910
N. F. Albanese and N. D. Chasteen
The Journal of Physical Chemistty, Vol. 82, No. 8, 1978
Origin of the Electron Paramagnetic Resonance Line Widths in Frozen Solutions of the Oxovanadium(1V) Ion Nlna F. Albanese and N. Dennls Chasteen" Department of Chemistry, Universi@ of New Hampshire, Durham, New Hampshire 03824 (Recelved November 23, 1977) Publication costs assisted by the National Institute of General Medical Sciences Grant GM 20 194-05
Comparison of experimental and simulated EPR line widths of V02+ indicates that unresolved electron-proton superhyperfine structure is a major source of line width in acidic and basic frozen solutions. For VO(HzO)s2t, the anisotropic dipolar electron-proton interaction is approximated by a point-dipolemodel in which the unpaired electron interacts with the protons or deuterons of four water molecules coordinated equatorially and one water molecule coordinated axially. Details of the calculation are discussed.
Introduction Vanadium(1V)in acidic and basic aqueous soldion has been the subject of several EPR line width studies above 0 "C. At room temperature, the dominant contribution to the line width is due tsmotional averaging of vanadium nuclear hyperfine and g tensors. The dependence of electron relaxation on nuclear orientation was first described by McConnell,' and leads to the well-known dependence of line width on the z component of the nuclear spin moment, MI.At high temperatures, a second contribution arises from the interaction of the rotational and spin magnetic moments, and was first treated by Kivelson.2 The spin-rotation contribution to line widths increases where T is the absolute temperature and q is the with T/q, viscosity. That part of the line width that cannot be explained by either of the above mechanisms is called the residual line width. For aquo vanadyl(1V)ion in acidic solution at ambient temperature, the residual line width has been variably reported as 2.8,3 2.85: and 3.3G.5 This residual line width has almost no temperature dependence and was originally attributed to unresolved isotropic proton hyperfine coupling. More recently, the major part of the residual line width has been attributed to a temperature-independent spin-rotation interactions6Residual line widths corrected for this contribution are 0.9 and 0.5 G in H20 and DzO, respectively, leading to an average contribution from proton hyperfine structure on the order of only 0.4 G. This is consistent with the isotropic coupling constant of 1.1 G obtained by Reuben and Fiat7 from deuterium NMR contact shift measurements. A corrected residual line width of 6.5 G was found for V02+ in basic solution6 which can be expected for the average isotropic coupling constant of 4.4 G for protons in VO(OH)3(Hz0)2-.8 At liquid nitrogen temperature (77 K) the spin-rotation contribution to EPR line widths is removed and an additional contribution from dipole-dipole interactions is expected. In low viscosity liquids the dipolar interaction is averaged to zero by molecular tumbling. Although numerous line width studies have been done on vanadyl solutions above 0 "C, the frozen solution spectrum has never been examined. A study of the line widths in frozen solution was prompted in part by the observation in our laboratory that vanadyl chelates and protein complexes with nitrogen ligands or coordinated water molecules exhibited somewhat broader EPR lines than complexes lacking these ligands. This raised the possibility that an analysis of the line widths of frozen solutions could provide information about the number of nitrogen or water ligands giving rise to unresolved superhyperfine structure and broadened lines in the EPR spectrum. In this paper, the
residual line width in frozen solution EPR spectra of the vanadyl ion in acidic and basic media is described.
