J. Phys. Chem. 1995,99, 12008-12015
12008
Solid-state 2Hand 13C NMR Studies of Hydrogen-Bond Dynamics in Ferrocene-1,l’-diylbis(diphenylmethanol) Abil E. Aliev, Kenneth D. M. Harris,* and Ian J. Shannon Department of Chemistry, University College London, 20 Gordon Street, London WClH OAJ, U.K.
Christopher Glidewell, Choudhury M. Zakaria, and Patricia A. Schofield School of Chemistry, University of St. Andrews, St. Andrews, Fife KY16 9ST, U.K. Received: February 16, 1995; In Final Form: April 28, 1995@
Dynamic properties of the hydroxyl groups in a selectively deuterated crystalline sample of ferrocene-1,l’-
diylbis(diphenylmethano1) (FBDPM) have been studied via variable-temperature wide-line *H NMR spectroscopy and high-resolution I3CNMR spectroscopy. In crystalline FBDPM, the molecules form hydrogenbonded dimers, with the 0 atoms of the four hydroxyl groups involved in this hydrogen bonding defining a folded trapezium. Each hydroxyl H atom is disordered between two equally populated positions, from which it is inferred that there are two plausible arrangements (clockwise and anticlockwise) of the eight-membered ring hydrogen bonded unit. The temperature dependences of the quadrupole echo 2H NMR line shape in the temperature range 293-370 K, the 2H NMR spin-lattice relaxation time in the temperature range 313-428 K, and the I3C C P M A S NMR spectrum in the temperature range 205-253 K demonstrate that the hydrogenbonding arrangement is dynamic; this dynamic process is interpreted as interconversion between the clockwise and anticlockwise hydrogen-bonding arrangements. The observed temperature dependence of the NMR spectra is consistent with the following dynamic models: (i) transfer of each hydroxyl H atom between adjacent hydroxyl 0 atoms; (ii) a two-site n jump motion of each hydroxyl group about its C - 0 bond. In either case, it is inferred that the motions of the four hydroxyl groups in the hydrogen-bonded dimer are highly correlated. In general, these dynamic models could be distinguished on the basis of *H NMR spectroscopy, but for the specific geometry of the intermolecular hydrogen-bonding arrangement in FBDPM, both of these models fit the *H NMR data. On the assumption of Arrhenius behavior for the temperature dependence of the jump frequency, the activation energy for the dynamic process is estimated (from 2H NMR spin-lattice relaxation time measurements and 2H NMR line-shape analysis) to be in the range 53-65 kJ mol-’.
Introduction The dynamic properties of hydrogen bonded solids have been the subject of detailed experimental and theoretical studies. Carboxylic acid dimers have received particular attention in this regard, with considerable debate surrounding the question of whether the dynamics take the form of proton transfer between oxygen atoms of different molecules or n flips of the complete hydrogen-bonded In this paper, we investigate the application of solid-state 2H NMR spectroscopy to probe the dynamic properties of a hydrogen-bonded arrangement of hydroxyl groups in a solid. A major advantage of applying solid-state *HNMR techniques in this area is that they provide the possibility to compare and distinguish different dynamic models which are considered plausible given the structure and symmetry of the system under investigation. As the subject of this study we consider ferrocene-1,1’-diylbis(diphenylmethanol) (FBDPM). The crystal structure of FBDPM has been determined recently by X-ray diffractiom6 Specifically (Figure l), the FBDPM molecules form a hydrogen bonded dimer with the Fe atoms lying on a crystallographic 2-fold rotation axis and the four 0 atoms defining a folded trapezium with two 0 0 distances equal to 2.762 8, and the other 0 Q distances equal to 2.714 and 2.865 8, (Figure 1). The positions of the hydroxyl H atoms are disordered, and X-ray diffraction suggests that, for each hydroxyl group, there are two equally populated H atom positions (each directed toward a neighboring
-
* Author to whom all correspondence should be addressed. @
Abstract published in Advance ACS Absrracrs, July 1, 1995.
0022-365419512099-12OO8$09.00/0
Fe
hydroxyl 0 atom) such that there are two half-occupancy H atom sites between each pair of 0 atoms. [As discussed below, it is important to emphasize that these H atom positions are not accurately determined from X-ray diffraction data, and therefore accurate geometric parameters defining the hydrogen bonding arrangement are not available.] Since it is implausible for both H atom positions along a given 0 0 edge to be occupied simultaneously, there are only two ways in which the set of H atom sites can be occupied. These two arrangements of the eight-membered hydrogen bonded ring are shown schematically below, and are subsequently denoted arrangement C (clockwise) and arrangement A (anticlockwise). Apart from the hydroxyl H atoms, there is no evidence from the X-diffraction results for disorder in the positions of any of the other atoms in the structure. In the work described in this paper, different aspects of 2H NMR spectroscopy, including 2H NMR line-shape analysis and 2H NMR spin-lattice relaxation time measurements, have been applied to investigate dynamic properties of the hydroxyl deuterons in the selectively deuterated material FBDPM-d2. We 0 1995 American Chemical Society
Hydrogen Bond Dynamics in FBDPM
J. Phys. Chem., Vol. 99, No. 31, 1995 12009
C
A
Figure 1. Dimer in the crystal structure6of FBDPM with clockwise (C, left side) and anticlockwise (A, right side) arrangements of the hydroxyl groups. The quoted 0* 0 distances are in A.
