~ O P ~ Cin.. S
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Chemical Instrumentation Edited by GALEN W. WING, Seton Hall University, So. Orange, N. J. 07079
T h s e articles are intended to serve the readers of THIS JOURNAL
by calling attention to new developments in the theory, design, or availability of chemical labmalory inalrumentalion, m r5y presenting useful insights and explanations of topics tho1 are of practical impmlance to those who use, m teach the use of, modern instrumentation and instrumental techniques. The edilor invites correspondence from prospective contFibutms.
LVI. Nuclear Quadrupole Resonance Spectroscopy. Part ~hree-chemical Applications (continued) J. A. S. SMITH, School of Molecular Sciences, University of Worwick, Coventry CV4 7AL, England
9. THE NUCLEAR QUADRUPOLE RESONANCE SPECTRUM AS A MOLECULAR 'FINGERPRINT' Despite the solid-state effects which we have been discussing in the previous sec-, tion, the differences in frequency between chemically different nuclei me often large and readily distinguished. In solid PClo for example, the PCL+8SCIT,frequencies near 32.3 MHz a t 77°K are very much different from the values for P C k near 30.0 MHz a t the same' temperature. R. J. Lynch, in the author's laboratory, has also shown that the mean PC4+ frequencies a t 77'K in many s d t s of this ion vary by little more than +ZOO kHs, despite considerable differences in the temoerature coefficients. so that the W l fre-
Qualitative analysis by nuclear quadrupole resonance is thus becoming an established technique, particularly in the analysis of heavily chlorinated carbon and boron compounds, where other kinds of spectroscopy are lacking in discrimination. This is oarticularlv , a oroblem with the chlorinated curboraa,ei ( I ' In wnle rrspects, the rruclrar q u n h p o l r rrwnbuce frequency I,rc.rnt!. rnther like the rhmmical shift in nuclear magnetic resonance, and recently Brame has published (61) s. "group frequency" table for 'C1 resonance which is reproduced in Figure 16. Thus if we were to apply the information in this table to the frequencies we have given previously the hexechlorocyclopentadiene (Section 8) we would conclude that the low-frequency group of four lines near 37 MHz could be safely migned to the vinylic chlorine. However, the highfrequency group of two lines near 39 MHz
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10. INDUCTIVE AND MESOMERIC EFFECTS IN MOLECULES Chemists are also interested in why a. quadrupole resonance frequency should have a. particular value. The theory of Townes and Dailey, which we have discussed in Section 3c, claims to answer this
N-CI
OALIPHATIC
is high for CCI, and it will be noticed in the table that there is considerable overlapping of the various group frequencies, as indeed would he expected from what we have discussed of solid state effects. The situation is not unknown in nuclear magnetic resonance, and the same care must be exercised in evaluating - "medium" effecta. On the whole. however. a6C11.auadruuole resonance spectroscopy is less discriminating than 'H magnetic resonsnce, but in compensation it enables the scientist to study nuclei such as 8'Br or whose magnetic resonance spectra in the liquid phase are often so broad as to he undetectable. Furthermore, it applies to solids as distinct from solutions, and can therefore give unique information on molecular structure in this phase; if for example the molecules under study dissociate or exchange in solution, a solid state method is often the only one available. For exsmple, W l quadrupole resonance of salts of the H C G ion show two kinds of species, as we have discussed in Section 8, whereas the 'H magnetic resonance of such salts in solution conceal this difference because of the much larger effects of dissociation and exchange. Another example occurs in the study of bortttes and borate glasses (62') where the quadrupole splitting of the "B magnetic resonsnce spectrum is characteristic of its stereochemistry in the glass, trigonal B having high values, (e.g., quadrupole coupling constants of 2.5-2.8 MHz with low n) rather than the low values (e.g., 0.3-0.7 MHa with high n) found in the tetrahedral B; such information is also pantilalive, e.g., W u resonance in CusO, a strong signal in the pure compound a t 26.5 MHz, can be used to analyze cuprite ores for their copper content (65).
-CCI~
0 V I N Y L CHLORIDE
0ALIPHATIC-CC12 0R - C l ALIPHATIC OXY. CHLORIDES
0I - C L 0 3 0s i c 1 19
22 25 Figure 16.
