF and Q-DMF.
collision-induced dynamics. The form of the Gaussian function is given by
The antisymmetrized version of the Gaussian line shape is used to satisfy the requirement that ~ [ R M K E s ( wgoes ) ] to zero as w goes to zero. For the case when the rotational diffusion part of the OHD-RIKES transient is not subtracted prior to the Fouriertransform analysis, the spike at small wavenumber values in the frequency domain can be fit to a sum of Lorentzian functions in the frequency domain: one Lorentzian for each exponential component in the time-domain data. The inverse Fourier transform of the I~[RRIKEs(w)] spectrum provides R~ms(t), which is the deconvoluted, pure nuclear coordinate response. This impulse response function is used to obtain a solvation energy time correlation function, Cy(t), using the theory proposed by Maroncelli et al.42 We have used their formalism to generate a polarizability autocorrelation function in place of Cl(t) and to generate an approximate CY(t) function that describes the solvation energy relaxation relevant to a strongly solvent-coupled charge transfer reaction. The calculation of a C,(t) function from an OHD-RIKES impulse response has been discussed p r e v i o u ~ l y . ~ ~ ~
Results The raw OHD-RIKES data obtained for the amide liquids are shown in Figure 1. The instantaneous response originating from the electronic hyperpolarizability of the sample follows the cross-correlation of our pump and probe pulses and is also shown in Figure 1. The rising edge of the pump-probe crosscorrelation is matched to the rising edge of the OHD-RIKES response by fitting the relative amplitudes and zero-time positions. The longer-time diffusive response is shown for d2-FA in Figure 2 over a range of about 100 ps. The rotational time
Dynamics of Formamide and N,N-Dimethylformamide
J. Phys. Chem., Vol. 98, No. 39, 1994 9715 TABLE 2: Parameters for Double-Exponential Decay Fits to the Long Time Rotational Reorientation Component (Normalized: 41 42 = 1)"
+
w, 0
d,-FA, OHD-RIKES Data
a1
Zl (PSI
a2
FA d2-FA [t(dz-FA)lt(FA)]
0.43 0.38
0.57 0.62
DMF
0.39 0.37
11.62 13.32 (1.15) 4.72 5.63 (1.19)
d7-DMF [t(d7-DMF)/t(DMF)]
T2
0.61 0.63
(PS)
1.45 1.45 (1.00) 0.82 1.07 (1.30)
The ratios of time constants between deuterated and undeuterated species are also given.
I 7
I
I
I
I
0
20
40 Time (ps)
60
80
Figure 2. Natural log plot of the longer time scale OHD-RIKES data for d2-FA at 297 K. The fit shown (line) corresponds to a doubleexponential decay function. Residuals for the double-exponential (dots) and triple-exponential (line) fits are also shown at top. TABLE 1: Principal Moments of Inertia for FA, DMF, and Isotopically Substituted Molecules"
3 f
a -E
DMF I
..... Total Im[RninEs(o)]
,
- Rotational subtracted Im[RR,KEs(w)]
'
6.95 8.46 (1.22) (1.10)
( m u A') 44.43 49.58 (1.12) (1.06)
( m u A') 51.39 58.02 (1.13) (1.06)
DMF Q-DMF [Z(d7-DMF)/Z(DMF)] [Z(d7-DMF)/Z(DMF)]o.5
56.6 76.5 (1.35) (1.16)
120.2 138.2 (1.15) (1.07)
170.5 202.0 (1.18) (1.09)
10 ( m u A')
Ib
Moments of inertia ratios for rotational constants comparisons and calculated frequency ratios for librations around these axes are also given. The inertial axis, c, is perpendicular to the ab plane. constants and their relative amplitudes from the doubleexponential fits for FA, DMF, and deuterated analogs are listed in Table 2. The frequency-domain representations of our OHD-RIKES data with the effective instrument response deconvoluted are shown for FA and DMF in Figure 3. The frequency representation of the longer time rotational diffusion dynamics is the lowest frequency feature: a sum of Lorentzian line shapes. In contrast to the spontaneous depolarized Rayleigh spectrum where the Rayleigh scatter obscures this low-frequency region, the deconvoluted OHD-RIKES spectrum clearly resolves the rotational diffusion and collision-induced dynamics contained within the Rayleigh wing region without any interferences from extraneous scattering. The OHD-RIKES low-frequency spectra of FA, DMF, and the deuterated analogs are compared in Figure 4. The Lorent-
. '.
!',... ; ".., ;
I
FA dz-FA [4&-FAY(FA)I [Z(d2-FA)/Z(FA)]o,5
.
;:,,,
I
I
,
zian line shape rotational bands have been subtracted to show the clear profile of the collision-induced, librational, and some intramolecular vibrational bands. Upon deuterium isotope substitution, the general trend of the band maxima shifting to the red can be observed. The band maxima of the impulsively excited intramolecular vibrational modes that we observe for DMF are 325.5, 356.3, and 407.5 cm-'. Those for d7-DMF are 202.2, 302.7, and 348.3 cm-'. These bands have been observed and characterized in detail p r e v i o u ~ l y . ~The ~ - ~results of normal-mode analysis s t ~ d i e show s ~ ~that ~ ~the bands for DMF originate from N(CH3)z symmetric scissoring deformation, C-N torsional, and N(CH3)z antisymmetric rocking deformation modes, respectively. For &-DMF, the bands originate from N-CD3 torsional, C-N torsional, and N(CD3)z antisymmetric rocking deformation modes, respectively. No intramolecular bands are observed for FA and Q-FA because their fundamental intramolecular bands lie outside the spectral range covered by our OHD-RIKES experimental setup. Figure 5 shows the fits to FA and DMF spectra using the functional forms discussed in the previous section. For DMF, the window of the fit was set to include the range 0-150 cm-'. This fit window was selected because of the existence of the higher frequency intramolecular vibrational bands and because
Chang and Castner
9716 J. Phys. Chem., Vol. 98, No. 39, 1994
- FA
too
0
200 Frequency (cm")
I
300
I
1.o
0.5
0.0
1.5
Time (ps)
Figure 4. Comparisons of low-frequency spectra (with diffusive )], rotational reorientation responses subtracted),I m [ R ~ ~ ( uobtained from the OHD-RIKES data. (A) FA and dZ-FA. (B) DMF and d7-
DMF.
Figure 6. Deconvolutednuclear coordinate impulse response function at room temperature (294-299 K) for (A) FA and Q-FA and (B) DMF
and Q-DMF.
