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Quadrupolar effects in the CPMAS NMR spectra of spin-12 nuclei
JOURNAL
OF MAGNETIC
RESONANCE
81,20
l-205 (1989)
COMMUNICATIONS Quadrupolar Effects in the CPMAS NMR Spectra of Spin-4 Nuclei ALEJANDRO Department of Chemistry, University ofIllinois
C. OLIVIERI at Urbana-Champaign,
Urbana, Illinois 61801
Received August 10, 1988
Since the early reports on the effect of 14N nuclei on 13CCPMAS NMR lines (l3), considerable effort has been devoted both to the experimental and to the theoretical study of this phenomenon. It has been explained as the result of the existence of a quadrupole coupling constant x = e2Qqz,/ h at the 14Nnuclei which interferes with the ability of the m a g ic-angle spinning (MAS) experiment to suppressdipolar 13C,14N interactions ( 4, 5). Recently, the application of a simple first-order perturbative approach allowed the derivation of an analytical equation for the observed 2: 1 splittings as a function of several parameters, such as (1) m a g n itude and sign of x, (2) asymmetry parameter 7 of the quadrupole tensor, (3) angles @ ’and LYEdefining the orientation of the vector connecting the 13Cand 14N nuclei in the principal axis system (PAS) of the quadrupole interaction, (4) Z e e m a n 14Nfrequency in the applied field ZN = Y~&/2i’r, and (5) dipOlX 13C,14NCOUphg COUStXlt D = yC&+h2( rCN)3 ( 6). This simple procedure has also been used to calculate powder pattern 13Clineshapesaffected by 14Nor 2H ( 7) and to successfully simulate 13CCPMAS spectra of compounds containing several 14Natoms (8). The discovery of similar residual dipolar coupling effects in other pairs of nuclei such as 31P,63@Cu(9) and ’19Sn35,37C1 ( 10, I1 ) merits further investigation on the extension of the perturbation approach to include quadrupolar nuclei with S > 1 as well as scalar coupling interactions. The analysis of the latter caseshas been restricted, so far, to rather qualitative discussions ( I1 ) or to time-consuming accurate calculations involving full 14N Hamiltonian diagonalization and space-partitioning procedures ( 9). In this communication, the previous first-order equations for the 13C,14N case are extended to any 1,s pair (I = f ; S > 1). The results should be applicable as far as the ratio x/Zs is not appreciably larger than 1 [as previously shown, the firstorder treatment provides reasonable accuracy even when the condition x/Zs G 1 is not achieved (6)]. The nomenclature previously used is repeated here, and only the m a in results will be shown (6). For the sake of clarity, however, the following m o d ifications are introduced: the unperturbed Z e e m a n S states are denoted I m) instead of ] ‘Pi) and the Zeeman-quadrupole eigenstatesare labeled I 1c/,,,> instead of I #si), where m is the Z component (along HO) of the angular momentum of the I m ) state from which ] qm) is derived by first-order perturbation. Therefore, I tim) are written as
[II
I1c/?n> = ;: 4mll~).
n=-S 201
0022-2364189 $3.00 Copyright 0 1989 by Academic Press, Inc. All rights of reproduction in any form reserved
202
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If the orientation of the internuclear vector ris in the Zeeman frame is defined by the polar and azimuthal angles Q and 4, respectively, then the frequency shift unI caused by the (II/,) state on the I line is given in this reference frame by vm
=-D(+,I&(l
-3cos2!d-~sinRcosfl(S+e~‘~+S~e’~)~~,j.
PI
Since the term (1 - 3 cos2a) vanishes with MAS, and the operators S+ and Sm.can only connect state ] m) with states I m + 1) and 1m - 1) , it can be shown that, to first order in x/Zs, Eq. [ 21 gives 1
v, = ;D sin Q cos Q[ VS( S + 1) - m( m + 1) (a;,,,, + dS(S+
e? + um,m-le’&)
1) - m(m - l)(aj$,-,e’”
+ um,m-le-ie)].
