ESR Studies and hMO Calculations on Benzosemiquinone

A Physical Chemistry Experiment

Rainer Beck and Joseph W. Nibler Oregon State University. Cowallis, OR 97330

Electron spin resonance (ESR) is a form of magnetic reso- nance spectroscopy often used to study the electronic struc- ture of molecules with unnaired electrons. The basic theorv (I) and several ESR expeiiments suitable for an undergrad- uate laboratorv have ameared in this Journal ( 2 4 ) . We describe here an experiment done a t Oregon ~ta teunivers i - tv that more fullv exploits the simple connection between experimental ESR hGperfine splitting patterns and the un- paired electron spin density distribution which can he ob- tained from e ~ e m k n t a r ~ mechanics (6-11).

For this laboratory study, several henzosemiquinone (BSQ) radical anions were chosen since they are long-lived and are easily made from inexpensive source materials. The effects of molecular svmmetrv and of different suhstituents attached to the aromatic ring system are also readily seen. Some of the more comnlex s ~ e c t r a demonstrate the value of computer-simulated ESR spectra in the determination of splitting constants from the experiment. Finally, a simple Hiickel molecular orbital (HMO) calculation for the unsuh- stituted radicals permits the comparison of the calculated charge distribution of the a-electron system with that de- duced from ESR hyperfine splittings. Several readily avail- able Project SERAPHIM' programs for an IBM PC can be used in these calculations (12-13).

Background The basic theory behind ESR is described sufficiently in

many widely used physical chemistry texts and hooks on ESR spectroscopy (6-9). In this experiment we make use of

' A variety of programs are available at nominal copying cosl from Projecr SERAPh M. NSF Eoucation. Department of Chem stry. East- ern Michigan Un verslry, Vpsilanli. MI 48197.

the fact that the unnaired electron eenerallv samnles the magnetic environment over much of the molecule. If the molecule contains nuclei with magnetic moments, especially protons, the electron-nuclear interaction produces charac- teristic splitting patterns in the ESR spectrum that can he used to deduce the number of different types of nuclei and their geometrical symmetry.

More specifically, the energy of interaction of the electron and the nuclear magnetic moments with a magnetic field B is, to first order:

electron nuclear electron- E = Zeeman + Zeeman + nuclear

energy energy coupling

~ = g , p & B - X$Nj~NjM~B + X i Q W 4 i (1)

Hereg, is theg factor of the unpaired electron, p. and p ~ i are the electronic and nuclear magnetic moments, and Ms and Mr; are the ouantum numbers eivine the snin comnonent along the fieid direction for theelecrron and nucleus i, re- snectivelv. The hv~erfine solittine constant a; is a character- istic parameter &; the interaction of the unpaired electron with a nucleus of type i. The nuclear Zeeman term in eq 1 does not change for levels involved in an ESR transition (M.is = -1) and is omitted in the following. Hence, the energy levels for an unpaired electron interacting with two different protons can be written as

E = Ms[g& + ~ I M I I + (2)

giving rise to the pattern and transitions depicted in Figure 1. The consequence of the electron-nuclear coupling in eq 1 is thus to split the free electron levels by an amount F %al F %a2 and to produce a quartet of lines whose spacings yield directly the hyperfine splitting parameters.

Volume 66 Number 3 March 1989 263

Free electron

Nuclear hyperfine splitting a1 a2

First nucleus

Second nucleus

Figure 1. Energy levels and spectral line panern (stick spectrum) for an unpaired electron lmeractlng with two nonequivalent protons whose spin Orientations are indicated at the right. The dashed levels and dashed transition arrow indicate the case tor an uncoupled free electron.

For equivalent protons (a, = a2), the two central transi- tions in Figure 1 merge and a triplet hyperfine pattern is produced with intensity ratios 1:2:1. In general, n equivalent protons give a spectrum of n + 1 lines equally spaced by the hyperfine splitting constant aH. The relative intensities equal the coefficients in a binomial expansion (1 + I)", and can be written in form of the so-called Pascal triangle.

