J . Phys. Chem. 1989, 93, 5371-5377 of molecules. It demonstrates that Morse potentials can be reasonably well simulated if the parameters are optimized. Alkali-metal dimers show a less satisfactory agreement while in many other cases it is even better. This is very interesting because it shows that the general behavior of the EHMO approach, including a two-body repulsive energy term, is correct.
5371
denotes the Slater-type atomic orbitals.
Acknowledgment. We thank Professor R. Gleiter, Heidelberg, for stimulating discussions and Konrad Hadener for his help in computational problems. This work is part of Project N F 2.025-0.86, financed by the Schweizerischer Nationalfonds zur Forderung der wissenschaftlichen Forschung, and of Project NEFF 329, financed by the Schweizerischer Nationaler Energieforschungsfonds.
Appendix To derive eq 17, let us start with E p ( R ) . With 2, and 2, for the core charges, we can write
s x m e a xdx = e " xmC ( - l ) P m!X m - P p=o ( m - p)!aP+' Integrals of this kind can be written as follows:32
bd is the occupation number of the atomic orbitals of the principal quantum number n and the azimuthal quantum number 1. xnl
leads to
Therefore we have
(32) Kauzmann, W. Quantum Chemistry; Academic Press: New York, 1957;p 286.
Molecular Inversion Dynamlcs of Bis(cyclopentadieny1)beryllium Inferred from Partially Relaxed Spin-Spin Coupling between Carbon-13 and Beryllium-9 Kerry W. Nugent, James K. Beattie,* and Leslie D. Field School of Chemistry, The University of Sydney, Sydney, N.S.W.2006, Australia (Received: June 3, 1988; In Final Form: January 23, 1989) The rate of molecular inversion of bis(cyc1opentadienyl)beryllium is estimated to be s-' in diethyl ether or cyclohexane bonding roles solutions at room temperature. Inversion occurs by the interchange of the central (v5) and peripheral of the two cyclopentadienyl rings and causes the hydrogen and the carbon atoms each to be dynamically averaged in their respective NMR spectra. The I3C spectra display fine structure, however, which arises from incomplete decoupling from the quadrupolar 9Be nucleus ( I = 3//2). The 'H-decoupled "C spectrum is a narrow doublet which collapses to a singlet as the temperature is lowered, with an apparent activation energy of 5.2 kJ mol-'. The line shape is independent of the magnetic field strength between 2.1 and 9.4 T and does not change significantly between the two solvents. These observations lead to the conclusion that the relaxation of the 9Be nucleus is predominantly caused by the molecular inversion and not by molecular tumbling. A precise value for the inversion rate cannot be calculated in the absence of the nuclear quadrupole coupling constant.
Introduction The IH N M R spectrum of bis(cyclopentadieny1)beryllium (BeCp2) in solution is a singlet, even at -135 O c . 1 - 3 Yet the molecule is polar in ~ o l u t i o n . ~This excludes the symmetrical (1) Morgan, G.L.; McVicker, G. B. J . Am. Chem. SOC.1968, 90, 2789. (2) Wong, C.; Lee, T. Y.; Lee, T. J.; Chang, T. W.; Liu, C. S . Inorg. Nucl. Chem. Lett. 1973, 9, 667. (3) Wong, C . ; Wang, S. Inorg. Nucl. Chem. Lett. 1975, 11, 677.
0022-365418912093-5371$01 SO10
ferrocene structure (Figure la) and implies that the equivalence of all of the Protons in the N M R spectrum is the consequence of some dynamical averaging process. The 9Be N M R spectrum is also a singlet at room temperature,' as would be expected for any of the structures which have been proposed for the molecule (Figure 1). (4) Fischer, E. 0.;Schreiner, S. Chem. Ber. 1959, 92, 938.
0 1989 American Chemical Society
5372 The Journal of Physical Chemistry, Vol. 93, No. 14, 1989
Nugent et al. TABLE I: NMR Parameters of BeCp, in Diethyl Ether Solution b H ~ppm 5.85 (from TMS) 6 -,~ D. D m 106.8 (from TMS) -21.9 ifrom 0.1 M Be(N03)2in H20) b e : PPm . >
'JC-H, Hz
168.5
Hz " 4 J ~ -H~ Z, J c - B ~Hz ,
6.6 4.9
233Jc_H,
2.0
Cyclohexane solution.
C)CS"
d)C,
Figure 1. Proposed structures for BeCp2: (a) symmetrical sandwich model; (b) u-T model; (c) unsymmetrical sandwich model; (d) slipsandwich model.
