The dynamics of ring rotation in ferrocene, nickelocene and ruthenocene by incoherent quadi-elastic neutron scattering

Chemical Physics57 (1981) 453-460 North-HoliandPublishingCompany

THE DYNAMXCS RUBHENOCENE

OF RING ROTA”I?JON IN FERROCENE, NXCKELOCENE AND BY INCOHERENT QUASI-ELASTIC NEUTRON SCAmERINGP

A. B. GARDNER,

J. HOWARD,

T. C. WADDINGTON

Chemistry Depnrrmenr, Science Laboratories, Durham

University, Sorrrh Road, Durham DHl

3LE, UK

and R. M. RICHARDSON and J. TOMKINSGN Nen*Gndivision.Rutherford and Appleton Lnboracories, Chilton, Didcot, Oron 0x11

OQX, (IK

Received20 October 1980

Incoherent quasi-elastic neutron scattering has been used to study the reorientational motions of the cyclopentadienyl rings in ferrocene, nickelocene and ruthenocene.The results for ferrocene show that the activation energy for ring rotation drops above the 164 K phase transition to 4.4~0.5 kl mol-’ (which is approximately half its low temperature value) but the rings still appear to jump between only live orient&ions on the observable time scale. At room temperature, the rings in nickelocene appear to behave the same as in ferrocene but in ruthenocene they reorientate much less frequently and resemble those in ferrocene below 164 K.

i Neutron scattering experiments were carried out at the Institut Laue-Langevin. Grenoble, FRIIW.

ferrocene to be disordered but not nearly as disordered as the plastic phase of ferrocene carboxaldehyde [8]_ For ferrocene, electron diffraction experiments [9] have shown that in the gas phase the CyclopentadienyI rings can rotate with an activation energy of 3.8 kJ mol-‘. F’ulsed NMR [lo] measurements have detected the ring reorientation in ferrocene (below 164 IS) and ruthenocene and have been able to measure the average residence time in each of the five possible orientations and the activation energy for ring reorientation, The pulsed NMR technique was not, however, able to provide such information above the phase transition in ferrocene because more than oat relaxation time was detected above 164 K. The principle aim of our work was to confirm the NMR results in ferrocene and ruthenocene and then to extend the ferrocene resuhs above the 164 K transition using incoherent quasielastic neutron scattering (IQBNS) from the protons in the molecules_ A brief summary of the theoretical background to

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1. Introduction The molecular structure of the metalocene compounds is a metal atom sandwiched between two cyclopentadienyl rings. Both ferrocene and nickelocene have transitions between two solid phases (ferrocene at 164 K [l], nickelocene at ~190 K [Z]), but ruthenocene does not appear to undergo such a transition [3]. At room temperature. ferrocene is monoclinic and on cooling it transforms to a triclinic form at 164 K. Below 250 K, both these fcrms appear to be metastable with respect to an orthorhombic form [4, S] but_recrystahzation into this phase takes place only after cooling below 164 K then annealing at ~200 K for several hours. In this work, therefore, only the monoclinic and trichnic phases have been studied. X-ray and neutron dif%action [6,7] have shown the monoclinic (room temperature) phase of

@ North-Holland

A.B. Gardner er al. / Dynamics of ring rotation

454

IQENS is given in section 2. Section 3 outlines the experimental method and section 4 discusses the analysis cf the results. These are discussed and compared with results of other techniques in section 5.

2. T&eoreticai background The IQENS technique has recently been reviewed (e.g. refs. [ll, 121) so only the most important points will be mentioned here. OnIy random motions that are sufficiently rapid to significantly broaden the instrumental resolution function are detected by IQENS. Translational diffusion is much too slow to be seen in these solids with the present experimental resolution. Vibrational motions only contribute a background (whose height depends upon Q’ .where htQ is the momentum transfer and Q is the scattering vector) and a Debye-WalIer factor in the quasielastic region. The incoherent scattering law, S(Q, o) (i.e. the scattered intensity as a function of neutron momentum and energy transfer) in the quasielastic region will have the form (for a powder sample): S(Q, w) = exp

~--Q*~rr~~)[-S,,,(Q, w)+B’(Q)I, (1)

where S,,,(Q, w) is the scattering law that would be observed if the molecule in the sample were only undergoing a random reorientational motion, (~~}~‘a is the root mean square amplitude of the periodic vibrations and B’(Q) is the inelastic background. This work has been done using the time-of-flight technique so spectra are measured at constant scattering angle and not at constant Q. However, S&Q, o) is peaked at hw = 0 (where Q = Q,J and it is only significant in the low IAol region (ho/_& C0.2) so the variation of Q across this i?o range is small. If (U2)1’2 is sufhciently small eq. (1) will (to a good approximation) be equivalent to S(Q> i) = CKUS,,(Q,

w)+B(Q,,).