In the present experiment, we are concerned with the hyperfine structure of the henzosemiquinone radical anions. The delocalized unpaired n electron is of course distributed over the entire molecular frame of six C atoms and two 0 atoms. For the unsuhstituted para-BSQ anion all four pro- tons are equivalent and (1 + x ) ~ = 1 + 4% + 6x2 + 4x3 + x4; hence, five hyperfine lines with relative intensities 1:4:6:4:1 are expected in the ESR spectrum of this radical. In con- trast, if one of the protons is substituted, the symmetry is lowered and each of the remaining three protons can possess a different splitting constant. A hyperfine structure pattern of eight unequally spaced lines of equal intensity is expected. The line splittings and relative intensities in ESR spectra thus convey information about the geometric arrangement of the atoms.

The hyperfine splitting parameters also yield information about the electron distrihution in the molecule. The theory of the electron-nuclear coupling interaction was first worked out by Fermi who showed that the constant a de- pends upon the electron density a t the nucleus. For a free hydrogenatom,a is given hythe Fermi contact interaction in the form (7-9):

a = (~*/~)&~L&~NILNP(O) (3)

where p(0) = 1$(0)12is the unpaired electron density a t the H nucleus. The wave function for the ground state of the H atom is J. = (rrao3)-'I2 exp (-rlao) where a0 = 0.529 A is the Bohr radius. The resultant value for a in gauss is 507 for this "pure" s orbital while values for p, d, f, and all other orbitals with a node a t the nucleus are zero.

For the molecular case, the essential conclusion is that the orbital must have some s (or a hvbrid) character for the unpaired electron to interact with a magnetic nucleus. Con- sider, however, the case of the benzene radical anion, where the electron is usually descrihed as being in a a orbital witha node in the molecular plane. As a consequence, no coupling with the proton nuclei is expected, a prediction clearly in conflict with the experimentally observed hyperfine split- ting of 3.75 gauss. How then does the unpaired a electron density appear a t the H nucleus?

The answer is that the electrons cannot be so neatly la- beled as a or * type, and part of the unpaired s electron densitv is transferred throueh the CH siema hondine elec- trons to the H nucleus throuih exchange ;nt~roctionG7-9). In thecaseofthe T electron in the planar methvl radical. this process, termed spin polarization,>esulta in a hyperfine con- stant of -23 gauss, about 5% of the limiting value of 507 gauss for an electron completely isolated on the H atom. Note that the sign of a is not directly determined in the ESR experiment but is negative according to theory. Thus one might say that the unpaired electron polarizes the CH bond- ing pair such that there is a net "negative spin excess of 5%" ahoutthe proton. For the benzene anion radical, the electron is equally distributed over six carbon atoms and one would expect a to he about -2316 = -3.83, a magnitude in good agreement with the experimental splittine of 3.75 eauss.

In the case of organic free radirals, ~ k o n n e l r ( l 4 ) has shown that a simpleempirical proportionalitycan be used to relate the observed hyperfinestructure constant aH to the unpaired electron spin density on the nearest carbon atom: au = QL. The constant Q is of the order of -20 to -30 eauss .. -. " " for aromatic hydrocarbons, and the benzene anionvalue of Q = -6 X 3.75 = -22.5 eauss is commonlv used. This relation may also he applied io give the hyperkne constant aH for splittings arisine from protons on the first carbon of a sub- stituentattacheb to acarbon in an aromatic system, e.g., each of three methyl hydrogens in the toluene radical cation. Again Q is in the range of -20 to -30 gauss, and a value of -28 is usually assumed (15) when an independent experi- mental determination cannot be made.