Experimental Section Concentrated stock solutions of VOSOl (Aldrich) were prepared in HzO (distilled, deionized) and DzO (J. T. Baker, 99.75 atom % D). Acidic solution samples were 0.1 M in HC1 or DC1 and nominally 3 X M in V02+. Samples contained 50% glycerin (by volume). Deuterated glycerin was prepared by mixing equal volumes of glycerin and DzO, followed by evaporation of water from the mixture under vacuum. Approximately 99 % exchange, as measured by proton NMR spectroscopy, was achieved by repeating this procedure three times. Final samples were about 94% in deuterium due to exchange with atmospheric H 2 0 during brief exposure of the highly hygroscopic glycerin to air. Basic solution samples were 0.2 M in NaOH or NaOD (pH ~ 1 2and ) nominally 3 X M in V02+. Addition of vanadyl sulfate under positive N2 pressure with rapid stirring and in the presence of excess base prevented formation of the gray precipitate which is probably VO(OH)z.9 All solutions were flushed with nitrogen to remove dissolved O2 and transferred between serumstoppered vessels with Hamilton microsyringes. EPR spectra were recorded at liquid nitrogen temperature (77 K) using a Varian E-4 spectrometer operating at X-band frequency (9.5 GHz) with 100 kHz magnetic field modulation. Care was taken to avoid line broadening due to overmodulation and power saturation. EPR parameters were determined using a DPPH (diphenylpicrylhydrazyl) marker (g = 2.0036) taped to the liquid nitrogen dewar insert. The magnetic field was calibrated with a proton nuclear magnetic resonance gaussmeter. Simulated powder spectra were calculated using a Fortran program for S = 1/2 systemslOmodified to include four different hyperfine interactions. First- and second-order perturbation theory are used for the ligand and metal nuclear hyperfine interactions, respectively. An intensity weighting feature placed equivalent nuclei under one spin value, and a three-point, Gauss-point method is used to integrate over all possible orientations. Calculations employed a DEC-10 computer and Calcomp plotter. Other details concerning the simulation are discussed further below. Line widths were measured directly from experimental and simulated spectra on an expanded scale (1 cm = 1 G). The full width at half-height for parallel lines found in the wings and the width between first derivative extrema for perpendicular lines are reported. Experimental line widths are the average of three spectral scans for five different
0022-3654/78/2082-0910$01.00100 1978 American Chemical Society
EPR Study of Oxovanadium(1V) Ion Frozen Solutions
The Journal of Physical Chemistry, Vol. 82, No.
8, 1978 9 11
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l
;
I
,
,
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8
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,
12
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16
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, 24
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, 28
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,I 32
[vo~.]( ~ 1 0 - 4 ~ ) Figure 2. Line width dependence on [V02+], MI= 3/2 perpendlcular , (O), and in H,O-glycerine mixture (A). line in HO , (0)in DO
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MAGNETIC FIELD (GAUSS)
Flgure 1. (A) Experimental H,O, (B) experimental D,O, and (C)simulated D20frozen solution EFR spectra, pH -2, of VO(H,0),2+. The instrument settings were as follows: time constant, 0.30 s; scan time, 8 min, modulation amplitude, 2.0 G, modulation frequency, 100 kHz; receiver gain, 1.25 X 10'; microwave power, 2 mW. Arrows in B denote forbldden lines.
TABLE I: Frozen Solution EPR Parametersa
VO(H,O),
+
1.933 f 0.001 1.978 f 0.002 182.6 f 0.2 70.7 * 0.1
g Ii g1
Al1(10-~ em-') Al(lO-' cm-) a Corrected for second-ordereffects.
VO(OH),(H,O 121.955i 0.002 1.974 f 0.002 161.7 f 0.2 53.5 f 0.2
samples ( N = 15). Standard deviations were calculated using N - 1 weighting.
Results and Discussion . 1. Concentration Dependence of Line Widths. Frozen solution spectra of V02+ in HzO and DzO at pH -2 are shown in Figure 1A,B. Lines are labeled from low to high field with negative to positive MI values because the vanadium nuclear coupling constant should be negative.ll Experimental EPR parameters listed in Table I are in good agreement with previously published values6 and are identical for VO(HzO),2+and VO(D20)52+. Unlike room temperature solution spectra,6 frozen solution spectra show a marked reduction in line widths in going from HzO to D20. Another striking feature of the D 2 0 spectrum .is the presence ... of forbidden transitions . I" mrrennnnninp A M .= =----.--- tn "- I.*l 1
-----I
~
1
1
+I -A
in .**
..