,
1
I i\
I
(A'
\
n n, V." I
7wp?&.&4+
k'
..
..... ... ... .. . .... ...
I
- DMF, total impulse response 1 -.- 60 cm" libration response . .. collision-inducedresponse
-a - rotational diffusion response
. ._
-0.01
-5-
1
1 '"\%.\
- DMF Im[R~in~s(W)l . ",..="~ I.
a 0,51 -E
.- . Gaussian lineshape
I,, -; ,
0.0
;,.,,
~.
"
0
100
---
I
Eq. (7) iineshape
, . 200 Frequency (cm")
I
0.0
300
1
Figure 5. Fits for the low-frequency OHD-FUKES spectra containing
the bands of intermolecular origin (librational and collisiodinteractioninduced dynamics). The Lorentzian line shape diffusive rotational reorientation component has been subtracted out. (A) The FA spectrum in the range from 0 to 250 cm-* was best fit to three Line shapes: two antisymmetrized Gaussian and eq 7. (B) The DMF spectrum in the range from 0 to 125 cm-I was best fit to an antisymmetrized Gaussian and eq 7. The residuals for the fits are included on top of each of the spectra. of increased noise at higher frequencies from the Fouriertransform deconvolution procedure.
0.2
I
0.4 Time (ps)
I
0.6
0.8
Figure 7. Total nuclear coordinate impulse response (bold) is shown along with the various subcomponent responses for (A) FA and (B) DMF.
The impulse response function for nuclear coordinate motions, RRIKES(t), is shown in Figure 6 for the amide liquids. This function is obtained from an inverse Fourier transform of the fit to the frequency spectra shown in Figure 5 with the readdition of the lowest-frequency Lorentzian rotational component. The R"s(t) represents the deconvoluted OHD-RIKES response within the spectral window that was set initially by the ultrashort optical pulse. Our analysis of the nuclear coordinate impulse response yields several subcomponents, shown in Figure 7, A and B, for FA and DMF, respectively. The underdamped librational responses with frequencies of 100 and 195 cm-' are shown along with a collision-induced response and the rotational
Dynamics of Formamide and N,N-Dimethylformamide
J. Phys. Chem., Vol. 98, No. 39, 1994 9717 1.0
,
-\
0.0 0.0
I
I
0.5
1 .o
1 5
Time (ps)
Figure 9. C&) functions calculated by our approximation to the Maroncelli-Kumar-Papazyan theory [ref 441 for &-FA and d7-DMF. 0
100 200 Frequency (cm")
for a strongly solvent-coupled charge transfer reaction and is obtained from the impulse response functions shown in Figure 6. The CY(?)correlation functions for dz-FA and d7-DMF are shown in Figure 9.
300
Discussion
0
50
100 Frequency (cm")
150
2bo
Figure 8. (A, upper) (A) Total OHD-RIKES frequency spectrum, Im[ R R J ~ ( w )for ] , FA. (B) RDRS(O)representation of SDRS(O) given by eq 5, and derived from ~ [ R ~ . I K E s ( using w ) ] eq 6. (C) Expanded ( x 100)
spontaneous depolarized Rayleigh/Raman spectrum,SD=(W), generated using Im[Rm(o)] and eq 4. Inset shows the normalized spectrum. (B, lower) (A) OHD-RIKESfrequency spectrum, I ~ [ R R I K E s ( wfor )], DMF. (B) RDRS(O)representation of SDRS(W)given by eq 5 and derived using eq 6. (C) Expanded (x25) spontaneous from ~~[RRIKES(W)] generated using Imdepolarized RayleighiRaman spectrum, SDRS(O), [R=(o)] and eq 4. Inset shows the normalized spectrum. reorientation response in FA. In DMF, damped librational (-60 cm-I), collision-induced and rotational reorientation responses make up the overall nuclear response. For the purpose of comparing the information provided by the OHD-RIKES and DRS spectra, the Raman spectrum, SDRS(a), and the RDRS(O)representation are calculated from the OHD-RIKES spectrum, I m [ R ~ ~ m ( a using ) l , eqs 4-6. These spectra for FA and DMF are shown in Figure 8, A and B, respectively. Following the procedure described p r e v i o ~ s l ywe , ~ ~invoke ~ a theory of Maroncelli et al.42 to generate a solvation energy relaxation function, C,(t). C,(t) is a time correlation function
The solvent dynamics covered by our OHD-RIKES data are in the frequency range from ca. 0.6 to 400 cm-'. This range covers both the low-frequency dynamics such as diffusive rotational reorientation as well as the higher frequency librational, collision-induced, and some intramolecular vibrational dynamics. Therefore, the time-domain OHD-RIKES technique provides comprehensive spectral information that can be obtained only in part by the other more traditional techniques such as microwave, far-infrared absorption, DRS, and dielectric relaxation spectroscopies. Details of the various types of solvent motions contributing to the overall OHD-RIKES response are discussed below. A. Inertial Response. Librational Dynamics. We observe significantly different librational responses from the protic FA and aprotic DMF liquids. We c o n f i the assignment of two librational bands for FA at -100 and 190 cm-l?l and we assign one librational band for DMF at 66 cm-'. All of these bands have Gaussian line shapes that indicate the inhomogeneous distribution of frequency oscillators about the band maxima. The low-frequency band profiles for FA have been observed previously by depolarized R a ~ l e i g h / R a m a n ~ ,and ~ ~ - far~~ infrared (far-IR)64spectroscopy studies. Information about the intermolecular dynamics contained within the wings of the Rayleigh spectrum is obtained by the transformation of the raw DRS spectrum into the RDRS(W) r e p r e s e n t a t i ~ n . ~Nielsen ~ . ~ ~ et a1.U,61,62have used the RDRS(W)representation to resolve the intermolecular Raman bands centered at 110 and 192 cm-' in liquid FA. Within experimental error, the higher frequency, 192 cm-I, is the same as that obtained from our OHD-RIKES spectrum, I ~ [ R R I K E s ( w )However, ]. significant deviation is observed for the lower frequency maximum (1 10 and 100 cm-' for RDRS(W) and h n [ R ~ ~ m ( wrespectively). )], We also observe nontrivial intensity profile differences between our OHD-RIKES spectrum and that given by the RDRS(W) representation. In fact, the Lorentzian line shape spectral feature corresponding to rotational reorientation observed in I~[RRIES(O)Ispectrum is completely suppressed in the RDRS(W)representation of the DRS spectrum. The relative intensities of the two prominent bands are also inverted between I~[RRIKEs(o)I and RDRS(O)spectra. These differences are explained by the fact that the RDRS(U)
Chang and Castner