'
0-H
..... 0/
I
n
H
/
.....H-
' 0
0
I
n
H
I
I C
A
also exploit the selectivity of high-resolution solid-state I3C NMR spectroscopy for distinguishing crystallographically inequivalent carbon sites, in order to study the dynamics of the hydrogen bonding arrangement in solid FBDPM-d2. It is relevant to note that FBDPM is a versatile host for the formation of hydrogen-bonded host-guest complexes exhibiting a wide range of structural types and hydrogen-bonding motifs?.s The present study may serve to lay the groundwork for a comprehensive investigation of the hydrogen-bonding dynamics in these systems. The crystallographic properties of several derivatives and structural analogues of ferrocene- 1,l'-diylbis(dipheny1)methanol have also been studied by X-ray diffract i ~ n , ~I -revealing ' a variety of different intermolecular hydrogen bonding arrangements. For example, crystalline triphenylmethanol contains tetrameric aggregates of triphenylmethanol molecules, in an approximately tetrahedral arrangement, with the four hydroxyl H atoms disordered (probably over the six 0m . 0 edges of the tetrahedron).I0
Experimental Section A sample of FBDPM-h2 (Le., with natural isotopic abundances) was prepared by reaction of phenyl lithium with 1,l'dibenzoylferrocene, followed by acidification. The melting point was 186 "C.' The selectively deuterated sample of FBDPM-d2 used in our NMR experiments was prepared from FBDPM-h;! by repeated exchange with aliquots of D20. The ' W H exchange was monitored using IR spectroscopy. The powder X-ray diffractograms of FBDPM-h2 and FBDPM-d2 were identical at room temperature. Differential scanning calorigrams of both FBDPM-h2 and FBDPM-d2 showed an irreversible endotherm at ca. 185 "C, corresponding to the onset of decomposition. 2H NMR spectra of FBDPM-d2 were recorded at 76.8 MHz on a Bruker MSL5OO spectrometer and at 46.1 MHz on a Bruker MSL300 spectrometer, using standard Bruker 5 mm high-power probes. The stability and accuracy of the temperature controller (Bruker B-VT1000) were ca. &1 K. Temperature calibration
of the probe was established via *H NMR studies of the melting transitions in CD30D (175 K) and D20 (277 K). The conventional quadrupole echo [(W"),,+-z- (9Oo),,+~~-z-acquire recycle] pulse sequenceI2 was used, with 90" pulse duration 1.5 ps (on MSL300) and 2.6 ps (on MSLSOO) and with echo delays z in the range 13- 150 ps. Phase cycling was employed to eliminate quadrature phase errors. Due to the low concentration of deuterons a large number of acquisitions (up to 5 x lo4) was required. The recycle delay was taken as ca. 1OTl and ranged from 0.5 s at 370 K to 420 s at 153 K. As a consequence of the very long recycle delay at low temperature and the low concentration of deuterons, the application of 2H NMR technique^^^,'^ for studying slow motions (time scales ca. 102-10-3 s) is not experimentally feasible for this material. 2H NMR spin-lattice relaxation times (TI) were measured at 46.1 MHz (on MSL300) using an inversion recovery pulse sequence modified for 2H nuclei: [(180"),-t-(90"),-z(9O0),-z-acquire-recycle]. The 180" pulse duration was 3.0 ps. The delay z was 13 ps and usually between 6 and 10 different values of t were used. Experimental T I values were derived from a three-parameter fit of peak intensity versus t. The quoted errors in activation parameters reflect only the errors in the least-squares fitting procedures. Simulations of quadrupole echo 2H NMR spectra were obtained using the program MXQET.I5 The spectral simulations were obtained by Fourier transformation of calculated echo decays, with both Gaussian and Lorentzian apodization applied before Fourier transformation. Calculations using the MXQET program include effects arising from the virtual free induction decay and from the echo, and corrections for imperfect spectral coverage (due to finite pulse powerI6) are also considered. The latter usually causes a reduction in the intensity of the shoulders of the experimental 2H NMR spectrum. Each 2H site involved in the dynamic process is specified via the Euler angles a,/3, and y (defined using the convention of Rose]') which define the orientation (relative to a space-fixed reference frame) of the site [strictly speaking the orientation of the principal axis system of the electric field gradient tensor VAS at the 2H nucleus (note: we use vas to denote the electric field gradient tensor, in its principal axis system, at the nucleus)]. In general, it is convenient to take the z-axis of the space-fixed reference frame parallel to the jump axis. Simulations of inversion recovery 2H NMR experiments were carried out using the program TURBOPOWDER.Is I3C NMR spectra of FBDPM-d2 were recorded at 75.5 MHz on a Bruker MSL300 spectrometer using a standard Bruker
Aliev et al.
