J. Phys. Chem. 1993,97, 7863-7869
7863
Anisotropic Nuclear Spin Interactions in K2Hg(CN)4: A Multinuclear Solid-state NMR Study Gang Wu and Roderick E. Wasylishen' Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4J3 Received: February 24, 1993; In Final Form: May I I , I993
Several anisotropic nuclear spin interactions in solid potassium tetracyanomercurate(II), K2Hg(CN)4, have been characterized using 13C, ISN, and Ig9HgN M R spectroscopy at 4.70 and 9.40 T. The carbon chemical shielding tensor is axially symmetric, with anisotropy, Au = ull - 61 = 329 f 2 ppm. From the 13C and Ig9Hg N M R spectra obtained with magic-angle spinning (MAS), 1J(199Hg,13C)i,= 1540 f 2 Hz; analysisof the Ig9Hg N M R spectra of a static powder sample indicates that this indirect spin-spin interaction is anisotropic, A1J(Ig9Hg,13C)= 950 f 60 Hz. The first report of 2J(199Hg,14/15N) in the solid state is obtained from an analysis of Ig9HgMAS N M R spectra: 12J(1g9Hg,14N)J= 20.6 f 2.0 H z and IZJ(199Hg,1SN)d= 29.0 f 2.0 Hz. The effective dipolar coupling between Ig9Hg and 14Nnuclei, R,tf = 20.0 Hz, is found to be significantly smaller than the direct dipolar interaction, RDD= 43.0 Hz. This reduction is attributed to anisotropy in the indirect spin-spin coupling; A2J(lg9Hg,14N)= 69 f 15 Hz. Analysis of lSN N M R spectra obtained with slow MAS indicates that the nitrogen chemical shift tensor is axially symmetric, with an anisotropy of 477 f 5 ppm.
Introduction Solid-state NMR techniquesprovide experimentalistswith an opportunityto characterize the orientation dependence of various NMR parameters.1.2 For example, the analysisof the NMR line shape resulting from an isolated spin '12 nucleus in a static powder sample allows one to measure the three principal components of the chemical shift tensor. If the spin 112 nucleus is coupled to an adjacent spin, one can, in principle, also obtain information about the direct dipoldipole coupling and the indirect, electronmediated spin-spin (J) coupling tensors. While information concerning the orientation dependence of carbon and nitrogen chemical shift tensors is available for most important functional groups in numerous compounds, much less is known about the anisotropy of indirect spin-spin tensors involving these nuclei. Recently,it has been demonstrated that several one-bond indirect spin-spin couplings involving mercury and phosphorus and platinum and phosphorus are anisotropic." The implication is that mechanisms other than the commonly accepted Fermi-contact mechanism must be important for these couplings. One of the primary objectives of the present study was to determine whether or not IJ(l*Hg,W) is anisotropic. Solid K2Hg(CN)4 is an ideal compound to investigate for this purpose since diffraction studies7Jindicate that the crystals are cubic; the space group is Fd3m. This places the mercury at the center of the symmetric Hg(CN)42- tetrahedron. The site symmetry at mercury makes solid-state 1WHg NMR studies feasible since the 1*Hg chemical shift anisotropy must be zero for Td symmetry. As well, the Jtensors involving mercury must be axially symmetric; this also simplifies the spectral analysis and the interpretation of the results. Furthermore, extensive 14N nuclear quadrupole resonance (NQR) studies of K'Hg(CN)4 have been carried out providing informationabout the 14Nnuclear quadrupolecoupling constant.gJ0 This information is important in the analysis of 199HgNMR line shapesobtained in magic-anglespinning (MAS) experiments. In the course of this study we also determined the orientation dependence of the 13C and 15N chemical shifts in K'Hg(CN)4. As well, we became aware of a number of subtleties associatedwith analyzing MAS spectra of spin 1 1 2 nuclei that are coupled to quadrupole nuclei. Since many of these have been neglected or misinterpreted in the past, we discuss them in some
* To whom all correspondence should be addressed. 0022-3654/93/2097-7863So4.00/0
detail. Before presenting the results of our study, a brief review of the background theory is provided.