9718 J. Phys. Chem., Vol. 98, No. 39, 1994 spectrum is biased toward the higher frequencies because of the multiplicative factor, w (given in eq 6), with respect to the I~[RRIKEs(w)] spectrum. In support of this argument, we find that the RDRS(O)spectrum we generate for FA using Im[R~ms(w)] and eq 6 (see Figure 8A(b)) is in excellent agreement with that obtained by Nielsen et a1.,61in terms of both the relative intensities and the frequency maxima of the two bands. It has been established through normal mode analysis, Raman, and far-IR studies that no fundamental intramolecular vibrations exist below 400 cm-' for FA.64 Both the 110- and 192-cm-' peaks in the RDRS(UJ) representation of the DRS spectrum have been assigned by Nielsen et al. to correspond to the librational modes arising from motions about the intermolecular H bonds. The results of their temperature-dependent, isotope-substitutiondependent, and salt-concentration-dependentlow-frequency Raman studiesa"' support this assignment. Itoh and ShimanouchiH have studied the structure of liquid and crystalline FA using both Raman and far-IR spectroscopy. The far-IR spectrum of liquid FA at 30 "C shows that the bands centered at 100 and 195 cm-' are also infrared-active, indicating the absence of a center of inversion symmetry for these bands. However, the assignment of these bands to a specific librational mode is complicated by the fact that the broad librational bands observed in liquid FA break up into several narrow bands in the far-IR spectrum of the crystalline FA at -165 "C. The observed bands are centered at 224, 212, 198, 155, 125, and 115 cm-', and they are assigned to correspond to the rotational lattice vibrations in the crystal. Because both C2h dimers and linear chains of FA molecules exist in the crystalline state,65 the center of inversion symmetry of the former means that some of the observed far-IR active bands much not be Raman active. However, these observations cannot be differentiated in the liquid state of FA because the observed bands are so broad and featureless. Thus, the assignment of the broad bands at 100 and 195 cm-' can only be made to the extent that they correspond to the librational modes about dissimilar rotation axes in the associated FA molecules. Additional support for the librational nature of these bands has been provided recently by a pressure-dependent lowfrequency Raman study of Goossens et al.63 Significantly different pressure-induced frequency shifts are observed for the protic vs aprotic amides and intermolecular vs intramolecular vibrations. Both the 114 and 189 cm-' bands for FA give frequency shift per pressure coefficient of approximately 2.5 cm-'kbar. In comparison, the intramolecular bands typically give a shift of less than 1 cm-'kbar. The 60 cm-I band for the non-hydrogen-bonded liquid DMF has a pressure-dependent shift of -4.0 cm-'&bar. The low-frequency band profile for DMF is much less structured than that of FA, as shown in Figure 5. In fact, the whole asymmetric feature for DMF with the band maximum at about 40 cm-' appears to match the lowest-frequency spectral feature for FA with the maximum also near 40 cm-'. This spectral component originates from the collision-induced dynamics. However, the fit to the I m [ R w ( w ) ]spectrum of DMF using only eq 7 is poor, and the best fit is obtained when eq 7 and one antisymmetrized Gaussian function (eq 8) are used. This need for a Gaussian line shape to achieve a good fit is evidence for the existence of a librational component that is overlapped with the component arising from the collisioninduced dynamics. No fundamental intramolecular vibrational modes exist below 200 cm-' in liquid DMF.58z59 The lowfrequency spectrum of the aprotic but strongly polar DMF liquid is similar to other polar liquids previously characterized by OHD-RIKES experiment^.',^,^,^,^,^^,^^ Unlike the intermolecular
TABLE 3: Parameters for I m [ R ~ ~ m ( oFitting )l Using Antisymmetrized Gaussian, Eq 8, and Eq 7 Line Shape@ Gaussian 1
Awl
Gaussian 2
Aw2
wI (cm-I)
(cm-I)
wz(cm-')
(cm-9
FA dz-FA [WAY w(dz-FA)I
99.8 94.7 (1.05)
78.5 82.9
190.1 182.1 (1.04)
96.4 87.9
DMF dT-DMF [w(DMF)/ w(d,-DMF)]
66.4 59.1 (1.12)
72.0
75.8
Litovitz wo (cm-9 a 26.2 21.9 (1.20)
1.1 1.1
28.2 27.5 (1.03)
1.2 1.0
The ratios of frequencies between deuterated and undeuterated species are also given.
H-bond librational dynamics observed in the liquid FA, the librational dynamics in DMF can only originate from the weaker dipole-dipole electrostatic interactions that give rise to some short duration orientational order because of the absence of strong H bonds. The effect of deuterium isotope substitution on the librational band frequencies for FA, DMF, and the deuterated species is summarized in Table 3. All of the librational bands are observed to red shift upon deuteration. In addition, the relative frequency shift indicated by the ratio of band maxima for undeuterated vs deuterated amides is 1.04 to 1.05 for FA and 1.12 for DMF. For FA, these observations are in good agreement with the lowfrequency, isotope-substitution Raman results of Nielsen et aL6' in which they obtain a ratio of 1.02 to 1.05. Their observation of the one-to-one correspondence between the experimental frequency ratios to the calculated frequency ratios for librations around three distinct rotation axes given by the square root of the moment of inertia ratio, [Z(d2-FA)/Z(FA)]o,5(see Table l), indicated that these bands are likely to be of librational origin. Although the isotope effect on intermolecular interactions in DMF was studied by Rodriguez and McHale using the DRS technique,52no specific information regarding the isotope effect on the librational dynamics was provided because they did not make a distinction between the collision-induced and librational dynamics in describing the observed RDRS(W)spectrum. Instead, they make a distinction between the rotational reorientation and the interaction-inducedcontributions to the overall polarizability anisotropy change. They do observe a frequency red shift of the overall band maximum in the RDRS(W)spectrum from 66 to 59 cm-' upon deuteration. They point out that the observed shift is complicated by the existence of both the reorientational and the interaction-induced dynamics that contribute to the spectral profile. To understand the relative importance of these two different types of dynamics in liquid DMF, they compared the spectral moments obtained from experimental data to those obtained by theory. The spectral moment calculations can provide insight into the relative contribution of reorientational vs collision-induced dynamics to an intensity profile because the moments are related to the angular correlation functions of pairs of molecules of interest. In the case of the angular correlation function based on the collective polarizability anisotropy, the spectral moment derivation involves the molecular moments of inertia and the mean square torque (which is the effective torque generated by the coupling of painvise and higher intermolecular interactions). Rodriguez and McHale found that the experimental moments are always in excess of the calculated moments and concluded that the collision-induced component contributes in a major way (60-65%) to the overall polari~ability.~~ We have computed the spectral moments of the RDRS(W)representation obtained from the Im[RNmS(w)] spectrum, and these are summarized in Table 4. Our spectral moments also indicate that the diffusive reorientational com-
Dynamics of Formamide and N,N-Dimethylformamide
TABLE 4: Average Frequencies, Normalized First, Second, ) Obtained and Fourth Moments of R D ~ ( oRepresentation from ~[RIUKES(O)I (WDRSY’ M1)/WO) W2YWO) W4YWO) (cm-*) (~m-~) (cm-I) (cm-*) DMF 83.6 2.93 1235.5 1.13 x 107 (1.19) (486) d7-DMF 79.7 2.70 1135.0 9.53 x lo6 (0.95) (387) a Average frequency is calculated using eq 1 in ref 53. The numbers in parentheses indicate the theoretical moments computed by Rodriguez and M ~ H a l e . The ~ ~ experimental moments are calculated for the spectral range of 0-200 cm-‘. The 202.2 cm-’ torsional mode is subtracted from the &DMF RDRS(O)spectrum prior to the moment calculation.