28 31 34 37 40 FREQUENCY IN Mc Group frequencier for
W
43
45
quadrupole resonance (all at 77°K).
explain the kind of di"fferenceb observed in halogen resonahces. The relationship to what the chemist lobsely calls the "ionic character" of the bond is clearly illustrsted by W 1 quadrupole resonance frequencies, with the high values for N (N-chlorosuccinimide, 54.1 MHB) +here the electronegativity difference is almost zero, and the low values for Ti and Th (ThCL, 5.92 MHz). I n ca~bon-chlorine bonds, the "Cl frequency is sensitive to other substituenta on the carbon atom, cf. the mean frequencies at 77'K of CC4 40.6 (Continued a page A%&)
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(16 lines), CHCL 38.28 (2 lines), CHpClz 35.991, and CHsCl 34.023 MHe. On the Townes-Dailev model. such dzerences would be expl"&ed b i e q n . (40) in tenns. of increasing polarity of the G C I bond, as each chlorine substituent is replaced by hydrogen, and the electron-withdrawing power of the substituents is reduced. On this model, of course, we must also expect changes in hybridisation and even Tcharacter to occur, although they are assumed to play a minor role. On the other hand, changing c-charctcter has been invoked in the case of the fluorocarbons to explain the fact that on going from CC1, to CFClr (mean frequency of 39.3 MHz) or CFKL (38.45 MHz) the W 1 frequencies decrease, rather than increase, as the higher electronegatimty of F would lead us to expect. Resonance structures of the kind
1 0.35 MHz
are held to he responsible.
whereas in RJLRsSiCI they find (66) u =
Despite the uncertainties which arise in such explrtnations, and the existence of solid state effects, substituent effects undoubtedly exist and W 1 quadrupole resonance frequencies can be related to such parameters as the Taft polarity parameter a C > Si, according to the "C1 quadrupole resonance evidence. In t.he author's laboratory (66) a parallel substituent effect has been found in transcomplexes of P t and Pd of the form RIMCL; in Pd(I1) the 'SC1 frequencies increase in the order piperidine < pyridine < BurAs < Burp < EtCN < PhCN aver a. range of 4 MHE, from 16.2 MHz in pip2PdClr to 20.6 MHs in ( P ~ C N ) X P ~ C I . making the W 1 frequency a sensitive indication of the donor 'ability of the lieand L and hence of cis influence. Thus &the donor ability of L rises, more charge is transferred to M and hence to C1, so that the quadrupole coupling constant of the latter drops; the few &-compounds which have been studied show a. similar trend, as Table 3 shows. The difference A between trans and cis follows the order RJP > py
> MerNH
which is also that of increasing lability of the tmans-C1 to replacement in the cis complex, the so-called "tmns effect". The parameter A may ifhereforeillustrate the operation of the "trans influence" in W l qusdrupole resonanoe. Mesorneric effects must also affect nuclear quadrupole resonance frequencies; in ascl spectroscopy, on the TownesDailey theory, they change the parameter in eqn. (41) and hence affect the raymmetry parameters through eqn. (42). Thus in 1,3,5-trichlorobensene (I),
Table 3. M e a n 'CI quadrupole reronance frequencies in some cis and trans-com~lexesof Ptllll. LzPtCla a t O°C
L
bans (MHz)
cis A(tmns-cis (MHz) (MHz)
(Continued on page A846)
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Chemical Instrumentation single q s t a l studies shown values for the 3 chlorines of 0.09, 0.11, and 0.13, higher than the values of 0.02 to 0.03 found in ?-benzene hexarbloride where the bonds, although lacking ~symmetry,should have little or no rr-character. In 1,3,5-trichloros-triasine (cyanuric chloride), (II), even higher q values are observed, viz., 0.23 m d 0.26, as would be expected if resonance structures like (111) can now contribnte. In 14N resonance studies of the mabenzenes, the r-electron effects appear in the Townes-Dailey theory as a change in populations of the 3p. orbitals on N. We may adapt the methods of Section 3c to the case of pyridine, for which microwave studies give egqQ/h = -4.88 MHz, q = 0.405 and solid state 1+N quadrupole resonance a t 77'K gives lezqQ/hl -- 4.584 MHz, n = 0.396; the directions of the principal components derived from the micxowave work are Figure 17. Plot of "Cl against "Ga quadrupola resononce frequencies a t 77'K in solnplexer of tho type LGaCls. The large circler mprasent the weighted mean "CI frequency for each mmpiox and the straight line is h e least-squara line through these poinh.
