J. Phys. Chem. 1993,97, 12685-12690
12685
Polycrystalline 59C0NMR Studies of Metal-Ligand Interaction in Axially Symmetric Diamagnetic Co(111) Complexes-Correlation of 6( 59C0)with NQCC/A&, S. C. Chung, Jerry C. C. Chan, and Steve C. F. Au-Yeung' Department of Chemistry, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
x. x u The Institute of Solid State Physics. Nanjing University, Nanjing, 21 0008, P.R. China Received: May 13, 1993; In Final Form: September 20, I993e
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The polycrystalline 59C0 N M R spectra (1/2 -1/2 transition) of the diamagnetic cobalt(II1) complexes Na3[Co(NOz)a] and trans-[Co(en)~(NOz)z]NO3 were measured a t 7.1 and 9.5 T. It is demonstrated that for axially symmetric diamagnetic cobalt(II1) complexes the 59C0 chemical shielding anisotropy (CSA) is semiquantitatively correlated (r = 0.998)with the product of the nuclear quadrupole coupling constant (NQCC) and the inverse of the weighted average of the first d - d electronic transition energies (A&,) through the similarity of the d-orbitals population imbalance in the expressions for the CSA and the NQCC. The application of the correlation in the determination of the orbital reduction factor ratio for D4h complexes containing nitrogen ligating atoms is presented.
Introduction
In the Ramsey formulation of chemical shift,' the shielding effect is separated into the diamagnetic and the paramagnetic parts. For metal complexes, it is well establishedz4 that the diamagnetic part is dominated by the core electrons whereas the paramagnetic part results from the motion of the electronsin the valence shells. Therefore, the paramagnetic part is affected by the different degrees of the quenching of orbital angular momentum upon variation of the ligands in the first coordination sphere. For cobalt(II1) and in general for the first-row transition metal complexes whereby the metal nuclei are situated at a site with cubic symmetry (e.g., oh, Td), a linear Freeman-MurrayRichard (FMR) type relationshipz4 has been well established between the metal chemical shift and the inverse first electronic transition energy.3 When the metal nuclei are not situated at a site with cubic symmetry,the principal components(ut,) of thechemical shielding (CS) tensor are not equal. Choosing the gauge origin at the metal nucleus, the paramagnetic shielding is expressed as4
where uXx= uyy, the expressions for the CS tensor are given below.
-
(r-3)sdmL('A1,
'E,) (2)
On the basis of eq 2, Juranie developed a method for the determination of the ratio of the orbital reduction factors k,'/k' (see eq 4 for definition). For D4h (t-coA&) complexes, the required equation is
?( kJ)zhF1(lAl, 8 k' 1 -W'('A1, 24
+
+ ;1i(~k,' ) A E ' - l ( l A l a 'E,) + 1 'E,) + j P E ' ( ' A l , 'A2J +
'E,)
+
+
+
3 2 p t k ' 2(r-3)3d
= 0 (3)
in which the orbital reduction factors (kJ are defined as6
where the symbols have their usual meanings. The summation in eq 1 corresponds to the matrix elements between ground 10) and excited In) states which have energies Eoand E,,,respectively. For diamagneticcobalt(II1) complexes, it has been establishedZJ that the paramagnetic shielding 6&9C0) is dominated by the first excited state transition energy, i.e., n = 1. The principal components of the CS tensor can be obtained by single-crystal NMR measurements or by measurements of the powder spectrum.5 The CS tensor elements in eq 1 are related to the metal-ligand bonding properties such as covalency along thedifferent molecular axes. For diamagneticcobalt(II1)complexes with D4h symmetry, Author to whom correspondence should be addressed. .Abstract published in Advance ACS Abstracts, November 1, 1993.