J. Phys. Chem., Vol. 98, No. 39, 1994 9719
calculated and experimentally obtained wo agreed well when m = 9 is used for monoatomic liquids such as AI and Xe and m = 13 is used for molecular liquids. We find that a,a floating parameter in eq 7, is close to unity for all of the liquids studied (see Table 3). Furthermore, the WO’Sfor FA and DMF are determined to be 26.2 and 28.2 cm-’, respectively. Isotope effects on wo are observed for both FA and DMF, and wo decreases on deuteration to 21.9 and 27.5 cm-’ for d2-FA and d7-DMF, respectively. We always achieve the best fits to our frequency-domain data when eq 7 is used for the low-frequency part of the spectrum in cases when the rotational component of the signal is present and when it has been subtracted prior to Fourier transformation. In very weakly interacting liquids such as carbon tetra~hloride,’~ cyclohexane, and methylcyclohexane, we find that the total intermolecular ponent contributes about 40% to the overall polarizability spectrum can be very well fit by eq 7 and not by any other anisotropy within the spectral region of 0-200 cm-’. However, model function we have tried. In these less complex liquids, in contrast to Rodriguez and McHale, we assign the rest to the low-frequency spectrum is certainly dominated by collisioncollision-induced (47%) and librational (13%) components. induced dynamics. While it is plausible that a line shape model Although we have carried out the spectral moment calcularooted in a binary-collision theory might work in part for the tions for DMF and d7-DMF liquids to compare with the previous strongly dipolar liquid DMF, it is hard to understand the success results, the same information can be obtained directly from the of this model in fitting the highly structured, hydrogen-bonded ~ [ R R I K E S ( spectrum W)] with greater accuracy. The integrated liquid FA. As shown in recent theoretical and molecular intensities of the diffusive reorientational, interaction-induced, dynamics simulations on the Raman spectrum of water, the and librational bands were calculated to estimate the relative interaction-induced (dipolehnduced dipole) dynamics lead to a contribution of each component to the overall band profile. very highly structured spectrum.77 We expect that the success Estimated in this way, the relative contributions are 33% of using eq 7 to model the bands centered at -40 cm-‘ in FA reorientational, 52% collision-induced, and 15% librational. In and d2-FA may be partially a coincidence. retrospect, the spectral moment analysis is shown to be able to B. Diffusive Rotational Reorientation Response. Because provide a rough estimate of the relative contribution of rotational FA and DMF molecules are asymmetric rotors (see Table l), it reorientational vs other collision-induced and librational dynamis expected that their rotational correlation functions will have ics. For the liquid FA, the relative contributions computed this multiple exponential decays. However, the analysis is compliway give 24% reorientational, 20% collision-induced, and 56% catd by the inherent overlap between the inertial and diffusive librational. The major contribution made by the librational responses near 1 ps. Also, in the case of FA, the intermolecular component indicates the strong effect that the intermolecular H bonds will hinder the rotational reorientation dynamics. H bonds has on both the overall structure and dynamics in FA Considering just the three distinct moments of inertia found liquid. in DMF,52 we would expect at least three rotational time Collision-Induced Dynamics. The collision-induced dynamics constants. Our observation of only two time constants may contribute to the low-frequency DRS and OHD-RIKES spectra underscore the fact that the third is contained well within the by inducing a macroscopic polarizability anisotropy. This subpicosecond response. An additional possibility is that the anisotropy arises from various intermolecular interactions different rotation axes of the molecule give rise to different involving molecular collisions and close encounters. The of polarizability change, which is then reflected in induction mechanisms include molecular frame d i ~ t o r t i o n s , 3 ~ , ~ , ~magnitudes ~ the overall diffusive reorientational response. In the case of dipole-induced dipole interaction^,^^^^^ and distortions in the DMF, the components of the molecular polarizability in relation electron cloud overlap.39 The assignment of the Rayleigh wing to the three rotation axes have been computed from the available intensity to collision-induced dynamics originally resulted from Kerr effect data78 and the use of a bond polarizability apthe DRS studies of dense noble gases and monatomic p r ~ x i m a t i o n .They ~ ~ are 9.06, 8.42, and 5.94 for G,a b , and f l ~ i d s . ~ In ~ ,these ~ ~ -studies, ~ ~ it was observed that the wing G,respectively. These polarizability values are not sufficiently feature disappears when the atomic density is lowered below a different to give rise to two effective rotational time constants critical density, indicating that the intermolecular interactions for liquid DMF. As discussed earlier in the data analysis are the source of this intensity. The DRS studies of atomic section, because the third time constant from the triplefluids were followed by the studies of molecular liquids where exponential decay fits for FA and DMF overlaps with the it was shown that the Rayleigh wing intensity is present in all subpicosecond inertial response, the long-time diffusive response l i q ~ i d s . ~ ~ ,In~ particular, ~ - ~ ~ s ~the~ DRS - ~ ~studies carried out is described in terms of the two time constants obtained from by Bucaro and L i t o ~ i t zare ~ ~notable , ~ ~ in that they were able the double-exponential fits for FA, DMF, and the deuterated to make correlations of the collision-induced dynamics observed analogs as summarized in Table 2. in a variety of liquids (protic, aprotic, polar, nonpolar, spherical, Other studies have also examined the rotational reorientation asymmetrical, etc.). They derived an analytic expression that dynamics of these amides. The dielectric relaxation study describes the collision-induced scattering component in the DRS carried out by Barthel et al. yields two Debye time constants spectra. This expression is a specific case for eq 7, given by each for FA ( t = ~ 37.3 and 1.16 ps) and DMF ( t = ~ 10.4 and 0.76 ps) in the observed frequency range 0.95-89 G H z . ~On ~ (9) the other hand, a depolarized Rayleigh scattering study carried out by Whittenburg et al. measured a single rotational time constant of 11.2 ps for FA at room temperature.*, From the and is based on a binary collision model initially introduced by latter study, additional rotation constants cannot easily be McTague and B i r n b a ~ m .Bucaro ~~ and Litovitz found that the
9720 J. Phys. Chem., Vol. 98, No. 39, 1994
Chang and Castner