(2)

can now be used as a scaling factor when fitting 2 model S&Q, w) to each experimental spectrum and I3(Q,3 can be used as a flat

inelastic background. C(Q,r)=exp

Since

(-Q%u’>),

(3)

the assumption that (u*)*‘~ is small can be checked by plotting In[C(Q,r)] versus Q:r and measuring the slope. For the samples in this work {zr‘}l” was always less rhan 0.45 .& and the variation of exp (-Q’{u’)) across the important part of a spectrum was 20% at worst and generally much less. For a locaiized, random molecular motion such as a rotation the incoherent quasielastic scattering law consists of an elastic term and a series of broadened terms, e.g. s,,,(Q,,,=A,(Q,sc,,i-~~*A,(Q)t(r,’),

(4)

is a lorentzian function of ener,y where L(r,‘) transfer with a half width at half maximum of r,r :

L(t,‘)

= 7”/7r(l t&2,).

(3

The 7, are related to the correlation time of the random molecular motion. Ao(Q) is known as the elastic incoherent stncture factor (EISF) and (for a constant Q spectrum) it is the fraction of the quasielastic intensity that is elastic (since CT+ A, = 1). The EISF is directly related to the geometry of the random molecuIar motion and so the approach in this work has been to measure the EISF a~ a function of Q,r and compare it with the calculated EISF for certain models. Having found a reasonable model (or models) we can then go on to use the width of the broadened terms to calculate the correlation time for the molecular motion. For some spectra, which were not much broader than the instrumental resolution function, it was not possible to measure the EISF. Fortunately in these cases we were able to assume a reasonable model for the geometry of the motion and thereby extract the correlation time.

3. Experimental

deta%

C(Q,l)

The samples of ferrocene, nickelocene and rnthenocene were made up by weight to scatter

A.B. Gardner et al. / Dynamics

10% to 15% of the neutron beam. They were contained in thin walled (0.5 mm) ahnninium cans and their temperatures were controlled by standard cryostats at the Institut Laue-Langevin (ILL), Grenoble. All the measurements were carried out on the multichopper time-of-flight spectrometer, IN5, at the ILL. The experimental conditions of the different measurements are summarized in table 1. Angles that were contaminated by Bragg reflections were not used.

4. Results

4.1. Dam reduction scheme The raw time-of-Right spectra were first corrected for scattering by the can, absorption and self-shielding and then converted to scattering law form using the programs PRIME and CROSSX [13] at ILL. This removed all the instrumental factors from the spectra except the effects of finite resolution and multiple scattering in the sample. The second stage of the data reduction scheme was to analyse the experimental scattering law using the program W3 [14] as described in the next sections (4.2 and 4.3). For some of the measurements it was considered worthwhile to estimate the effects of multiple scattering on the results. This procedure is described in section 4.4.

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455

4.2. Ferrocene aboue I64 K and nickelocene results The spectra from ferrocene above 164 K and nickelocene at 303 K both showed considerabie broadening. Fig. 1 shows the quasielastic spectra from ferrocene at 343 K where clearly distinct elastic and broadened components can be seen. The data for ferrocene above 164 K and nickelocene have been analysed by extracting the EISF and the correlation time from the experimental spectra using the following method. The first step in the process was to choose a physically reasonable model for the random motion. For these samples, 5 or 10 fold jump reorientation of the cyclopentadienyl groups was chosen [15]. The “elastic” to “broadened” intensity ratio must be a variable so a (smah) parameter D was added. The model scattering law, for a powder sample, then becomes: S&Q,

01 = [Bo(QaI+DlW~)

(6j where B, (Qa 1 =N-’

t

In=1

jo(2Qa

sin rim/N)) cos (Zs;nm/N) (7)

Table 1 Summary of experimental details Sample

Temperature V/K)

Incident waveIen$h &/A)

Resolution (fwhm/reV)

Maximum Q,, (A-‘)

ferrocene ruthenocene ferrocene nickelocene ferrocene

286 286 303 303 303 343 393 193 174 154

8.2 8.2 5.5 5.5 8.0 8.0 8.0 8.0 8.0 8.0

53 53 106 106 50 50 50 37 37 37

1.42 1.42 2.12 2.12

ferrocene

fenocene ferrocene ferrocene ferrocene

1.45

1.45 1.42 1.42 1.42 1.42

Fig. I. The points represent rhe measured incoherent quasielastic scattering law of ferro=ne at 343 K. The solid lines are rhe best Fits of the five-fold jump model [es. (6), N = S] to the data, the short dashes separate the elastic and broadened terms and the longerdashes are a fitted inelastic background.