1.
tnn nnrnonrfimilnr r&nV w " I . " r"Ar"AAU."U'UL & 'i"n Un
of the spectrum (Figure 1B). This feature is distinguished by its absence in the simulated D20 spectrum (Figure IC). Preliminary work revealed several concentration-dependent line broadening effects. VOSOl dissolved in dilute perchloric acid produces a multispecies EPR spectrum with line width dependence on perchlorate concentration. Perchlorate is known to bind to the vanadyl ion.12 In hydrochloric acid, there is a slight dependence of line width on HC1 concentration down to 0.1 M HC1 while below 0.1 M the EPR spectrum loses signal intensity. Multispecies vanadyl ion EPR spectra have been reported for frozen
solutions at very high C1- concentrations due to replacement of H20 by C1- in the first coordination sphere,13 The most pronounced effect is the dependence of line width on vanadyl ion concentration even in dilute solution (Figure 2). In both H 2 0 and D20 in the absence of glycerin, the line width of the MI = -3/2 perpendicular line decreases linearly with decreasing ion concentration. The MI = perpendicular line behaves similarly. Upon freezing, solute aggregation evidently occurs, leading to a nonmagnetically dilute sample. As shown in Figure 2, addition of glycerin removes this concentration depenglycerin prevents nucleation dence. According to and growth of crystals by retarding the rate of diffusion, thus favoring glass formation. No concentration dependence was observed for V02+in basic solution and, accordingly, glycerin was not used with these samples. 2. Calculation of Ligand Superhyperfine Coupling Constants. Ligand superhyperfinecoupling constants arise from both isotropic contact and anisotropic dipolar interactions. The only significant superhyperfine interaction is between proton and electron spin angular momenta involving first coordination sphere water molecules. Since the average electron-proton distance is greater than 2 A, a point-dipole model is a good approximation.ls The dipolar coupling constant is then given by
where y is the angle between the vanadium-proton direction and the applied magnetic field and r is the vanadium-proton distance. The principal values of AD are obtained when y = 0 or 90°. g(6) is given by g(e ) = gil
cos2
e + gL2sin2 e
(2)
where 6 is the angle between the field direction and the symmetry axis of the complex, in this case the V02+bond axis. Terms arising from noncoincidence of g and electron-proton dipolar coupling tensors have been ignored. Second-ordereffects arising from off-diagonal terms in the spin dipolar tensor due to mixing of /PeaN) and states and, deuterium nuclear quadrupole16effects on the EPR spectrum are negligible and have been omitted from our calculations. Total ligand superhyperfinecoupling constants are sums of isotropic and dipolar terms
Ai = A D i + u (3) where i = X,Y, or 2 and a is the isotropic proton coupling constant. Covalent bonding delocalizes unpaired spin density from 3d metal orbitals onto ligand orbitals. In VO(H20),2+
912
N. F. Albanese and N. D. Chasteen
The Journal of Physical Chernistty, Vol. 82, No. 8, 1978
TABLE 11: Proton Superhyperfine Coupling Constantsa Nuclei A,, 1.07b Protons 1, 2, 5, 6 1.07b Protons 3, 4, 7, 8 o.looc Protons 9, 10 a Units of cm-l. Reference 7 .
AD,
ADy
ADZ
-4%
A,
A,
2.47 -1.27
-1.27
-1.27 - 1.27 2.32
3.54
- 0.20
- 0.20 -1.09
3.54 -1.09
- 0.20 -0.20 2.42
-1.10
2.47 - 1.10
Reference 19.
TABLE 111: Frozen Solution EPR Line Widths ( G ) Experimentala Complex A. Aquo
LineC -7/2il - 5 / 2 1I -3/21 +1/21
Simulatedb D2O
H2O 9.86 ?I 8.74 12.30 f 11.61
0.10 0.11 0.08 0.10
* * 17.72 * 0.30
6.04
i
0.07 0.04
4.64 f 6.15 f 0.05 5.06 f 0.05
fJd
3.2 i 0.1 2.4 f 0.1 3.3 0.1 2.5 i 0.1
*
HZ0
D2O
8.5 f 0.1 7.4 f 0.1 13.05 j: 0.1 10.3 f 0.1
6.1 f 0.1 4.6 i 0.1 6.0 0.1 5.1 0.1
* *
B. Trihydroxo -l/2ll 9.27 f 0.15 a Values are averages of three spectral runs on five different samples, 2 one standard deviation. Modulation amplitude = 0.5 G. Uncertainty in reported values reflect the uncertainty in u and the measurement of line widths of the simulated Line widths of parallel lines are half-widths at half-height of absorption curve. Line widths of perpendicular spectra. lines are widths between first derivative extrema. Obtained by fitting simulated D,O to experimental D,O line widths.
