J. Phys. Chem. 1996, 100, 2045-2052
2045
Multinuclear NMR Study of HFeCo3(CO)9[P(OCH3)3]3 in the Solid State and in Solution Pierre Kempgens, Je´ roˆ me Hirschinger,* Karim Elbayed, Je´ sus Raya, and Pierre Granger Institut de Chimie, UMR 50 CNRS, Bruker Spectrospin, UniVersite´ Louis Pasteur, BP 296, 67008 Strasbourg Cedex, France
Jacky Rose´ Laboratoire de Chimie de Coordination, URA 416 CNRS, UniVersite´ Louis Pasteur, 4 rue Blaise Pascal, 67070 Strasbourg Cedex, France ReceiVed: August 21, 1995X
and 59Co NMR have been applied to study the structure and dynamics of the tetrahedral mixed-metal cluster HFeCo3(CO)9[P(OCH3)3]3 both in the solid state and in solution. The 31P chemical shift (CS) anisotropy, the direct (D) and indirect (J) dipolar 31P-59Co interactions, and the relative orientation of the CS, D, and J tensors have been determined by iterative fitting of the 31P MAS NMR spectra at two magnetic field strengths (4.7 and 7.1 T). The quadrupole coupling constant as well as the isotropic part and anisotropy of the CS tensor at the 59Co nucleus has been evaluated by a moment analysis of the solid-state central transition line shape. The 31P and 59Co NMR data, which are both influenced by second-order quadrupolar shifts, clearly show a departure from the C3V molecular symmetry due to a solid-state packing effect. Using the static interaction parameters obtained by solid-state NMR, it was possible to evaluate the overall rate of molecular motion in solution from 59Co relaxation measurements. The analysis of the solution-state 31P NMR saddleshaped spectrum gives the same 1J(31P-59Co) coupling constant as in the solid state. Moreover, no Q-CS relaxation interference effects are detected in agreement with the very weak contribution of the CS anisotropy to the 59Co relaxation predicted by the solid-state NMR data. 31P
I. Introduction Multinuclear NMR spectroscopy has proved to be a very powerful tool for studying molecular structure and dynamics in solution and in the solid state.1-8 Hence, in principle, the NMR technique provides a bridge between the solution and solid-state molecular structures.9 In addition, the fixed arrangements found for molecules in the solid state allow the determination of static NMR interaction parameters that are necessary for the interpretation of the relaxation time measurements in solution.1,3,5,7,8 The field of solid-state NMR methods applied to organometallic and coordination chemistry is growing rapidly.10 In particular, 59Co NMR has been recently applied to the study of tetrahedral clusters both in solution11-15 and in the solid state,16,17 these compounds being of structural and catalytic interest.18 Moreover, in derivatives containing phosphorus ligands, complementary information may be obtained by 31P NMR.19 However, as a result of the existence of a large quadrupole coupling constant QCC ) e2qQ/h at the high-spin 59Co nucleus, care must be taken in the analysis of the experimental data. Indeed, in solution, the multiplet structure of the scalar-coupled 31P spin1/ nucleus is expected to be strongly influenced by the fast 2 59Co spin relaxation.20-22 On the other hand, in the solid state, the so-called quadrupolar second-order effects at the high-spin nucleus are known to be transmitted to the spin-1/2 nucleus through the magnetic dipolar interaction between both nuclei.19,23-28 Clearly, using both the solution- and solid-state NMR data, the microdynamical behavior of these molecules in solution may be accessed.29-31 In the present article, the tetrahedral mixed-metal cluster HFeCo3(CO)9[P(OCH3)3]3 is studied by 59Co and 31P NMR in the solid state and in solution. Since a definitive structure X
Abstract published in AdVance ACS Abstracts, January 1, 1996.