Boltzmann prefactor w [ 1 - e~p(-hw/kT)l,@~~' the RDRS(O) representation is greatly biased toward the higher frequencies, and the spectral features below 100 cm-I are systematically suppressed and approach complete suppression toward 0 cm-'. The treatment of the measured SDRS(O) spectrum necessary for the study of Rayleigh wing features in the DRS investigations causes artifacts to appear, such as the inaccurate relative intensities and frequency maxima of the low-frequency bands. Since the I~[RNKEs(w)] spectrum is free of the data distortions required to generate the RDRS(W)representation, the former spectrum provides far more detailed and accurate information regarding the low-frequency molecular dynamics. It is appropriate to recall here that the I~[RMKES(O)I spectrum is directly obtained from the observed birefringence transients bond^.^^,^' without invoking any models during the analysis. In accord with the increase in all of the moments of inertia E. C&), Solvation Energy Time Correlation Function. upon deuteration, we observe that rotation time constants The solvent nuclear coordinate dynamics may dictate the course become longer in d2-FA and d7-DMF liquids relative to the of a condensed-phase chemical reaction. This situation occurs undeuterated species. The increased rotation times for the for those reactions where the reaction coordinate is strongly deuterated liquids may well be explained by moment-of-inertia coupled to the solvation energy relaxation coordinate. In the arguments for DMF. However, the ordered structure of liquid case of a charge transfer reaction, for example, the reaction is FA that results from H-bonding interactions means that any thought to be solvent controlled when the free energy barrier connection between moments of inertia and rotational diffusion between the donor and acceptor is small or negligible. Because is very complex, and the apparent agreement may require a more the impulse response function R"s(t) describes the nuclear detailed explanation. dynamics of the pure solvent, it can be used to approximate C. Impulse Nuclear Response Function. The inverse the time-dependent solvation energy relaxation and, in turn, the Fourier transformation of the I~[RMKEs(w)] spectrum gives rise solvent-controlled charge transfer or even photoisomerization to a time-domain function that represents a pure nuclear reaction dynamics. The calculated C,(t) functions for d2-FA coordinate OHD-RIKES impulse response, RRIKES(t).23,45 and d7-DMF are shown in Figure 9. The Cv(t)functions for Because the frequency content of the initial excitation pulse FA and DMF were given previou~ly.~ As has been observed limits the spectral window provided in I~[RNKEs(w)], the in several molecular dynamics simulations22-25.27-29-*3,84 and R R I K E S (is~ )also subject to this limitation and describes only also in recent time-dependent fluorescence Stokes shift studthose dynamics within the range of the I~[RNKEs(o)]spectrum. ies,26,30we can observe a Gaussian-shaped inertial regime on a For the amide liquids studied, the spectral window of ca. 400 time scale of less than 200 fs and a diffusive regime for times cm-' covers all of the intermolecular and diffusive rotational longer than several hundred femtoseconds. Some wiggles reorientation dynamics. The R R I K E S for ( ~ ) FA, DMF, and the arising from oscillatory librational contributions are also apdeuterated analogs are shown in Figure 6, and the subcompoparent in the C,(t) of d2-FA. The average solvation time, zs, nents corresponding to reorientational, librational, and collisionobtained from the zeroth moment of the Cv(r)trace is 0.75,0.79, induced responses are shown for FA and DMF in Figure 7. All 0.48, and 0.50 ps for FA, dz-FA, DMF, and d7-DMF, respecof the subcomponent responses start at time zero with an tively. It is interesting to note that the solvation energy inertially limited rise. The librational responses in FA are relaxation in the inertial regime for FA and d2-FA is significantly observed to be oscillatory, and they resemble damped sinusoidal faster than it is for DMF and Q-DMF and that the trend is functions. The DMF librational response is shown to be almost reversed in the diffusive regime. These observations are critically damped. The damped nature of the librational explained by the intermolecular H-bond network present in FA responses is connected to the inhomogeneous dephasing rate, and d2-FA liquids that significantly affects both the inertial and /3, which is proportional to the librational line width, Av,by /3 diffusive reorientation dynamics. Considering the numbers for = Avnc/(2 In 2)'". The time-domain response of the collisionzs, the DMF liquids provide a faster relaxation overall as induced band peaked at 40 cm-' for both the FA and DMF compard to the FA liquids primarily because the rotational shows an exponential-like decay in the subpicosecond regime. dynamics occur faster since there are no intermolecular H bonds. As discussed earlier, the diffusive reorientational responses are The z,'s also reflect the deuterium isotope effect on C,(t) with described by multiple exponential decay functions that extend slightly longer zs observed for the deuterated analogs. out to the picosecond regime. The impulse response functions shown in Figure 7 do not include the responses arising from Summary the intramolecular vibrational modes. The intramolecular vibrational responses have been observed to dominate the overall We have studied in detail the total solvent relaxation profile OHD-RIKES response in the case of CC4 and other halogenated of the dipolar liquids FA, DMF, and their deuterated species m e t h a n e ~ . ' JHowever, ~ ~ ~ ~ ~for ~ ~the amide liquids studied here, using the Fourier-transform OHD-RIKES technique. The the overall response is dominated by the intermolecular and inertial solvent motions were observed on a time range spanning diffusive reorientational dynamics, and the intramolecular several hundreds of femtoseconds. The diffusive solvent responses are observed not to contribute significantly. motions are a result of these same molecular motions observed D. I~[RRIKEs(o)Ivs RDRS(O). Using the I~[RRIKEs(w)] on a longer time scale following many molecular collisions and representation of our OHD-RIKES data, we have calculated the interactions. The librational dynamics are observed to be low-frequency spontaneous Raman spectrum, SDRS(W),and the significantly different between FA and DMF liquids because of the protic and aprotic nature of the two liquids, respectively. RDRS(W)representation using eqs 4-6. These spectra are shown for FA and DMF in Figures 8, A and B, respectively, and are Two distinctly underdamped H-bond librational modes with compared with the I~[RNKEs(w)I spectrum. Because of the frequencies of 100 and 195 cm-I are observed in the FA liquid extracted from the depolarized Rayleigh spectrum because the Rayleigh line scatter overwhelms the Lorentzian line shapes in the wings of the DRS spectrum that arises from the diffusive rotational reorientation dynamics. From our analysis as well as that from Barthel et al., the rotational time constants for DMF are shorter than those for FA despite the fact that the moments of inertia of DMF are significantly larger than those of FA. This effect is caused by the presence of intermolecular H bonds in FA that significantly hinder the rotational motions. In fact, the results of the temperature-dependent study of this slowest reorientational relaxation indicate that the diffusive reorientation in FA is connected to the making and breaking of the intermolecular H