N M R Spectra. The IH satellite spectrum was recorded with a Bruker WM400 spectrometer. The I3C spectra were recorded with Jeol FX60Q, Bruker HX90, and Bruker WM400 spectrometers. The 9Be spectra were recorded with Bruker WM400 and Jeol FX90Q spectrometers equipped with multinuclear probes. The 9Be T , measurements were made at 56.2 MHz on the WM400 spectrometer with the standard 180-~-90" pulse sequence. The spectra were analyzed by using a Hewlett-Packard 9835A computer. The data were transferred from the spectrometer to this computer by plotting the region of the peak using a scale of 1 Hz/cm, and digitizing the data from this plot using the computer and a Hewlett-Packard 7225A plotter equipped with a digitizing sight.
Until a preliminary account of the present work was commuResults n i ~ a t e d ,the ~ I3C spectrum of BeCp, apparently had not been reported. The I3C spectrum also displays a single resonance, but I3C N M R Studies. The proton-decoupled 13C spectrum of with a temperature-dependent fine structure which is ascribed to BeCp, in diethyl ether solution at room temperature appears as incomplete decoupling with the 9Be nucleus. Analysis of this a broad doublet. The chemical shift is 106.8 ppm from T M S temperature dependence and its solvent dependence suggests a (Table I). The spectrum of this solution at -100 "C shows no mechanism for the relaxation of the quadrupolar 9Benucleus. This exchange broadening; instead, the line becomes narrower at lower requires some extension of the published theory for quadrupolar temperatures. The temperature dependence of the line width is rela~ation.~,~ illustrated in Figure 2. The 13C spectrum of the compound in X-ray crystal structure analysis indicates that in the solid state cyclohexane solution similarly shows a decrease in line width with the molecule possesses the novel "slip-sandwich" s t r u c t ~ r e . ~ ~ * ~a ~decrease in temperature (Figure 3). Analysis of the infrared spectrum in solutionlo and in the vapor The room temperature 'H-coupled I3C spectrum comprises two phase" indicates that the slip-sandwich structure persists in these multiplets with a separation of 168.5 Hz equal to IJCwH.This value states. The molecule is disordered in the crystal with two for ' J is rather lower than those for cyclopentadienylberyllium equivalent sites for the beryllium atom. This disorder exchanges bromide (1 79.1 Hz) and cyclopentadienyl(pheny1)beryllium (177.4 the roles of the two cyclopentadienyl rings between central and Hz),13 reflecting the fact that these compounds contain only a peripheral bonding. The interpretation of the N M R spectrum centrally bonded cyclopentadienyl group, whereas the coupling leads to the conclusion that in solution the molecule undergoes for bis(cyc1opentadienyl)beryllium is the average of the coupling this inversion with a lifetime of the order of s. constants for the centrally and peripherally bonded rings. The quintet structure of the multiplet (Figure 4) is similar to Experimental Section The multiplet arises that published for cy~lopentadienyllithium.'~ Sample Preparations. Bis(cyclopentadieny1)beryllium was from the virtual coupling of the remaining four protons with an prepared by the method of Fischer and Hofmannl, as described apparent coupling constant 233Jc-H of 6.6 Hz. in detail elsewhere." Caution! Beryllium compounds are very The doublet fine structure of the quintet arises from partially toxic by inhalation and in contact with the skin, are irritating to relaxed coupling to the 9Be nucleus and will be discussed in detail the respiratory system, and present the danger of very serious below. irreversible effects. ' H N M R Studies. The 'H N M R spectrum has been described The N M R samples were prepared on a vacuum line by first previously.I4 The chemical shift in diethyl ether is 5.85 ppm from subliming BeCp, into the N M R tube and then condensing the TMS. The I3C satellites in the proton spectrum were examined. solvent into the tube. The sample was then frozen in liquid Only the outer satellites (due to hydrogen atoms directly bonded nitrogen and the tube sealed. Samples were prepared in diethyl to a 13Catom) were clearly resolved. The separation of the outer ether, approximately 50% Merck Sharp & Dohme Isotopes disatellites is equal to lJc-H, with a value of 168 Hz, the same as ethyl-dIoether (99 atom % D) and 50% stock ether dried over is observed in the I3C spectrum. The satellite is close to symsodium wire, and in cyclohexane, Aldrich Gold Label cyclometrical, with five rather broad lines separated by 4.9 Hz. This ' D). Two attempts to prepare an N M R hexane-dlz (99.5 atom % is the average value of the three-bond and four-bond H-H coupling sample of BeCp, in decalin failed, with the N M R tubes breaking, constant, 394JH-H.One of the outer satellite peaks is illustrated apparently due to thermal expansion of solid decalin. in Figure 5 . 9Be N M R Studies. The 9Be spectrum of BeCp, in cyclohexane shows a single sharp peak at -21.9 ppm from aqueous 0.1 M ( 5 ) Nugent, K. W.; Beattie, J. K. J . Chem. Soc., Chem. Commun. 1986, beryllium nitrate. The difference between this value and the 186. (6) Bacon, J.; Gillespie, R. J.; Quail, J. W. Can.J . Chem. 1963, 41, 3063. reported value' of -18.3 ppm for the same compound in me( 7 ) Suzuki, M.; Kubo, R. Mol. Phys. 1963, 7 , 201. thylcyclohexane solution is possibly due to a concentration de(8) Wong, C. H.; Lee, T. Y.; Chao, K. J.; Lee, S.Acta Crystollogr. 1972, pendence of the chemical shift of the reference, beryllium nitrate. B28, 1662. The line width at room temperature was 5.25 Hz, which appeared (9) Nugent, K. W.; Beattie, J. K.; Hambley, T. W.; Snow, M. R. Aust. J . Chem. 1984, 37, 1601. to be significantly less than that of the reference signal. (IO) Pratten, S. J.; Copper, M. K.; Aroney, M . J.; Filipczuk, S. W. J . Chem. SOC.,Dalton Trans. 1985, 1761. ( I I ) Nugent, K. W.; Beattie, J. K. Inorg. Chem. 1988, 27, 4269. (12) Fischer, E. 0.;Hofmann, H. P. Chem. Ber. 1959. 92, 482.