The derivation of eq 3 involves several assumptions. The first assumption neglects *-bonding in the metal-ligand bond; this assumption leads to the result that kl'and kz'in eq 4 are equal. Second, the factor 3 2 p ~ * k ' ~ ( r ~is) 3assumed d constant provided that the ligators concerned are in the same period. Finally, the electronic transition energies 'AI, 'E8and 'AI, 'A* are
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0022-3654/93/209112685$04.00/0 Q 1993 American Chemical Society
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12686 The Journal of Physical Chemistry, Vol. 97, No. 49, 1993
assumed to be separable and can be measured on the optical spectrum. Thus, the ratio of k,’/k’can be determined from eq 3. In this approach, the S9Co CSA is determined through the anisotropy of the electronic transitions. In short, this method is inapplicable to cases where the energy differences between IAz8 and ‘E, states are too small. It is important to note that the factor 32p~zk’~(r’)3d, which is extracted from the plot of 6(59C0) against AE(lTlg)-l, is difficult to apply when the ligators are from a different period in the periodic table,3c because a welldefined slope is difficult to obtain for these cases. The objective of this paper is to demonstrate and establish that (i) for axially symmetricdiamagneticcobalt(II1) complexes where the equatorial ligands remain unchanged a semiquantitative relationship exists between the 6iso(59C0) and NQCC/M,, and that (ii) the results obtained from the correlation in (i) are applicable to the determination of the ratio of k,’/k’ for cases where the optical transition energies cannot be resolved. This is a commonly occurring situation when the ligators concernedutilize a common donor atom for the formation of the metal-ligand bond.
Chung et al. When the electric field gradient (EFG) tensor and the CS tensor are coincident, only two Euler angles are involved in the calculation. The overall frequency shift is simply the summation of the uCsand wQ. Baugher9 calculated the powder line shape function using this procedure. In this method, the critical points of the pattern are obtained by using the standard method of optimal points calculation. This treatment often produced results containing errors because of the assumption that the two tensors are coincident. If the principal axis systems of the EFG and the CS tensor are not coincident, a complete set of angles relating the two tensors must be used to completely elucidate the system. The NQCC and the CS tensor components must be obtained by computer simulation. Very recently, the calculation of the NMR powder pattern of the quadrupole nucleus has been formulated by several authors.sJ”lz If the Euler angles between the two principal coordinates (CS and Q) are a,0, and y (Edmonds’conventionl3), the C S tensor can be expressed in the principal coordinate of the EFG tensor by the transformation
Experimental Section Synthesis. The trans-dinitrobis(ethylenediamine)cobaltate( 111) nitrate’ was synthesized by a literature method. Potassium cobalticyanide and sodium cobaltinitrite were purchased from Strem Chemicals, U S A . , and were used without further purification. The compounds were characterized by the known UV-vis spectrum as well as solution 59Co N M R chemical shift measurements. Solid-state 59Co NMR Measurement. The static 59C0N M R powder spectra were recorded on Bruker MSL-300 and MSL400 superconducting FT-NMR spectrometers operating at 7 1.21 and 95.5 MHz, respectively. A 10-mm high-powered solenoid broad-band probe was used. N o shimming and lock of the magnetic field were necessary due to the large bandwidths of the peaks. The ECHOCYC and SOLIDCYC sequences were used alternately whenever appropriate at 71.21 MHz, and the QUADECHO sequence was used at 95.5 MHz with quadrature phase cycle. All spectra were recorded at room temperature ( a 2 3 “C). Typical spectral acquisition settings were as follows: 2.5-MHz spectral width, 4000 data points, and 90” pulse width of 3 ps at 71.21 MHz, and 1.66-MHz spectral width, 4000 data points, 90’ pulse width of 3.5 ps, and 0.2-s pulse repetition time at 95.5 MHz. 59Co N M R chemical shifts were referenced to a 1 M K ~ C O ( C Nsolution )~ in D20. UV-vis Spectral Measurements. Solution UV-vis spectra were recorded on a Hitachi U-2000 spectrometer. A quartz cell of 1-cm path length was used. The concentration of solution was kept to a high dilution during the measurements. Reflectance spectra were measured using a Varian Techtron Model-635 UVvis double-beam spectrometer with Bas04 as the solid reference. Computer Simulation. The solid-state N M R spectra were simulated on a Sigma AT-486 personal computer using the program SECQUAD developed by Wasilyshen et aL8 Results and Discussion
Polycrystalline W o NMR StaticSpectra. The powder patterns of Na3[Co(N02)6]and rrans-[C~(en)~(NO~)~]NO~ were measured. When the CSA and the quadrupolar interactions are of comparable magnitude, the analysis of the static N M R pattern is not straightforward. In the presence of strong quadrupolar interaction (NQCC = 10 MHz), the satellite transitions cannot be observed. For nuclei with half-integer spin ( W o I = 7/2), it has been demonstrated that the central transition is not influenced by the first-order quadrupoleperturbation. The central line of the quadrupole nucleus can be treated by the second-order perturbation theorye9 The effect of the chemical shift anisotropy can be determined using the first-order perturbation treatment.