Experimental The semiquinone radicals are produced by base-induced oxida-

tion of 1,4-dihydroxyhenzene (hydroquinone) or 19-dihydroxyben- zene (catechol) by molecular oxygen, present in dissolved form. Prepare 5-10 mL of concentrated solution (1 M or greater) of the hydroquinones in methanol (ethanol or acetonitrile can also be used as solvents). A basic NaOH solution in methanol (1 M or greater) can be made by adding 1 g NaOH to 25 mL of alcohol. With a syringe, place 1-2 mL of the hydroquinone solution into a small beaker, and then add a drop of basic methanol. Stir until the solu- tion turns yellow, then transfer to a quartz ESR tube and record the spectrum. A scan range of 10-20 gauss and a modulation amplitude of 0.01 gauss would be suitable starting parameters.

The spectra can be recorded in conventional 5-mm-0.d. ESR (or NMR) tubes. The hieh dielectric constant of methanol can make the cavit;diffieult to tune: this ~roblem can he reduced hv insertine the ~ ~ ~ ~~~ ~,~ ~.~ ~~~~~~~~~~ ~~~~~~~~~~~ , ~~ ~~~~~~~n ~~~-

tuhesothat thesolurionertendsonly partially into thecavity rcgim or, better, by using a 2-mm-o.d. ESR tube. Sperial ESH tubcs for aqueous solutions are also available that have a flat rectangular sample section that can he oriented to maximize the sample volume at the central plane of the cavity where the electric field has a node, giving lower dielectric loss.

After preparation the parent p-benzosemiquinone radical anion mav eraduallv increase in concentration as oxidation occurs and will lasiahout 2 h The merhylor t-butyl substiturcd radicalstormmore quickly and have lifetimes of about I5 min due to radical-radical reactions and other processes that destroy the anions. The culur serves as some guide to the optimal concentration; a reddish color suggests that too much base has been added while a brown-black color indicates that radical-radical combination has occurred. A satisfactory spectrum for the o-benzosemiquinane anion is more difficult to obtain by the above method because the radical-radical reaction is much faster. One simple way to promote the oxidation of the parent to provide areasonable anian concentration is to increase

264 Journal of Chemical Education

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'son with valuescalculated from theow. S i m ~ l e HMO theorv, reviewed in refs 6. 8, and 10, is satisfactor). for calculati& electron densities in aromatic hvdrucarbuns. HMO theory

Floss 2. Experirnenra (lefl)ano carcu~atedlrlghtlESR spechs oltheanlonsof la) pars-BSQ. 10) t-Duty-BSQ. (c) metnyl.BSQ. (dl 2.3dlmetnyl-BSQ. (el orthp BSO The scan range is 10 gs~ss lor a. b. and e, an0 20 g a d s for c and d.

the surface area of the solution to give greater access hy oxygen in the air. This can he done hy adding one drop each of catechol solution and base to a 5-mm-0.d. EPR tube. Turn the tube to form a green film of solution on the wall; a brown color is the result of radial-radical reaction. Shake any excess solution from the tube and record the spectrum immediately. It may he necessary to ex- periment a hit to obtain good spectra and two 3-h laboratory periods are recommended. ~ . - ~~~~~~-~~~~~~

Spectra for substituted ratechola ran he ohtained in the samr way as for the hydroquinones, hu t these anLm are much less stable, and interference by other radical intermediates makes the interpreta- tion of these spectra more difficult. Thus it is suggested that spectra be obtained for the parent o- and p-benzosemiquinones and for one or more of the suhstituted methyl-, 2,3-dimethyl-, or t-butyl para forms. All the expected lines in the parent anion spectra should be clearly resolved. For the methyl compound, it may be difficult to obtain a recording showing all 32 expected lines clearly separated, hut at least 20 separate lines should be readily distinguishable. Resolution of all the hyperfine structure of the dimethyl and t-hutyl species will depend on the instrument and the sampling conditions.