0022-3654/96/20100-2045$12.00/0
determination of this trimethyl phosphite tris-substituted derivative has been reported via X-ray32 and neutron diffraction33 methods, special attention is paid to the relationship between the static solid-state structure determined by diffraction techniques and the motionally averaged one which exists in solution. II. Theoretical Considerations A. Solid State. In a strong magnetic field B0, the internal Hamiltonians Hλ (λ * Z) can be treated as perturbations of the Zeeman coupling HZ. We consider a spin-1/2 nucleus I which is coupled via direct dipolar (λ ) D) and indirect (λ ) J) interactions to a quadrupolar nucleus S (S > 1/2), both the I and S spins being also submitted to their respective chemical shift coupling (λ ) CS). Applying static perturbation theory up to the second order, the effective Hamiltonians in the Zeeman interaction representation governing the evolution of the I and S spin systems may then be written2-4,34 I I(1) IS(2) IS(2) Heff ) HCS + HDIS(1) + HIS(1) + HQD + HQJ J
(1)
S S(1) Heff ) HQS(1) + HCS + HQS(2)
(2)
where the superscript (i) refers to the perturbation order. In eqs 1 and 2, we have considered that the quadrupolar interaction (λ ) Q) predominates over all other internal couplings (|HQ| >> |Hλ|) and that the D and J interactions are much smaller than the chemical shift anisotropy at the S nucleus (|HSCS| >> |HDIS|, |HIS J |). Indeed, it has long been recognized that the spectra of quadrupolar nuclei are influenced by second-order effects corresponding to HQS(2).28,35,36 The resulting orientation dependent shifts have been analyzed in considerable details by line shape simulation17,36-38 as well as moment description.17,39-41 Moreover, it has been observed that the second-order effects © 1996 American Chemical Society
2046 J. Phys. Chem., Vol. 100, No. 6, 1996
Kempgens et al.
may be transmitted to spectra of spin-1/2 nuclei by the D and J IS(2) IS(2) interactions,42,43 the HQD (HQJ ) cross terms between HQS and IS IS HD (HJ ) being responsible for this phenomenon.23,24,28 In the case of a moderate quadrupole coupling constant, QCC < ν0S, and provided that νr >> DISQCC/ν0S, where ν0S ) ω0S/2π is the resonance or Zeeman frequency of nucleus S and DIS ) (µ0/ 3 ) is the dipolar IS coupling constant, it has 4π)(γIγSh/4π2rIS been shown that the second order effects essentially cause a gradual increase in the J-multiplet splitting but have a negligible contribution to the spinning side band (ssb) intensities.25-27 Hence, the quadrupolar coupling effect may be conveniently introduced as a correction to the line shifts, the ssb intensities being accurately predicted by the first-order perturbation treatIS(2) IS(2) ment.19,44 Ignoring the HQD and HQJ cross terms, eq 1 then reduces to I Heff ) ωCSIz + (ωD + ωJ)IzSz
1 4π(2S + 1) S
×
π
2 CD,J 1 ) 3(1 - 2 cos β) sin 2χ cos Γ +
3(sin2 χ cos 2Γ - 3 cos2 χ + 1) sin β cos β 2 SD,J 1 ) 3(sin 2χ sin Γ cos β - sin χ sin 2Γ sin β)
CD,J 2 ) 3 [sin2 χ cos 2Γ(1 + cos2 β) + (3 cos2 χ - 1) sin2 β] + 2 3 sin 2χ cos Γ sin β cos β 2 SD,J 2 ) -3(sin 2χ sin Γ sin β + sin χ sin 2Γ cos β)
with Γ ) R + ξ. D,J It is seen that the angle ψ is absent from the CD,J n and Sn coefficients due to the axial symmetry of the D and J interactions. Moreover, when the D, J, and CS tensors are coincident (χ ) 0 or 180°) and the CS tensor is axially symmetric (ηICS ) 0), the FN functions are independent of R, so that the powder average over this angle is unnecessary.