[3]
In Eq. [ 31, ‘v, is a function of time and must be averaged over one cycle of rotation about the spinning axis. Using the expressions for the coefficients u~,~+* and &m-1 as given by perturbation theory (6)) Eq. [ 31 leads to I v, = (3Dx/4Zs)[S(2Sl)]-‘[S(S+ 1) - 3m2]sin Q cos 8 X[3sin~cosBcos~+17sin6cos6cos(p-~)--sin~costcos(~-~)],
[4]
where the angles 6, t, and 0 are the polar angles made by the x, y, and z principal axes of the quadrupole S tensor with HO, and p and 7 are the azimuthal angles used to define the orientations of the x and y axes in the Zeeman frame, respectively (cf. Fig. 1 in Ref. (6)). As has been shown (6), ‘v, is orientationally dependent and therefore defines a powder pattern. Using the same arguments as in Ref. (6)) the centers of mass of these lines are computed by suitable mathematical manipulation of Eq. [4] followed by spatial averaging. The result is the isotropic shift b, = (3Dx/20Zs)[S(2S-
l)]-‘[S(S+
1) - 3m2] X (3 cos2pD - 1 + n sin2pDcos 2aD)
[5]
showing that the line positions depend on m2 and thus the I +,,) states produce the same shift. Figures la and lb show the effect predicted by Eq. [ 51 when S = 1 and S = 5, respectively. Equation [ 51 can be used to calculate the spectra of spin-f nuclei affected by the presence of quadrupolar nuclei dipolar coupled to them. However, since in some cases there has also been detected a scalar 1,s coupling in the CPMAS spectrum of the I nucleus (9-11), it is worthwhile to extend this simple approach to include the effects of Jis . In its PAS, this interaction is represented by the Hamiltonian (in frequency units) zJ
= J xxxI S x + JyyIySy + J,,I,S,.
PI
If an axially symmetric J tensor is assumed, and the secular approximation is applied to the spin operator I, then Eq. [ 61 becomes (in the Zeeman frame) 2~
= Jidzsz
+ (AJ/3)[3~zqz(S,q)
-
~zXzl>
[71
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COMMUNICATIONS
A ,;,b
A ,Ja “1
“2
“1
h
Jiso
IA-La-L “1
“2
hJiso
C
I
“3
“2
d I
“1 “2
“3
“4
FIG. 1. Schematic representation of the CPMAS spectrum of a spin-f nucleus affected by a quadrupolar nucleus S. In all cases x > 0, oD = p” = 0, 7 = 0, D - A J/ 3 > 0, and Y increases from right to left. (a) S = 1; Jls = 0: v, = (6Dx/ 10Zs); U~=-(~DX/~~Z~);(~)S=~;J,~=O:~,=-~,=(~DX/IOZ~);(C)S = 1; Jls f 0: u, = 1J,,I - $D - AJ/3)(x/Zs); “1 = $0 - AJ/3)(x/Zs); v3 = -I J,,I - &(D - AJ/ 3)(x/Zs);(d)S=i; J~sZO:~l=~lJi,l +d;vz=tlJi,j -d;V3=-flJlsoI -d;uq=-$lJisa/ +d:d
= -&CD- AJ/3)(xlZd.
where Jiw = 4 (J, + Jyy + J,,), A J = J,, - 4 (J, + Jy,,) and qz is the Z component of the unit vector q directed along the z principal axis of the J tensor. It can be appreciated that the first term will be responsible for the multiplet structure observed in the spectra, whereas the second term will give a shift analogous to that previously discussed for the dipolar interaction, D being replaced by - A J/ 3. The complete expression for the shift produced by the ] qm) state of the quadrupolar nucleus is therefore which, upon evaluation to first order in x/Z, and spatial averaging, leads to I = -mJiso + (3x/20Zs)[S(2Sl)]-‘[S(S+ 1) - 3~2’1 urn X[(-AJ/3)(3cos2fl--
1 +~sin2@cos2aJ) + D( 3 cos2pD - 1 + 17sin2@‘cos 2aD)],
[9]
where p” and cyJfix the orientation of the unique z axis of the J tensor in the PAS of the quadrupolar tensor. Figures lc and Id sketch the effect of introducing the 1,s