Dynamics of Formamide and N,N-Dimethylfomamide that appear in the time-domain OHD-RIKES data as oscillating features. The librational mode at 66 cm-I observed for the DMF liquid is almost critically damped and is assigned to arise from the dipole-dipole electrostatic interactions between the molecules. Both liquids seem to exhibit similar collision-induced dynamics. The deuterium isotope substitution has a noticeable effect on both the librational and collision-induced dynamics. We have compared the spectral information provided by the two related techniques, DRS and OHD-RIKES. Although the low-frequency molecular motions and intermolecular interactions have been studied extensively in the past using DRS spectroscopy, we show that the RDRS(O)representation does not provide as accurate and detailed information as that provided by OHD-RIKES. Specifically, the equation used to generate the RDRS(W) representation (eq 5) gives rise to incorrect relative contributions of collision-induced, librational, and diffusive rotational dynamics. In addition, we find that the librational frequency maxima obtained from RDRS(W)are systematically higher than the values measured from I m [ R m s ( w ) ]because of the multiplicative frequency factor given in eq 6. Because the spectral profile given in Im[R"(w)] describes the liquid dynamics directly without any additional treatment of the data, it provides unique and important insights into the solvent motions that comprise the overall liquid dynamics. In addition to the Rayleigh wing feature, I~[RRIKEs(o)] shows the lowestfrequency Lorentzian line shape profile, arising from rotational reorientation dynamics, that is free from the dominant Rayleigh line intensity contained in the DRS spectra. Another advantage of the OHD-RIKES technique is that all of the spectral features can also be examined in the time domain for further analysis. For example, we have analyzed the diffusive rotational reorientation dynamics in the time domain to find that this response exhibits nonexponential decay behavior. The multiple rotational time constants required to describe this response can be explained by the fact that these amide molecules are asymmetric rotors with three different moments of inertia. We also observed that the diffusive response for DMF was faster than that for FA despite the large moments of inertia for the DMF molecule. The significant hindering of the rotational reorientation dynamics by the intermolecular H-bond network in the FA relative to DMF is responsible for this effect. The rotational response shows a predictable deuterium isotope effect for both FA and DMF. The rotational time constants are measured to be longer for the deuterated species, and they are correlated with the increase in the moments of inertia upon deuteration. After characterizing the neat solvent dynamics, we would like to be able to make some predictions of how these ultrafast solvent motions will affect the dynamics of a condensed-phase chemical reaction. Toward this end, we have examined the role that the inertial and diffusive solvent motions will play in barrierless charge transfer reaction dynamics. The solvation energy time correlation function, C,(t), which describes the dynamics of both the solvation and reaction for this case, is obtained by calculating a polarizability autocorrelation function from the OHD-RIKES impulse response function. As has been confirmed by the recent e ~ p e r i m e n t a l , ~theoretical, , ~ ~ . ~ ~ and computer simulation22-29,83,84 results, we observe both the inertial and diffusive regimes of the Cv(t)function. The protic FA liquid exhibits faster relaxation in the inertial regime and slower relaxation in the diffusive regime as compared to the aprotic DMF liquid. The H-bond librational dynamics that dominate the inertial solvent motions in the FA liquid give rise to the accelerated solvation energy relaxation in the f i s t few hundreds to femtoseconds whereas the same H bonds that hinder the rotational reorientation dynamics decelerate the relaxation
J. Phys. Chem., Vol. 98, No. 39, I994 9721
in the picosecond diffusive regime. The Cv(t) correlation function obtained in this way from the OHD-RIKES data complements the C,(f) obtained by the time-dependent fluorescence Stokes shift Because the time resolution of the OHD-RIKES technique is approaching sub-10 fs, a more comprehensive examination of the ultrafast solvent dynamics and their effect on reaction dynamics is possible using the OHD-RIKES technique. A question that remains is how our new experimental results on the intermolecular dynamics in complex liquids can be connected with results from theory and computer simulations. Molecular dynamics simulations allow a detailed and comprehensive view of the intermolecular dynamics. The weakest aspect of current dynamical simulations in complex molecular liquids is often the lack of a detailed intermolecular potential. A good dynamics simulation would reproduce the intermolecular dynamics we have observed here. Though the problem of inverting the intermolecular potential based upon our dynamics is most difficult, our results do provide the detailed data required for a consistency check for those working out new potentials. A promising approach toward a detailed theoretical understanding of the liquid-phase intermolecular dynamics presented here is the work using the instantaneous normal modes (INM) p i c t ~ r e . ~ ~In- ~essence, l the classical dynamical matrix for the total ensemble of molecules in the sample is formally inverted, yielding well-defined normal modes for all of the intermolecular motions occurring at short times. In fact, the time scales on which the INM description break down seem to be at around 0.5 ps, which is where we observe that the dephasing of the inertial intermolecular motions is complete and the transition to wholly dissipative dynamics is Occurring. One major challenge in the INM description is to understand the unstable imaginary-frequency dynamics that result from saddles in the intermolecular potentials, as opposed to the stable harmonic modes that arise from the parabolic harmonic potentials. Both purely analytic theories and analytic theories combined with molecular dynamics simulations have recently been completed. Another important question has been whether the measured polarizability arises from motions that can only be described in a collective fashion or whether the polarizability may be represented as a sum of independent single-molecule oscillators. Recent work of Stratt and Cho provides a simple and insightful answer, namely that either single-particle or all-collective descriptions of the intermolecular dynamics will be correct for short times.87 Specifically, for times during which the INM description remains valid, Le., during the inertial part of the solvent relaxation, the collective and single-molecule dynamical pictures are related by an orthogonal matrix transformation. Though the progress in INM theories is most encouraging, we are not yet able to apply these results directly to our solvent dynamics data. To understand our OHD-RIKES data on a molecular level, we have done a careful spectral decomposition of the measured dynamics. One advantage of this approach is that we may directly make the connection between the solvent polarizability time correlation function and chemical reaction dynamics.