We first assign the electrons to localized orbitals, ar below (for a CNC bond angle of 120°), A
Orbital
Deswiptia
$1
cbonding
with p < 2 bwause of r-handing of N(2p,) to the nng. Assigning contributmns to the electric field gradient along z from d l orbitals (as in Section 3c), wederive
constants can be measured for the same molecule, the interpretation of the coupling constants is not consistent; in crystalline oyanuric chloride, (II), the difference between its "C1 asymmetry parameter and that for 1,3,6trichloro-
Populatwn P
benzene leads from eqn. (42) to a change in r of 0.055, whereas the differences in the '4N coupling constant and asymmetry parameter between this molecule and s-triazine (IV)
6
NvN
and
(W
Now taking (esqQ/h).t, as -8.0 MHE, one calculates for p a value of 1.100 and for b 1.250, in comparison with MOcalculated values far p of 1.100 (67). Unfortunately, the agreement is worsened if the correct value of 117'34' for the CNC angle is incorporated into the model. However the theory in pyridine is consistent with the negative value of the quadrupole coupling constant and with the observed directions of V.. and V.,. Unfortunately, when 14Nand ajC1 coupling
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predict a change in p of 0.204. I n the first oase, the increase in r is attributed to the increase in the p, population on the N atom caused by increased delocaliaation of the C1 3pr orbitals, and this should therefore be very closely similar to the difference between (11) and (IV). Where the errors lie has yet to be olearly established; it is clearly unwise to mix experimental data from hoth gas and solid, and the validity of an unmodified TownesDailey theory when applied to the prediction of orbital populations and "N quadrupole resonance frequencies in cyanides has recently been questioned (68).
11. INORGANIC COMPOUNDS AND METAL COMPLEXES Mmy compounds of this kind can give quadrupole coupling constants for stoms at hoth ends of a. chemical bond; this should be true for example of nitrogenhalogen, antimony-halogen, boron-halagen, gallium-halogen, cobalt-halogen, halogen-halogen and many intermetallic bonds. Unfortunately, relatively few studies of this kind have been attempted by nuolear resonance spectroscopy. quadruple M6ssbeuer speetroshopy can he useful here; although its resolving power is low, it can also give information on the sign of the coupling Constant, so that for example the technique shows the electric field gradient a t iodine in L to be positive and in IOs- and ICL- to be negative. In Wa-Wl bonds in complexes of the GaClr (L ligrtnd), both 6nGa type L and W 1 quadrupole coupling coistafits have been collected for a variety of ligands L, and as Figure 17 shows, the 8'Ga couplhg constants shows a much greater sensitivity than those of "Cl to changes in the electronic structure of L (6.9). Moreover, hoth sets of frequencies in some six complexes (encircled in Fig. 17) show an excellent correlation with the gas-phase heats of formation of the donor-acceptor bond, providing yet another example of a relationship between donor ability and halogen quadrupole coupling constants. Many transition metal nuclei should in principle be amenable to study by quadrupole resonance spectroscopy; for example, we may mention "V, =Mn, Wo, "Cu, 9PNb,' 8 6 I l e , and 'O'Au. In recent years, there has been an increasing effort to find these resonttnces, and SMn, Wa, 8nd '"Re signah have been detected in several dirtmagnetic complexes of these elements. Some d%tafor "Co are collected in Table 4. Notice the near zero asymmetry (Cmtinued a page AS.@)
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parameter for 'Co resonance in the [Co(C6Hs)zl+ ion, as would be expected from its sandwich structure. Rather more surprising is the low q in [Co(1,2 B&Bu).l-, wbere (in Fig. 18) stoms 1,2 are carbon and 4,7,8 boron. Either the carborane groups are undergoing rapid reorientation, whioh seems unlikely st 77°K in a solid, or more likely the carbon and boron positions in the framework are almost identical in their charge distribution and their ability to donate charge to cobdt. The high asymmetry parameter in Cor(C0)s is understandable in view of tbe known structure
Toble 4.
wbere two of the "octahedral" positions around Co are occupied by bridging CO ligands and a third on the same face by an orbital engaged in bonding to the other cobalt atom, giving a configuration lacking in axial symmetry. On the other hand, in the [CO(NHS)&~]'+ ion, where an axis of symmetry might have been expected, the rather large 1 shows the significant iduence of solid state effects; in [Co(NHa).COal+, the large n is clearly s. consequence of the cis-stereochemistry. A striking feature of the W o quadrupole coupling constants is their wide range, showing an extreme sensitivity to eleotronio effects within the molecule. The values appear to be dominated by the unbalance in the 3d orbital populations (in contrast to current interpretations of W1 quadrupole coupling constsnts, wbere the 3 p orbital unbalance is important); thus in CodCO)s, a major contribution to the ohsewed quadrupole coupling constant comes from the 3d population differenca of about 0.17 electrons between the orbitals engaged in forming the Cc-Co bond and the other bonding orbitals (70).