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indirect coupling. It follows that the effect of the anisotropy in J coupling will be difficult to distinguish from the purely dipolar interaction, unless information is available regarding rIs distance and quadrupole data for the S nucleus. In this case. Eq. [9] can be used not only to account for the appearance of the spectra but also to estimate the relative contributions of D and A J. When S = $, Eq. [ 91 predicts an I spectrum consisting of a distorted quartet (Fig. Id). According to this figure, the distances between the lines will be uI - v2 = 1Ji,, 1 1Jiso ] - 2 d. Therefore, the quantity d can be easily +2d;v2-~3= IJ~~,I;V~-U~= extracted from the spectrum, and its value can be compared with that predicted by the equation d = -(3~/202,)[(-AJ/3)(3cos2@-
~)+D(~cos~~~-
l)],
[lOI
where an axially symmetric quadrupole tensor has been assumed. Two specific examples wiIl be examined. The effect of the i 19Sn,35C1 coupling has been recently noted in the ’19Snhigh-resolution solid-state NMR spectrum of triphenyltin chloride, which shows the superposition of two distorted quartets arising from two crystallographically inequivalent sites (11). If the anisotropic term A J is neglected in Eq. [lo] and the following values are introduced: (1) ] x I = 33.7 MHz ( 12)) (2) 2s = 29.4 MHz ( 35C1Zeeman frequency at 7.05 T), (3) rSnCl= 2.32 A (I.?), (4) /ID = 0 (z axis of the 35C1quadrupole tensor along the Sn-Cl bond), d is estimated as $120 Hz. Since the experimental shift d at 7.05 T is about +80 Hz ( 11)) it appears that the effects of A J should also be taken into account. If this is the case, the use of Eq. [lo] shows that A J should be -350 Hz (with the further assumptions that x < 0 and /3”= 0, and taking into account the negative sign of ysn). A second case deserving attention is the 12 1 MHz 31P spectrum of solid (PPh3)2C~(N03) (9), which has been previously analyzed by computer methods, assuming that the axially symmetric electric field gradient at the Cu nucleus points along the P-Cu bond and neglecting A J effects ( 9). However, as revealed by the Xray diffraction study of this compound ( 14)) the molecule lies on a twofold crystallographic symmetry axis which bisects the P-Cu-P angle. This suggeststhe following likely orientations for the z axis of the Cu quadrupole tensor: ( 1) in the P-Cu-P plane, bisecting the P-Cu-P angle (PD = 65”); (2) perpendicular to this plane (/3n = 90”); and ( 3) perpendicular to the former two directions (@’ = 25”). If 7 is assumed to be zero, using I x ] = 30 MHz (15, 16), 2s = 79.5 MHz for 63Cu at 7.05 T, D = 1120 Hz for a 3’P,63Cu pair at 2.26 ,& ( 24), Eq. [lo] predicts the values of d shown in Table 1, under the assumption that effects of A J can be neglected. Since none of the calculated values of d is in agreement with the experimentally observed value of - 150 Hz (9)) a A J anisotropic contribution should be included in Eq. [lo]. Table 1 presents the magnitudes of A J for each p” orientation for both positive and negative x ( p” = pD is considered). In a recent theoretical report on ‘j3Cu quadrupole interactions in a closely related tetrahedral environment involving phosphine ligands, the z axis was placed as bisecting the P-Cu-P angle ( I 7). This implies /?’ = 65”leading, according to Table 1, to seemingly large A J effects. It may well be that the assignment of the relative orientation of the quadrupolar PAS in these molecular frames needs to be revisited.
205
COMMUNICATIONS TABLE 1 Analysis of the Effect of 3’P,63CuCoupling in the 12 1 MHz “P CPMAS Spectrum of (PPh,)2Cu(NO)) Using Eq. [lo]
x>o PD 25" 65” 90
xc0
da,g” (A@/Hz
d,,l=Ou(A/)b/Hz
-92(-1,710) +29(19,345) +63(10,780)
+92(8,430) -29(-12,625) -63(-4,060)
n d,,=, is the value of d at 7.05 T calculated with Eq. [lo] and assuming A J = 0. b In parentheses are given the values of A J calculated with Eq. [lo] in order to match the theoretical and experimental values of d.
