4780
J. Phys. Chem. 1994,98, 4780-4786
ARTICLES Solution-State N M R Measurement of the Carbon and Proton Chemical Shift Tensors, the C-H Bond Distance, and the Molecular Correlation Time in Phenylacetylene Thomas C. Farrar,. Michael J. Jablonsky, and Joe L. Schwartz Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706 Received: October 26, 1993; In Final Form: February 25, 1994" N M R relaxation times were measured for the acetylene carbon and hydrogen nuclei in the coupled two-spin system H5C6-C=l3C-H. For the experiments reported here, 0.15 and 0.30 M solutions of phenylacetylene in pure d-8-toluene and in 50/50 mixtures of fully deuterated toluene/methanol and toluene/2-propanol were studied. The values obtained a t 7.0 T between 163 and 189 K for the carbon-hydrogen bond distance, rcH, corrected for vibrational averaging and the carbon and proton chemical shift anisotropies (AS), are 109.1 f 1.0 pm, -159.6 f 7.2 ppm, and -13.7 f 0.3 ppm, respectively. Within experimental error, these parameters are independent of temperature, magnetic field strength, and solvent. The temperature dependence of the 13C isotropic chemical shift (which can be measured more precisely than the AS value) is approximately -0.017 ppm/K; it is not linear and can be described (in units of ppm) by the quadratic equation Si, = (5.608 X lO-s)P - 0.0410T 82.30, where T i s the temperature in degrees Kelvin and Si, is the isotropic chemical shift relative to TMS. In terms of the components of the proton and carbon chemical shift tensors (relative to TMS), we obtain: 6 p = -6.31 ppm, S y = 7.39 ppm, Sf = -27.76 ppm, and :S = 131.84 ppm :6( = 2.82 ppm and ,,a: = 78.64 ppm in a 50/50 toluene/methanol mixture). Using the Redfield formalism, simultaneous information about the two CSA values, the bond distance, the correlation time, and the intermolecular interactions can be obtained a t a single fixed temperature and a single magnetic field value while observing a single nucleus. The relative contributions of the dipolar, CSA, and intermolecular interactions depend on different components of the spectral density function and are, consequently, temperature (i.e., correlation time) dependent.
+
1. Introduction
The work reported here is part of a long-range effort to learn more about solvent-solute interactions and molecular correlation times and to further develop nuclear magnetic resonance (NMR) relaxation methods, in both coupled and decoupled spin systems, for the accurate measurement of molecular structure and molecular dynamics. We are particularly interested in the measurement of bond distances, chemical shift tensors, and molecular correlation times in small molecules and ions. An experimental measurement of the carbon chemical shift anisotropy (CSA or A6) in phenylacetylene is of special interest in light of a recent ab initio calculation' of the carbon chemical shielding tensor which has predicted a value of Au = +166 ppm. This value is surprising since most other reported carbon Au values for substituted acetylenes are in the range 200-240 ppm.2 In past N M R literature, chemical shielding and chemical shift have been used loosely and interchangeably, making it particularly arduous for the reader to determine which of these the authors is reporting (the chemical shift anisotropy (CSA) is the negative of the anisotropy of the chemical shielding (ACS)). It is for this reason that we distinguish between the two by denoting chemical shift anisotropy (CSA) as A6 and the anisotropy of the chemical shielding (ACS) as Au. Chemical shift tensor components will be denoted by 6, and chemical shielding tensor components will be denoted by u. For clarity between shift and shielding, we will refer to the chemical shift anisotropy as CSA and the anisotropy of the chemical shielding as (ACS). For further information and/or clarification see the discussion in ref 2. With the advent and increasing use of N M R spectrometers which operate at high magnetic field strengths (4.7-14 T and
* Author to whom correspondence should be addressed.
* Abstract published in Adoance ACS Abstracts, April 1, 1994.