in which pcs is the component of the CS tensor in the spherical basis and DEL, is the second-rank Wigner rotation matrix. The analysis of the powder patterns involves the variation of all eight parameters. They are the C S tensor components 611, 622, and 6 3 3 (6111 622 2 633 following literature conventions), the NQCC, the asymmetry parameter 7,and the three Euler angles (a,0, and y) between the EFG and CS principal coordinates. The initial parameters used for the simulation are often difficult to estimate. Hirschinger12 applied the method of moment to obtain an initial guess of the range of the CS tensor and the EFG tensor components. Another method, which is practically useful for analysis, is the determination of the singular points for a preliminary set of parameters before the simulation is carried out. For the case where the EFG and CS coordinates are coincident, the analytical expression is available. For the case where the two tensors are not coincident, explicit analytical expression cannot be obtained in general.” In this work, the singularity points used for the initial guess were calculated based on the method of Baugher et aL9 The powder patterns of Na3[Co(NOz)b] at 7.1 and 9.5 T are given in Figure 1. The splitting of the peak at 7605 ppm at 7.1 T collapses at 9.5 T. Therefore, this splitting is caused by the quadrupole effect, and the spectrum clearly displays an axially symmetric tensor line shape at 9.5 T. The spectra observed in this work are in good agreement with those observed at five different magnetic field strengths by Eaton et a1.14 Using a 59C0 MASS experiment, they have also confirmed the presence of only one crystallographic site for cobalt. The values of the CSA and NQCC were reported to be 180 ppm and 9.4 MHz, respectively. Therefore, the problem of fitting eight parameters is greatly reduced because seven of the eight parameters are essentially known. These values provide an excellent initial guess for the simulation of the spectra. The NQCC obtained through simulation is 8.2 MHz with 7 = 0, and the origin of the nonzero EFG arises from site symmetry lowering at the cobalt as a result of the combined effects of steric repulsion between nitro groups and crystal packing forces. The NQCC value obtained by simulation is 1.2 MHz smaller compared to the value of 9.4 MHz determined earlier14 using the method of Baugher9 (a difference of =l3%). The CS tensor is determined to be axially symmetric with 611 = 7748 ppm > 622 = bj3 = 7568 ppm. The simulation also reveals that the EFG tensor is coincident with the CS tensor where a, 0, and y were determined to be Oo, 90°, and O”, respectively. The N M R central transition (1/2 --1/2) of S9C0at the two field strengths in trans-[Co(en)2(N02)2]NO3 is shown in Figure
Polycrystalline 59C0NMR Spectra of Co Complexes
20
10
0
-10
The Journal of Physical Chemistry, Vol. 97, No. 49, 1993 12687
-20
I
I
I
I
300
200
100
0
kHz
I
-100
1
1
-200
-300
kHz
Figure 1. 'To experimental (upper spectrum) and simulated (lower spectrum) powder pattern of Na3[Co(NO2)6] at (a) 9.5 T and (b) 7.1
Figure 2. 59C0experimental (upper spectrum) and simulated (lower spectrum) powder pattern of truns-[Co(en)2(N02)2]NO3 at (a) 9.5 T and (b) 7.1 T.