equatorial water molecules participate in u bonding through al donor molecular orbitals7J7J9and in T bonding through bl and b2 donor orbitals,7J6while the axial water molecule is involved mainly in u bonding through a1 donor orbitals, where al, bl, and b2 are the irreducible representations of the C4upoint group of VO(H20)52+.Since a1 and b2 molecular orbitals of water contain hydrogen 1s character, covalent bonding through these donor orbitals directly places unpaired spin density on water protons, resulting in positive isotropic coupling constants.'J9 The sign of the dipolar contribution is determined by the (3 cos2 y - 1) term in eq 1. The VO(H20)2+complex is shown in Figure 3A. It was assumed that the vanadium nucleus lies along the bisector of the lone pair orbitals of coordinated water molecules, as in other transition metal hydrates.20 For coordinated water molecules, the average 0-H bond length is 0.987 A and the H-0-H bond angle is 108°.21 Vanadium water oxygen bond lengths were taken from Ballhausen et a1.22 The model shown in Figure 3 assumes that the equatorial water molecules lie in the X-Y plane of the complex (contrary to 0-V-0 bond angles published for crystalline VOS04.5H20)and that the protons of each coordinated water molecule are averaged by rotation around the V-0 bond (Figure 3b). The values of r reported in Figure 3b are the vanadium-averaged proton distances. Since the dipolar tensor has its origin at the proton and is diagonal only if r points along one of the coordinate axes, an x, y, z system was constructed at each averaged proton position. Two sets of equivalent equatorial protons are defined: protons 1, 2, 5, 6 and protons 3, 4, 7, 8. The protons of the axial water molecule constitute the third set of equivalent protons. The calculated coupling constants for H (gN = 5.575486) are listed in Table 11. Values for D can be obtained by multiplying the H values by g,/gH = 0.1538.
Simulations were carried out using the total ligand superhyperfine coupling constants and the following ratios of intensity: 1:4:6:4:1 for each set of equatorial protons, 1:2:1 for axial protons, 1:4:10:16:19:16:10:4:1for each set of equatorial deuterons, and 1:2:3:2:1for axial deuterons, where IH = l/z and ID = 1. These three superhyperfine interactions produce a hyperfine manifold composed of 75 lines for VO(H20),2+and 405 lines for VO(D20)52+.Line width parameters (u, Table IV) were obtained by fitting simulated D20 line widths to experimental D20 line widths. u is defined as the half-width at half-height of the absorption curve. A different line width parameter is used
tZ
AZ
*Z
x ~ I4 9,lo~y Figure 3. Structural model of VO(H,0)52+. (A) Bond lengths (A) and X, Y , Z, molecular axes shown. (B) Average proton-vanadium distances (A) and x, y , z axes shown.
for each line to account for a small line width dependence on MI in frozen solution. These values of u along with the proton superhyperfine coupling constants were then used to simulate the line widths of VO(H20)2+. A Lorentzian line shape function was used, leading to an unresolved packet of Lorentzian lines with a non-Lorentzian line shape. 3. Comparison of Experimental and Simulated Line Widths. Experimental and simulated line widths of the M I = -7/2, - 5 / 2 parallel and MI = +ll2perpendicular lines of VO(HzO)52+and VO(D20),2+are listed in Table 111. Single crystal EPR line widths of V02+ Tutton salt grown from D20 solution exhibit comparable reductions in line while room temperature solution spectra exhibit line width reductions on the order of only 0.4 G in D20a6 The average difference between experimental and simulated VO(H20)52+line widths is 7.5%; the average simulated and experimental reductions in line width in going from HzOto D20differ by about 17%. Despite these
The Journal of Physical Chemistry, Vol. 82, No. 8, 1978 913
EPR Study of Oxovanadium(1V) Ion Frozen Solutions
?