Acknowledgment. This research was carried out at Brookhaven National Laboratory under Contract DE-AC0276CH00016 with the US.Department of Energy and supported by its Division of Chemical Sciences, Office of Basic Energy Sciences. References and Notes (1) McMorrow, D.; Lotshaw, W. T.; Kenney-Wallace, G. A. IEEE J. Quantum Electron. 1988, 24, 443.
9722 J. Phys. Chem., Vol. 98, No. 39, 1994 (2) McMorrow, D.; Lotshaw, W. T.; J . Phys. Chem. 1991,95, 10395. (3) Hattori, T.; Terasaki, A.; Kobayashi, T.; Wada, T.; Yamada, A.; Sasabe, H. J . Chem. Phys. 1991, 95, 937. (4) Wynne, K.; Galli, C.; Hochstrasser, R. M. Chem. Phys. Lett. 1992, 193, 17. (5) Cho, M.; Rosenthal, S. J.; Scherer, N. F.; Ziegler, L. D.; Fleming, G. R. J . Chem. Phys. 1992, 96, 5033. (6) Cho, M.; Du, M.; Scherer, N. F.; Fleming, G. R.; Mukamel, S. J . Chem. Phys. 1993, 99, 2410. (7) Chang, Y. J.; Castner, E. W., Jr. J . Chem. Phys. 1993, 99, 113. (8) Chang, Y. J.; Castner, E. W., Jr. J. Chem. Phys. 1993, 99, 7289. (9) Castner, E. W., Jr.; Chang, Y. J. In Femtosecond Reaction Dynamics; Wiersma, D. A,, Ed.; North-Holland: Amsterdam, 1994; p 255. (10) Righini, R. Science 1993, 262, 1386. (1 1) Kohler, B.; Nelson, K. A. J . Phys. Chem. 1992, 96, 6532. (12) Ruhman, S.; Joly, A. G.; Nelson, K. A. J . Chem. Phys. 1987, 86, 6563. (13) Ruhman, S.; Joly, A. G.; Nelson, K. A. IEEE J. Quantum Electron. 1988, 24, 470. (14) Becker, P. C.; Fragnito, H. L.; Bigot, J. Y.; Brito Cruz, C. H.; Fork, R. L.; Shank, C. V. Phys. Rev. Lett. 1989, 63, 505. (15) Bardeen, C. J.; Shank, C. V. Chem. Phys. Lett. 1993, 203, 535. (16) Nibbering, E. T. J.; Duppen, K.; Wiersma, D. A. J . Chem. Phys. 1990, 93, 5477. (17) Nibbering, E. T. J.; Wiersma, D. A,; Duppen, K. Phys. Rev. Lett. 1991, 66, 2464. (18) Kang, T. J.; Yu, J.; Berg, M. J . Chem. Phys. 1991, 94, 2413. (19) Fourkas, J. T.; Berg, M. J . Chem. Phys. 1993, 98, 7773. (20) Yu, J.; Berg, M. J . Phys. Chem. 1993, 97, 1758. (21) Muller, L. J.; Bout, D. V.; Berg, M. J . Chem. Phys. 1993,99, 810. (22) Perera, L.; Berkowitz, M. J . Chem. Phys. 1992, 96, 3092. (23) Perera, L.; Berkowitz, M. J . Chem. Phys. 1992; 97, 5253. (24) Phelps, D. K.; Weaver, M. J.; Ladanyi, B. M. Chem. Phys. 1993, 176, 575. (25) Maroncelli, M. J . Mol. Liq. 1993, 57, 1. (26) Maroncelli, M.; Kumar, P. V.; Papazyan, A,; Homg, M. L.; Rosenthal, S. J.; Fleming, G. R. In International Workshop on Ultrafast Reactions Dynamics and Solvent Effects;Simon, J. D.; Ed.; Kluwer: Abbaye de Royaumont, France, 1994. (27) Chandra, A.; Bagchi, B. J . Chem. Phys. 1993, 99, 553. (28) Roy, S.; Komath, S.; Bagchi, B. J . Chem. Phys. 1993, 99, 3139. (29) Smith, B. B.; Staib, A.; Hynes, J. T. Chem. Phys. 1993, 176, 521. (30) Rosenthal, S. J.; Xie, X.; Du, M.; Fleming, G. R. J . Chem. Phys. 1991, 95, 4715-4718. (31) Chang, Y. J.; Castner, E. W., Jr. In 6th International Conference on Time-Resolved Vibrational Spectroscopy; Lau, A,, Ed.; SpringerVerlag: Berlin, 1994; pp 145-147. (32) Clarke, R. J. H. In Advances in Infrared and Raman Spectroscopy; Clarke, R. J. H., Hester, R. E., Eds.; Heyden: London, 1978; Vol. 4, p 109. (33) Madden, P. A. In Phenomena Induced by Intermolecular Interactions; Birnbaum, G., Ed.; Plenum Press: New York, 1985; p 399. (34) Evans, M.; Evans, G. J.; Coffey, W. T.; Grigolini, P. Molecular Dynamics and Theory of Broad Band Spectroscopy; John Wiley & Sons: New York, 1982. (35) Bucaro, J. A.; Litovitz, T. A. J . Chem. Phys. 1971, 54, 3846. (36) m b e a u , M.; Oksengom, B.; Vodar, B. J . Phys. 1968, 29, 287. (37) Lallemand, P. Phys. Rev. Lett. 1970, 25, 1079. (38) Levine, H. B.; Birnbaum, G. Phys. Rev. Lett. 1968, 20, 439. (39) McTague, J. P.; Bimbaum, G. Phys. Rev. Lett. 1968, 21, 661. (40) Gabelnick, H. S.; S t r a w , H. L. J . Chem. Phys. 1968, 49, 2334. (41) Eesley, G. L.; Levenson, M. D.; Tolles, W. M. IEEE J . Quantum Electron. 1978, QE-14, 45. (42) Maroncelli, M.; Kumar, V. P.; Papazyan, A., J . Phys. Chem. 1993, 97, 13. (43) Lund, P. A.; Nielsen, 0. F.; Praestgaard, E., Chem. Phys. 1978, 28, 167. (44) Nielsen, 0. F.; Christensen, D. H.; Have Rasmussen, 0. J . Mol. Struct. 1991, 242, 213.