2a,b. The powder patterns show a major doublet at both magnetic fields. The splitting decreases from 26.3 kHz at 7.1 T to 21.1 kHz at 9.5 T. This feature is consistent with the prediction that the quadrupole interaction is dominant over the effect of the CSA. The single-crystal X-ray structure for the complex trans[C0(en)~(NO2)2]N03has been reported.'* The CS tensor components (axx = 6200 ppm,,6 = 6500 ppm, ,a = 6100 ppm) and the NQCC (e2qzzQ/h = 13.22 MHz, 7 = 0.73) were first determined by Spiessand Hartmann using the single-crystalN M R method.I6J7 In the analysis of their results, the two tensors are assumed coincident because of the high symmetry of the complex. Therefore, of the eight parameters involved in the simulation, we had excellent prior knowledge of six of the parameters. These values were used as the initial guess for the simulation, but repeated attempts failed to obtain a reasonable simulation of the experimental spectra. When the assumption of coincidence between the two tensors was removed and the Euler angles were allowed to vary, a fair spectrum was obtained on each of the two field strengths. The best Euler angles obtained from simulation are Oo, 3.5O, and Oo. The chemical shifts obtained from computer simulation of 611, 622, and 633 are 6444, 6144, and 6044 ppm respectively. The slight differences between the airobtained here and those obtained from single-crystal N M R probably arise from either one or both of two factors: (i) the accuracy of the measured frequencies was low since the single-crystal work was carried out at low field, Le., 1.4 T (60 MHz IH), and (ii) the shielding and EFG tensors are assumed coincident in the treatment of the data. Itshouldbenoted that theEuleranglesOO, 3S0,and00 determined here were marginally different from (Oo,Oo,Oo). In other words, Hartmann'sl6 original assumption that the two tensors were coincident was indeed a good one. Its effect probably exemplifies itself because of the small anisotropies for this particular complex. The line widths in the simulated and the experimental spectra are alsoquite different. Although the program SECQUAD provides the line-broadening function, we found that the intensity pattern
TABLE I: Summary of 6,~. NWC, and Euler Angles Na3 [CO(N02)61 trans- [Co(en)2(N02)2]NO3
T.
7748 15 7568 f 15 7568 15 7628 8.2 (9.4)b 0.0
*
lY
OD
B
90'
Y
OD
* *
6444 25 6144 25 6044 25 621 1 13.3 (13.22)c 0.735 (0.73)c 00 3 9 00
The conventions 611,622, and 633 are magnitude based whereas ,6 and 6,, are symmetry based. For the complex trans-[Co(en)z(N02)2]NO3,the single-crystalNMR shieldingtensor has been reported16 (6, = 6200 ppm, 6, = 6500 ppm, 6, = 6100 ppm). Therefore, a direct mapping between ( i = 1 , 2, 3; this work) and ajj, 0' = x, y , z) can be carried out by magnitude comparison. Based on these data, 611 =, ,a 622 = 6,,, and 633 = For axially symmetric system, 6, = ,,S thus 6,, corresponds to 611 for Na3[CO(NO2)6]. b Reference 14. Reference
, , ,a
16.
of the simulated spectrum altered significantly when large line broadening was used. Therefore, the criteria for the correctness of the simulations were judged solely by the fitness of the singularity points and the relative intensity of the peaks. The broadening of the line due to relaxation effects as well as direct and indirect J-coupling to the nitrogen may contribute to the line width and cannot be simulated by the program on hand, Table I summarizes the experimental shielding tensor components and the NQCC values. Correlation of CSA with NQCC/A& in the Solid State. The recent availability of supercomputers has greatly enhanced the development of ab initio calculation on the chemical shielding constants of transition metals. Ab initio molecular orbital calculations of the isotropic shielding constants of M o , ~ ~ -Mn?I ~O
12688 The Journal of Physical Chemistry, Vol. 97, No. 49, 1993
and Zn,22-24 as well as those of Ag, Cd, and Cu have been Despite theavailability of a largechemical shift range of -20 000 ppm which provides excellent sensitivity for the testing of any calculation procedure, no ab initio molecular orbital calculation has been carried out for W o . Since the problem of treating transitionmetals is not a trivialone, semiempiricaltheories are more attractive for the treatment of experimental data. The need for the development of an ab initio molecular orbital calculation scheme on the shielding tensor of 59Co remains essential. Using the parametrized FPT-CNDO/INDO method, Webb25 has shown that the nonlocal paramagnetic shieldingterms are negligibly small for 59Co. This finding provides some justification for theuse of semiempiricaltheories for the treatment and interpretation of S9Coshielding data presented in this paper. The starting point for our discussion of the correlation between A6(S9Co)and NQCC/aEa, is based on the semiempiricalaverage excitation energy method (see the Appendix). (eqs A 1-A3) given in the Appendix can The expressions26~27 be simplified for the case where the d-orbitals do not mix in a single molecular orbital. That is, PWy= 0 for p # u in oh, D4h, and Cb systems, and the ails become
Chung et al. TABLE II: Summarv of Solid-state CSA. NOCC. and AE.
