interpretive experiment/
edited by FRANKDEHAN Occidental College Los Angeies. CA 90041
Nuclear QuadrupoleResonance of R3SbX2Compounds T. B. Brill University of Delaware, Newark. DE 19711 In contrast to NMR, nuclear quadrupole resonance (NQR) spectroscopy depends primarily on the interaction between the nuclear quadrupole moment and electric field gradients produced hy the electron distrihution in a crystalline compound. NQR spectroscopy is a specialized technique which can provide important information in well-chosen systems. In principle, the technique may be applied to any nucleus with spin greater than or equal to unity and whenever a non-zero electric field gradient exists. In ~ractice.the techniaue is somewhat more restricted. unsuitable relaxation times and the occasional difficulty in findine the Droner . . snectrometer conditions may providd the user with no spectrum a t all. As a result, students rarely have the opportunity to see and interpret NQR spectra. Described here is an interpretive experiment aimed a t showing how electron density shifts, bonding trends, and structural information can he extracted from NQR data in a series of compounds. Pentavalent arsenic, antimony, and bismuth form compounds having the stoichiometry R3MX2 where R is an organic group and X is a halogen. The antimony compounds are the central focus of this experiment. Several possible structures can be envisioned for R3Shx2. insert cut 98473 Antimony, chlorine, and bromine possess quadrupolar nuclei. Hence NQR is spectroscopy can he used to ascertain changes in electron density as R and X are varied a s well as to indicate the structure adopted. &
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This feature presents "dry lab" experiments involving the work-up and interpretation of data obtained from expensive or especially sensitive instruments or from those otherwise unavailable to most undergraduate students. Frank DeHaan received an A.B. degree in chemistry from Calvin College in 1957. As a graduate National Science Foundation Fellow under Professor H. C. Brown's direction, he received his doctorate from Purdue University in 1961. Through a NSF Science Faculty Fellowship he spent 1968169 studying spectroscopy at Caltech with Professor Harrv Grav. Since 1961 Dr. DeHaan has taught physical and inorganic chemistry at Occidental College where he is now C. F. Braun Professor of Chemistry. In collaboration with undergraduate students and through the support of the Research Corporation and National Science Foundation, he is actively involved in kinetics research, the results of which have been published in the Journal of the American Chemical Society. In 1974 he was the recipient of the Graham L. Sterling Award, given by Occidental for "strong teaching, service to the College, and distinguished professional achievement".
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Table 1. Nuclear Data a for Isotopes Encountered In this Experiment Element 61 CI
Isotope
37 35
101 (in barns) 0.079
I 312 312
Natural Abundance ( % )
25 75
0.10
'Fuller, G. H.. J ~ h pChem. . Ref. mta. 5,835 I19761
Theory The reader is directed to extensive presentations of NQR theory.'f2 The principles described here are intended to define some of the terms used in this experiment. Chemists are usually interested in the distrihution of electron density around the atom in question. T h e nucleus is the "antenna" used in NQR spectroscopy. T h e distrihution of electron densitv in the eround state of the molecule can he extracted from thkgradie& of the electric field (electric field gradient, EFG) a t the nucleus. T h e EFG is a second order symmetric tensor whose ij components are -qjj = d2V/Jxjdxj, where V is the electrostatic potential a t the nucleus and xixj are Cartesian coordinates. A symmetric tensor is described most conveniently in aprincipal axis system where the three diagonal elements are q,, ,qyy. and q,,, and the off-diagonal elements are zero. Laplace's equation stipulates the ~~
9rr + 4 y y
+ 41r = 0
~~~
~~
(1)
a t the nucleus. By convention lq,, I > Iqyy 12 Iq,, I so that the nucleus will preferentially detect the q, direction. q,, is often represented as eq where e is.the protonic charge. The asymmetry parameter of the electric field gradient is defined a s . . 41s
and measures the departure of the EFG from axial symmetry about the z direction. When q,, = q,, then q = 0and the EFG is axially symmetric. When q,, # q,, q can have a value between 0 and 1. Crystal lattice packing may produce slight distortions in the EFG and can lead to values of 7 up to 0.15 in molecules which are otherwise axiallv svmmetric. T h e antenna for the experiment, t h e nuclear quadrupole moment, eQ, represents the departure of the nucleus from spherical charge symmetry. The important nuclear data for this experiment are tabulated in Table 1. If the nucleus has
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Drago. R. S.. "Physical Methods in Chemistry." W. 6. Saunders, Philadelphia. 1977, pp. 510-527. Smith, J. A. S., J. CHEM. EDW., 48, 39, A77. A147, A243 (1971).
Volume 58 Number 6 June 1981
519
Table 2. Relalire Frequencies lor the Allowed Transnions between MI I = 512 andI = 712 -. -.Levels 01 9
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20
1 = 512 112 = 312 312 = 512
3.0000 3.0013 3.0052 3.0118
3.0209 3.0326
6.0000 5.9995 5.9980 5.9950 5.9922
3.0468
5.9879 5.9826
3.0635 3.0827 3.1043
5.9764 5.9696 5.9614
3.1282
5.9526
112 * 312
2.0000
2.0029 2.01 16
2.0260 2.0459 2.0713
1 = 712 312 512 512 = 712 6.0000 4.0000 3.9991 5.9998
=
3.9964 3.9919 3.9858
5.9990 5.9978 5.9962 5.9940
2.1372 2.1773 2.2218
3.9780 3.9688 3.9583 3.9495 3.9336
5.9846 5.9805
2.2703
3.9198
5.9758
2.1018
5.9913 5.9882
a he hequencies are relative foraglvenvalueat I.Frequencier for different valuesat I OhWld nn be armpared.