( )
-ω2 1 exp 2∆ω2 ∆ωx2π
(10)
is a normalized Gaussian broadening function of standard deviation ∆ω ) 2π∆ν accounting for unresolved dipolar interactions, relaxation effects, etc. The powder averaged shift of the Nth side band corresponding to the m state of the S spin appearing in eq 4 is written
1
2π exp{i[-NΦ + ∫ 0 2π 2
∑ Cnm sin(nΦ) - Snm cos(nΦ)]} dΦ
G(ω) )
(4)
where
FN )
I SCS 2 ) 2ηCS cos β sin 2R
+∞
∫0 ∫0 ∑ ∑ FN*FNG(ω - ωmN) dR sin β dβ m)-S N)-∞ 2π
I I 2 CCS 2 ) (3 + ηCS cos 2R) sin β - 2ηCS cos 2R;
(3)
Under magic angle spinning (MAS) with a frequency νr ) ωr/2π, the orientation dependent frequencies ωλ (λ ) CS, D, J) are periodic functions of time.4,45 Remarking that Iz commutes with IzSz, the NMR MAS spectrum is readily expressed from I as4 Heff
I(ω) )
I CS I CCS 1 ) -(3 + ηCS cos 2R) sin 2β; S1 ) 2ηCS sin β sin 2R
(5)
I + m2πJiso + Nωr + 2π∆m ωmN ) ω0Iσiso
n)1
where19,25-27
with
C1m )
x2 J,D [(ν δI /2)CCS 1 - mD′ISC1 ] 3νr 0I CS
(6)
S1m )
x2 J,D [(ν δI /2)SCS 1 - mD′ISS1 ] 3νr 0I CS
(7)
C2m )
1 J,D [(ν δI /2)CCS 2 - mD′ISC2 ] 6νr 0I CS
(8)
S2m )
1 J,D [(ν δI /2)SCS 2 - mD′ISS2 ] 6νr 0I CS
(9)
∆m )
( )[
]
3CQD S(S + 1) - 3m2 20ν0S S(2S - 1)
(11)
(12)
with
where ν0I ) ω0I/2π and the pseudodipolar coupling constant D′IS is defined as DIS - ∆J/3 with ∆J the anisotropy of the J coupling. The Cλn and Sλn coefficients depend solely on the orientation and the asymmetry parameter ηλ of the interaction tensor λ .46 For simplicity, we have considered in eqs 6-9 that the J tensor is axially symmetric (∆J ) J| - J⊥) and that the principal axes of the J and D tensors are coincident (CDn ) D J J,D CJn ) CJ,D n ; Sn ) Sn ) Sn ; ηJ ) ηD ) 0). If we choose first to transform by the Euler angles (ψ, χ, ξ) the D (and J) tensor from its principal axes system (PAS) into the PAS of the CS tensor of the I spin, which itself is related to the rotor frame by the angles (R, β, γ), the Cλn and Sλn coefficients of eqs 6-9 are written44,46
CQD ) QCCD′IS(3 cos2 θ - 1 - ηQS sin2 θ cos 2φ) (13) Equations 12 and 13 show that the second-order isotropic shift ∆m induced by the quadrupolar S nucleus to the spin-1/2 nucleus I through the D and anisotropic J interactions depends on the polar angles θ and φ, fixing the orientation of the D and J tensors in the PAS of the Q tensor at the S nucleus.25,26 Because the shift of the outermost lines ∆(S appears to be independent of S, the following parameter is also conveniently defined19
∆ ) ∆(S ) -
3CQD 20ν0S
(14)
B. Liquid State. In solution, all possible anisotropic interactions, namely chemical shift anisotropy (CS), dipoledipole interactions (D), quadrupole interaction (Q), etc., are averaged to zero due to the rapid isotropic molecular motion.4,47 Since both the D and Q tensors are traceless, the static part of the internal Hamiltonian in a liquid sample is reduced to the isotropic chemical shift and the scalar spin-spin indirect
Multinuclear NMR Study of HFeCo3(CO)9[P(OCH3)3]3
J. Phys. Chem., Vol. 100, No. 6, 1996 2047
couplings. However, the time-dependent anisotropic part of the interactions leads to relaxation mechanisms which are quantified by relaxation times. In the case of the IS spin system examined above, the relaxation of the quadrupolar nucleus S is in principle due to S both the pseudodipolar (HDIS and HIS J ), quadrupolar (HQ), and S shift anisotropy (HCS) interactions. However, since we have considered that |HQS|, |HSCS| >> |HDIS|, |HIS J |, the pseudodipolar contribution to the relaxation may be neglected. In the extreme narrowing condition with a single correlation time τC, the CS relaxation of the S spin is described by the longitudinal TS1CS and transversal TS2CS relaxation times47
1 S T1CS
)
6 1 3 S ) ω20SCCS τC 7 TS 10
(15)
2CS
1 S 2 S S 2 ) (δCS ) 1 + (ηCS ) CCS 3
[
]
(16)
S and transUnder the same conditions, the longitudinal T1Q S versal T2Q quadrupolar relaxation times are given by47
1 3π2 2S + 3 1 C τ ) ) S S 10 S2(2S - 1) Q C T1Q T2Q
(17)
with the quadrupolar parameter
1 2 CQ ) QCC 1 + (ηQS)2 3
]
(18)