In conclusion, it has been shown that a simple extension of the first-order perturbative treatment can be useful in analyzing the CPMAS spectra of spin-$ nuclei dipolar and scalar coupled to quadrupolar nuclei, provided that data are available concerning the quadrupole interaction, yIs distance, and isotropic Jrs coupling constant. In addition, information about the anisotropy in the 1,s indirect coupling tensor can be obtained. ACKNOWLEDGMENTS A partial fellowship from CONICET (Consejo National de Investigaciones Cientificas y Tecnicas, Argentina) and a postdoctoral research associateship from the University of Illinois are gratefully acknowledged. REFERENCES 1. S. J. OPELLA, M. H. FREY, AND T. A. CROSS, J. Am Chem. Sot. 101,5856 (1979). 2. C. L. GROOMBRIDGE, R. K. HARRIS, K. J. PACKER, B. J. SAY, AND S. F. TANNER, J. Chem. Sot. Chem. Commun., 174(1980). 3. M. H. FREY AND S. J. OPELLA, J. Chem. Sot. Chem. Commun., 474 (1980). 4. N. ZUMBULYADIS, P. M. HENRICHS, AND R. H. YOUNG, J. Chem. Phys. 75,1603 (1981). 5. J. G. HEXEM, M. H. FREY, AND S. J. OPELLA, J. Chem. Phys. 77,3847 (1982). 6. A. C. OLIVIERI, L. FRYDMAN, AND L. E. DIAZ, J. Mugn. Reson. 75,50 (1987 ). 7. A. C. OLIVIERI, L. FRYDMAN, M. GRASSELLI, AND L. E. DIAZ, Mugn. Reson. Chem. 26,615 (1988). 8. A. C. OLIVIERI, L. FRYDMAN, M. GRASSELLI, AND L. E. DIAZ, Magn. Reson. Chem. 26,28 1 (1988). 9. E. M. MENGER AND W. S. VEEMAN, J. Magn. Reson. 44,257 (1982). IO. R. A. KOMOROSKI, R. G. PARKER, AND A. M. MAZANY, J. Mugn. Reson. 73,389 (1987). 11. R. K. HARRIS, .I. Mugn. Reson. 78,389 (1988). 12. P. J. GREEN AND J. D. GRAYBEAL, J. Am. Chem. Sot. 89,4305 (1967). 13. N. T. BOKII, G. N. ZAKHARONA, ANDYU. T. STRUCHKOV, Zh. Strukt. Khim. 11,895 (1970). 14. G. G. M E S S M E RAND G. J. PALENIK, Inorg. Chem. 8,275O (1969). 15. T. OKUDA, M. HIURA, K. YAMADA, AND H. NEGITA, Chem. Lett., 367 (1977). 16. H. NEGITA, M. HIURA, K. YAMADA, AND T. OKUDA, J. Mol. Struct. 58,205 (1980). 17. M. OHSAKU, M. C. BGHM, T. OKUDA, AND H. NEGITA, J. Mol. Struct. THEOCHEM 104, 253 (1983).
OF MAGNETIC
RESONANCE
81,20
l-205 (1989)
COMMUNICATIONS Quadrupolar Effects in the CPMAS NMR Spectra of Spin-4 Nuclei ALEJANDRO Department of Chemistry, University ofIllinois
C. OLIVIERI at Urbana-Champaign,
Urbana, Illinois 61801
Received August 10, 1988
Since the early reports on the effect of 14N nuclei on 13CCPMAS NMR lines (l3), considerable effort has been devoted both to the experimental and to the theoretical study of this phenomenon. It has been explained as the result of the existence of a quadrupole coupling constant x = e2Qqz,/ h at the 14Nnuclei which interferes with the ability of the m a g ic-angle spinning (MAS) experiment to suppressdipolar 13C,14N interactions ( 4, 5). Recently, the application of a simple first-order perturbative approach allowed the derivation of an analytical equation for the observed 2: 1 splittings as a function of several parameters, such as (1) m a g n itude and sign of x, (2) asymmetry parameter 7 of the quadrupole tensor, (3) angles @ ’and LYEdefining the orientation of the vector connecting the 13Cand 14N nuclei in the principal axis system (PAS) of the quadrupole interaction, (4) Z e e m a n 14Nfrequency in the applied field ZN = Y~&/2i’r, and (5) dipOlX 13C,14NCOUphg COUStXlt D = yC&+h2( rCN)3 ( 6). This simple procedure has also been used to calculate powder pattern 13Clineshapesaffected by 14Nor 2H ( 7) and to successfully simulate 13CCPMAS spectra of compounds containing several 14Natoms (8). The discovery of similar residual dipolar coupling effects in other pairs of nuclei such as 31P,63@Cu(9) and ’19Sn35,37C1 ( 10, I1 ) merits further investigation on the extension of the perturbation approach to include quadrupolar nuclei with S > 1 as well as scalar coupling interactions. The analysis of the latter caseshas been restricted, so far, to rather qualitative discussions ( I1 ) or to time-consuming accurate calculations involving full 14N Hamiltonian diagonalization and space-partitioning procedures ( 9). In this communication, the previous first-order equations for the 13C,14N case are extended to any 1,s pair (I = f ; S > 1). The results should be applicable as far as the ratio x/Zs is not appreciably larger than 1 [as previously shown, the firstorder treatment provides reasonable accuracy even when the condition x/Zs G 1 is not achieved (6)]. The nomenclature previously used is repeated here, and only the m a in results will be shown (6). For the sake of clarity, however, the following m o d ifications are introduced: the unperturbed Z e e m a n S states are denoted I m) instead of ] ‘Pi) and the Zeeman-quadrupole eigenstatesare labeled I 1c/,,,> instead of I #si), where m is the Z component (along HO) of the angular momentum of the I m ) state from which ] qm) is derived by first-order perturbation. Therefore, I tim) are written as
[II
I1c/?n> = ;: 4mll~).