12010 J. Phys. Chem., Vol. 99, No. 31, 1995
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I53
Figure 2. Experimental (left side, 76.8 MHz) and simulated (right side) 2H NMR spectra for FBDPM-Q. The simulated spectra were calculated assuming model (i) and model (ii) discussed in the text (these dynamic models each result in the same lineshape at each value of K ) . Static quadrupole coupling constant x = 215 kHz and static asymmetry parameter 17 = 0.09 in the temperature range 293-358 K; y, = 210 kHz and 7 = 0.09 at 370 K.
magic-angle sample spinning (MAS) probe with double-bearing rotation mechanism. The standard IH-l3C cross-polarization (CP) technique was employed (I3C 90" pulse duration = 3.5 ps; 'H 90' pulse duration = 4 ps; CP contact time = 5 ms; MAS frequency 4-5 kHz), with high-power IH decoupling applied during acquisition. The difference in the duration of the 'H and 13C 90" pulses arises from a difference in the rise times for the two pulses. The pulse sequence for total suppression of spinning sidebands (TOSS)'9,20and its combination with dipolar dephasing2I were also used. The accuracy of the temperature measurements was c a f 3 K. 13C chemical shifts are given relative to tetramethylsilane. Powder X-ray diffraction patterns of FBDPMd2 were recorded in transmission mode on a Stoe Stadi-P powder X-ray diffractometer with the sample loaded in a capillary. Temperatures below room temperature were obtained using a cryostream cooler (Oxford Cryosystems Ltd), with liquid nitrogen as coolant.
Results and Discussion Definition of Dynamic Models. We consider three dynamic models for interconverting arrangements C and A of the eightmembered hydrogen bonded ring in solid FBDPM-d2. Model (i): transfer of each hydroxyl H atom between adjacent hydroxyl groups. Model (ii): x jumps of each hydroxyl group via rotation about its C - 0 bond. Model (iii): x flips of the FBDPM dimer about the crystallographic 2-fold rotation axis passing through the two Fe atoms in this dimer. 2HNMR Line-Shape Analysis. 2H NMR spectra of FBDPM-dz, recorded in the temperature range 153-370 K, are shown in Figure 2. The spectrum recorded at 153 K is characteristic of a "static" 2H NMR powder pattem, and the best-fit simulation of this spectrum (Figure 2) is obtained assuming no motion of the deuterons and with static quadrupole coupling constant 01 = e2qQh) equal to 227 kHz and static asymmetry parameter (7) equal to 0.13 (assuming the same values of x and 7 for all 'H environments in the sample). [Note:
I
I
I
200
0
-200
kH2
Figure 3. Simulated "static" 2H NMR spectra using (a) x = 227 kHz, 17 = 0.13; (b) x = 215 kHz, 17 = 0.09; (c) 10 different values of x in the range 215-233 kHz, 7 = 0.09; (d) = 227 kHz, 10 different values of 7 in the range 0.03-0.17. (c) and (d) illustrate the effect of a distribution of x and 7 values, respectively, on the 'H NMR line shape.