Theoretical Background To describe the NMR spectrum of a spin nucleus (e.g., 13C, l5N, Ig9Hg)in a solid powder sample made up of a collection of crystallites, one must consider the orientation dependence of several nuclear spin interactions. First, the chemical shielding experienced by a particular nucleus in any given crystallite will depend on the orientation of that crystallitein the applied magnetic field, BO. Second, the spin 112 nucleus under observation (the I spin) may be spin-spin coupled to a neighboring nucleus, S, via two different interactions, a direct dipoledipole interaction and an indirect electron mediated spin-spin interaction. The direct dipolar interaction depends on the inversecube of the internuclear separation, rs-', and on the orientation of the internuclear vector in BO. Although indirect spin-spin coupling constants, J(I,S), are often assumed to be scalars (isotropic), they too, in principle, may be anisotropic. In the case of the tetrahedral Hg(CN)42- ion all nuclei lie along C3 axes. Under these conditions the carbon and the nitrogen chemical shift tensors are axially symmetric as are the indirect spin-spin interactions. For such a spin pair, the resonance frequency of the I spin is given by the equation
where
and Jb is the isotropic value of the indirect spin-spin coupling tensor. In these expressions 0 is the angle between any given C3 symmetry axis and BO,u b is the isotropic value of the chemical shieldingtensor, ha is the chemical shielding anisotropy,and & is the effective dipolar coupling constant. These parameters are defined in eqs 2-4 0 1993 American Chemical Society
Wu and Wasylishen
7864 The Journal of Physical Chemistry, Vol. 97, No. 30, 1993
--i
where the direct dipolar coupling constant, R D D , is (h/4r)(ynsh/2a) ( r ~ s -and ~ )theanisotropyin the indirect spinspin coupling is defined as AJ = Jll - JI. The total spin l / 2 NMR powder line shape is obtained by considering all possible angles 6. Each of the 2s 1 transitions (ms = S, 4 + 1, ..., S - 1, S) must be added to give the total I-spin powder spectrum. Equation 1 is only strictly valid for cases where both Z and S spins are spin 1/2 nuclei. If the S spin is quadrupolar (e.g., 14N, S = l), the pure Zeeman states of the quadrupolarnucleus, p,ms), may not be eigenstates of the total Hamiltonian. However, provided the ratio of the quadrupolar to Zeeman energies is small, Olivieri and co-workers11J2have presented a simple first-order perturbation approach which is useful for calculating eigenstates of quadrupolar nuclei. For the Hg(CN)d2-ion, x(14N) = -4.047 MHz9 and VL(I~N) = 14.5 and 29.0 MHz at BO= 4.70 and 9.40 T, respectively, so that x/4v~(’4N)is -6.98 X l e 2 and -3.49 X 1P2.Also, it is important to point out that the electric field gradient (EFG) at 14N in the cubic phase of K2Hg(CN)4 is axially symmetricwith the largest component along the m N bond (the C3 axis). Under these conditions earlier work from our laboratory indicates that the breakdown of the high-field approximation will have a negligible influence on the I3CNMR spectra of static powder samples.13 In contrast, MAS line shapes will be more sensitive to the breakdown of the high-field approximation, and Olivieri‘s first-order perturbation approach11J2must be implemented. This approach will be used to calculate the spin l / 2 MAS line shapes exhibited by the 13C-14N and 199Hg-14N spin pairs of Hg(CN)P.
+
Experimental Section Crystallinesamplesof K2Hg(CN)4 were prepared by dissolving 0.020 mol of KCN and 0.010 mol of Hg(CN)2 in methanol and then evaporating the solvent. A partially 13C enriched sample was also prepared by this procedure, except that a 3:l mixture of KCN and K W N was used. Sizable colorless crystals of l5Nlabeled K z H ~ ( C Nprecipitated )~ from an aqueous solution of Hg(CN)2 (252.0 mg) and an excess of KC15N (420.8 mg). These crystals were removed from the solution and dried. The 15N enrichment of the resultant K2Hg(CN)4 sample was about 70%. Carbon-13 NMR spectra were obtained at 4.70 T on a Bruker MSL 200 NMR spectrometer operating at 50.3 MHz. In both MAS and static experiments, the recycle time was 60 s and 60° pulses were used due to the long 13C spin-lattice relaxation time of solid K2Hg(CN)4. Typical spinning frequencies in the MAS experiments were 2.5-3.5 kHz. Carbon-13 chemical shifts are referenced with respect to TMS using solid adamantane as a secondary reference.14 Nitrogen-15 NMR spectra of a partially 15N enriched sample were recorded at 4.70 T on a Bruker MSL 200 spectrometer operating at 20.3 MHz. A recycle time of 120 s and 60° pulses were used. Spectra were obtained at several sample spinning frequencies in the range 2.0-4.0 kHz. Nitrogen-15 chemical shifts were referenced using solid 15NH4NO3, which has a shift of 23.80 ppm with respect to liquid ammonia at 20 OC. All nitrogen chemical shifts are reported with respect to liquid ammonia. Mercury-199NMRspectra wereobtained at 35.83 MHz (4.70 T) and 71.63 MHz (9.40 T) using Bruker MSL 200 and AMX 400 spectrometers, respectively. A typical sample spinning frequency in the MAS experiment was 3.0 kHz at 4.70 T and 5.0 kHz at 9.40 T. A recycle time of 30 s was used at both fields.