Usually, as a consequence of the predominance of the quadrupolar interaction (|HQS| >> |HSCS|), the experimental relaxation times of the S spin, TS1 and TS2, are completely S , and controlled by the quadrupolar interaction; i.e., TS1 ≈ T1Q S S T2 ≈ T2Q. Hence, provided that the quadrupolar parameter CQ is known, τC may then be directly deduced from eq 17. The NMR line shape of the spin-1/2 nucleus I, which is scalarcoupled to the quadrupolar nucleus S, is also predicted to be strongly affected by the relaxation of the S spin.20,47 Indeed, the usual well-resolved I multiplet can then be changed into a broad or coalesced pattern without any clear multiplet structure. Using the stochastic approach, the NMR line shape of the spin1/ nucleus I is then written47 2
I(ω) ∝ Re[W‚A-1‚1]
∑
Rm,m′
(21)
m′*m
The transition probabilities Rm,m′ depending on the strength of the interactions at the S spin and also on the molecular motion can be expressed as a function of the relaxation times TS2CS and S 21,22 . Remarkably, it has been demonstrated21 and recently T2Q observed22 that interference terms between the quadrupolar and chemical shift interactions lead to differential line broadening, which results in asymmetric line shapes even in the case of a S /TS2CS ≈ 0.01). When the relatively weak CS interaction (T2Q relaxation of the S spin results solely from the fluctuating quadrupolar interactions, i.e., neglecting the Q-CS interference terms, the probabilities of the allowed transitions between the spin states of nucleus S are given by the following expressions:
Rm,m(2 )
with the chemical shift parameter
[
τm-1 )
(19)
where W is a row vector of populations of the 2S + 1 spin states of the S nucleus (all equal to (2S + 1)-1); 1 is a (2S + 1) unit column vector; A is a (2S + 1) × (2S + 1) matrix with elements given by the expression
Am,m′ ) I - ω + m2πJiso) - 1/TI2 - 1/τm]δm,m′ + Rm,m′ [i(ω0Iσiso
(20) δm,m′ is the delta function; 1/πTI2 is the natural line width of any one of the (2S + 1) components of the I multiplet in the absence of relaxation at the S spin; Rm,m′ is the total probability per unit time of transitions occurring between the states m and m' of the S spin; and τm is the average lifetime of the m state of the S spin expressed by
1 (S - m)(S ( m + 1)(S - m - 1)(S ( m + 2) (22) S 2(2S + 3)(2S - 1) T2Q 1 (S - m)(S ( m + 1)(2 m ( 1) S 2(2S + 3)(2S - 1) T2Q
2
Rm,m(1 )
(23)
Generally, the relaxation rate of the I spin (1/TI2) is negligible against the one of the S spin, so that I(ω) will depend S S ) T2Q and Jiso. exclusively on T1Q III. Experimental Section A. Sample Preparation. HFeCo3(CO)9[P(OCH3)3]3 has been synthesized from the tetranuclear mixed metal carbonyl hydride HFeCo3(CO)12 and P(OCH3)3 according to the published procedure.32 X-ray powder diffraction patterns show that the crystal structure is identical to the one previously reported.32 B. NMR Measurements. 31P (I ) 1/2) and 59Co (S ) 7/2) NMR measurements were carried out on Bruker MSL-300 (B0 ) 7.1 T, ν0I ) 121.50 MHz, and ν0S ) 71.21 MHz) and ASX200 (B0 ) 4.7 T, ν0I ) 81.01 MHz, and ν0S ) 47.47 MHz) spectrometers. In the solid state, 59Co static spin-echo, 31P single-pulse MAS, and 13C CP/MAS experiments were performed with high-power proton decoupling during acquisition using a Bruker high-speed CP/MAS probe with cylindrical 4-mm-o.d. zirconia rotors. The selective two-pulse Hahn echo sequence was applied to the fictive spin 1/2 central transition of the 59Co nucleus, as described previously.17 In 31P resonance, nonselective π/2 pulses of ∼2 µs and a relaxation delay of 30 s were used. The liquid state 59Co and 31P single-pulse spectra were recorded on the MSL-300 spectrometer with a standard 5 mm broad-band probe. HFeCo3(CO)9[P(OCH3)3]3 was dissolved in CD2Cl2 or CDCl3. All spectra were broad-band decoupled from protons. 59Co T1 and T2 measurements were performed using the standard inversion-recovery (π-τ-π/2) and Hahn echo (π/2-τ-π-τ) sequences, respectively. At least 12 values of τ for each relaxation experiment were employed. The length of the π/2 pulse was 8 µs, and the recycle delay was 50 ms. T1 and T2 relaxation times were respectively obtained using a three- and two-parameter exponential curve fit of the experimental data. In 31P resonance, the pulse length was 4.5 µs and the recycle delays corresponding to the lowest values preventing from saturation effects ranged from 1 to 15 s between 241.5 and 296 K. This means that the phosphorus T1 relaxation time (TI1) is long and can indeed be neglected in theoretical calculations (section II.B). The temperature was controlled with
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Kempgens et al.