x
(a) the components of VAS are taken such that lVzzl1 IV,l 2 lVyyl; (b) 7 is defined as 7 = (IV,l - lVyyl)/lVzzl and is in the range 0 5 7 5 1; (c) the z axis of VAS is assumed to lie along the direction of the 0-D bond]. At 153 K, the 2H NMR spinlattice relaxation time (TI) for FBDPM-d2 is long, and it was necessary to use a recycle delay of 420 s to obtain 2H NMR spectra with acceptable signallnoise ratios. The high value of TI is consistent with the conclusion that there are no motions of the deuterons on the 2H NMR time scale at 153 K. The values of x and 7 [x = (227 f 5 ) kHz; 7 = 0.13 f0.031 should be compared with those of water-& [x = 213-236 kHz; 7 = 0.1-0.2],22 methanol-d [x = 202.7 kHz; 7 = 0.1741, and tribenzylmethanol-d [x = (241 f 2) kHz; 7 = 0.04 f 0.01 (determined at 128 K)].23 In contrast to FBDPM-Q, the hydroxyl groups of tribenzylmethanol-d are not involved in hydrogen b ~ n d i n g ,resulting ~ in a larger value of x for tribenzylmethanol-d. In crystalline FBDPM-d2, there are four crystallographically inequivalent 2H environments6 which could, in principle, have different values of x. A distribution of values of x (resulting from a distribution of 0-D bond lengths and/or D 0hydrogen bond distances) should give rise to loss of definition of the outer edges and shoulders in the 2H NMR line shape.24 The observed 2H NMR lineshape at 153 K for FBDPMd2 suggests that there is indeed a distribution of x values (Figure 3). An accurate determination of x for each environment requires single-crystal 2H NMR measurements (for example, it has been shown25for the hydroxyl deuterons in Dianin's compound (4-p-hydroxyphenyl-2,2,4-trimethylcroman) that the difference in x values for inequivalent 2H environments does not exceed 2.4 kHz). We assume here that the static quadrupole interaction parameters for the crystallographically inequivalent deuteron environments do not differ significantly in the temperature range 293-370 K. Thus, for spectral simulations, it was assumed that all *H sites have the same values of the static quadrupole interaction parameters. 2H NMR spectra for FBDPM-d2 recorded in the temperature range 293-370 K (Figure 2) show features characteristic of a dynamic process on the timescale of the 2H NMR technique (ca. 10-3-10-7 s). In particular, the relative intensity of the maxima at ca. f-31 kHz increases gradually from 293 to 370 K. It is important to note that the evolution of the *H NMR line shape with temperature shown in Figure 2 is usually interpreted in terms of a x jump model with the z axis of VAS forming an angle of ca. 60" with the jump axis. However, as
Hydrogen Bond Dynamics in FBDPM
J. Phys. Chem., Vol. 99, No. 31, 1995 12011 and static asymmetry parameter (7) than those determined from the "static" spectrum recorded at 153 K. The values of and q giving rise to the best fit between the simulated and experimental spectra were = 215 kHz and q = 0.09 in the temperature range 293-358 K, and = 210 kHz and q = 0.09 at 370 K. We propose that this arises from an increase in the amplitudes of rapid small-angle motions of the 0-D bonds about their equilibrium orientations. It is also possible that the exact nature of the hydrogen bonding and the temperature dependence of the 0-D bond polarization in these systems may have a critical influence on the temperature dependences of and q, particularly as the motion involves breakage and formation of hydrogen bonds. We now consider model (ii), shown in Figure 4b. For this model, the simulated 2H NMR line shape is very sensitive to the angle (8) between the jump axis and the z axis of VAS, and the best-fit simulations are obtained with 8 = 65". This value of 8 implies that the C-0-D bond angle is 115", which is in agreement with the approximate values determined by X-ray diffraction for the four hydroxyl groups: 117", 118", 118", 126". Thus, the geometry of this dynamic process is consistent with the average geometry of the dimeric aggregate. We also note that the jump angle inferred from the positions of the hydroxyl H atoms determined from X-ray diffraction are 172" and 178" rather than the 180" assumed in the n-jump model. However, the overall 2H NMR line shape is not significantly different using jump angles of 172", 178", and 180" in spectral simulations for model (ii), with the variation of the jump angle affecting only the relative intensity of the inner peaks in the spectrum at ca. f 3 1 kHz. This observation, together with the fact that the positions of the hydroxyl H atoms are not determined accurately from X-ray diffraction data, justifies our use of 180" as the jump angle for model (ii). Clearly both model (i) (with 4 = 130") and model (ii) (with 8 = 65") can fit the experimental 2H NMR line shape equally well, with geometric parameters that are consistent with the known crystallographic information. It is important to emphasize that this coincidence arises as a consequence of the special geometry of the intermolecular hydrogen bonding arrangement in FBDPM (compounded, to some extent, by the fact that the positions of the hydroxyl H atoms have not been located accurately by X-ray diffraction). For other similar hydrogenbonding arrangements, differing only in the exact values of the geometric parameters that define the hydrogen bonding arrangement, it would be possible to distinguish model (i) and model (ii) on the basis of 2H NMR spectroscopy. The reason that the same *H NMR line shapes are obtained for model (i) with 4 = 130" and model (ii) with 8 = 65" arises from the fact that, for jump models, the 2H NMR line shape is determined by the orientation of VAS at each site populated during the dynamic process, and therefore, in certain cases, different dynamic processes can give the same line shape if there is a special relationship between the geometric parameters defining these different dynamic processes. For example, rotation of n about an axis forming an angle 8 with the z axis of VAS (with y = 0') gives rise to the same *H NMR line shape as rotation of 4 = 28 about an axis perpendicular to the plane containing the z axes of VAS (with y = 90') for the two sites involved in the motion. Model (iii) may be consistent with the observed line-shape changes if the angles between the 0 - D bonds (or, strictly, the z axis of VAS for the 2H nucleus) and the jump axis (Le., the crystallographic 2-fold rotation axis passing through the two Fe atoms of the dimeric aggregate6) are all ca. 65". The corresponding angles obtained by X-ray diffraction for the four
x
x
x
x
Figure 4. Dynamic models for the hydroxyl H atoms in FBDPM-d2. The orientations of the principal-axis systems ({XI,y ~ Z,I } and ( ~ 2 y2. , z2}) for deuteron sites 1 and 2 and the orientation of the space fixed reference frame {X, Y, z> are specified in each case. (a) Model (i): the jump axis is perpendicular to the plane containing 01-Hl and 0 2 . Euler angles {a,p, y > are {0", 90°, 90") for site 1 and {@,go", 90a} for site 2 . As discussed in the text, the optimum value of @ has been found to be 130". (b) Model (ii): a two-site n jump model for reorientation of each hydroxyl group about its C-0 bond axis. Euler angles {a,p, y } are {O", 8,O") for site 1 and {180", 8, O"} for site 2 ; the yl axis and Y axis are perpendicular to the page and directed out from the page; the y2 axis is perpendicular to the page and directed into the page. As discussed in the text, the optimum value of 8 has been found to be 65".