400
350
300
250
200
150
LOO
-2
SO
-3
0
-50
-100
Chemlcal S h i f t lppml
Figure 1. I3C MAS NMR spectrum of KzHg(CN), at 4.70 T. The spinning frequency was 2945 Hz. The isotropic region together with spinning sidebands is shown. The order of the sidebands to high frequency of the isotropic peaks is indicated by positive integers.
Mercury- 199 chemical shifts were referenced to Hg(CH3)z by comparing the observed 199Hg NMR frequency of solid K z H ~ ( C Nwith ) ~ that of Hg(CH3)2, which is 17.910 841 MHz in a magnetic field such that the protons of TMS resonate at exactly 100.0 MHz.15 The 13C“isotropic MAS NMR powder spectrum”wasobtained by adding the intensities of all the spinning sidebands in the MAS NMR spectrum. Carbon-13 MAS NMR spectra were calculated using the first-order perturbationmethod of Olivieri,IlJ2 incorporating the POWDER routine of Alderman, Solum, and Grant.16 Simulations of 199Hg static and MAS NMR spectra were based on a FORTRAN programdeveloped in this laboratory.
Results and Discussion Carbon-13 MAS N M R Spectra. A typical 13C MAS NMR spectrum of K2Hg(CN)4is shown in Figure 1, where the sample spinningrate was 2945 Hz. The isotropic region consists of three asymmetric doublets: the central intense asymmetric doublet is due to 13C nuclei attached to magnetically inactive mercury nuclei while the doublets which flank the central doublet are due to l3C nuclei bonded to 199Hg(I = ‘/2, natural abundance = 16.84%). From separations involving the outer doublets, 1J(199Hg,13C)i, = 1540 & 2 Hz. This coupling constant is much smaller than that found in Hg(CN)2, 3158 Hz.17 This observation is in agreement with qualitative arguments based on the “s-character” of the mercury-carbon bond;l8 however, such simple arguments must be treated with caution (vide infra). Although splittings due to 3lP, 201Hg couplings (201Hg,Z = 3/2, natural abundance = 13.22%) have been recently observed in 31PMAS NMR spectra of mercury phosphine c o m p l e ~ e s no , ~ ~splittings ~ ~ ~ due to 13C, 201Hgcoupling were observed in the 13CMAS NMR spectra of K z H ~ ( C N ) ~The . absence of 201Hgsatellite peaks is attributed to rapid zolHg spin-lattice relaxation (T,(201Hg) 0). Several theoretical treatments of this problem have been developed. Among them, a simple approach based on first-order perturbation theory has been shown to be convenient.*lJ2 However, all theoretical treatments of this problem are based on the assumption that the 13C chemical shift anisotropy (CSA) is negligible or that the fast-spinning limit is satisfied. It has been previously noticed
Anisotropic Nuclear Spin Interactions in K2Hg(CN)4
J 400
U 800
0
L -200
-400
Hz
Figure 2. (a) + 1, (b) 0, and (c) -2 order spinning sidebands, and (d) the sum of all spinning sidebands in the I3C MAS NMR spectrum of KzHg(CN)d; (e) calculated I3C NMR spectrum using R(13C,14N),n= 1.29 Wz, x(14N) = -4.0MHz, u ~ ( l ~ N =)14.4 MHz, and IJ(I3C,l4N) = 5.1 Hz. Note that the plus sign indicates a high-frequency spinning sideband.
that the detailed line shape of the isotropic doublet in the 13C MAS NMR spectrum of NH4SCN cannot be reproduced with the theoretical simulation when several spinning sidebands exist.13 Recently, Sethi et ~ 1 . 3 have 0 shown that it is possible to calculate the detailed spin NMR line shapes of the isotropic and MAS sideband peaks under conditions where the spin '12 nucleus is dipolar coupled to a spin 1 nucleus and the high-field approximation is not strictly valid for the quadrupolar nucleus. They found that the calculated MAS line shapes differ for the different order spinning sidebands. Here we present an experimental example which clearly demonstrates that the MAS line shape changes dramatically for the different order spinning sidebands as predicted by theory. For KzHg(CN)4, the carbon chemical shift anisotropy is quite large (vL - vi > 15 kHz at BO = 4.70 T), and the presence of several spinning sidebands is inevitable at normal spinning rates (see Figure 1). In Figure 2, several of the spinning sidebands are shown on an expanded scale for easy comparison. It is obvious that the MAS line shapes vary for the different order spinning sidebands. The detailed I3C MAS NMR line shapes observed for solid K z H ~ ( C Nresemble )~ those calculated by Sethi et