j&r) = sin (x)/x,

(8)

5;, = 7,,/2 sin’ (zn/N),

(9)

a is the radius of gyration of the protons (2.2 A), N is the number of sites (5 or lo), and 7rcs is the mean residence time in any one site. This scattering law was folded with the instrumental resolution function and fitted to the measured SpeCiNm by varying D and ‘;res (as well as the scaling factor, C, and a flat inelastic background, B). Typical fits are shown in fig. 1. The value of (&+D) giving the best fit to the experimental results is taken as the experimep tal EISF and the results for ferrocene at 303 K are plotted in fig. 2. The values of D were generally small and negative (always 0.05 > D > -0.1) which indicated that the original choice of model was good. The values of ‘i-1were constant to within 15% over the Q range which again confirms the merit of the model. There was little difference in the values of the EISF given

Fig. 2. The symbols represent some of the experimentally determined elastic incoherent structure factors (EISFsj. With the exception of the solid circles, they have all been eorrected for the effects of multiple scattering (MSC). The different symbols represent the fallowing experimental conditions: Ca- ferrocene at 303 K and A0 = 5.5 A (no MSC), O-ferrocene at 303K and &,=S.S& O-ferrocene at 303 K and A,, = 8.0 A, B - feenocene at 173 K and A,,= 8.0 pi. E - nickelocene at 303 K and A0 = 5.5 A. The solid linesrepresent the theoretical ElSF expected for u&&al jump reorientation OF the cyclopentadienyl goups between 5 sites (upper solid line) or 10 sites (lower solid line) and the dashed line is the EISF expected if the whole molecule were tumbling.

by the five- and ten-fold jump models except at Q > I.2 -4-l. At the higher Q values the spectra were SO broad that it became very difficult to separate the fiat inelastic background from the wings of the spectrum. The five- and ten-fold jump models differ most in the wings, SO it is probably the difficulty in finding the background that produced the differences in the results for Q > 1.2 A-‘. In fig. 2 we have plotted the average of the two sets of results for the experimental EISF (i.e. for the five- and tenfold jump models) and represented the differences by error bars. There was no significant difference between the -rl values given by the five- and ten-fold jump models. The values of rrfs were calculated using eq. (9) with the appropriate value of N substituted. The effects of multiple scattering on the EISF and r,, were estimated and corrected as described in section 4.4.

4.3. Ferrocene below 164 K and rutt%enocene, results and discussion There was only a small (but nevertheless detectable and measurable) broadening of the resolution in the scattering from ferrocene (below 164K) and ruthenocene (see figs. 3 and 4). Since it is not possible to separate the elastic and broadened components to obtain the EISF, it is not possible to measure directly the geometry of the random molecular motion on these sampIes (although it could be done with a higher resolution spectrometer)_ However, there is much evidence [3, lo] to suggest that the motion is a five-fold jump reorientation of the rings. Furthermore, structural determinations of ferrocene below 164 K l163 and ruthenocene [3] have not offered any evidence to suggest that the rings are disordered so the reorientation is almost certainly between five indistinguishable sites. We have, therefore, assumed this model to be correct and have extracted the correlation time by fitting eq. (6) (with N = 5, D = 0 and ‘i-1, the scaling factor C and background B as fittable parameters) to the data. No multiple scattering corrections were made for these measurements, but the mean residence times (shown in table 2) were calculated from the high

Fig. 4. The points represent the measured scattering law of ruthenocene at 286 K (Q = 1.38 A-‘). The solid iine is a fit

of the five-fold jump model to the data as errplained in the text and the dashed line is an unbroadened resolution function. The fitted inelastic background is too low to be disringuishable.

Q resu!ts where the corrections are expected to be small. Table 2 also compares the mean residence times with those found by Campbell et al. [lo], using NMR. Bearing in mind the fact that the IQENS results were only just detectabIe with the experimental resolution used, the agreement wit’h NMR is most satisfactory. 4.4. Mtdtipie scattering corrections

-00

a20 hi-&f r’ Fig. 3. The points represent the measuredscatteringlawof

ferrocene at 154 K (Q 4 1.42 A-‘). The solid line is a fit of the five-fold jump model to the data as explained in the text and the dashed line is 2n unbrmdened resolwion function. ‘l’be fitted inelastic background is too low to be dhtinguizh-

able.