TABLE IV: Line Width Reduction of MI= t 1 1 , Perpendicular Line for Some Vanadyl Complexes in D,O Obsd
ComDlexa VO (EDTA)'VO (NTA )VO(1DA) VO (TIR )' VO(SSA)-
reduction, G 0.2 0.1 2.8 2.4 2.5
No. of equatorial water molecules
Proposedb 0 0 1-2 2 2
CalcdC 0.13 0.06 1.8 1.5 1.6
a EDTA (ethylenediaminetetraacetate),NTA (nitrilotriacetate), IDA (iminodiacetate), TIR (1,2-dihydroxybenzene-3,5-disulfonic acid), SSA (5-sulfosalicylate). Reference 27, from NMR data. e Calculated assuming four equatorial water molecules in VO(H20)52+ are mainly res onsible for 6.55-G reduction in line width of MI = perpendicular line; thus, 6.55/4 = 1.6 G per H,O.
MAGNETIC FIELD (GAUSS)
Flgure 4. (A) Experimental HzO and (B) experimental DzOfrozen solution EPR spectra, pH N 12, of VO(HzO)AOH)3-. The instrument settings were as follows: time constant, 1.0 s; scan time, 0.5 h; modulation amplitude, 2.0 G; modulation frequency, 100 kHz; receiver gain, 1.25 X lo3; microwave power, 2 mW.
differences the data provide strong evidence that a major contribution to line widths in frozen solutions of aquo vanadyl is unresolved superhyperfine splitting from coordinated water protons. Although our model predicts reasonably well the experimental reduction in line width upon exchanging DzO for H20, it is instructive to examine other contributions to the line width not taken into account here. First, it is possible that differences between H20and D20as solvents and ligands alter the microenvironment of the paramagnetic species and hence, its relaxation processes. In hydrogen bond are D20 ice, the D-0 bond and 0---D stronger, the OD bond has a smaller vibrational amplitude, D20 molecules undergo a slower rate of molecular reorientation and migration, and the dielectric relaxation time is longer than in H20 ice.25 These properties and others may alter phonon interactions of the type which lead to spin-lattice relaxation (Tl). Thus, T1may be different for VO(DzO)52+and VO(Hz0),2+ leading to different comf aDzO). ponent line widths for the two species (i,e., aHQO A second consideration is that different protons of coordinated water molecules have different principal axes which diagonalize the dipolar tensor and cannot be rigorously treated as equivalent protons as has been done here. Other considerations include small contributions from dipolar interactions between the unpaired electron and protons in the second coordination sphere. This contribution should be about 1/10 that of the first coordination sphere water. Moreover, because of covalency, the simple point-dipole representation may not be adequate. The lack of detailed information concerning the distribution of electron spin density among the various orbitals on the coordinating oxygen atoms does not permit covalency to be taken into account rigorously.26 Uncertainty in the value of r used to estimate the dipolar term,
and the isotropic coupling constants is also quite important. An estimate of the uncertainty in calculated coupling constants from this source alone is roughly 10-20%. Agreement between experimental and simulated line widths is within this range. 