Table 3. Nuclear Ouadrupole Resonance Frequencies Spin, I
The complete NOR spectrum of (CHS)~S~CI~. The expanded insert shows the appearance of a resonance multiplet. Frequencies are given in megahertz.
Table 4. Antimony and Chlorine NOR Frequencies In MHz at 300°K
a finite quadrupole moment, then its energy depends on its orientation with respect to q,,; that is, on its magnetic quantum numher, fmr. An i n ~ uoft enerav ... in the radio freauenw region cnn reorient the nudrus betwrrn the degrncrate f m~ levels. A total uf 1-112 resonance frequencies occur for halfinteger nuclear spins. The nuclear quadrupole resonance frequency, u, depends on the magnitude of the product of eq and eQ. This product defines the nuclear quadrupole coupling constant, e2Qqlh (in MHz).The frequency also depends on 7. The effect of 7 on the transition frequencies for I = 512 and I = 712 nuclei is shown in Table 2.3 T h e experimental resonance frequencies are directly proportional to the values given there. Equations describine the deuendence of u on n and e2Qo/h ... for various nuclear spins are given in Table 3. Note that u is directly ~ r o ~ o r t i o nto a l the EFG but that the sien of the c o u ~ l i n e con&ant cannot he determined. A unique value of an2 e2Qqlh can be extracted routinely in a polycrystalline sample when I has a value other than 312. For I = 312, e2Qqlh is approximately equal to 2v for small values of 7. T h e intensities of NQR transitions approximately correlate with the abundance of the isotopes of a given element except when the energy is divided among several transitions as in the case of antimony. T o he useful to a chemist, e2Qqlh and 7 need to be related to bonding parameters. The assumption in many approximate EFG models is that the couoline constant of an atom in a molecule is proportional to i h a t o f the atom acted on by a single valence shell electron in a p orbital.
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In the cases that .mine in this ~ x p e r i r n ~ tpi tcan be related to the electron . ~ o.n u l a t i o nin thr indivirlunl valence shell D orhitals, Np,, according to 520
Journal of Chemical Education
where q,, coincides with the p, orbital. This orbital also coincides with the highest-fold rotation axis in an axially symmetric or pseudo-axially symmetric molecule. Since (e2Q,lh).t,, is a constant for a given atom, the trend in the coupling constants for a series of molecules is determined by the relative magnitude of Np, versus (Np, N p )I2 on the atom containing the quadrupolar nucleus. In a simiiar manner, the asymmetry parameter, 7 , can he thought of as a measure of the difference between the population of the p, and p, orbitals as shown in eqn. (5).
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The Experiment The Data
The NQRspectrum of (CH&SbC12isshown inFigure 1. However, this spectrum is compressed as required for illustration; the actual spectrum covers nearly 20 ft of chart paper! An expanded insertdetailing the appearance of one of the resonances is shown. For eonvenience the complete set of accurately measured nuclear quadrupole resonance frequencies for (CHs)$3bC12 and also (CsH6)sSbC12 is tabulated in Table 4. In addition to these raw data, the values of e2Qqlh and 7 determined from the resonance frequencies of antimony in other RsShXz compoundsalong with halogen resonance frequencies are compiled in Table 5. These data were obtained on a Wilks Sei-, entific NQR-1A super regenerative oscillator spectrometer. The multi~letof lines of a sin& resonance shown in the insert (seefipure) results from the ooeratknal characteristics of this oseiilator.-~h.
Energy level diagrams are available which graphically give thaw data in necessarily somewhat less precise form. For example, see Brown, T. L., Acch of Chem. Res., 7,408 (1974)andWang, T. C., Phys. Rev., 99, 566 (1955). Shenoy, G. K., andDunlap, B. D., Nucl. Instrum. Methods, 71,285
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(1969).
Table 5. Antlmony NQR data and Bromine NOR Frequencies at
300°K e20q/h.MHz Compound 121sa 1235, (CH&SbBra 630.6 803.9 (CsHsCH2hSbC12 600.6 763.3 a (CBHSCH~JS~B~Za (CeHshSbFz 603.9 769.9 (CeHrhSbBrs 565.6 720.9 (C6HdsA~Br2 (CsHshBiBr2
q(Sb) 0.0 0.0 a 0.07 0.04
~(312= 112).MHz 798, 81, 115.1 96.13 120.4
100.6
127.1 145.4 114.0'
106.1 121.5 9 5 . ~ ~
Not Observed. dAverage of three closely spaced resonances. a
.. .
61 Usine the annronriatestrueture for RxSbXl - .extracted in ouestion 151,onc n r the prmcipal axe,