Figure 1. Schematic of the HFeCo3(CO)9[P(OCH3)3]3 cluster.
a Bruker B-VT 1000 unit and calibrated using the difference of chemical shift between the two types of proton of methanol in a capillary tube that has been placed inside the 5 mm NMR tube. Chemical shifts are reported downfield from the external references, i.e., K3[Co(CN)6] saturated in D2O and an aqueous solution of H3PO4 (85%) for 59Co and 31P resonances, respectively. The 31P spectra in both the solid and liquid states were simulated directly in the frequency domain according to eqs 4 and 19, respectively. The NMR parameters were determined by iterative nonlinear least-squares fitting of the experimental line shapes using Powell’s method48 from the numerical recipes package.49 Subsequently, the accuracy of each parameter was obtained by the postoptimal analysis for nonlinear least-squares fitting performed by the subroutine SV02A of the Harwell subroutine library. IV. Results and Discussion A. Solid State. Figure 2 shows the experimental 31P MAS spectra of HFeCo3(CO)9[P(OCH3)3]3 for B0 ) 4.7 and 7.1 T. In both spectra, the 31P-59Co J-coupled octet centered at ∼150 ppm and its associated ssb manifolds are clearly apparent. As described in section II.A, the gradual variation of the multiplet line intensities may be easily explained by the effect of the 31P59Co dipolar and (or) anisotropic J couplings in addition to the chemical shift interaction at the 31P nucleus. However, closer inspection of the center band at B0 ) 7.1 T (Figure 3) demonstrates the presence of an additional peak which is unresolved at lower field (Figure 2a). Since the D and J couplings are independent of the applied magnetic field and the second-order effects increase with decreasing B0 (eq 12), it is concluded that, at least, two nonequivalent crystallographic 31P sites having different isotropic chemical shifts must be considered to describe our NMR data. Indeed, as seen below, the 31P line shape is analyzed by the sum of two distinct resonances having a 2:1 intensity ratio. This fact is in agreement with the 13C CP/MAS spectrum where the methyl resonance is split into a 2:1 doublet (not shown). At first sight, these results are in contradiction with the expected C3V geometry of the molecule (Figure 1). However, it is well-known that the crystal lattice forces may impose a lower molecular symmetry. The solid-state spectrum which is very sensitive to the local molecular environment then exhibits more signals than the corresponding solution-state spectra.9 Note that such a solidstate packing effect has already been observed for 31P bonded to 55Mn and 59Co in similar compounds.19 Indeed, the structure of HFeCo3(CO)9[P(OCH3)3]3 determined by X-ray32 and neutron33 diffraction shows that the crystallographic asymmetric
Figure 2. Experimental and fitted 31P NMR MAS spectra of HFeCo3(CO)9[P(OCH3)3]3 (Table 1) at (a) 4.7 T (νr ) 8.98 kHz) and (b) 7.1 T (νr ) 10.36 kHz): (1) experimental; (2) simulated; (3) difference spectra.
Figure 3. Center band of the 31P NMR MAS spectrum of HFeCo3(CO)9[P(OCH3)3]3 at 7.1 T (νr ) 10.36 kHz).