(13) Fisher, P.; Stadelhofer, J.; Weidlein, J. J . Organomel. Chem. 1976, 116, 65.
The Journal of Physical Chemistry, Vol. 93, No. 14, 1989 5373
Molecular Inversion Dynamics of BeCp,
1A i 260 K
3M
290 K
I:
215 K
230 K
220 K
Figure 2. Temperature dependence of the proton-decoupled 13C spectrum of BeCp, in diethyl ether solution. Each spectral plot is 15 Hz in width.
330 K
320 K
310 I:
300 K
304 K
ZW K
285 I:
Figure 3. Temperature dependence of the proton-decoupled I3C spectrum of BeCp, in cyclohexane solution. Each spectral plot is 15 Hz in width.
D
10
20
15
Figure 5. One of the outer I3C satellites in the IH NMR spectrum.
-40
0
40
Hz
Figure 4. One of the pair of multiplets comprising the C-H coupled 13C N M R spectrum.
A direct measurement of the beryllium spin-lattice relaxation time, T I ,was made at room temperature, with cyclohexane as solvent, and gave a value of 130 ms. A estimate of T I can also be obtained from the beryllium line width. Under extreme narrowing conditions, the beryllium spectrum should consist of a single Lorentzian peak with width in hertz at half-height of l / r T , * . At 21 OC, the line width of the 9Be resonance of BeCpz in cyclohexane of 5.25 Hz corresponds to a T2* value of 61 ms. This value can be considered as a lower limit for T I ,for any other contribution to the line width of the 9Be resonance would result in an increase in the estimated T 1 value. 9Be-13CCoupling. The splitting of the resonance lines in the 'H-decoupled I3Cspectrum can only be attributed to coupling of the carbon nucleus to the 9Be nucleus (spin 3/2). The coupling
cannot be resolved, however, to give the expected four line pattern for a spin I / , nucleus coupled to a spin 3 / 2 nucleus. The line appears as a doublet at higher temperatures, but the line shape shows a strong temperature dependence as shown in Figures 2 and 3. The low-temperature spectra show the beryllium nucleus to be effectively decoupled from the 13Cnucleus. This is attributed to rapid spin relaxation of the beryllium nucleus. The unusual doublet observed at room temperature must therefore be a result of coupling to a beryllium nucleus at an intermediate rate of relaxation. This results in a situation similar to chemical exchange, and the variation of line shape with relaxation rate has been calculated.6,7 This theory may be used to estimate the relaxation rate of the beryllium nucleus, and thus the temperature dependence of the beryllium relaxation time, from the carbon line shape. A value of the 9Be-13C coupling constant is required to be able to fit the spectra. Best fits were obtained with values of 2.0 Hz for the diethyl ether solution and 1.8 Hz for the cyclohexane solution, as described below. Theory of Quadrupolar Relaxation. The naturally occurring isotope of beryllium, 9Be, has a nuclear spin of 3/2 and a quad-
Nugent et al.
5374 The Journal of Physical Chemistry, Vol. 93, No. 14, 1989 I
q2= 1000
___-__
q2= 8
.
. . .. . ,. .. ... ,. . .,. .. q2= 1 5
-_--
q2= 2
.._
q"
.
. 00 1
Figure 6. Line-shape function, eq 2, as the parameter 7 is varied.
rupole moment, Q,of 0.05 barns. It has been shown by Abragam14 that the spin-lattice relaxation time, T1,for a nucleus of spin I = 3/2, due to coupling of the nuclear quadrupole moment of the nucleus to a fluctuating electric field gradient is given in the "extreme narrowing case", U T ,