higher), N M R relaxation can become rather complex, especially when both dipolar and chemical shift anisotropy (CSA) contribute significantly to the relaxation. Both the longitudinal (or spinlattice, T I ) relaxation and the transverse (or spin-spin, Tz) relaxation for a two-spin system are functions of the internuclear distance, rCH; the thermally averaged bond distance; the components of the chemical shielding tensors, 611,UZZ, and u33for both nuclei; and the components of the rotationaldiffusion tensor, 71, 72, 7 3 . If none of these parameters is known a priori, it is possible in favorable cases to obtain all of these parameters from experiments at a fixed field and a fixed temperature while observing a single nucleus. The data analysis and the experiments are greatly simplified, however, if the number of parameters to be simultaneously fit can be reduced, either by symmetry considerations or by accurate a priori knowledge of some of the parameters. In the present case for the acetylene carbon and proton in phenylacetylene, symmetry simplifies the analysis since, to a good approximation, the molecule in solution may be considered to have axial symmetry. Consequently, there are only two different components of the chemical shielding tensor (UII= u22 = uL and 6 3 3 = all) and a single component ( T ~of ) the rotational diffusion tensor (7, = 72 = T~ and 7 3 = 711). Since rotation about the symmetry axis does not change the orientation of the internuclear vector with the Bo magnetic field, 711may be ignored. It has been our experience that if the CSA values for both nuclei are comparable in magnitude to the dipolar parameter and if the two-spin system has C3" symmetry or higher, it is possible via N M R relaxation time studies of a coupled system to obtain quite accurate values for the dipolar parameter (and hence the bond distance) and both components of the chemical shielding tensor (uil and ul) for each nucleus. In the present case, in a magnetic field of 7.0 T, the '3C Au (ACS) factor, rBo(ull - ul), is about
0022-3654/94/2098-4780SO4.50/0 0 1994 American Chemical Society
The Journal of Physical Chemistry, Vol. 98, No. 18, 1994 4781
Solution-State N M R Measurement 3-9% of the dipolar term, (YCYHh/2rCH3)(p0/4?r);excellent fits were still possible. The relative ACS contribution is a function of the molecular correlation time and is a maximum when UT, N 1. At 11.7 T, the relative ACS contribution varies from about 10%to 30%. In addition, such experiments provide simultaneous information about the molecular correlation time and the intermolecular contributions (usually from the deuterated solvent molecules) to the relaxation. If accurate information is available concerning the internuclear distances and/or the components of the chemical shielding tensors for the relaxing nuclei, the data analysis for the molecular diffusion time, T,, is greatly simplified and the accuracy and precision of rCvalues are improved. For systems of low symmetry, it has been our experience that there are too many parameters involved in the nuclear relaxation process to obtain accurate values for all of them via N M R relaxation time measurements of the coupled spin system. It is then essential to have accurate data about internuclear distances and the components of the chemical shielding tensors. In the present case, the analysis is relatively simple and straightforward since the C-H spin pair has essentially axial symmetry and the principal axis of the chemical shielding tensor and the dipolar tensor are coincident. The work reported here is part of a long-term effort to obtain experimental data from chemical shielding tensors in both the liquid and the solid state and to investigate how these tensors change as a function of molecular conformation and geometry, physical state, and solvent. Both solid-state line shape studies and liquid-state relaxation time studies provide information about the components of the tensors. Recent advances in a b initio calculations have made it possible, a t least for hydrocarbons, to calculate the components of the chemical shielding tensor with a high degree of accuracy. In order to compare the calculated results with experimental data, we have used solid-state N M R methods to obtain chemical shift tensor data for a neat, polycrystalline sample of phenylacetylene. The data obtained thus far have been of poor quality. Nuclear magnetic raonance (NMR) relaxation methods areoften used to obtain information about molecular structure and dynamics in liquids3-5 and also to provide an alternate method for obtaining chemical shift tensor data. Until recently, most N M R experiments have been carried out in relatively low magnetic fields (2.3 T or lower), where the primary relaxation mechanism is the dipoledipole interaction. If intramolecular dipolar relaxation is the sole relaxation process present, then the spin-lattice (or longitudinal) relaxation rate, R l ,for a system of two spins, I and S,each of spin- 1/2, is usually given in the form6
distance, h is Planck's constant divided by 2 r , WI and US are the N M R resonance frequencies (in units of s-I), Ea is the activation energy for rotational diffusion, T~ is the molecular correlation time, and TO is a pre-exponential factor. and are obtained by interchanging I and S in the above expressions. These equations accurately predict the typical biexponential decay of the free induction decay (FID) signal for either spin I or spin S and show clearly that the I, and S, magnetizations decay a t the same rate. Note that I, is the sum of the magnetizations for both lines in the I-spectrum; each line relaxes at the same rate. A similar condition holds for S,. In other words, for dipolar-only relaxation all four spectral lines relax a t the same biexponential rate and only two molecular parameters, p , the dipolar parameter, and T ~the , molecular correlation time are needed to describe the relaxation of the system. An analysis of the temperature dependence of the relaxation in the dispersion region, where U T , N 1, provides information about the dipolar parameter, p (see eq 4) and hence the internuclear distance, rIs. The temperature-dependent data in the dispersion region also provide information about the pre-exponential factor, TO,and the activation energy, Ea, for rotational diffusion. Once these parameters are known, longitudinal relaxation times can be directly related to the molecular correlation time. In the above analysis one has assumed an isolated two-spin system with dipolar-only relaxation and molecular motions which can be described by a single correlation parameter, T,. In most experiments, however, there are intermolecular contributions to the relaxation of the spin pair. The intermolecular interactions are usually between the spins of interest and the deuterons in the solvent molecules such as D20, d6-DMS0, and so on. The magnitude of these interactions can be measured experimentally via isotope dilution e~periments.3,~ With the increasing availability of high magnetic fields (7 T and higher), for most spin-1/2 nuclei other than hydrogen the chemical shift anisotropy (CSA) interaction contributes significantly to the relaxation. In this event the relaxation may become much more complex. Four different parameters are then required to describe the transverse relaxation' (one parameter for each spectral line), and 12different parameters are required to describe the longitudinal relaxations (the longitudinal relaxation for each line is described by a triple exponential). Although the analysis of the experimental data is now much more complex, a wealth of additional new information is available from these high-field experiments. Details of the theory are available in numerous papers in the 1iterature;Gl'J a brief summary is given in the Theory section of this article.