tranr-[Co(en)2C12]C1.HCI'
3100
71.7
18 233c
[CO(NH~)~CN]CI~"J -1500 -26.6 28359'4 tram-[Co(en)2(N02)2]NO3'~ 2 W 13.2' 22 666e [Co(NH3)5OH]Brf
Na3[Co(N0z)61bs
9200 0.99h (0.99)' 700 6211 1.31 (1.08)
233b 13.2' 2060 54.80 205OObJ 180 8.2 22222' 7628 0.91 18of 9.4, -720 -9.3 15389' 12076 800 18.8 19608' 9700
Co(acac)3 d ~ [CO(NH~~CO~IBP Reference 16. This work. Reference 17. Reference 38. e Reference 4. /Reference 14. XSign deduced from Figure 3 and ref 29. Calculated using eq 16. i Calculated using eq 3. Measured in solution. Le., P(xz-y2)- P(z2),eqs 10 and 11 are combined, which allows a correlation to be established between A6(59C0)and NQCC (eq 12):
Assuming the magnitude of qIattis small, the second term in the square bracket of eq 12 can be replaced by an average value. Expressing the transition energiesin wavenumberand the shielding tensor in chemical shift, eq 12 becomes
ai,
e2qzZQ 1
- bll = A-
h
-AEav
where where the abbreviation Pi= P,, is used. The shielding anisotropy is given as
1
UL - QIpz(ll) =j'4x+ u;y - 2U%,,))
For non-U bonding system, Pxy = Pxz = Py,, eq 9 becomes
The orbital population parameters on the right-hand side of eq 1 0 cannot be evaluated explicitly. The calculation of NQCC using the theory of Towns and Daily28~29 is given by eq 11
Y
in which 1
4 = pxy- p,,+ PYJ + PXLY*- p*2 = PXLY2- p,, where R and 7..are the Sternheimer antishielding factors. On the basis of the resemblance of the orbital population imbalance,
and
Equation 13 is tested using the CS tensor, NQCC, and the electronic transition energy data obtained in this work and those previously reportedl6.17 (Table 11). The straight-line plot of CSA versus NQCC/AE,, in Figure 3 supports the assumptions made. The calculation of the value of A in eq 13 required the knowledge of the contribution of the valence electron to the antishielding factor R. This value is generally in the range 0 < R < 1,3O but a range of values is not available for Co3+. The R value, +0.32, for the isoelectronic Fe2+species has been estimated by Watson.31 Assuming this value is applicable to Co(II1) and setting P,, = 2 as well as Q(59Co) = 0.40 X m2, A in eq 13 is calculated to be 6.4 X l e 7 cm-l s. To determine the slope of the graph in Figure 3, point G ([Co(NH3)5CN]Brz) is excluded because the complex contains the "-ligand CN. It is not expected to obey eq 13, which is confirmed experimentally. Therefore,a new analytical expression is needed for *-complexes. Based on data points A to F, the experimental slope is determined to be 8.36 X lO-' cm-I s ( r = 0.998). This approach produces an error of =23% compared to the calculated A value. The intercept (-160 ppm) determined from the plot in Figure 3 supports the assumption that the average lattice contribution is small. The scattering of the data off the correlation line for the rrans-[Co(en)2(N02)2JNOJ most likely
i
PolycrystallineW o NMR Spectra of Co Complexes
3
0
-1.5
The Journal of Physical Chemistry, Vol. 97, No. 49, 1993 12689 sion for the determination of k,'/k'
where
1.5
3.0
4.5
Figure 3. Correlation of b i , - 61 with NQCC/AE,, of s9C0in the solid state: (A) rrunr-[Co(en)2Cl2]Cl.HCI, (B) [Co(NH3)5OH]Br,(C) [Co(NH3)4C03lBr, (D)trunr-[Co(en)2(N02)21NO3, (E)Na3[Co(N0z)6l1 (F) Co(acac)l, and (G) [Co(NH3)sCN]C12.