Chang and Castner (45) McMorrow, D. Opt. Commun. 1991, 86, 236. (46) Nielsen, 0. F.; Christensen, D. H.; Lund, P. A,; Praestgaard, E. Proc. 6th Int. Conf. Raman Spectrosc. 1978, 2, 208. (47) Nielson, 0. F. Chem. Phys. Lert. 1979, 60, 515. (48) Nielsen, 0. F.; Lund, P. A. J . Chem. Phys. 1983, 78, 652. (49) Perrot, M.; Brooker, M. H.; Lascombe, J. J . Chem. Phys. 1981, 74, 2787. (50) Brooker, M. H.; Perrot, M. J . Chem. Phys. 1981, 74, 2795. (51) Rodriguez, R.; McHale, J. L. J . Chem. Phys. 1988, 88, 2264. (52) Rodriguez, R.; McHale, J. L. J . Chem. Phys. 1988, 88, 2273. (53) Gordon, R. G. J . Chem. Phys. 1964, 40, 1973. (54) Dardy, H. D.; Volterra, V.; Litovitz, T. A. J . Chem. Phys. 1973, 59, 4491. (55) Bruining, J.; Clarke, J. H. R. Mol. Phys. 1976, 31, 1425. (56) Ladanyi, B. J . Chem. Phys. 1983, 78, 2189. (57) Gordon, R. G. Adv. Magn. Reson. 1968, 3, 1. (58) Durgaprasad, G.; Sathyanarayana, D. N.; Patel, C. Bull. Chem. Soc. Jpn. 1971, 44, 316. (59) Jao, T. C.; Scott, I.; Steele, D. J . Mol. Struct. 1982, 92, 1. (60) Schmid, E. D.; Brodbeck, E. J . Mol. Struct. 1984, 108, 17. (61) Nielsen, 0. F.; Lund, P.-A.; Praestgaard, E. J . Chem. Phys. 1982, 77, 3878. (62) Nielsen, 0. F.; Lund, P.-A.; Chem. Phys. Lett. 1981, 78, 626. (63) Goossens, K.; Smeller, L.; Heremans, K. J . Chem. Phys. 1993, 99, 5736. (64) Itoh, K.; Shimanouchi, T. J . Mol. Spectrosc. 1972, 42, 86. (65) Ladell, J.; Post, B. Acta Crystallogr. 1954, 7, 559. (66) McMorrow, D.; Lotshaw, W. T. Chem. Phys. Lett. 1990,174, 85. (67) Lotshaw, W. T.; McMorrow, D.; Kalpouzos, C.; Kenney-Wallace, G. A. In Ultrafast Phenomena VI, 1st ed.; Yajima, T., Yoshihara, K.; Harris, C. B., Sionoya, S., Eds., Springer-Verlag: New York, 1988; p 537. (68) Bucaro, J. A.; Litovitz, T. A. J . Chem. Phys. 1971, 55, 3585. (69) McTague, J. P.; Birnbaum, G. Phys. Rev. 1971, A3, 1376. (70) Fleury, P. A.; Daniels, W. B.; Worlock, J. M. Phys. Rev. Lett. 1971, 27, 1493. (71) An, S. C.; Montrose, C. J.; Litovitz, T. A. J . Chem. Phys. 1976, 64, 3717. (72) An, S. C.; Fishman, L.; Litovitz, T. A.; Montrose, C. J. J . Chem. Phys. 1979, 70, 4626. (73) Bartoli, F. J.; Litovitz, T. A. J . Chem. Phys. 1972, 56, 413. (74) Howard-Lock, H. E.; Taylor, R S. Can. J . Phys. 1974, 52. (75) Posch, H. A.; Litovitz, T. A. Mol. Phys. 1976, 32, 1559. (76) Castner, E. W., Jr.; Chang, Y. J.; Melinger, J. S.; McMorrow, D. J . Lumin. 1994, 60&61, 723. (77) Sastry, S.; Stanley, H. E.; Sciortino, F. J . Chem. Phys. 1994, 100, 5361-5366. (78) h o n e y , M. J.; LeFevre, J. W.; Singh, A. N. J . Chem. Soc. 1965, 3179. (79) Barthel, J.; Bachhuber, K.; Buchner, R.; Hetzenauer, H. Chem. Phys. Lett. 1990, 165, 369. (80) Whittenberg, S. L.; Jain, V. K.; McKinnon, S. J. J. Phys. Chem. 1986, 90, 1004. (81) Chang, Y. J.; Castner, E. W., Jr. Manuscript in preparation. (82) Back, R.; Kenney-Wallace, G A.; Lotshaw, W. T.; McMorrow, D. Chem. Phys. Lett. 1992, 191, 423. (83) Bader, J. S.; Chandler, D. Chem. Phys. Lett. 1989, 157, 501. (84) Neria, E.; Nitzan, A. J . Chem. Phys. 1992, 96, 5433. (85) Barbara, P. F.; Jarzeba, W. In Advances in Photochemistry; Volman, D. H., Ed.; Wiley: New York, 1990; p 1. (86) Buchner, M.; Ladanyi, B. M.; Stratt, R. M. J . Chem. Phys. 1992, 97, 8522. (87) Stratt, R. M.; Cho, M. J . Chem. Phys., submitted. (88) Wan, Y.; Stratt, R. M. J . Chem. Phys., submitted. (89) Cho, M.; Fleming, G. R.; Saito, S.; Ohmine, I.; Stratt, R. M. J . Chem. Phys., submitted. (90) Wu, T. M.; Loring, R. F. J . Chem. Phys. 1992, 97, 8568. (91) Wu, T. M.; Loring, R. F. J . Chem. Phys. 1993, 99, 8936.