e'
q'
2. Experimental Section
ds, = -*(I, dt
- I,) - Rfs(Sz - So)
(4)
where I and S are the spin quantum numbers for the two spins, 71and 7s are their gyromagnetic ratios, rIs is the internuclear
The samples were degassed by a t least eight f r e e z e p u m p thaw cycles on a high-vacuum line and sealed under high vacuum. The N M R tubes were carefully cleaned before use and treated with sodium EDTA solutions toremove any trace of paramagnetic ion contaminants. Measurements made over a period of 12months show no change in the relaxation times for a given set of experimental conditions, and they show no exchangeof the proton directly bonded to the acetylene carbon atom when stored at a temperature of -80 OC. A convenient lock signal was provided by the methyl deuterons in the toluene solvent, even at the lowest temperatures. In the relaxation experiments performed here, temperature stability is of paramount importance. For this reason we designed and built a temperature controller which is capable of holding the temperature constant to better than f0.035 OC for periods up to 36 h or longer (the carbon-13 chemical shift provided an internal check on the temperature and its stability). This device has been described elsewhere.23 Typical carbon 90° pulse widths were about 20 ps; proton 90° pulse widths were approximately 14 ps. All spin inversions were accomplished with composite
4782
The Journal of Physical Chemistry, Vol. 98, No.18, 1994
Farrar et al.
pulses designed to compensate for R F inhomogeneity (9OX- 180,
- 90,).24 Relaxation delays of 10 times the relaxation time for the most slowly relaxing of the four spectral lines were used. A spectral width of about 500 Hz was used (the value of JCH is 25 1 Hz). FIDs were zero-filled and line-broadened prior to Fourier transformation to provide a t least 15 data points above the half height for each peak. As shown in an earlier paper,zs in order to obtain reliable values for the CSAs, the dipolar parameter, and the correlation time, it is necessary to execute, as a minimum, two or more of the following experiments (each of these experiments constitutes a boundary condition): (1) broad-band (non-selective) inversion recovery of 13C, followed by observation of 13C;(2) broad-band inversion of the lH lines followed by observation of 13C;and (3) simultaneous broad-band inversion of the lH lines and the I3C lines followed by observation of 13C. Twenty-five 7 values for each experiment were collected, two or three of which were a t least 10 times greater than T I ;these were used to check the long-term stability of the system and the reproducibility of the data. At a field of 4.7 T, between 12 and 24 h were required to collect one set of data for the experiments described above (of course, shorter times were required to achieve the same signal-to-noise ratio for data obtained at the higher field strengths). To minimize the effects of spectrometer instability, the program cycles through the three experiments in the following manner:
- -
(EXPl(7") EXP,(7*) EXP3(7,)), where n indicates one of the 25 7 values and EXPI, EXP2, and EXP3 are experiments with the three different boundary conditions. Eight scans are collected for each value of n,and then the entire sequence is repeated m times to give the required signal to noise ratio. This cycling reduces the stability required of the spectrometer to only the few minutes necessary to collect eight scans for each of 75 FIDs instead of the many hours required for theentire experiment. Peak heights were used for magnetization intensities. These were then scaled to account for the differences in height that result from the differential line broadening. Reproducibility between equilibrium values was 0.5 % (std. dev.) or better. For the work described here, all three of the above boundary conditions were used in the fit routines. The temperature dependence of the 13C isotropic chemical shift is approximately -0.017 