The Journal of Physical Chemistry, Vol. 97, No. 30, 1993 7865 where it was assumed that the unique components of the spin chemical shift and spin 1 EFG tensors were coincident. Clearly, this assumption is valid for K*Hg(CN)4 where both the carbon chemical shift and nitrogen EFG tensors are axially symmetric with the unique component lying along the linear Hg-C-N bonding axis. As mentioned above, when a large number of spinning sidebands exist, the isotropic part of the MAS NMR spectrum cannot be reproduced by previous NMR line shape calculations. Sincethose line shape calculations are based on averaging over one rotor period, they should be associatedwith the "isotropic MAS NMR powder spectrum", a spectrum obtained by synchronous acquiWhen spinning sidebands are present, it is the sum of all spinning sidebands, rather than the center band, which represents the "isotropic MAS NMR powder spectrum". Therefore, one must compare the sum of all spinning sidebands with the line shape calculated by previous methods such as that based on perturbation theory.llJ2 This is clearly illustrated in Figure 2. While the different order spinning sidebands vary markedly, the sum of all spinningsidebands (Figure 2d) compares well with the MAS line shape calculated using Olivieri's approach.ll.12 In a recent 13C solid-state NMR study of [(n-C3H,)4N] [Cd(SCN)3], the first measurement of IJ(13C,l4N) in a solid sample was reported.32 In the 13C MAS NMR spectrum of K2Hg(CN)4, no splitting due to 1J(14N,13C)was observed at the high-frequency region of the asymmetricdoublet, indicatingthat the coupling is small. In fact, lJ(13C,l4N) is expected to be approximately 5.1 Hz, based on a solution NMR study,33in which a value of 7.2 Hz was reported for lJ(l3C,ISN)in Hg(CN)d2-. One of the standard techniques for determining the principal components of a spin '12 chemical shift tensor in powdered samples is to use an ingenious procedure proposed by Herzfeld and Berger.34 MAS spectra are obtained at two or more spinning frequencies, and the relative intensities of the spinning sidebands are analyzed using a graphical approach. However, for K2Hg(CN)4 this approach is not applicable sincethe 13Cis strongly coupled to 14Nvia the direct dipolar interaction (R = 1.29 kHz, vide infra) which also modulates the spinning sideband intensities. Furthermore, the breakdown of the high-field approximation for 14Nfurther complicates the intensity distribution of the spinning sidebands as previously mentioned. Attempts to use the conventional Herzfeld-Berger approach under these conditions will lead to erroneous conclusions. For example, Nunes et a]. recently indicated that the principal components of the l3C chemical shift tensor obtained in this way for tetracyanoquinodimethane (TCNQ) appear to be dependent on the MAS spinning frequency.35 However, as shown previously,l3 the principal components of the I3C chemical shift tensor can be easily obtained from an analysis of the powder pattern of a static sample. Analysis of the 13C NMR spectrum of a static sample of K2Hg(CN)4 yields an axially symmetric chemical shift tensor: 61 = 262.8 ppm, and 611 = -66.3 ppm. The chemical shift anisotropy, A6 = 61 - 611= 329.1 ppm, compares well with corresponding values found in organicnitriles;s6however, all three principal components of the carbon chemical shift tensor of K2Hg(CN)4 are deshielded relative to those in organic nitriles. The isotropic 13Cchemical shift of K2Hg(CN)4 is approximately 30 ppm greater than the values reported in typical organic nitriles. The carbon CSA observed in K2Hg(CN)4 is also comparable to that found for the low-temperaturephase ( T I 278 K) of NaCN, 3 15 ppm;37 however, each of the principal components appears to be more deshielded by about 20 ppm in NaCN. Carbon-13 CSA data are available for several metal cyanide complexes: K2Pt(CN)4Bro,3.3H20studied by Stoll et al.,3*K2M(CN)4.3H20 (M = Ni, Pd, Pt) studied by Kim and and a mixed copper-zinc cyanide complex, recently reported by Curtis et ~ 1 Again, the 13C CSA obtained in K2Hg(CN)4 is similar to those reported for these metal cyanides.
.
~
Wu and Wasylishen
1866 The Journal of Physical Chemistry, Vol. 97, No. 30, 1993
9.40 T
4.70 T
b a 800
400
0
-400
-800
Hz Figure 3. Experimental (a) and calculated (b) IwHg NMR spectra of a static, partially 13Cenriched powder sample of solid K2Hg(CN)4.