Fig. 2 shows that there is a very small difference between the EISF expected for a five- or ten-foid jump model in the region measured and so the accuracy of the experimental EISF was considered important enough to warrant correcting for multiple scattering. In order to calculate the multiple scattering correction (MSC) for a spectrum, the scattering law of the sampIe must be known and so arriving at a precise MSC is usually a lengthy iterative procedure. For the present purposes it was considered adequate to estimate the elect 0: multiple scattering on the parameters that were derived from the spectra (i.e. the EISF and ~~3. This was done by generating spectra that represented neutrons having undergone up to five scattering processes in the sample using the Monte Carlo program DISCUS [17]. The input

A.B.

458 Table 2 Comparison Substance

fexocene ruthenocene

Gardner et al. / Dynamics of ring rotation

of IQENS and NMR results Temperature

‘;rcr (NMR)[lO]

w

ilo-'"s)

;‘r=, (IQEN.9 (lO-‘Os)

154 303

2.9 4.1

2.150.4 l._si 1.0

scattering law was assumed to be that for a fivefold jump reorientation [eq. (6) with N = 5, D = 0 and cl fixed at the experimentally determined value]. Tine spectra were then fitted by the same program as used for the real data. Dividing the EISF and rrc. of the input model by those found by the program gave “first-order” correction factors for the experimentai results. The correction factors always tended to increase the EISF by ~15% of its value and some of the corrected values are plotted in fig. 2. The correction factors also improved the constancy of rres across the Q range, and the values of r,, in fig. 4 are corrected for multiple scattering and ihen averaged over the Q range.

5. Discussion 5.1. Geometv of the ring rotation in ferrozene abor2e164K The experimentally determined EISF values appear to be practically independent of temperature which shows that, as expected, the geometry of the random motion being observed does not vary with temperature (only the correlation time changes). In fig. 2 the experirnental EISFs are compared with the EISF expected if the rings were jumping between 5 or 10 sites on a circle b.e. eq. (7) with n = 0, N = 5 or 101. Only one set of points extends to suCiently high Q for these models to be distinguishable and it clearly favours the five-fold jump model. Further experiments, going to even higher values of Q, are planned to confirm this point. X-ray [4] and neutron [73 difiraction from ferrocene in its high temperature phase has .been explained by a disorder model involving a

super-position of two different molecular orientations. This is consistent with the rings having ten equilibrium sites but it is not necessarily true ihat the rings can explore all ten sites on the neutron time scale. Our IQENS experiment has detected a rapid jumping of protons amongst five-fold sites but it has not precluded the possibility of slower relaxation between two sets of five-fold sites belonging to different molecular orientations. Since the presence of two different molecular orientations has only been detected by diffraction studies we cannot say what the time constant for interchange between them is. We plan to explore this further with a very high resolution IQENS experiment. The broken line (line c) in fig. 2 represents the EISF expected if the molecules were tumbling isotropically about their centres of gravity, i.e. EISF=j;(Qa),

(10)

where a is 3.2 A, the distance from the protons to the centre of gravity. The strong disagreement between the measurements and the broken line shows that we can definitely conclude that the molecules are not tumbling and that the observed motion is essentially uniaxial ring rotation between at least five equilibrium sites. 5.2. The dynamics of the ring rotation in ferrocene above 164 K In order to estimate the energy barrier to rotation of the cyclopentadienyl rings we have assumed that the mean residence time in a site follows an Arrhenius type of activation law: rrs(T)

= 7s eq

%/KB

T).

(111

Fig. 5 is an Arrhenius plot of mean residence time (assuming the five-fold jump model) against the inverse temperature and the slope implies an activation energy of 4.41 0.5 kJ mol-‘. Since the activation energy is derived from the sIope of the graph, assuming N = 10 instead of 5 does not change its value. In table 3 thii value is compared with the values

A.B.

Cfurdner

of ringmrati~n

et al. 1 Dynamics

459

that were used in this work, &hp near ineiastic features in the spectra are swamped by multiphonon effects and the quasi-elastic scattering, but at 5 K the lowest inelastic feature is seen at 2.7 meV. For this energy transfer, (2~)~’ = 7.5 x lo-,13 s which is in excellent agreement with the pre-exponential factor given by assuming N = 5. The apparent simikrity between the high temperature (five-fold jump) and the low temperature pre-exponential factors suggests that the five-foId jump model is correct, but confirmation must await the availability of inelastic data for this high temperature phase. 2-0

3-o

LO

5.0

6.0

5.3.

ldK/T

Fig. 5. An Arrhenius plot of the mean residence time in a site. 7,. against reciprocal temperature. The slope gives the activation energy to ring rotation.