unit is a complete molecule. Moreover, although the molecule shows near perfect C3V symmetry, a detailed inspection of the crystallographic data reveals that bond angles at the phosphite ligands depart from each others by 5-10°. Such slight distortions of the molecule which are favored by the large ligand size agree with the presence of the nonequivalent signals observed in the 31P and 59Co NMR spectra. Note that this slight departure from perfect C3V symmetry has not been detected by infrared and Mo¨ssbauer spectroscopies.32 Furthermore, it may be inferred from the 2:1 line intensity ratio that the distorted molecule still has approximately a local mirror plane symmetry (Cs). This result is clearly confirmed by the line shape fits of Figure 2 corresponding to the interaction parameters of Table
Multinuclear NMR Study of HFeCo3(CO)9[P(OCH3)3]3
J. Phys. Chem., Vol. 100, No. 6, 1996 2049
TABLE 1: Fitted Interaction Parameters for the 31P NMR MAS Spectra of HFeCo3(CO)9[P(OCH3)3]3 at B0 ) 4.7 and 7.1 T interaction parameter
site 1
site 2
|Jiso| (Hz) I σiso (ppm) I (ppm) δCS I ηCS |D′IS| (Hz) CQD (Hz2) |CQD/D′IS| (MHz) ξ (deg) χ (deg) fraction ∆ν (Hz) at 7.1 T ∆ν (Hz) at 4.7 T
825 ( 1 149.7 ( 0.1 -181.4 ( 1.6 0.15 ( 0.15 951 ( 25 -(2.82 ( 0.10) × 1010 29.7 ( 1.8 0 or 180 ( 5 0.659 ( 0.002 300 ( 5 254 ( 3
832 ( 2 143.8 ( 0.1 -181.0 ( 3.0 0.27 ( 0.08 739 ( 46 -(2.20 ( 0.19) × 1010 29.8 ( 4.5 0 or 180 ( 14 0.341 ( 0.002 270 ( 7 248 ( 5
1, the signal of each site being given by eq 4. Indeed, an excellent agreement between the experimental and calculated line shapes is obtained at both magnetic fields (4.7 and 7.1 T). As mentioned above, the main site population (site 1) is very close to 2/3. Moreover, Figure 2 demonstrates that the system is adequately described by a tightly coupled 31P-59Co spin pair, the unresolved homonuclear 31P-31P and 59Co-59Co interactions being well accounted for by G(ω). Table 1 also shows that a good precision is achieved for all the parameters, except the angle ξ, which is found to be completely undetermined within our precision criteria (Table 1). This is not surprising, since the line shape becomes insensitive to ξ as ηICS tends toward 0. Moreover, within experimental accuracy, it is seen that sites 1 and 2 are only distinguished by their isotropic I . Indeed, the differences observed for |Jiso| chemical shift σiso and |D′IS| are not large enough to be significant. Note that |Jiso| ≈ 830 Hz is found to be larger than in the HFeCo3(CO)11PPh3 and Co4(CO)11PPh3 clusters.19 For both crystallographic sites, the axially symmetric (ηICS ≈ 0) CS tensor, which is characterized by an anisotropy δICS of ca. -181 ppm, appears to be collinear with the 31P-59Co dipole (and J) coupling within experimental error (χ ≈ 0 or 180°). These results, which are reasonable considering the threefold rotation symmetry of the trimethyl phosphite ligand (Figure 1), substantiate the coaxiality and axial symmetry assumptions of the J coupling (see section II.A). The experimental pseudodipolar coupling constant D′IS may then be compared with the dipolar coupling constant DIS corresponding to the internuclear distance deduced from the Co-P bond length measured by X-ray32 and neutron diffraction33 methods. Since the gyromagnetic ratios of the 31P and 59Co nuclei both are positive, calculations based on an internuclear distance rIS of 2.17 Å32,33 give DIS ) 1125 Hz. At this point, it should be noted that only the relative signs of D′IS and Jiso can be determined experimentally: the spectra of Figure 2 show that D′IS and Jiso have the same sign. Indeed, a negative Jiso × D′IS product exchanging the m and -m spin states would inverse the sense of the modulation of the multiplet intensity by the dipolar interaction (eqs 6-9 and 11). Therefore, assuming that the difference between the calculated DIS and experimental |D′IS| values is entirely due to the J coupling anisotropy, we get for sites 1 and 2 (Table 1) (i) ∆J(1) ) 522 ( 75 Hz, ∆J(2) ) 1158 ( 138 Hz if Jiso, D′IS > 0 and (ii) ∆J(1) ) 6228 ( 75 Hz, ∆J(2) ) 5592 ( 138 Hz if Jiso, D′IS < 0. There are only a few reliable data on the anisotropy of indirect spin-spin coupling tensors in the literature.50-53 However, it may be remarked that the relative anisotropy |∆J/ Jiso| has always been observed to be smaller than ∼1. Hence, considering also the fact that the sign of Jiso ) 1J(31P-59Co) is expected to be positive from double-resonance solution-state
Figure 4. Experimental 59Co NMR static spin-echo line shapes of HFeCo3(CO)9[P(OCH3)3]3 at (a) 4.7 T and (b) 7.1 T.