ppm/K. It is not linear and can be described (inunitsofppm) by thequadraticequation 6i, = (5.608 X lO-S)P - 0.04107' 82.30, where T is the temperature in degrees Kelvin and 6i, is the chemical shift relative to TMS; see Figure 1. This was measured a t both 4.7 T (200 MHz IH) and 11.7 T (500 MHz 1H); this information served as an additional method to monitor changes in the temperature of the sample. These measurements were made without deuterium lock to avoid convoluting the temperature dependence of the deuterium isotropic chemical shift of the lock solvent with the carbon isotropic chemical shift of the phenylacetylene. The temperature was independently measured with a platinum resistance thermometer (PRT) inserted into the probe before and after the measurements. Carbon longitudinal relaxation time experiments were performed a t 4.7 and 7.0 T using the home-built temperature controller mentioned above. The measurements done a t 8.5 and 11.7 T employed a commercial temperature controller which was much less stable and gave substantially greater errors. Measurements were carried out in three different fully deuterated solvents: toluene, a 50/50 mixture of toluene/methanol, and a 50/50 mixture of toluene/ 2-propanol. In addition, both 0.15 and 0.30 M concentrations of phenylacetylene in a 50/SO mixture of toluene/methanol were studied.
+
3. Theory The theory of spin-lattice relaxation in coupled spin systems has been treated in detail by a number of authors (refs 7, 8, 27,
9
76.5
1
a,
€ 1
'a
Q Q
v
I
,
,
,
200
,
I
,
,
250
Temperature (K) Figure 1. I3Cisotropicchemical shift (62)relative to TMS as a function of temperature. The data can be described by the quadratic quation (5.608 X 10-s)P - 0.0410T+ 82.30 ppm where Tis the temperature in degrees Kelvin. This data set was taken at 4.7 T. The system is 0.1 5 M phenylacetylene in 50/50 toluene/2-propanol.
20 and refs 11-1 3,19,29) and is not repeated in detail here. The populations of the energy levels are represented by the diagonal elements of the density matrix uti, and the spin-lattice (or longitudinal) relaxation is described by the differential equation given in eq 6. Note that the form of this equation is almost identical to that used to describe two-dimensional NOESY experiments.17J8
The elements of the relaxation matrix, &iff, for the case of two spin 1/2 nuclei relaxed by the dipolar and CSA interaction are calculated by the theory developed by Redfield19and by Shimizu27 and are given below. Two isotropic random field terms, A and E (for 13Cand 'H, respectively), were included in the analysis to account for the residual intermolecular dipolar interactions of the solvent deuterium nuclei with carbon and proton spins. In general, the random field terms also include any spin-rotation contributions to the carbon or proton relaxation? in the present case the spin-rotation contribution is negligible. The random field terms A and E allow for motionally noncorrelated intermolecular relaxation (primarily with the deuterons in the solvent) and are of the form y f B ? ~ iwhere , Bi is the randomly fluctuating field produced by spins external to the C-H spin pair and 71is the correlation time for the deuteron-carbon or deuteron-proton interaction. The random termsdepend upon temperature because of the implicit dependence on T ~ and , they provide information about solvent/solute interactions. Experimentally, one observes not populations of energy levels but population differences, or line intensities. In order to use the line intensities directly in the analysis, the relaxation matrix was transformed to the line intensity basis: dI/dr = R'[I - I(=)] where I is a vector whose four components are the intensities of the four N M R transitions and I(=) is a vector whose components are the equilibrium intensities for those same four transitions. The solution to this set of differential equations is
+
I = cleXlrvl c,eX2'v,
+ c3eX3'v3+ c4ehrv4+ I(..)