4. VO(H,O),(OH),- and Other Vanadyl Complexes. The frozen solution EPR spectra of VO(OH)3(Hz0)2-and VO(OD)3(D20)z-are shown in Figure 4; corresponding EPR parameters are listed in Table I. Again, dramatic reduction of line width occurs in D20;in this case, the line width of the MI = -l J 2 perpendicular line is decreased by 8.45 G in D20. Line width data (Table 111) were not obtained for lines other than the MI = -1/2 perpendicular line because, in DzO, the spectrum was of low intensity making it difficult to measure the other line widths accurately. The much greater reduction in line width for VO(H,O),(OH),- compared to VO(HzO),2+is a consequence of the greater covalency of the metal-ligand bonds in the former; this results in an average equatorial isotropic proton coupling constant four times greater for VO(H2O)2(OH)3-.7-9Attempts to model the reduction in line width for VO(H,O),(OH-), were unsuccessful because of insufficient information on the structure. Preliminary measurements on a number of other vanadyl complexes in HzO and D20 were performed to establish whether reduction in line widths in D20 could be used to determine the number of equatorally coordinated water molecules in vanadyl chelates. The results summarized in Table IV are in agreement with structures of these complexes proposed by Wuthrich and C ~ n n i c k . ~ ~ These results are only approximate because the frozen solution spectra of these complexes, particularly the 1:l complexes of bidentate ligands, are influenced by the presence of minor amounts of other species. Nevertheless, the number of water molecules predicted by the EPR line widths is in accord with NMR results of Wuthrick and C~nnick.~~
Summary Simulated line widths based on calculated values of proton and deuteron superhyperfine coupling constants agree with experimental EPR line widths of V02+in acidic aqueous solution within the limitations of the model. While contributions to line widths in frozen solution can arise from several sources, a major source of line width is unresolved proton superhyperfine splitting of first coordination sphere water molecules. References and Notes H. M. McConnell, J. Chem. Phys., 25, 709 (1956). (2) P. W. Atklns and D. Klvelson, J. Chem. fhys., 44, 169 (1966), (1)
914
The Journal of Physical Chemistry, Vol. 82, No. 8, 1978
(3) N. D. Chasteen and M. W. Hanna, J . Phys. Chem., 78, 395 (1972); and correction, bid., 80, 778 (1976). (4) D. C. McCain and R. J. Myers, J . Phys. Chem., 71, 192 (1967). (5) R. N. Rogers and G. E. Pake, J . Chem. Phys., 33, 1107 (1960). (6) M. M. Ianuzzi, C. P. Kubiak, and P. H. Rieger, J . Phys. Chem., 80, 541 (1975). (7) J. Reuben and D. Fiat, Inorg. Chem., 8, 1821 (1969). (8) W. C. Copenhafer and P. H. Rieger, submitted for publication. (9) M. M. Ianuzzi and P. H. Rieger, Inorg. Chem., 14, 2895 (1975). (10) L. K. White and R. L. Belford, J. Am. Chem. Soc., 98, 4428 (1976). (11) B. R. McGarvey, J . fhys. Chem., 71, 51 (1967). (12) 0. BenalCBakchand E. Wendling, Rev. Chim. Miner., 12, 223 (1975); Chem. Absfr., 83, 1985405(3975). (13) H. Kon and N. E. Sharpless, J. Phys. Chem., 70, 105 (1966). (14) R. T. Ross, J . Chem. Phys., 42, 3919 (1965). (15) B. A. Goodman and J. B. Raynor, Adv. Inorg. Chem. Radiochem., 13, 135 (1970).
H. N. Cheng and H. (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27)
S.Gutowsky
M. Weissman, J. Chem. Phys., 44, 422 (1966). C. J. Ballhausen and H. B. Gray, Inorg. Chem., 1, 111 (1962). B. 9.Wayland and W. L. Rice, Inorg. Chem., 5, 54 (1966). G. Vislee and J. Seibin, J . Inoro. Nucl. Chem., 30, 2273 (1968). G. Firaris and M. Franchini-Angela, Acta Crysta//ogi.,Secf.‘B, 28, 3572 (1972). Z. M. El Saffar, J . Chem. fhys., 45, 4643 (1966). C. J. Ballhausen, 8. F. Djurinskij, and K. J. Watson, J . Am. Chem. Soc., 90, 3305 (1968). A. Carrlngten and A. D. McLachlan, “Introduction to Magnetic Resonance”, Harper and Row, New York, N.Y., p 30. R. H. Bocherts and C. Kikuchi, J . Chem. Phys., 40, 2270 (1964). D. Eisenberg and W. Kauzrnann, “The Structure and Propertles of Water”, Oxford University Press, New York, N.Y., 1969. H. M. McConneil and J. Strathdee, Mol. Phys., 2, 129 (1959). K. Wuthrich and R. E. Connick, Inorg. Chem., 7 , 1337 (1968).