data,54 we may infer that (i) is the most probable solution, i.e., ∆J(1)/Jiso ≈ 0.6 and ∆J(2)/Jiso ≈ 1.4. The root-mean-square (rms) deviation of the simulated relative to the experimental spectra was observed to decrease by a factor 2 when introducing the parameter CQD. Hence, although weak, the second-order quadrupolar effects are found to be significant for both crystallographic sites (Table 1). Indeed, since ∆(1) ) 89 Hz at B0 ) 4.7 T, the second-order line shifts clearly are not negligible. On the other hand, ∆ν is still large enough against ∆ so that the second-order orientationdependent line broadening corresponding to each line of the multiplet may fortunately be neglected.19,25-27 Indeed, since the second-order line shifts are inversely proportional to B0, the IS(2) IS(2) fact that ∆ν is not controlled by HQD and HQJ is confirmed by the slight increase of ∆ν with increasing B0 (Table 1). Since, strictly speaking, the cluster has no elements of symmetry, this increase of ∆ν could mean that the three crystallographic sites might be resolved at higher magnetic fields. We may finally deduce from the 31P NMR line shape analysis the absolute value of the ratio CQD/D′IS, which only depends on QCC and the relative orientation of the D and Q tensors (eq 13). Table 1 shows that |CQD/D′IS| lies very close to 30 MHz for both sites. Since |CQD/ D′IS| e 2|QCC|, it may be inferred that the absolute value of the quadrupole coupling constant at the two cobalt sites is higher than 15 MHz. The experimental 59Co NMR spin-echo spectra of HFeCo3(CO)9[P(OCH3)3]3 at the two available field strengths are reported in Figure 4. As previously observed on analogue compounds,17 the central transition line shape varies with B0, demonstrating that the magnitudes of the second-order quadrupolar and first-order chemical shift interactions are comparable. Hence, both the CS and Q tensors as well as their relative orientation may, in principle, be determined by line shape simulations.17,37,38 Alternatively, these powder spectra exhibit
2050 J. Phys. Chem., Vol. 100, No. 6, 1996
Kempgens et al.
prominent features such as shoulders, steps, or singularities (peaks) corresponding to critical points in the orientationdependent transition frequencies which can be related to the tensorial interaction parameters. Baugher et al.36 have determined the locations of the critical frequencies assuming that the principal axes of the electric field gradient and the shielding tensor are coincident. In this case, for a single resonance, there can be at most two positions for peaks and four positions for shoulders. Extending this approach to noncoincident interaction tensors, Chu and Gerstein37 have shown that a maximum of three peaks may then be observed in the spectrum. Therefore, the presence of four peaks in the experiment at B0 ) 4.7 T (Figure 4a) cannot be explained assuming three equivalent cobalt atoms in the molecule. In accordance with the 31P MAS NMR results, (at least) two 59Co distinct sites must be considered in the unit cell. However, despite considerable efforts, our attempts to match simulated line shapes with the experimental spectra of Figure 4 remained unsuccessful. Indeed, each cobalt site being in principle described by nine parameters,17 finding a good starting guess parameter set for iterative powder pattern fitting was revealed to be a formidable task. A possible solution would be to apply sample reorientation techniques in order to average the CS anisotropy (MAS34 experiments) or both the CS and Q anisotropies (DAS55 or DOR56 experiments). However, these techniques do not permit us to average the strong inhomogeneous and homogeneous broadening leading to the observed line shape breadths of ca. 200 kHz (Figure 4). Indeed, using a MAS synchronized spin-echo experiment with νr ) 15 kHz, we verified that the 59Co spectrum of HFeCo3(CO)9[P(OCH3)3]3 at 7.1 T has no resolved side bands; i.e., the line shape is essentially unaffected by MAS. The spectral resolution is not expected to be significantly improved by the DOR experiment, since external-rotor spinning speeds are limited to ca. 1-1.5 kHz.57 Moreover, the short 59Co spin-lattice relaxation time precludes the use of the DAS technique.57 Note that this problem may nevertheless be solved by the recently developed multiple-quantum transition method.58 Alternatively, as previously shown,17 the relevant interaction S , CQ, and CSCS, may be evaluated from the first parameters, σiso and second moments of the line shapes (M1, MCG 2 ) at two different magnetic field strengths. When this method is applied in the presence of a site distribution, it is readily shown that S and C h Q are then directly derived the averaged parameters σ j iso from the measurement of the first moment M1 at two magnetic field strengths. The average P h of the interaction parameters P(1) and P(2) corresponding to the two inequivalent sites 1 and 2 is simply defined by