(7)
where vi are the eigenvectors, XI are the eigenvalues, and the ci
Solution-State N M R Measurement
The Journal of Physical Chemistry, Vol. 98, No. 18, 1994 4783
are constants of the integration which depend on the boundary values for the various experiments. In the analysis program the relaxation matrix is calculated based on estimated values of AUC,A u H , ~rC, , A, and B which are defined below. This is then numerically diagonalized to give eigenvalues XI through & and eigenvectors v1 through v4. Note that since the number of nuclei is constant, one of the eigenvalues is zero and the relaxation is described by a triple exponential. Using the initial conditions (which depend upon the pulse experiment) and the equilibrium line intensities, the constants c1 to c4 are obtained, and then the predicted line intensities are calculated as a function of time. Nonlinear least-squares methods are used to find the set of best fit parameters. Similar information can, in principle, be obtained from transverse (Tz) relaxation time measurements. It is straightforward to show that for nondegenerate eigenstates the transverse relaxation rates are described by simple, single-exponential functions,7 and the line widths of the four single quantum coherences are given by
Figure 2. Energy level diagram for a carbon-hydrogen spin system: (a) for a finite magnetic field, but no spin coupling; (b) for a spin coupling
greater than zero; and (c) for a spin coupling less than zero. Note that thechangesin the energy levelsdue to the J-coupling aregreatlymagnified. is positive, thecorrect energy configurationis that given in part SinceJCH b.
where
ko = 7J5,
k, =
kc =
70
5 [1
+ oc27,2]
one might at first glance think that, in principle, it would be possible to obtain accurate values of the molecular parameters by measuring the widths of the four spectral lines and solving the four equations. In practice, this has not been a reliable method for obtaining accurate values for the molecular parameters. This is in large part due to the difficulty in obtaining accurate values for the line widths (the TZor the R,, values)” and because at least four additional random field terms are needed to describe the transverse relaxation of the coupled two spin system. We have found that much more accurate and precise values of the above molecular parameters can be obtained by measuring the longitudinal relaxation rates, the Riijp The longitudinal relaxation for each of the four lines is a triple exponential. In order to obtain the parameters via longitudinal relaxation time experiments, the experimental data are fit to solutions of the set of coupled differential equations described in eq 7. In the nonlinear least-squares fit programs, eight parameters are actually fit: the four molecular parameters, two random field parameters (the A and B terms), and two additional parameters which define the boundary conditions of the experiment. To obtain unique, meaningful fits of the parameters, the data from three complete sets of experiments with different boundary conditions are fit simultaneously. Details are given elsewhere.s.9 For some molecular or ionic systems, it has been found that the temperature dependence of the correlation time may be accurately described by an Arrhenius equation
70
5 [1
+ (OH f WC)’~:]
Note that in the case of Cj”symmetry or higher ull = 4 2 2 = uI and 433 = 411so that Aui = [all - alli, where i can be C o r H. The full line width a t half-height for the coherence between states i andj is denoted by Rijij/.rr= (Atqp)ij. Similar equations describe the line widths for the two proton resonance signals. The i and j indices in the Ri,i, terms refer to the eigenstates involved in the four single quantum coherences for this two-spin system. This is shown in Figure 2. Each of the four transverse relaxation rates, Riji,,is a function of the four molecular parameters: AUC, the carbon chemical shielding anisotropy; AUH, the proton chemical shielding anisotropy; p, the proton-carbon dipolar parameter; and rC,the molecular correlation time. Since one has four relatively simple equations in four unknowns (if intermolecular interactions and slow exchange processes are unimportant),
where Ea is the activation energy for isotropic reorientation, T is the absolute temperature, and TO is a pre-exponential factor which is often interpreted as an inverse collision frequency. For our work with phenylacetylene, and most systems, we find that much better fits are obtained by using the Vogel equation
where TOis a constant. In the present case, where twodifferent nuclei and twodifferent relaxation mechanisms are present several different spectral density functions contribute to the relaxation. As the correlation time becomes longer, each of these spectral densities passes through a maximum. Since thevarious spectral density functions pass through their maxima at different temperatures, a multiparameter fit of the parameters in eq 7 should, in principle, be
Farrar et al.
4784 The Journal of Physical Chemistry, Vol. 98, No. 18, 199'4
I/
> c v, Z
W
160
-
140
-
-I
z
so0
ma
100
0
-100
HI
Figure 3. Carbon NMR spectrum for the acetylene carbon in phenylacetylene rccorded at 7.05 T. The sample was a 0.3 M solution of phenylacetylene in a fully deuterated 50/50 toluene/methanol mixture at a temperature of 175 K. The value of JCHis 251 Hz. The frequency
increases from right to left.
l
l
l
l
l
.5
l
l
l
.