discussed below, other dynamic models can also be consistent with this evolution of the *H NMR line shape. For model (i) (see Figure 4a), the simulated 2H NMR spectra are shown in Figure 2. The frequency separation between the "inner" intensity maxima in the simulated 2H NMR spectrum depends critically upon the jump angle for the 0 - D deuterons, and the best agreement between simulated and experimental spectra recorded in the temperature range 293-370 K is obtained with the jump angle (4) within the limits 4 = 130" & 1". Since the asymmetry parameter is nonzero, different results could be obtained for different values of y , and the bestfit simulations are obtained with y = 90" for both 2H sites. It is important to emphasize that, for jump models, the duration of the jump itself is assumed to be negligible on the time scale of the 2H NMR technique; hence, at any instant in time, the system is described by the Hamiltonian of one of the welldefined 2H sites. Under this assumption, the 2H NMR line shape is determined by the orientation of VAS at each site populated during the dynamic process, rather than the trajectory by which the *H nucleus moves between these sites. It is therefore impossible to establish the trajectory of motion of the deuteron in model (i) on the basis of 2H NMR line-shape analysis. The best-fit spectral simulation at each temperature in the range 293-370 K is shown in Figure 2 (right side). On the basis of previous X-ray diffraction studies and I3CNMR results (see below), we assume that the populations of the 2H sites in arrangements C and A are equal and independent of temperature. To achieve good agreement between these simulated spectra and the experimental spectra, it was necessary to use slightly smaller values of the static quadrupole coupling constant 01)
Aliev et al.
12012 J. Phys. Chem., Vol. 99, No. 31, I995
1
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'
100000
"
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I
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'
E HERTZ
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-100000
Figure 5. Experimental (left side, recorded at 343 K, 46.1 MHz) and simulated (right side, calculated using K = 2 x lo6 s-I) 2H NMR spectra for FBDPM-dl at different echo delays t.The expeniental spectrum for t = 50ps and the corresponding simulated spectrum are normalized such that they have the same maximum intensity. The spectra for t = 100 ps and t = 150 p s are normalized by factors given by their total integrated intensities divided by those for the experimental or simulated spectrum for t = 50 ,us.
inequivalent hydroxyl H atoms are 20", 7 5 O , 74O, 23". Notwithstanding the low accuracy in the determination of the positions of the hydroxyl H atoms from X-ray diffraction data, there are clearly two inequivalent orientations of 0-D bonds with respect to the crystallographic 2-fold axis, forming angles of ca. 20" and 75" with respect to this axis. Due to the critical dependence of the observed line shape on the angles between the 0 - D bond and the jump axis, a substantially different 2H Nh4R line shape (with at least two pairs of "inner" peaks at ca. f 4 8 and 439 kHz (values determined from spectral simulations)) should be observed for model (iii). Furthermore, for model (iii), it is probable that the complete rotation of the dimeric aggregate in the crystal represents a process that is too high in energy to be observed at room temperature. From our discussion above it is clear that model (i) with 4 = 130" and model (ii) with 8 = 65" give rise to the same simulated 2H NMR line shapes (for a given value of jump frequency K ) , and these models therefore cannot be distinguished on the basis of 2H NMR line-shape analysis. Figure 5 shows the experimental (recorded at 343 K) and simulated (using K = 2 x lo6 s-I) 2H NMR line shapes as a function of pulse spacing t (for 5 = 50, 100, and 150 ,us). The use of model (i) (with 4 = 130") and model (ii) (with 8 = 65") at each value of t in spectral simulations results in the same line shape, and the z dependences of the line shape and the echo intensity therefore do not allow these dynamic models to be distinguished. O n the assumption of Arrhenius behavior (Le., K = A exp(-E,/RT)) for the temperature dependence of K , the activation parameters [determined from a graph of ln(K/s-') versus T-'/K-I] are estimated t o be Ea = (65 f 3) kJ mol-', A = (1.1 0.3) x 10l6 s-l. zHNMR Spin-Lattice Relaxation Time Measurements. Detailed dynamic information can also be obtained from measurement and analysis of the 2H NMR spin-lattice relaxation time ( T I ) which , permits dynamic processes with motional frequencies K between Y x and Y x IO3 to be studied26(Y denotes the Larmor frequency of the 2H nucleus). Theoretical expressions for 2H NMR spin-lattice relaxation times can be derived for specific dynamic processes, allowing the correct dynamic model to be established by comparison of theoretical
*
tlms 320 I60 80 40 20 10 5
25
-
.