resulted from the combined experimental errors in the measurements of the solid-state shielding tensor, NQCC, as well as the optical spectrum. Given the large number of approximations used in the derivation of eq 13,the agreement can be considered fair. When the equatorial ligand remains unchanged within a given series, 61in eq 13 remains constant. A linear plot between 6i, and NQCCIAJZ,, produces 61 by extrapolating to the CS axis. A plot of the required solid-state data for trans-[Co(en)2Cl2]CbHCl and trans-[Co(en)2(N02)2]N03 produces a slope of 8.66 X lo"cm-1 sand an intercept of 5795 ppm. The intercept carries a 5% error when compared with the value of bZz(ll)= 6100 ppm determined by Hartmann.'6 These values again support the assumptionsmade earlier because the value of the slope is similar to that of the graph in Figure 3. Appllcrrtioato the Study of Cobalt-Nitrogen Interaction. From eq 2, the average excitation energy A&,. can be expressed in terms of the shielding tensor components as shown in eq 14.Simple algebraic manipulation gives eq 15. U +
3&"
-
2UL = -32~(:(r-~)~~Ma;' (14) 3[(&'+ 3&,')/412 32a,
3[a1/3
+ 3 2 ~ , Z & ' ~ ( r - ~ )ma;'] ,,
= [l
+ 3(&,'/&?12 (15)
The second term in the denominator in the LHS of eq 15 can be transformed into experimentally accessible parameters for the symmetry types treated here. A&,-' is obtained directly from eq 13 whereas 3 2 ~ ( ~ 2 k ' Z ( r 3is) obtained ~ through -ai&?(lA1g+lT1g) for the shielding equation of the corresponding octahedral parent complex of the same series. Substitution into eq 15 followed by rearrangement gives the final expres-
The calculated ratio of the orbital reduction factor k,'/k' for trans-[Co(en)z(NO2)2]N03 is 1.31 (Table 11). It is in fair agreement with thevalueof 1.08 calculated usingpolarizedoptical spectraldata and eq 3. Therefore, thevalidity of eq 16 is checked. The ratio k,'/k'> 1 clearly supports the known chemistry that NO2 is a stronger ligand than ethylenediamine. For Na3[Co(NO&], the determined k,'/k'ratio is 0.91 if 0 4 h symmetry is assumed. This ratio cannot be obtained using the method described by eq 3 since the optical energies cannot be resolved. In addition to packing effects, which often give rise to deviation from cubic symmetry in the solid state, the value 0.91 could also suggest that the ligand field strength of the axial NO2 is weaker than those of the equatorial ones. Two pieces of evidence support this latter suggestion: (i) Contrary to the kinetic inertnesstoward substitution for most diamagnetic cobalt(II1) complexes in aqueous solution, the [ C o ( N 0 ~ ) 6 ]anion ~ undergoes rapid substitutionreaction32 to produce predominantly trans-substituted products. (ii) Steric repulsion was attributed to be the cause of the unusual behavior observed in (i), and the observed ~ ( W O ) for cobalt nitro complexes is consistent with an additiverepulsion model whereby the ligand field strength of NO2 was found to be weakened successively when the number of adjacent NO2 groups increased in the c0mplex.~3Hence, metal-ligand interaction is extremely sensitive to the shielding tensors as revealed through the ratio of the orbital reduction factor. For trans-[ C O ( ~ ~ ) ~ C ~ ~ ] C I . H the C ~calculated . ~ H ~ O ,value of k,'/k' is 0.99. Since the ligand field strength of C1 and ethylenediamine is not comparable, the physical implication of the anomalous value is rationalized in the following way. In the derivationof eq 16 from eq 2,the radial factors of the 3d electrons are assumed not to vary significantlyfrom complex to complex. While this assumption is shown to work properly in systems where the six ligating atoms are from the same period, its limitation is clearly revealed in the result of trans-[C~(en)~Cl~]Cl~HCl. Therefore, it is inferred that in mixed ligand systems the analysis proposed is not valid when the ligating atoms are from different periods in the periodic table.