Analysis of the static 13CNMR spectrum of K2Hg(CN)4yields an effective 13C-14N dipolar coupling constant of 1.29 kHz, which implies a C-N bond length of 1.19 A assuming A1J(13C,14N)= 0. The bond distance derived from the analysis of the 13CNMR static spectrum is somewhat longer than that obtained from the neutron diffraction study, 1.16 A.8 As is well-known, the dipolar coupling constant measured in NMR experiments is an effectiue value, Re~.41,42It is clear from eq 4 that any derivation of internuclear distances from the observed Rcfr is based on two assumptions: (1) anisotropy in the J tensor is negligible, and (2) motional averaging is negligible. Since lJ(13C,14N)is only 5.1 Hz, A1J(W,14N) is expected to be negligible;43thus, the smaller value of Rea observed compared with that calculated using m4 . = 1.16 A (RDD= 1.399 kHz) must be attributed to motional averagingof the direct dipolar interaction. Based on the calculated value of RDDand the observed value of Rcn,the reduction of the direct 14N, 13Cdipolar coupling constant due to motional averaging of the CN vector is approximately 8%. Analysis of the '99Hg NMR Spectra of a Static Powder Sample. The 199Hg NMR spectrum of a partially 13C enriched powder sampleof K2Hg(CN)4consistsofa central peakand twosatellites; see Figure 3a. The separation between the two satellites, 1540 Hz, confirms the value of lJ(lg9Hg,l3C)h,which was obtained from the 13C MAS NMR spectrum. The full line width at halfheight of the central peak, 218 Hz, is essentially independent of the applied magnetic field, providing further evidence that the site symmetry at mercury is Td and that the lWHgchemical shift tensor is isotropic. The line width of the central peak is mainly due to thedipolar and Jinteractions with four adjacent 14Nnuclei in the molecule (uide infra). The 1WHg chemical shift of solid K2Hg(CN)4 is -463 ppm with respect to Hg(CH3)z. It is readily seen from Figure 3 that the line widths of the I3C satellites are approximately the same as that of the central lg9Hg NMR peak. Analysis of the static line shape yields the effective dipolar coupling constant between lWHg and l3C nuclei, R('99Hg,13C)cn = 225 f 20 Hz. Note that the lWHg NMR line shapes of the 13Csatellites depend on the relative sign of 'J(lWHg,W) andR(199Hg,13C)ea.MSince thesign of 1J(1wHg,13C) in several organomercury compounds is known to be positive,4our analysis indicates that R(1WHg,13C)cty is positive. The lg9Hg NMR spectrum obtained at 9.40 T was very similar to the spectrum obtained at 4.70 T except that the half-height line width, 288 Hz, was slightly larger than the value at 4.70 T, 218 Hz. The value of R c ~225 , Hz, was also confirmed by fitting the I99Hg NMR spectrum obtained at 9.40 T. Based on the Hg-C bond length of 2.152 A from diffraction studies: the calculated direct dipolar coupling constant, RDD,is 542 Hz. Thus, Refi is approximately 60% less than RDD.Since motional averaging in solid K2Hg(CN)4onlyresults in an 8%reduction inR(14N,13C)DD, the larger reduction of R(lWIg,l3C)dcompared to R(1WHg,l3C)~~ cannot be attributed to motional averaging. Since &n has the same sign as RDD,A1J(lg9Hg,13C)is estimated to be 950 f 60
I 300
I
I
-300
0
I 300
I 0
I -300
Hz
Hz
Figure 4. Experimental (a), calculated (b, c) IwHg MAS NMR spectra. 12J(1wHg,14N)I = 20.6 Hz and d = 1.65 and 0.82 Hz at 4.70 and 9.40 T, respectively. In (b) a Gaussian line broadening of 16 Hz is used. Note that resolution enhancement was applied before Fourier transforming the experimental spectra.
Hz. This value compares well with that obtained for Hg(CHp)z in a liquid crystal solvent, A1J(lWHg,13C)= 864 H Z . ~Since ~ 1J(199Hg,13C)in K*Hg(CN)4 can be assumed '41= 2170 f 60 Hz and lJL= 1220 f 60 Hz, indicating that a stronger electron-nucleus interaction exists when the magnetic field lies parallel to the Hg-C bond as opposed to being perpendicular. Previously, it has been found that 'Jll > lJLfor several other indirect spin-spin coupling tensors such as 1J(199Hg,31P),3--5 13(195Pt?lP)6 and 1J(65Cu,31P).50 Analysis of *-HgMAS N M R Spectra. The 199Hg MAS NMR spectra of solid K2Hg(CN)4 at 4.70 and 9.40 T are shown in Figure 4. Compared with the lg9HgNMR spectrum of a static sample, shown in Figure 3, the line width is reduced to about 100 Hz, and some splittings are clearly visible. As discussed above, an asymmetrical doublet is generally observed in the MAS NMR spectra of spin l / 2 nuclei that are dipolar coupled to a spin 1 nucleus such as 14N. If the Jcoupling between these two nuclei is large enough to be resolved, a triplet pattern with nonequal spacingresults. The two separationswithin the triplet can be written a d 2
IJiJ
+ 3d
and IJJ - 3d
(5)
Here, d is defined as
where Renis the effective dipolar coupling constant between the spin l / 2 and spin 1 nuclei, x is the quadrupolar coupling constant of the spin 1 nuclei, and YL(S) is the Larmor frequency of the spin 1 nuclei. It should be noted that eq 6 is valid only for an axially symmetric EFG tensor at the spin 1 nucleus with the unique component lying along the internuclear vector, as is the case in K2Hg(CN)4. More general expressionscan be found el~ewhere.~' Since the lg9Hg nucleus is adjacent to four equivalent 14N nuclei in KzHg(CN)d, the resultant multiplet is rather complicated; however, one can still analyze these spectra. In Figure 4 the calculated stick spectra and the spectra convoluted with a Gaussian function of 16 Hz are shown. The best fit of the 1WHg MAS spectra yields 12J.,(199Hg,14N)( = 20.6 f 2.0 Hz; d = 1.65 f 0.4 and 0.82 f 0.4 Hz at 4.70 and 9.40 T, respectively. It is known that the resultant pattern is independent of the signs of Jim and 4~but is sensitive to the sign of x.51952 The positive sign obtained ford indicates that x( 14N)is negative. Negative values for x(14N) have been reported for other compounds containing the cyano group.32~53
Anisotropic Nuclear Spin Interactions in K z H ~ ( C N ) ~
i\
C
2.L
b
400
200
0
-200
Hz Figure 5. Calculated lWHgMAS NMR spectra as a function of d (a) 1.20, (b) 1.60, (c) 2.00, (d) 2.40, and (e) 2.80 Hz. In all cases, 12J(199H,14N)1 = 20.6 Hz.