n=-S 201
0022-2364189 $3.00 Copyright 0 1989 by Academic Press, Inc. All rights of reproduction in any form reserved
202
COMMUNICATIONS
If the orientation of the internuclear vector ris in the Zeeman frame is defined by the polar and azimuthal angles Q and 4, respectively, then the frequency shift unI caused by the (II/,) state on the I line is given in this reference frame by vm
=-D(+,I&(l
-3cos2!d-~sinRcosfl(S+e~‘~+S~e’~)~~,j.
PI
Since the term (1 - 3 cos2a) vanishes with MAS, and the operators S+ and Sm.can only connect state ] m) with states I m + 1) and 1m - 1) , it can be shown that, to first order in x/Zs, Eq. [ 21 gives 1
v, = ;D sin Q cos Q[ VS( S + 1) - m( m + 1) (a;,,,, + dS(S+
e? + um,m-le’&)
1) - m(m - l)(aj$,-,e’”
+ um,m-le-ie)].
[3]
In Eq. [ 31, ‘v, is a function of time and must be averaged over one cycle of rotation about the spinning axis. Using the expressions for the coefficients u~,~+* and &m-1 as given by perturbation theory (6)) Eq. [ 31 leads to I v, = (3Dx/4Zs)[S(2Sl)]-‘[S(S+ 1) - 3m2]sin Q cos 8 X[3sin~cosBcos~+17sin6cos6cos(p-~)--sin~costcos(~-~)],
[4]
where the angles 6, t, and 0 are the polar angles made by the x, y, and z principal axes of the quadrupole S tensor with HO, and p and 7 are the azimuthal angles used to define the orientations of the x and y axes in the Zeeman frame, respectively (cf. Fig. 1 in Ref. (6)). As has been shown (6), ‘v, is orientationally dependent and therefore defines a powder pattern. Using the same arguments as in Ref. (6)) the centers of mass of these lines are computed by suitable mathematical manipulation of Eq. [4] followed by spatial averaging. The result is the isotropic shift b, = (3Dx/20Zs)[S(2S-
l)]-‘[S(S+
1) - 3m2] X (3 cos2pD - 1 + n sin2pDcos 2aD)
[5]
showing that the line positions depend on m2 and thus the I +,,) states produce the same shift. Figures la and lb show the effect predicted by Eq. [ 51 when S = 1 and S = 5, respectively. Equation [ 51 can be used to calculate the spectra of spin-f nuclei affected by the presence of quadrupolar nuclei dipolar coupled to them. However, since in some cases there has also been detected a scalar 1,s coupling in the CPMAS spectrum of the I nucleus (9-11), it is worthwhile to extend this simple approach to include the effects of Jis . In its PAS, this interaction is represented by the Hamiltonian (in frequency units) zJ
= J xxxI S x + JyyIySy + J,,I,S,.
PI
If an axially symmetric J tensor is assumed, and the secular approximation is applied to the spin operator I, then Eq. [ 61 becomes (in the Zeeman frame) 2~
= Jidzsz
+ (AJ/3)[3~zqz(S,q)
-
~zXzl>
[71
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COMMUNICATIONS
A ,;,b
A ,Ja “1
“2
“1
h
Jiso
IA-La-L “1
“2
hJiso
C
I
“3
“2
d I
“1 “2
“3
“4
FIG. 1. Schematic representation of the CPMAS spectrum of a spin-f nucleus affected by a quadrupolar nucleus S. In all cases x > 0, oD = p” = 0, 7 = 0, D - A J/ 3 > 0, and Y increases from right to left. (a) S = 1; Jls = 0: v, = (6Dx/ 10Zs); U~=-(~DX/~~Z~);(~)S=~;J,~=O:~,=-~,=(~DX/IOZ~);(C)S = 1; Jls f 0: u, = 1J,,I - $D - AJ/3)(x/Zs); “1 = $0 - AJ/3)(x/Zs); v3 = -I J,,I - &(D - AJ/ 3)(x/Zs);(d)S=i; J~sZO:~l=~lJi,l +d;vz=tlJi,j -d;V3=-flJlsoI -d;uq=-$lJisa/ +d:d
= -&CD- AJ/3)(xlZd.