P h ) xP(1) + (1 - x)P(2)
(24)
S , CQ, or CSCS. On where x is the fraction of site 1 and P ) σiso the other hand, because the site distribution intrinsically about the center of contributes to the second moment MCG 2 gravity of the line shape, C h SCS cannot be determined. However, it is easily demonstrated that the following relation still holds
S S S S )C h CS + 5x(1 - x)[σiso (1) - σiso (2)]2 ) K h CS CG 5[MCG 2 (ω′0) - M2 (ω′′0)]
+ (ω′0)2 - (ω′′0)2 ω′′0M1(ω′0) - ω′0M1(ω′′0) 115 f(x,CQ) 7 (ω′0)2 - (ω′′0)2
[
with
]
2
(25)
f(x,CQ) ) 1 +
[
]
CQ(1) - CQ(2) 2 30 g1 x(1 - x) 23 C hQ
where M1(ω0) and MCG 2 (ω0) are the first and second moments at the corresponding Larmor frequencies ω′0 and ω′′0. Of course, in the case of a single site (P(1) ) P(2) or x ) 1), we obtain the same result as in ref 17. More interestingly, when two sites are present, it is seen that a lower limit on the chemical h SCS)min, can be obtained from the shift parameter K h SCS, called (K moment analysis by fixing f(x,CQ) to 1 on the right-hand side h SCS, it is remarked that of eq 25. Moreover, since C h SCS e K S S h CS. In fact, this means that K h CS represents an upper limit for C h SCS and, thus, (δSCS)2 (eq 16), if the (K h SCS)min is close to C S distributions of σiso and CQ have weak or similar contributions to MCG 2 . The moment analysis applied to the experimental line S ) -2492 ppm, (C h Q)1/2 ) 17 shapes of Figure 4 then gives σ j iso S 1/2 h Q, eqs 18 and 24, it MHz, and (K h CS)min ) 695 ppm. From C
( )
1/2
2 lies between 14.8 and 17 MHz. may be inferred that QCC Note that this result is consistent with the 31P NMR data showing h SCS)1/2 that |QCC| g 15 MHz. Finally, it is remarked that (K min is in the range of previously reported shift anisotropies in analogue clusters.17 B. Liquid State. The 59Co NMR spectrum consists of a single broad featureless line, as already noted by Saito and Sawada.12 The chemical shift at room temperature, σS ) -2646 ppm, may be compared with the averaged isotropic part of the S ) -2492 ppm. CS tensor determined in the solid state, σ j iso This difference, which is probably due to solvent and solidstate packing effects, is within the range of values previously observed in similar clusters.17 As usual in transition metal NMR,7 σS is temperature dependent and increases linearly by 0.8 ppm/K between 240 and 290 K. The line widths at half height ∆ν1/2 of the corresponding spectra are given in Table 2, along with the experimental TS1 and TS2 relaxation times. (π∆ν1/2)-1, which is found to be equal to TS1 below 260 K, increasingly departs from T1 approaching room temperature. This is not surprising, since additional line broadening must then be caused by scalar J coupling between the 59Co and 31P nuclei (Jiso ≈ 830 Hz). The extreme narrowing condition (T1 ) T2) is verified in the whole studied temperature domain. Moreover, Figure 5 shows that TS1 follows the Arrhenius law with an activation energy for the molecular motion Ea of 11.2 kJ/mol. This fact supports the hypothesis of a single correlation time τC and validates the use of eqs 15 and 17. It also indicates that the relaxation is not influenced by the carbonyl scrambling process which has often been proposed to occur in tetrahedral clusters.59 As already mentioned, the main contributions to relaxation must arise from the quadrupolar and chemical shift interactions, the corresponding relaxation times being given by eqs 15 and 17. It is further remarked that the interaction parameters CSCS and CQ appearing in eqs 15 and 17 may be h Q values respectively approximated by the (K h SCS)min and C determined in the preceding section by line shape moment analysis of the 59Co NMR spectra in the solid state. With these S /TS1CS is estimated assumptions, the dimensionless quantity T1Q -4 to be about 2.5 × 10 so that the chemical shift anisotropy contribution to the 59Co relaxation can effectively be neglected S ). The τC values directly deduced from the experi(TS1 ≈ T1Q mental TS1 data (Figure 5) using eq 17 are reported in Table 2. They are in the range of correlation times expected for small molecules and confirm that, over the studied temperature range, the extreme narrowing condition holds (ω0SτC