Nickelocene

Since nickeIocene appears to have a similar order-disorder phase transition to ferrocene it is not surprising that the random reorientation of the cyclopentadienyl rings give very similar IQENS results to ferrocene. The mean residence time in a site (3.9 x lo-“s at 303 K) is practically the same as for ferrocene and the slight systematic difference in the EISFs is probably due to some of the nickelocene sample being oxidised to “non-mobile” hydrogen containing compounds which give an extra elastic contribution to the spectra.

given by other techniques for various phases of ferrocene. Campbell et al. [lo] have proposed a scheme in which the potential experienced by a cyclopentadienyl ring as it rotates is due to a combination of intramolecular bonding forces and intermolecular non-bonding forces (ref. [SO] iig. 9). Although they could not predict exactly the total barrier to rotation, the vaIue found in our work is quite compatible with their scheme. The pre-exponential factor c, is 8 X IO-l3 s if 5 sites are assumed (2 X lo-l3 s for 10 sites). The first value is in good agreement with the value found by NMR [lo] in the low temperature phase, given in table 3. Following Brot [lpil we expect ~2’ to be comparabIe with twice the frequency of libration in one of the weIls in the potential. At the relatively high temperatures

6. Condusion We have shown that the activation energy for rotation of the cyclopentadienyl groups in ferrocene drops above the order-disorder transition at I64 K. The balance of the evidence suggests strongly that the rings reorient in a

Table 3 Activation energies and pre-exponential factors for ferrocene Phase

Technique

Activation eners

Pre-exponeotial factor (5 sites),

(E&i

(GJS)

mol-‘1

g=

electron diffraction [9]

3.8t1.3

solid > 164 K

IQENS

4.4r05

8 X lo-”

solid< 164 K

NMR [lOI

8.33

6.16X lo-‘3

460

i--B. Gardner et al. / Dynamics

five-fold potential on a time scale of lo-” s. This can only be fully confirmed, and the details of the potential explored, by IQENS measurements at higher momentum transfers and a detailed analysis of the inelastic scattering. Both are in progress. The presence of random molecular motions in the disordered phase on a time scale slower than lo-” s also remains to be searched for by a higher resolution experiment. At room temperature, the dynamics of the rings in nickelocene and ferrocene seem to be practically the same, whereas in ruthenocene, the rings reorientate much less frequently and behave more Iike ferrocene below 164 K.

References [I] J.W. Edwards, G.L. Kingtton and R. Mason, Trans. Faraday Sot. i5 (1959) 660. [2] G. CaIverin and D. Weigel. J. Appl. Cry%. 9 (1976) 212. [?I M.J. Bennett ar.d W.L. Hutcheon. Paper No. 236, 57th Canadian ChemicaI Conference, Regina Saskatchewan, 1974.

of ring rotation

[4] K. Ogasahata,

M. Sorai and H. Suga, Chem. Phys. 68 (1979) 457. [53 J.F. Barar, G. C&a&, D. Weigel, K. ChIor and C. Pommier, J. Chem. Phys. 73 (1980) 438. [6] P. Seiler and J. Dun&z, Acta. Cry%. B35 (1979) 1068. [7] F. Takusagawa and T-F. KoetzIe, Acta Cryst. 835 (1979) 1074. [8] M.F. Daniel, A.J. Leadbetter, RE. Meads and W.G. Parker, Trans. Faraday Sac. II 74 (1978) 456; M.F. Daniefs. A.J. Leadbeaer and R.M. Richardson, to Ire published. 191 A. Haaland and J.E. Nilsson, Chem. Cornsnun. 88 (1965). [IO] A.J. Campbell, CA. Fyfe, D. Harold-Smith and K.R. Jeffrey. Mol. Cryst. Liquid Cryst. 36 (1976) 1. [ll] A.J. Lesdbetter, in: The plasticaIly crystalline state, ed. J. Sherwood (Wiley, New York, 1979) ch. 8. [12] A.J. Leadbetter and R.M. Richardson. in: The molecular physics of liquid crystals, eds. G.R. Luckhurst and G.W. Grey (Academic Press, New York, 1979). [13] A..!. Dianoux. R.E. Ghosh, H. Hervet and R.E. Lechner, ILL Internal Technical Report No. 75D16T. [14] R.M. Richardson, Rutherford Laboratory Report No. RI_-79-095. [15] J-D. Barnes. J. Chem. Phys. 58 (1973) 5193. [16] P. SeiIer and J. Dun&, Acta. Cryst. B35 (1979) 2020. [17] M.J. Johnson, Atomic Energy Research Establishment Report No. AERE-R7682. [18] C. Brat, Chem. Phys. Letters 3 (1969) 319. Letters