I
1 .o
I
,
,
,
I
,
1.5
,
,
,
I
2.0
TIME (seconds)
possible. A major advantage of measuring the relaxation of a fully coupled spin-1 /2 pair is that the dipolar, chemical shielding, and correlation time parameters as well as the intermolecular contributions to the relaxation can all be obtained at a single, fixed temperature and a single, fixed value of the magnetic field while observing a single nucleus. We can obtain information not only on the 13C nucleus but also on the 1H chemical shielding tensor and the 1H intermolecular interactions by observing its coupled I3C partner. This is particularly appealing since solidstate N M R determination of proton chemical shielding tensors is not trivial. In the solid, the proton spectrum is normally convoluted with line shapes of other chemically different protons, and theinterpretation of thespectrumisoftendifficult. Inaddition to this, multiple-pulse techniques are required to separate the homonuclear dipolar contribution to the line width from that of the CSA contribution to the line width. Since the coupled relaxation time measurements give information about the chemical shift anisotropy, A6 = 611 - 6*, and highresolution experiments give the isotropic chemical shift, 61, = ( 1 / 3 ) ( ~ 5 ~ ~622 15~3)= (1/3)(26* all), simple algebra then gives the components of the chemical shift tensor in terms of these two measured quantities:
+ +
+
6, = 6i,-
l
.o
(1/3)A6
6,,= (2/3)A6
+ 6i,
Both 6 k and 6k were determined at 177.7 K in a 0.3 M methanol/toluene solution and are referenced to tetramethylsilane (TMS); the values obtained are: 6 = 2.82 ppm and 6k = 78.64 ppm. We can also obtain the values of the chemical shielding tensor components from the equation 6 = u,f - u where u,,f is the chemical shielding of a reference compound relative to the bare nucleus; in this case, a,,f is that of TMS. 4. Results and Discussion
A typical proton-coupled carbon-13 N M R spectrum at 175 K for the acetylene carbon a t a magnetic field of 7.05 T is shown in Figure 3; the sample was a 0.3 M solution in a fully deuterated 50/50toluene/methanol mixture. Since it is known from solidstateNMR data of a sample of phenylacetylene that thechemical shielding anisotropy (Auc) for the protonated acetylene carbon is positive, the fact that the high-frequency carbon-1 3 resonance line (the coherence between states 3 and 4) is broad indicates that the absolute sign of the carbon hydrogen spin-coupling constant, JCH,is positive. This follows from eqs 8 and 9 for the line widths of the two carbon- 13 resonance signals given above.
Figure 4. Time evolution of the carbon magnetization following a 180°
broad band, nonselective, inversion pulse on the proton magnetizations. The squares are the experimental data for the low-frequency carbon coherence, and the triangles are for the high-frequency coherence. The solid lines are best-fit curves obtained from the fitting routines. Typical longitudinal relaxation recovery curves obtained at a temperature of 169.3 K and a magnetic field of 7.0 T are shown in Figure 4. For the data in Figure 4, both of the proton magnetizations were initially inverted and the time evolution of the carbon magnetizations was monitored as a function of the time interval following the proton inversion pulse. The solid lines are the least-squares best fits to the data, the squares are experimental data for the low-frequency carbon line, and the triangles are the data for the high-frequency carbon line. The molecular parameters used to generate these best-fit curves were rCH = 113.7 pm, AUC = +159.2 ppm, AUH = +13.6 ppm, 7c = 7.44 X 10-lo s, A = 0.207 s-l, and B = 0.151 s-l. As discussed elsewhere? in order to obtain unique, meaningful fits two or more sets of boundary conditions must be fit simultaneously. For the molecular parameters obtained here the three different boundary conditions described above were all fit simultaneously. Typical results for the coupled spin system of 0.3 M phenylacetylene dissolved in a 50/50toluene/methanol mixture are shown in Table 1. Experiments were run for solutions of phenylacetylene in pure toluene, in a 50/50 toluene/2-propanol solvent mixture, and in a 50/50 toluene/methanol solvent mixture. In addition, 0.15 and 0.30 M phenylacetylene in 50/50toluene/methanol solutions were studied. All samples were run over a wide range of temperatures (163-21 8 K) and a t four different magnetic fields, 4.7,7.0,8.5, and 11.7 T. At 4.7 and 7.OT, theinterference terms between the dipolar and the CSA interactions are small and the correlation coefficients in the fit routine between the different parameters are all close to unity. For this reason, we used data a t 8.5 and 11.7 T to carry out fits in which no parameters were fixed. These fits were unique and gave a bond distance value of 1 13.7 pm from the dipolar parameterp. This value o f p was then used as a fixed parameter in the fit routines for data obtained a t 4.7 and 7.0 T. At 7.0 T, if the bond distance was changed by more than f 2.0 pm from the 113.7 average value, the residuals in the fits increased significantly. Typical values for the other parameters obtained from fits with a fixed bond distance of 1 13.7 pm are shown in Table 1. In most of the fits there was considerable scatter in the values of the random field terms. In order to obtain bettter values for these A and B terms, ACTH,AUC, and p were fixed to the average values shown in Table 1, the values for the correlation time were taken from the best fit plot of ln(r,) versus