i m ~ m
8 HERli
-1BBWB
188888
8
I80808
HERTL
Figure 6. Experimental (left side, recorded at 363 K, 46.1 MHz) and simulated (right side) partially relaxed inversion recovery lH NMR spectra for FBDPM-d2 with echo delay t = 13 ps. The simulated spectra were calculated assuming the two-site n jump model (model (ii)) for reorientation of each hydroxyl group about the relevant C-0 bond with jump frequency K = 7.0 x lo6 s-I.
and experimental r e s ~ l t s . ~The ~ . ~calculated ~ inversionrecovery line shapes are only slightly anisotropic (Figure 6) and spin-lattice relaxation data were analyzed using the expression for the powder average (denoted (UT,)) of the 1/Tl values. As discussed in ref 29, the expression for (UTI) for a two-site n-jump model with equal equilibrium populations of the sites is:
(UT,)=
where w is the Larmor frequency of the 2H nucleus in rad s-I, and pes(1) and peq(2)are the equilibrium populations of the two
J. Phys. Chem., Vol. 99, No. 31, 1995 12013
Hydrogen Bond Dynamics in FBDPM
/I
120 K
I
295 K
00024
00026
00028
0003
0 0032
K/T
Figure 7. Plot of ln((l/T$l/s) versus T-I/K-'. The open circles represent experimental values (measured at 46.1 MHz), whereas the solid line represents the best fit determined using eq 1.
and sites. 8 represents the angle between the z axis of VAS the jump axis. For a two-site jump motion, the jump frequency K and correlation time r, are related by r, = ( ~ K ) - I ,In our analysis of the spin-lattice relaxation data, we have assumed that the amplitudes of any librational motions occurring around the potential minima are too small to affect the spin-lattice relaxation (the fact that two discrete positions of each hydroxyl hydrogen atom were located (albeit inaccurately) from X-ray diffraction data6 supports the assumption that the librational amplitudes of these atoms are small). The powder average (UTI) of the reciprocal of the 2H NMR spin-lattice relaxation time was measured for FBDPM-d2 using inversion-recovery experiments at 12 different temperatures between 313 and 428 K. As an illustration, the results from the inversion recovery experiment carried out at 363 K are shown in Figure 6 together with the corresponding set of bestfit simulated spectra for model (ii) with K = 7.0 x IO6 s-'. As in the case of the 2H NMR line-shape analysis (see above), the results of spectral simulations for model (i) with 4 = 130' and model (ii) with 8 = 65" are indistinguishable. A graph (Figure 7) of ln((l/TJ-'/s) versus T-'/K-' was used to determine activation parameters (see below). On the assumption of Arrhenius behavior (r, = ro exp(E,/RT)) for the temperature dependence of tc(assuming that the equilibrium populations of the two sites occupied by each deuteron are equal), the activation parameters and the value of the (determined from the graph of ln((l/Tl)-l/s) versus T'/K-'and eq 1 using the method of nonlinear least squares) are E, = (53 & 1) kJ mol-'; ro = (1.2 f 0.6) x s (corresponding to A = (4.3 k 2.2) x 10l6 s-'); = 191 f 10 kHz. The two-parameter fit with fixed at the value (215 kHz) determined from line-shape analysis for the temperature range 293-363 K results in the following activation parameters: Ea = (52 f 1) kJ mol-'; t o = (2.3 f.
x
x
x
0.7) x 10-15 s.