Quadrupole coupling constants and asymmetry parameters in some Cobalt complexes Com~ound
leJQ/hl I Hel
Temp. f°Kl
Figure 18. Structure of the [(1,2-B~4HrdnCo],on.
(Continued a page A#60)
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Table 5.
12. IONIC LATTICES A N D METALS I n this concluding section, we turn our attention to quadmpole w u p h g wnstants in two rather different kinds of solid, namely ionic lattices and metals, where the calculation of the electric field gradient follows rather different principles to those described in Section 3 of the first article. Taking ionic lattices first, quadrupole coupling wnstants can be measured in many noncubic crystals by such methods as electron%pin resonance, nuclear acoustic resonance, or MBssbauer spectroscopy, sprtrt from the techniques of nuclear magnetic resonance; in cubic crystals, such as NaC1, quadrupole splitting can be observed in crystals deformed by point defects, e.g., from Waions adjacent t o K + substitutional sites. I n ionic lattices eood where overlm of the ions is small.. .. vsluen of the lnttire energy cm be calculatrd by the "point-charge model", where thr ions ere replawd hy point charges at their atomic centers and the corrections needed to account for departures from this model, e.g., due to the finite polarizibilities of the ions, me relatively small in the majority of cases. However, the poinbcharge model is not generally valid for predicting the quadrupale wupling constant, which therefore becomes a much more sensitive criterion of the electron distribution in the crystal. ~
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B e 0 Lattice; lattice parameter a = 2.6979
0- QuadPoint-charge O-- dipole ruple Nuclear contribution wntribution contribution Q site (e/aa) (e/a8) (e/aq (X10-%mal .. . .. . .. . . . (1 . - r-) . . 'Be -0.0910 0.7050 -0.2765 f0.05 0.811 "0 0.0181 -0.0265 29.22 0.0910 (mntrZution) -
(kHz) . . 49 200
Note: The values of the electric field gradient in this table are expressed in units of electrons/as, where a = 2.6979 X 10-8 om; to derive the coupling constant, multiply by the factor ZeaQ(l - 7-)/ha'. S w i n g with the point-charge model, we need the sum of Ze(3 cm'S - I)/rVwhere Ze is the ionic charge and 8 the sngle of the interionic vector of length r with respect to V,) over all ions in the crystal apart from the one we are wnsidering; this sum wnvergea relatively slowly-in fact, were it not for the angular term, it would not wnverge at &-and in a crystal like AIDI one needs to sum over a t least 30 unit cells in a volume around the "A1 nucleus under wnsideration in order to derive a wnvergence of about 1%. Various procedures have been proposed to accelerate the rate of convergence, and such calculations have now been perf o d for a wide variety of orystals. Here, we wntrast two crystals; CurO and BeO. The W u resonance frequency in the former a t 77°K is near 26.0 MH5; the lattice contains Cu+ ions lying on a faweentered cubic lattice and the 0'- ions on a body-centered cubic lattice, so that the electric field gradient a t Cu+ arises entirely from the 0%-ions. Since the
latter lie a t centers of symmetry, they have no induced dipole moment hut there wuld be higher multipole moments such as quadrupole. Neglecting the latter, the poinbcharge calculations (71) are wnsistent with experiment if one assumes a value of 8.5 for (1 - r,), which is not unreasonably far from Sternheimer's prediction of 16.0. Here therefore the poinb charge model works fairly well, in agre* ment with the conclusions from the high pressure dtudies to which we referred in Section 8. In BeO, the *Be quadrupole coupling constant is 41 f 4 kHz; the compound has a Wurteite structure and both Bea+ and 0'- wntribute to the electric field gradient. The value of the sub-lattioe displacement parameter u [O-- lies at (O,O,u) and (%,,s!l '/I u)l is not known with suffinent acnvscy for a reliable calculation to be made, but if we assume a value of 0.3770 b, then Table 5 shows. the contributions to the electric (Continued on page Asfig)