where Jiw = 4 (J, + Jyy + J,,), A J = J,, - 4 (J, + Jy,,) and qz is the Z component of the unit vector q directed along the z principal axis of the J tensor. It can be appreciated that the first term will be responsible for the multiplet structure observed in the spectra, whereas the second term will give a shift analogous to that previously discussed for the dipolar interaction, D being replaced by - A J/ 3. The complete expression for the shift produced by the ] qm) state of the quadrupolar nucleus is therefore which, upon evaluation to first order in x/Z, and spatial averaging, leads to I = -mJiso + (3x/20Zs)[S(2Sl)]-‘[S(S+ 1) - 3~2’1 urn X[(-AJ/3)(3cos2fl--
1 +~sin2@cos2aJ) + D( 3 cos2pD - 1 + 17sin2@‘cos 2aD)],
[9]
where p” and cyJfix the orientation of the unique z axis of the J tensor in the PAS of the quadrupolar tensor. Figures lc and Id sketch the effect of introducing the 1,s
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indirect coupling. It follows that the effect of the anisotropy in J coupling will be difficult to distinguish from the purely dipolar interaction, unless information is available regarding rIs distance and quadrupole data for the S nucleus. In this case. Eq. [9] can be used not only to account for the appearance of the spectra but also to estimate the relative contributions of D and A J. When S = $, Eq. [ 91 predicts an I spectrum consisting of a distorted quartet (Fig. Id). According to this figure, the distances between the lines will be uI - v2 = 1Ji,, 1 1Jiso ] - 2 d. Therefore, the quantity d can be easily +2d;v2-~3= IJ~~,I;V~-U~= extracted from the spectrum, and its value can be compared with that predicted by the equation d = -(3~/202,)[(-AJ/3)(3cos2@-
~)+D(~cos~~~-
l)],
[lOI
where an axially symmetric quadrupole tensor has been assumed. Two specific examples wiIl be examined. The effect of the i 19Sn,35C1 coupling has been recently noted in the ’19Snhigh-resolution solid-state NMR spectrum of triphenyltin chloride, which shows the superposition of two distorted quartets arising from two crystallographically inequivalent sites (11). If the anisotropic term A J is neglected in Eq. [lo] and the following values are introduced: (1) ] x I = 33.7 MHz ( 12)) (2) 2s = 29.4 MHz ( 35C1Zeeman frequency at 7.05 T), (3) rSnCl= 2.32 A (I.?), (4) /ID = 0 (z axis of the 35C1quadrupole tensor along the Sn-Cl bond), d is estimated as $120 Hz. Since the experimental shift d at 7.05 T is about +80 Hz ( 11)) it appears that the effects of A J should also be taken into account. If this is the case, the use of Eq. [lo] shows that A J should be -350 Hz (with the further assumptions that x < 0 and /3”= 0, and taking into account the negative sign of ysn). A second case deserving attention is the 12 1 MHz 31P spectrum of solid (PPh3)2C~(N03) (9), which has been previously analyzed by computer methods, assuming that the axially symmetric electric field gradient at the Cu nucleus points along the P-Cu bond and neglecting A J effects ( 9). However, as revealed by the Xray diffraction study of this compound ( 14)) the molecule lies on a twofold crystallographic symmetry axis which bisects the P-Cu-P angle. This suggeststhe following likely orientations for the z axis of the Cu quadrupole tensor: ( 1) in the P-Cu-P plane, bisecting the P-Cu-P angle (PD = 65”); (2) perpendicular to this plane (/3n = 90”); and ( 3) perpendicular to the former two directions (@’ = 25”). If 7 is assumed to be zero, using I x ] = 30 MHz (15, 16), 2s = 79.5 MHz for 63Cu at 7.05 T, D = 1120 Hz for a 3’P,63Cu pair at 2.26 ,& ( 24), Eq. [lo] predicts the values of d shown in Table 1, under the assumption that effects of A J can be neglected. Since none of the calculated values of d is in agreement with the experimentally observed value of - 150 Hz (9)) a A J anisotropic contribution should be included in Eq. [lo]. Table 1 presents the magnitudes of A J for each p” orientation for both positive and negative x ( p” = pD is considered). In a recent theoretical report on ‘j3Cu quadrupole interactions in a closely related tetrahedral environment involving phosphine ligands, the z axis was placed as bisecting the P-Cu-P angle ( I 7). This implies /?’ = 65”leading, according to Table 1, to seemingly large A J effects. It may well be that the assignment of the relative orientation of the quadrupolar PAS in these molecular frames needs to be revisited.