Based on the Hg-N separation obtained from the neutron diffraction study? 3.312 A, and the 14N quadrupole coupling constant, -4.047 MHz, obtained from NQR measurements: d was calcualted to be 3.55 Hz at 4.70 T using eq 6. This calculated value of d is significantly larger than the observed value of 1.65 Hz. Similar discrepanciesare also evident from the data at 9.40 T where the calculated and observed d values are 1.78 and 0.82 Hz, respectively. From the value of d, the effective dipolar coupling constant, Rem is determined to be 20.0 Hz, which is significantlysmaller than the calculated value for the direct dipolar coupling between lg9Hgand 14Nnuclei, RDD= 43.0 Hz. It should be emphasized that the MAS multiplet simulation is sensitive to small variations in d. To illustrate the sensitivity of the 1WHg MAS multiplet to d, several calculated spectra are shown in Figure 5 , in which d varies from 1.20 to 2.80 Hz in steps of 0.40 Hz. Clearly a change in d, even as small as 0.40 Hz, can cause noticeable variation in the lg9HgMAS multiplet. This can be rationalized by noting that any change in d is first amplified by a factor of 3 (see eq 5 ) and then further enhanced by a factor of 4 because of the presence of four equivalent 14N nuclei. As we have already established from our analysis of the static lg9HgNMR spectrumof 13Clabeled K2Hg(CN)4, thesmallvalue of R(lggHg,l3C),m relative to R( l g 9 H g , l 3 C )implies ~~ that u(lg9Hg,l3C)is nonzero. Similarly, the observation of a significantly smaller Ree between 199Hg and l4N nuclei suggests that 2J(1WHg,14N) is also anisotropic. Several other possible factors that could be responsible for the reduction in R(199Hg,14N)en were considered. Motional Averaging. Because lg9Hgis at the center of the Hg(CN)4 tetrahedron and is relatively far from the terminal nitrogen atoms, RDI,is not very sensitiveto the motional averaging of the cyano group. This can be appreciated if one considers a
The Journal of Physical Chemistry, Vol. 97, No. 30, 1993 7867 plot of RDDas a function of internuclear separation. Since RDD a l/r3, the sensitivity of RDDto variations in r is attenuated at long internuclear separations. At r = 3.312 A, a displacement of 0.20 A, which is unreasonably large, causes only an 18% reduction in RDD.As we have indicated above, the C-N separation derived from our 13C NMR study, which is a measure of a motionally averaged C-N distance, differs from the neutron diffraction result by only 0.03 A. The neutron diffraction study of K2Hg(CN)4 indicated that the crystal structure is relatively independent of temperature, suggesting rather rigid Hg(CN)4 tetrahedra.8 An inelastic neutron scattering has shown that librational motion (rotation) of the Hg(CN)4 about [ 1 111 is associated with theobservedphasetransition at 111K. However, this motion cannot provide an explanation for the observed reduction of d, because (a) the librational amplitude is small (=2S0 at 298 K) and (b) this librational motion would also affect the 13C-14N dipolar coupling. Validity of Eqs 5 and 6. Since eqs 5 and 6 are based on a first-order perturbation approach, it is important to estimate corrections due to higher-order perturbationterms. As is known,l2 second-orderperturbation terms do not affect isotropic positions of the MAS line shapes and so d is constant to (x/v~("N))3.In the present case, the ratio x / v ~ ( l ~ N equals ) 0.28 and 0.14 at 4.70 and 9.40 