The Journal of Physical Chemistry, Vol. 98, No. 18, 1994 4785
Solution-State N M R Measurement
TABLE 1: Fit Parameters in 50/50 CD~OD/d-8-Toluene,0.30 M, 7.0 T’ temp (K) IC (s x 1010) Awl (PPm) Am(PP~) 163.29 167.09 169.32 169.43 173.26 177.03 179.05 181.55 182.17 182.28 182.28 184.50 188.14
14.67 8.680 7.442 7.158 5.204 3.039 3.607 3.367 3.553 3.227 3.382 2.651 2.126
13.41 13.23 13.62 13.76 13.35 13.55 13.86 13.57 13.49 13.74 13.69 14.37 13.99 13.66 0.30
avg a
A (s-I)
175.25 156.64 159.18 161.83 170.38 154.07 161.43 153.51 149.84 156.08 152.43 159.48 164.67 159.60 7.25
0.584 0.134 0.207 0.232 0.265 0.058 0.136 0.049 0.036 0.081 0.067 0.129 0.103
B
B (SI) 0.130 0.134 0.151 0.161 0.120 0.137 0.145 0.125 0.106 0.140 0.1 17 0.168 0.199
0.728 0.921 0.885 0.877 0.827 0.871 0.770 0.731 0.698 0.729 0.709 0.732 0.703
For all of the fits in the above table, the bond distance was fixed to a value of 113.7 pm.
TABLE 2 Fit Parameters in 50/50 CD~OD/&8-Toluene, 0.30 M, 7.0 T’ temp (K) sC(s x lolo) A (s-l) B (s-I) B 167.09 169.32 169.43 173.26 179.05 181.55 182.17 182.28 182.28 184.50 188.14
8.954 7.553 7.491 5.652 3.778 3.200 3.073 3.051 3.051 2.646 2.110
0.268 0.247 0.264 0.151 0.110 0.080 0.128 0.122 0.136 0.158 0.094
0.115 0.134 0.116 0.003 0.130 0.169 0.165 0.153 0.156 0.154 0.127
0.879 0.872 0.852 0.828 0.750 0.741 0.748 0.751 0.745 0.730 0.710
The correlation time was fixed to the value determined from a bestfit line of h ( s c ) vs 1/T,the bond distance was fixed to 113.7 pm, and the boundary conditions were fixed to average values. Only the random field terms and the 0 term (Cole-Davidson distribution) were allowed to float.
1/ T, and then the data were refit to obtain to the optimum values for A, B, and /3 (a parameter in the Cole-Davidson distribution). The results are shown in Table 2. At a field strength of 11.7 T, the interference effects of the two relaxation processes are much greater and the correlation between parameters is greatly reduced; in this case all parameters can be fit simultaneously. The results obtained for the parameters at 1 1.7 T are the same as the results at 7.0 T. The residuals are, of course, greater at the lower field strength. Within the limits of experimental error, the carbon-hydrogen bond distance and the two chemical shielding anisotropies were independent of temperature, solvent, and magnetic field strength. The average values obtained over all experiments using the toluene/methanol or toluene solvents are rCH = 113.7 f 1.0 pm, AUC = +159.6 f 7.2ppm,andAa~=+13.7*0.3ppm. Intermsofthecomponents of the proton and carbon chemical shift anisotropies and chemical shift tensors (relative to TMS), we obtain the following: A6c = -1 59.6 ppm, A ~ = H-1 3.7 ppm, 6f = -6.3 1 ppm, 6 y = 7.39 ppm, 6; = -27.76 ppm, and :6 = 131.84 ppm. This value reported above for the C-H bond distance is the thermal average value in the liquid sample. This value is longer than the values usually reported in the chemical literature, which have been “corrected” for thermal (vibrational) averaging. That is, the revalue reported in the literature is one which does not take into account the lengthening of the bond due to molecular vibrations. This is convenient for comparison with ab initio calculations, which also do not take molecular vibrations into account. In an N M R experiment, however, the molecule is vibrating, and this does result in an average bond distance which is systematically longer than those obtained in ab initio calculations. In this case that value is 113.7 f 1.O pm. If we “correct” this value for a molecule which is not vibrating, we obtain (see ref 38 for details) a value of 109.1 f 1.O pm. This is longer than