Conclusion Many correlations between the chemical shift and the NQCC have been Masod7 correctly demonstrated that the 6(14N) is proportional to NQCC(14N)/AEaVfor a series of axially symmetric R-NO compounds. All other authors concluded that the isotropic chemical shift is directly proportional to the NQCC for low-symmetry complexes. For WOand in general for the first-row transition metal complexeswith total symmetry, the isotropic chemical shifts are linearly related to the inverse of the first transition energy (Le., the well-known FMR plot). For an axially symmetric a-bonded metal complex, it is the CSA which is proportionalto the product of NQCC/A&,. It is important to note that the direct proportionalityof the chemical shift and the NQCC is generally incorrect since the orbital imbalancein the chemical shift equation and that in the NQCC equation are not exactly equal. The correlation established here can also be applied to the determination and resolution of axially symmetric tensor components in soiution through the use of relaxation techniques. We have alsodemonstratedthat the S9CoNMR shieldingtensor obtained from polycrystalline powder spectra is a very sensitive
12690 The Journal of Physical Chemistry, Vol. 97, No. 49, 1993
probe for the study of metal-ligand interaction. The use of the shielding tensor serves as an alternative method of obtaining indirect information on the relative difference in the orbital covalency for diamagnetic cobalt(II1) complexes. This is particularly useful when the optical anisotropy cannot be resolved on the optical spectrum and is made possible with the advent of high-powered spectrometers, which have greatly enhanced the ability to determine the experimental shielding tensors to fair accuracy. However, the development of the theoretical aspect of the 59Co shielding calculation has disappointingly lagged far behind that of experimental development.
Acknowledgment. The authors wish to thank Prof. Chaohui Ye of the Wuhan Institute of Physics, The Chinese Academy of Science for the measurement of the solid-state spectra at 400 MHz and The Institute of Solid State Physics of Nanjing University for providing the MSL-300 NMR facility for the measurement of the low-field spectra. This research was supported by a RGC Earmarked Grant (CUHK 85/93E). Also, financial assistance in the form of a traveling grant to S.AuYeung and C. S.Chung from a private donation by Prof. H. N. C. Wong is gratefully acknowledged. Appendix Adopting the so-called Yatom-in-a-molecule”model, eq 1 can be simplifiedby the followingp r o c e d ~ r e : 2(i) ~ *The ~ ~ denominator E, - EOin eq 1 is replaced by an average energy denominator Ma”. (ii) The contribution to up from all orbitals on atoms other than the one being considered as well as the s and p contributions on the cobalt atom is neglected. (iii) The radial factor is averaged over the radial part of the atomic wave functions. Within the LCAO-MO framework, the relevant equation for d-orbitals was given by Jameson and G u t o w ~ k yas~ follows: ~
Chung et al. The orbital population PNyis defined as
a
where na is the number of electrons in the ath filled molecular orbital and ai is the coefficient of the ith d-orbital in the ath MO.
References and Notes (1) Ramsey, N. F. Phys. Rev. 1950, 78, 699-703. (2) Bramley, R.; Brorson, M.; Sargeson, A. M.;SchHffer, C. E. J . Am. Chem. Soc. 1985, 107,2780-2787. (3) (a) Jameson, C. J.; Mason, J. Mulrinuclear N M R Mason, J., Ed.; Plenum: New York, 1987; pp 51-88. (b) Kidd, R. G.; Goodfellow, R. J.
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