T, respectively. Therefore, high-order corrections to d will be less than 2%. If higher-order terms were operative, one would expect a better fit for the spectrum obtained at the higher field, 9.40 T. In contrast, we are able to reproduce both spectra using the sameset of parameters, indicatingthat high-order terms are indeed negligible. It then seems impossible to rationalize the observed reduction in d without introducing a sizable anisotropy in *J('*Hg,14N). Based on the calculated and observed d values, A2J(lWHg,l4N) = 69 f 15 Hz, assuming that %m has the same sign as RDD.The error of f15 Hz was estimated assuming that the uncertainty in d is 0.4 Hz. From the ratio of +N)/7(14N), AV(1WHg,15N) is expected to be -97 f 20 Hz. Since the magnitude of A2J(lg9Hg,14N)is greater than the corresponding isotropic value, 2J(l99H,l4N)im,it is possible that 2Jll and VI may have opposite signs. To date, there have been few reportsof AzJin the literature. For acetonitrile, Diehl et al.55reported A2J(13C,15N)= -16 Hz. In a more recent and extensive study of acetonitrile in several liquid crystal solvents, a value of -18 Hz was obtained for A2J(13C,15N).56 This value can be compared with the results of a molecular orbital calculation, -8 Hz.43 Although the agreement is only qualitative, it is probably significant that the calculations indicated that the anisotropy in 2J(13C,15N) is dominated by the cross term between the Fermi contact and spin-dipolar interactions.43 Since reliable MO calculations involving heavy atoms such as mercury are still difficult, a complete understanding of indirect spin-spin interaction requires much more effort from both theoreticians and experimentalists. Nevertheless,the large anisotropy observed in 2J(199Hg,14J5N) implies that non-Fermi contact terms are important in transmitting nuclear spin information via electrons. In two recent solid-state NMR studies, AJ values have been reported in phosphinecopper(1) complexes50 and hexachl~roplatinates~~ by analyzing quadrupole-perturbed MAS spectra of 31Pand Ig5Ptnuclei, respectively. Mercury199 MAS experiments were also carried out on a 70% l5N enriched sample of KzHg(CN), at 4.70 T; a typical spectrum is shown in Figure 6a. For this particular sample it is easy to show that the probability of a lg9Hgnucleus being bonded to four, three, two, one, and zero Cl5N groups is 0.2401,0.4116, 0.2646,0.0756, and 0.0081, respectively. The l*Hg MAS line shape has been calculated using these relative populations (see Figure6b). The parametersused tocalculate thespectrumshown in Figure 6b are I2J(lWHg,lsN)kl = 29.0 Hz, 12J(1*Hg,14N)J = 20.6 Hz, and d = 1.65 Hz at 4.70 T. The agreement between
Wu and Wasylishen
7868 The Journal of Physical Chemistry, Vol. 97, No. 30,19'93
n
TABLE I: Calculated Direct Dipolar (RDD),Observed and Indirect Spin-Spin (J) Effective Direct Dipolar (h), Interactions in Solid K2HdCN)P
l3C, I4N 1399 1290h 50 199Hg, 542 22% 20 199Hg,I4N 43.0 20f5 199Hg,I5N -60.3 -28f 5 a All parameters are in Hz.
*
1540 2 20.6k2.0 29.0 f 2.0
*
950 50 69* 15 -97 f 15
TABLE 11: Chemical Shift Parameters46 Obtained for Solid K2He(CNh nucleus 6iW 61 611 A6 = 6 1 - 611 1 3 c
200
100
0
-100
-200
Hz Figure6. (a) Experimentaland (b) calculated 199HgMAS NMR spectra of a partially I5Nenriched K2Hg(CN)4 at 4.70 T. Parameters used in the simulationare IzJ(199Hg,14N)I = 20.6Hz, 12J(199Hg,15N)I= 29.0 Hz, and d = 1.65 Hz. A Gaussian line broadening of 16 Hz is used in (b).