Powder X-ray Diffraction. To investigate the possibility of a solid-solid phase transition in FBDPM-d2, variabletemperature powder X-ray diffraction experiments were carried out in the temperature range 120-295 K (Figure 8). The only observable difference between the diffractograms recorded at 120 and 295 K is a shift of the peaks to higher 28 due to contraction of the crystal on decreasing the temperature. There was no evidence for any structural phase transition, and
201
Figure 8. Powder X-ray diffractograms of FBDPM-& recorded (Cu K a l radiation) at (a) 120 K and (b) 295 K.
consequently the observed changes in the I3C NMR spectrum with temperature (see below) are interpreted in terms of a dynamic interconversion between the two equally populated hydrogen-bonding arrangements C and A. High-Resolution 13C N M R Spectroscopy. Since the observed dynamic process is rather slow on the time scale of the 2H NMR technique, it may be expected that, at low temperature, the frequency of the motion will approach the time scale of high-resolution I3C NMR spectroscopy. Conventional highresolution I3C NMR line-shape analysis is based on studying, as a function of temperature, changes in the positions and line widths of peaks in the I3C NMR spectrum, with particular interest in the study of coalescence phenomena. Figure 9 shows high-resolution solid-state I3C NMR spectra of FBDPM-d2, recorded at 293 K. In the following discussion, we consider only the peaks corresponding to CI of the ferrocene fragment and the C atom directly bonded to the 0 atom (denoted C,); these are the C atoms closest to the hydroxyl groups (occupying /?and y positions relative to the hydroxyl H atom) and are well resolved in the I3C NMR spectrum (Figure 9). In the average crystal structure determined at room temperature? there are two (rather than four) different crystallographic environments (denoted Cl(1) and Cl(2)) for C I carbon atoms, and two (rather than four) different crystallographic environments (denoted Cc(l) and Cc(2)) for C, carbon atoms. This arises from the fact that the FBDPM dimer has a 2-fold symmetry axis in the average crystal structure (Le., averaging over the interconversion between the A and C hydrogen-bonding arrangements). For a given hydrogen-bonding arrangement (Le., A or C), however, there cannot be a 2-fold symmetry axis, and therefore four different crystallographic environments for CI carbon atoms and four different crystallographic environments for C, carbon atoms should be expected. At 293 K, the C1 and C, carbons each give rise to a pair of relatively narrow (line widths ca. 40 Hz) peaks in the highresolution solid-state I3C NMR spectrum, as a consequence of the crystallographic inequivalence between the Cl( 1) and CI(2) environments (chemical shifts 100.5 and 96.2 ppm, respec-
Aliev et al.
12014 J. Phys. Chem., Vol. 99, No. 31, 1995
1;s
1:s
iia
IL
(
1x0
rrm
inn
ga
sa
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'
1
70
80
Figure 9. High-resolution solid-state I3C NMR spectrum of FBDPMd2 recorded at 293 K using (a) the TOSS pulse sequence and (b) the combined NQS/TOSS pulse sequence (MAS frequency 5 kHz in both cases). Signals in the regions 66-73,79-80,96-101, 126-128, and 146-150 ppm are due to pentadienyl CH, C,, CI, phenyl CH, and phenyl quaternary C, respectively. 100
tively), and between the Cc(l) and Cc(2)environments (chemical shifts 79.3 and 78.9 ppm, respectively) in the average crystal structure at this temperature.6 On lowering the temperature, spectral changes characteristic of a dynamic process are observed for the peak assigned to Cl(1) (Figure 10) with broadening (up to 150-170 Hz) in the coalescence region (ca. 229-233 K). In the range 160-205 K, there are two peaks for the Cl(1) carbons, separated by Av = 120 Hz and with approximately equal integrated intensities. This reflects the fact that the interconversion between the A and C hydrogen-bonding arrangements is slow ( K < 270 Hz) with respect to the I3C NMR time scale, resulting in the local symmetry being lower than the average crystallographic symmetry at room temperature. The fact that the peak for Cl(2) at high temperature is not observed to evolve into two resolved peaks at low temperature (as discussed above for the Cl(1) carbons) is presumably due to the difference between the chemical shifts at low temperature being small. Analogous line-shape changes are observed for the signals assigned to the C, carbons, although the smaller chemical shift difference between Cc(l) and Cc(2) (in comparison with the chemical shift difference between Cl(1) and Cl(2)) results in these changes being less well-defined than for the CI carbons. Although line-shape analysis for high-resolution solid-state I3C NMR spectra containing spinning sidebands requires consideration of the whole spinning sideband pattern rather than just the isotropic peak,30we have estimated the free energy of activation using a method based upon considering the coalescence temperature for a pair of lines of equal inten~ity.~'The value of AG* predicted by this method is 46 W mol-' at the coalescence temperature (231 i 2 K).