the value of 106.3 pm for acetylene obtained from gas-phase microwave experiments. Given the ease with which one can exchange the acetylenic proton with a deuteron, one might, perhaps, anticipate that there would be an observable solventsolute interaction which would lead to a small increase in the C-H bond distance. The temperature dependence of the random field terms is very interesting andindicates that theremay besomesubstantial solvent interactions present. In other systems which we have studied (e.g., the PH032- and PF032-anions), the random field terms, which are relaxation rates arising from fluctuating magnetic fields generated by the deuterium solvent nuclei, both go through a maximum at about the point where W T ~cy 1. The “A” and “B” random field terms represent the acetylene carbon-solvent and the acetylene proton-solvent interactions, respectively. As can be seen in Table 2, theB term (for the proton-solvent interaction) is small and shows very little temperature dependence. The A term is significantly larger than the B term a t lower temperatures and goes through a minimum rather than a maximum. This is surprising since the proton-solvent dipolar interaction is usually larger than the carbon-solvent interaction. The present results are consistent with an interaction of the phenylacetylene with the solvent in which the proton on the phenylacetylene is hydrogen bonded with the oxygen on an 0-D group of either the d-8-2propanol or the d-Cmethanol; this puts the solvent deuterons closer to the carbon than to the proton. The strength of the interaction increases with decreasing temperature. For experiments carried out above the dispersion region (Le., usC
7,
(13)
The spectral density function, given by the Fourier transform of this distribution, is given by
The decrease in J(w.6) with decreasing j3 value is quite apparent.
4786 The Journal of Physical Chemistry, Vol. 98, No. 18, 1994
As 6 becomes less than one, the center of the spectral density shifts toward, and becomes weighted more for, lower frequencies. As can be seen from Table 2, the j3 parameter is significantly less than unity, indicating a substantial deviation from a Lorentzian spectral distribution function (when 8 = 1, the Cole-Davidson distribution function becomes equivalent to the Lorentzian distribution function). This is to be expected from a glassy sample. The large temperature dependence of the isotropic carbon chemical shift (see Figure 1) is a clear indication that there are appreciable solvent-solute interactions present in solution. This temperature dependence is consistent with the observation above that the random field term for the carbon-solvent interaction (the ‘A” term) is larger than the proton-solvent interaction and increases with decreasing temperature. Of course, such behavior has been noted before.39 It is now generally agreed that the temperatureeffects are primarily related to changes in thedensity of the fluid system. As the temperature increases, the volume expands and the solvent-solute interaction decreases. In the solutions used here there is a liquid volume increase of about 25% in going from 196 to 300 K (room temperature). In summary, we have shown that for a coupled carbon-hydrogen spin pair, even when the CSA contributes only 5-1076 of the total relaxation (as it does for sp-hybridized carbons a t 7.OT), accurate values for the bond distance, the CSA values, the molecular correlation time, and the random field parameters can be obtained. In general, the higher the field and the greater the CSA, the more accurate are the values obtained for the parameters. The great advantage of the coupled relaxation time experiments is that at a fixed magnetic field strength and a fixed temperature values for all of the parameters may be obtained simultaneously. For decoupled experiments, measurements must be done at several field strengths and as a function of temperature and the extent of deuteration of the solvent in order to obtain the same information. The value of Aac is in good agreement with ab initiocalculations and is significantly smaller than other reported values for substituted acetylenes. (Values of 133.2 and 143.8 ppm were obtained using the IGLOand LORG ab initiomethods, respectively. In both cases the calculations were done at the 6-31G* coupled Hartree-Fock level with 132 basis functions.) Given the fact that for the experiment there are substantial solvent-solute interactions present and the calculations are done for an isolated molecule in the gas phase, the agreement is surprisingly good. We know of no other values for the tensor components of UH in acetylenes. It is interesting to note that our value for u? is almost the same as that for other acetylenes. The major change in uf is due to the fact that the molecule is no longer symmetric or linear.
Acknowledgment. We thank Dr. John Decatur and Dr. Jon Trudeau for the number of helpful discussions and for correcting a number of errors in a draft of this manuscript. We thank Dr. Ilene Carpenter of Cray Research Co. for calculating the components of the carbon chemical shift tensors in phenylacety-
Farrar et al. lene, and we thank a reviewer for a number of very helpful comments and suggestions. We gratefully acknowledge the support of the National Science Foundation for the support of this research (NSF Grant Number CHE-9102674).
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