Temperature Dependence of Lanthanide Induced Chemical Shiftst H. N. Cheng$ and H. S. Gutowsky” Department of Chemistry, University of Illnois, Urbana, Illinois 6 180 1 (Received August 8, 1977; Revised Manuscript Received November 28, 1977)
Questions have been raised in the literature about the nature of lanthanide induced shifts (LIS) in nuclear magnetic resonance. Theoretical treatments by Bleaney, by Horrocks, and by Golding and Pyykko differ in approach and conclusions, the most readily apparent difference being the temperature dependence predicted for the induced shift. Comparison of theory with experiment is often complicated by the temperature-dependent equilibrium between the lanthanide shift reagent (LSR) and the substrate for which the LIS is observed. In this study of Pr(fod)8-dimethylacetamide (DMA) solutions in tetrachloroethane, a careful analysis was made of the LSR-DMA equilibrium; and the proton LIS of the three methyl groups in DMA were separated into equilibrium and intrinsic temperature-dependent components of comparable magnitude. The resulting intrinsic LIS can be fitted by either a T1or T 2dependence over the temperature range studied.
Introduction The use of lanthanide shift reagents (LSR) has become a standard technique in nuclear magnetic resonance (NMR) spectroscopy.lI2 The basis of the technique is the ability of the LSR to interact with substrate molecules in a solution and produce isotropic shifts that spread out and simplify the NMR spectra of the substrate. In this connection, a problem of fundamental importance is the nature and the origin of the isotropic shift. It is generally agreed that for protons the pseudocontact (dipolar) interaction is the predominant contribution, and in the last few years several theories have used it as a point of departure to elucidate the shift mechani~rn.~-~ The first extensive investigation of transition metals using density matrix methods is that of Murland and M ~ G a r v e y . ~Besides the anisotropic g tensor their treatment included anisotropy in the magnetic susceptibility. Subsequently, for the lanthanides, Bleaney proposed an elegant model based solely on anistropy in the Susceptibility? His result was very similar to Kurland and McGarvey’s, and agrees a t least semiquantitatively with experiments on several lanthanide complexes.6 The Bleaney model was extended by Golding and Pyykko? who observed small but noticeable deviations from Bleaney’s results. Recently, Horrocks and his co-workersld8attacked some of the assumptions of Bleaney’s theory. They made extensive calculations and obtained results differing from ?This work was supported in part by NSF Grants MPS 73-04984 and CHE 77-04585. *Present address: GAF Corporation, Wayne, N.J. 07470. 0022-3654/78/2082-09 14$01.OO/O
those of Bleaney. A major difference is their prediction dependence of the LIS rather than of an approximate T1 Bleaney’s T 2result. Tests of the theories by comparison with experiment are complicated by the possibility that the temperature dependence of the observed LIS includes a significant contribution from changes in the equilibria between shift reagent and the substrate in question. This possibility is enhanced by the need to observe the temperature dependence of the LIS over a large range of temperatures and a T 2dependence to differentiate clearly between a T1 and to establish an accurate intercept for T 03. In this paper we have undertaken to separate the observed temperature dependence of the LIS into its equilibrium and intrinsic components, which is not a simple task. The intrinsic temperature dependence is then compared with the theoretical predictions of it.
-
Theory of the LIS To a first approximation, the approaches employed by Bleaney,6 Horrocks,8 and Golding7 are similar. The isotropic shift is assumed to arise from anisotropy of the magnetic susceptibility tensor, obeying the general equation
( A H / H ~=) ( r - 3 / 2 ~ ) [ ( X - z-js)(3 cos2 e (x, - x,) sin2 e cos2 $1
-
1)+
(1)
The susceptibilities can be obtained by expanding the susceptibility as a power series in T1(as in Abragam and Bleaneyg),or by employing Van Vleck’s equation.lOJ1 In 0 1978 American Chemical Society