Concluding Remarks Dynamic properties of the hydroxyl deuterons in selectively deuterated crystalline ferrocene- 1,l'-diylbis( diphenylmethanol)
,
90
~
PPR
"
88
'
~
70
~
'
"
"
~
Figure 10. High-resolution solid-state I3CNMR spectrum of FBDPMdz recorded as a function of temperature using the TOSS pulse sequence, with MAS frequency % 4-5 kHz.The spectrum at 205 K was fitted using the standard line-fitting procedure LINESIM, from which the ratio of integrated intensities for the C1 peaks at 96.0, 99.7, and 101.2 ppm is estimated to be 2.03:1.OO :1.04.
have been studied by variable-temperature wide-line 2H NMR in the temperature range 153-370 K and by variable-temperature I3C CPMAS NMR in the temperature range 205-253 K. The observed temperature dependences of these spectra indicate that the disorder of the hydrogen-bonding arrangement is dynamic, and this dynamic disorder is interpreted in terms of interconversion between two equally populated hydrogenbonding arrangements with clockwise and anticlockwise arrangements of the hydroxyl groups. Various plausible dynamic models describing the mechanism of this interconversion have been considered, and the following are consistent with the solidstate NMR results discussed above: (i) transfer of the hydroxyl H atoms between adjacent hydroxyl groups; (ii) a two-site n jump motion of each hydroxyl group its C - 0 bond. In the absence of accurate information on the geometry of the hydrogen bonded unit in FBDPM-4, these dynamic models cannot be distinguished on the basis of the solid-state NMR experiments reported here. In this regard, it is important to note that the dynamic models considered here assumed that after the transfer (model (i)) or rotation (model (ii)) of the hydroxyl H atom from its initial site (denoted HI), the new H atom site (denoted H2) is in the same plane as 02**Q-H1 for model (i) (see Figure 4a) and in the same plane as C-0-HI for model (ii) (see Figure 4b). From the approximate positions of the four different hydroxyl H atoms estimated from X-ray diffraction data, the angles between the O-Hz bond axes and the relevant planes specified above are 9", 1l0, 12", and 14" for model (i) and 2", 3", 8", and 8" for model (ii). The fact that these values lie
'
i
Hydrogen Bond Dynamics in FBDPM within experimental error of 0" justifies our use of the idealized geometries (Figure 4)for the dynamic models. Nevertheless, a more accurate experimental determination of the positions of the hydroxyl H atoms (e.g., from neutron diffraction) should allow the geometric details of the dynamic models to be refined, allowing model (i) and model (ii) to be distinguished on the basis of the reported *HNMR results. It is relevant to note that models analogous to (i) and (ii) were considered in order to interpret single-crystal 2H NMR results for the hexagonal hydrogen bonding arrangement (involving six hydroxyl groups) in the host structure of Dianin's compound (containing ethanol guest molecules),z5and analysis of zHquadrupole coupling tensor components led to model (i) being ruled out. The dynamic process was assigned as concerted jumps of the six hydroxyl groups via rotation about their C-0 bonds, and the activation energy was determined to be 33.1 kJ mol-'. Similar concerted rotational jumps of hydroxyl groups and water molecules have been assigned for P-cyclodextrin undecahydrate from neutron diffraction studies.3z It is noteworthy that the activation energy for the concerted two-proton transfer process in solid carboxylic acids is in the range 3-10 kJ mol-] (refs 33 and 34) and is considerably lower than the activation energy for the hydrogen-bond dynamics in Dianin's compoundz5 and in FBDPM. Given the geometry of the hydrogen bonding arrangement in FBDPM, it is probable that the dynamic process (whether model (i) or model (ii)) must necessarily be highly correlated, in the sense that it is improbable for two H atoms to lie simultaneously between the same pair of 0 atoms (as assumed in our interpretation of the dynamic process as an interconversion between the C and A hydrogen bonding arrangements). Independent (uncorrelated) transfer (model (i)) or rotation (model (ii)) of different hydroxyl H atoms would allow the possibility for two H atoms to lie simultaneously between the same pair of 0 atoms, implying that the dynamics must indeed be correlated to some extent. It is clearly interesting to consider whether the dynamic process consists of all four hydroxyl H atoms moving completely in unison, or whether one hydroxyl H atom begins to move first, triggering the motions of the other hydroxyl H atoms. A deeper understanding of mechanistic aspects of the dynamic properties of the hydrogen-bonding arrangement in FDBPM (with particular regard to the degree of correlation of the motions of the different hydroxyl groups) could be obtained from the application of computer simulation techniques, as demonstrated recently35 for another system containing a hydrogen-bonded arrangement of hydroxyl groups.
Acknowledgment. We thank University of London Intercollegiate Research Services for the provision of facilities for solid state NMR spectroscopy, and E.P.S.R.C. for financial support (postdoctoral fellowship to A.E.A. and general support to K.D.M.H.). Professor R. G. Griffin is thanked for providing the TURBOPOWDER program.
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