205
COMMUNICATIONS TABLE 1 Analysis of the Effect of 3’P,63CuCoupling in the 12 1 MHz “P CPMAS Spectrum of (PPh,)2Cu(NO)) Using Eq. [lo]
x>o PD 25" 65” 90
xc0
da,g” (A@/Hz
d,,l=Ou(A/)b/Hz
-92(-1,710) +29(19,345) +63(10,780)
+92(8,430) -29(-12,625) -63(-4,060)
n d,,=, is the value of d at 7.05 T calculated with Eq. [lo] and assuming A J = 0. b In parentheses are given the values of A J calculated with Eq. [lo] in order to match the theoretical and experimental values of d.
In conclusion, it has been shown that a simple extension of the first-order perturbative treatment can be useful in analyzing the CPMAS spectra of spin-$ nuclei dipolar and scalar coupled to quadrupolar nuclei, provided that data are available concerning the quadrupole interaction, yIs distance, and isotropic Jrs coupling constant. In addition, information about the anisotropy in the 1,s indirect coupling tensor can be obtained. ACKNOWLEDGMENTS A partial fellowship from CONICET (Consejo National de Investigaciones Cientificas y Tecnicas, Argentina) and a postdoctoral research associateship from the University of Illinois are gratefully acknowledged. REFERENCES 1. S. J. OPELLA, M. H. FREY, AND T. A. CROSS, J. Am Chem. Sot. 101,5856 (1979). 2. C. L. GROOMBRIDGE, R. K. HARRIS, K. J. PACKER, B. J. SAY, AND S. F. TANNER, J. Chem. Sot. Chem. Commun., 174(1980). 3. M. H. FREY AND S. J. OPELLA, J. Chem. Sot. Chem. Commun., 474 (1980). 4. N. ZUMBULYADIS, P. M. HENRICHS, AND R. H. YOUNG, J. Chem. Phys. 75,1603 (1981). 5. J. G. HEXEM, M. H. FREY, AND S. J. OPELLA, J. Chem. Phys. 77,3847 (1982). 6. A. C. OLIVIERI, L. FRYDMAN, AND L. E. DIAZ, J. Mugn. Reson. 75,50 (1987 ). 7. A. C. OLIVIERI, L. FRYDMAN, M. GRASSELLI, AND L. E. DIAZ, Mugn. Reson. Chem. 26,615 (1988). 8. A. C. OLIVIERI, L. FRYDMAN, M. GRASSELLI, AND L. E. DIAZ, Magn. Reson. Chem. 26,28 1 (1988). 9. E. M. MENGER AND W. S. VEEMAN, J. Magn. Reson. 44,257 (1982). IO. R. A. KOMOROSKI, R. G. PARKER, AND A. M. MAZANY, J. Mugn. Reson. 73,389 (1987). 11. R. K. HARRIS, .I. Mugn. Reson. 78,389 (1988). 12. P. J. GREEN AND J. D. GRAYBEAL, J. Am. Chem. Sot. 89,4305 (1967). 13. N. T. BOKII, G. N. ZAKHARONA, ANDYU. T. STRUCHKOV, Zh. Strukt. Khim. 11,895 (1970). 14. G. G. M E S S M E RAND G. J. PALENIK, Inorg. Chem. 8,275O (1969). 15. T. OKUDA, M. HIURA, K. YAMADA, AND H. NEGITA, Chem. Lett., 367 (1977). 16. H. NEGITA, M. HIURA, K. YAMADA, AND T. OKUDA, J. Mol. Struct. 58,205 (1980). 17. M. OHSAKU, M. C. BGHM, T. OKUDA, AND H. NEGITA, J. Mol. Struct. THEOCHEM 104, 253 (1983).