observed and calculated spectra is good. The ratio of I2J(199Hg,lsN)d to12J(199Hg,l4N)hl, 1.41,agreeswellwith theratio of l7(lsN)/7(l4N)1 = 1.403. This further confirms the results obtained from the analysis of 199HgMAS NMR spectra of an unenriched sample. To the best of our knowledge, the observations reported here represent the first report of 2J(199Hg,14JsN)in a solid sample. The only values of 2J(199Hg,I4N) available in the literature have been obtained for organomercury fulminates, RHgCNO (R = Me, Ph, CNO), in DMSO and THF solutions.58 It is noted that the value of 2J(199Hg,14N)for K2Hg(CN)4 is significantly smaller than the values reported for the mercury fulminates, 89-260 H Z . ~ ~ *5NMAS NMR Spectra. Nitrogen- 15 MAS NMR spectra of K2Hg(CN)4 were also obtained using the partially lSNenriched sample (=70%). The isotropic peak, centered at 280.9 ppm, was flanked by several spinning sidebands when the magic-angle spinning frequency was in the range 2.0-4.0 kHz. Using the Herzfeld-Berger method, the principal components of the nitrogen chemical shift tensor can be recovered from the relative intensities of the spinning sidebands. Assuming that the nitrogen chemical shift tensor is axially symmetric, analysis yields 61 = 440 ppm and 611 = -37 ppm. The chemical shift anisotropy, 477 ppm, is about 70 ppm larger than typical values reported for organic nitriles.36 The isotropic I5N chemical shift of the cyano group in K2Hg(CN)4 is approximately 30 ppm to high frequency (deshielding) of the values in organic nitriles. Comparing the principal components of the l5N chemical shift tensor of K2Hg(CN)4 with those of the organic nitriles reveals that this highfrequency shift is mainly due to changes in the 61 components. The principal components of the nitrogen chemical shift tensor in KzHg(CN)4 were found to be comparable to those in NaCl5N, the anisotropy being approximately 460 ppm in the latter ~ a l t . 5 ~ Nitrogen-15 MAS NMR spectra of KzHg(CN)4 at higher spinning frequencies were also recorded. The natural half-height line width of the 15N isotropic peak and the MAS sidebands (ca. 40 Hz) precluded resolution of 199Hgsatellites; however the base of each peak was broadened due to 199Hg,I5N indirect spin-spin coupling.
Conclusions Nuclear spin-spin &upling data and chemical shift parameters obtained for solid K2Hg(CN)4 are summarized in Tables I and 11, respectively. The results indicate that the indirect spin-spin interactions involving mercury are anisotropic. The magnitude of A15(199Hg,13C) in solid K2Hg(CN)4 is comparable to the value reported for dimethylmercury. Although values of A I J from the
153.1
262.8
-66.3
329.1
15N 440 -37 477 280.9 199Hg 463 -463 -463 oc All values are in ppm. 611 and 61 are the chemical shifts when the applied magnetic field is parallel and perpendicular, respectively, to the C3 axis along the Hg-mN direction. Required by the sitesymmetry. liquid crystal solvent NMR studies are often treated with skepticism, the results obtained for A1J(199Hg,13C)in dimethylmercury agree with the qualitative conclusion obtained in the present study (Le., 1J('99Hg,13C)is anisotropic). Since the Fermicontact mechanism leads to an isotropic coupling tensor, the observation of an anisotropic indirect spin-spin coupling tensor implies that other mechanisms must be operative.18,60 The implication is that it is dangerous to simply relate the magnitude of 1J(199Hg,13C)to the percent "s-character" of the mercurycarbon bond since such relationships assume that only the "isotropic" Fermi-contact mechanism is operative.ls.60 In addition, our experiments show that it is possible to measure extremely "small" indirect spin-spin couplings involving quadrupole nuclei in the solid state. Such measurements are not feasible in solution due to the efficiency of the quadrupolar relaxation mechanism.61 The carbon and nitrogen shift tensors reported here for the cyano group are similar to those reported for the cyano moiety in other metal cyanides and a variety of organic nitriles. The implication is that electronic energy levels responsible for the nuclear magnetic shielding characteristics of the cyano group are not significantly altered when the cyano group is bonded to different groups. Finally, the I3C MAS NMR spectra of K z H ~ ( C Nnicely )~ demonstrate some of the subtleties associated with analyzing l3C spectra of the I3C-l4N spin pair. In principle, similar multinuclear solid-state NMR studies as reported here are applicable to other metal cyanide complexes. Further investigations are in progress in our laboratory.
Acknowledgment. We thank Mr. Ken Wright for preparing a sample of KzHg(CN)4 and Dr. Klaus Eichele for developing a computer program which was used to calculate the 199Hg MAS NMR spectra reported in this work. We are also grateful to Professor T. S. Cameron and Dr. B. M. Borecka for helpful discussions concerning the crystal structure of K2Hg(CN)4. This work was financially supported by the Natural Sciences and Engineering Research Council of Canada. References and Notes (1) Mehring, M. Principles of High Resolurion NMR in Solids, 2nd 4.; Springer-Verlag: Berlin, 1983. (2) Fyfe, C. A. Solid Stare NMR for Chemists, CFC Press: Guelph, Ontario, Canada, 1983. (3) Penner, G. H.;Power, W. P.; Wasylishen, R. E. Can.J . Chem. 1988, 66,1821. (4) Power, W. P.; Lumsden, M. D.; Wasylishen, R. E. J. Am. Chem.Soc. 1992. 113. 8257. (S) Power, W. P.; Lumsden, M. D.; Wasylishen, R. E. Inorg. Chem. 1991, 30, 2991.
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