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Chemical Instrumentation field gradient a t the Be and 0 nuclei which have been derived (78) and with the nuclear Q-values snd shielding parametem quoted, one estimates the coupling constants in the find column. The 0-dipole contribution srises from the fa05 that the ion does not lie s t s site with 1 symmetry, and so is p o l a r i d by the lattice; it was calcull~ted assuming a polariaibility of 2.19 La, which is larger than the optical value of 1.29 1 'because of the effects of the lattice. The electric quadrupole moment of the 0-- ion was taken as 7.0 from a theoretical calcnls, tion for this ion. Note that for %e the dipolar contribution is apparently the predominant one, with even the quadrupolar contribution being larger than that of the mint-chsrees. - . a remarkable difference from the lattice energy calcnll~tions for BeO, and one which gives a deeper physical insight into the electronic structweaf the crystal. We may now consider b r i d y the application of the so-called ionic model to met&. On this model, we imagine spheres drawn around the lattice nuclei such that adiscent spheres just touch; inside the sphere, we have a local wntributiou to the electric field gradient from conduction electrons close to the host ion, which as we saw in Section 3a will be
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(1 - Rg)ptm.r; outside the sphere, we have a lattice contribution (1 - y..kl.ttia. from the lattice charges (considered as points) and the remaining conduction electrons, which are generally assumed to have a uniform charge distribution in this region. Again the lattice sums converge rather slowly; for example, in an hexagonal close-packed lattice, the nearest neighbor ions contribute only 50% of the total pointcharge contribution. Nevertheless, closed formulas have been derived for the pobt-charge contribution in several common lattices, so that with the best value of Q wailable, one can estimatethe contribution to the quadrupole mupling constant far qt.tti,.. In tetrttgonal indium (75), for example, the four "&In quadrupole resonance frequencies (I = 9/2) observed at 4.2% lead to a qus, drupole coupling constant of 45.19 MHe (7 = 0 bemuse of the fourfold point symmetry of the nuclea.~site); the calculation, assuming (1 - y,) for I n to be 21, predicts (eZqQ/h)l,tti.. to be 9.2 MHa. In this erystal, there is therefore a large local contribution, which may possibly arise from a p-electron unbalance caused simply by the small distortion from cubic symmetry. In both metals and ionic crystals, a great amount of work clearly remains to be done before accurate predictions of quadrupole coupling constants can be made, but we will then have s. considerably greater insight into the electronic structure of these crystals.
References (60) Bnymaov*, E.V., B ~ m a oV. . I.. K~rarov*. A. I., TIPOVA. N.8., and S m m . G. K.,Zh. Sfrukk K i m . , 9 , 3 9 (1968). (81) Bnaul. E. G.. JR., And. Chom., 39, 918 (1867). (62) BWT, P. J.. Esw~nos.J. 0.. 0'Kmnm. J. G.. Roae. V. F.. and Imau~aax,I.. J. Cham.Phva..35,435 (1881). (83) Swmwvs. H. D.. and KARR.C.. Jr.. And. Chem., 41.661 (1969). (84) Bmmmov, I. P., and Voaoarov, M. G..
Collect. Czech. Cham. Commun.. 32, 830 (1967). (66) B ~ a r m o v .I. P., Vo~ox=ov,M. G., add S ~ r m ,I . A,. Tern. Eks. Khim. Akod. Nouk. mr. 8. S.R.. 1,124,373 (1966). I (66) FRrms, C. W., and 8 m r ~J.. A. S., J. Chem. Soc., A. 1029 (1970). (67) Ref. ((I), p. 236. (68) B o ~ ~ o o o a s R.. x . Sc~occo.E., and Tornas, J.. J. Chem. Phya., 50,2940 (1969). (69) T o m . D. A,. Cham. Conmun., 790 (1969).
.. 8.. PI EBB, 8.W., GARRETT, (10) M o o a l s s ~E B. B.. and Samrm. R. K.. J. Chsm. Phya.. 51.1970 (1969). (71) Bmsoxn, R., J. Chcm. Phvs., 29,326 (1958). (72) T ~ n o s T ..T..and DM, T.P., Phyus. Rsn.. 133A,m1327 (1964).
C., P., (73) Bryxona. W. W.. and S ~ O A T E R Phya. R a . . 121.l680 (1961).