Results and Discussion

Figure 2 shows the spectra for several BSQ radical anions in methanol as ohtained on a Varian E-9 ESR spectrometer. (A relatively inexpensive teaching ESR instrument that may he suitable for this experiment is available from MICRO- NOW Instruments, Skokie, IL.) Also shown are simulations done on an IBM PC usine the Droeram ESR-SIM (12). The ~~~ ~ ~ ~ - . - hyperfine splitting constants deduced from the spkctra are indicated in the fieure. These denend somewhat on concen- tration and solveit, with variaGons of 10 to 20% or more common for values summarized in reference (16). For the more complex spectra, the computer s i m u l a t e d ~ ~ ~ spectra can he verv helpful in the determination of a set of constants that give a besi fit to the observed spectra.

The experimental hyperfine splittings and the McConnell relationship allow us to calculate spin densities for compari-

assumes that a a molecular orbit& delocalized over n atoms, can he written as a linear comhination of n atomic p, orbi- tals: $ = Z,c,p,. The corresponding one-electron a density at atomi is given by p,, = c , ~ . We omit the intermediatesteps in the HMO calculation and eive onlv the results in Tables 1 and 2 for the two u n s u h s t h e d parent radicals. Both the original secular determinants and the simpler block diagonal forms obtained from symmetry considerations are shown in the tables. Although group theory is not necessary for an understanding of the HMO results, the calculations provide an excellent opportunity for the discussion of group theory and symmetry in the laboratory lecture or for independent student study.

As usual i n ~ ~ M 0 theory, a , and B,, in the tables represent the Coulomb inteeral and the bond interral, respectivelv. For oxygen it is conventional to take a, = a, + hp, ,, = k& = kp where h and k are empirical p a r e e t e r s set equal to h = 2 and k = 2'12 in the SERAPHIM HUCKEL program (13). Values of h = 1 and k = 1 are also common choices for oxygen, and Vincow and Fraenkel(17) suggest that values of h = 1.2 and k = 1.56 are best for BSQ anions. The students are encouraeed to reneat the calculations of Table 1 usine these value;

The BSQ anions have nine a electrons. so the un~a i red electron resides in the $6 orbital in the HMO description. The unpaired electron densities ohtained from the experi- mental ;esults and the McConnell relation are p2 = 0.101 for para HSQ and 0, = 0.033. p4 = 0.150 for ortho BSQ. These are in reasonahle agreement with calculated values of p2 = 0.100 and p3 = 0.055, p4 = 0.124, respectively, when one considers the simplicity of the McConnell assumption and the HMO theory. Note that the calculations provide a basis for the assignment of the two a parameters in the ortho compound.

Since the total unpaired spin density over the molecular framework must be one. the densitv on the CO atom airs canalso hededuced from the experiment and compared'wirh the HMO result. It is instructive to draw valence bond reso- nance structures for these molecules to see whether the oh- served spin densities are consistent with resonance forms expected to have highest weight. Molecular orbital calcula- tions for the methyl and t-butyl-substituted BSQ anions have also been done (10). In these cases, the transfer of unpaired spin density from the a system t o the proton is explained in terms of hyperconjugation (8).

Literature Clted 1. Bunce. N. J. J. Chom. Edue. 1987.64.907-914. 2. Eeatman, M. P. J. Chem.Edue. 1982,59,677-879. 3. Dreenblatt, M. J. Chem. Edue. 1980.57.546551. 4. D8rcy.R. J.Chem.Edue. 1980.57.907-908. 5. Watts. M. T.: Van Reet. R. E.: Eastman M. P. J. Chem. Educ. 1913.50.287-288.

20. 7. Draga. R. S. Physical Metho& in Chemistry. Saunders: Philedelphie, 1977; Chapters

14.9, 13. 8. carrington, A,: McLachlan. A. D. Introduction to Mqgnefie Roaommo, H a w . and

Row: New York. 1967; pp 1-23.72175. 9. Wertz, John E.; Bolton. J. R. Electron Spin Reaomnca: Elementory Theory m d

Ploetieol Appiicotiom: MeGraw-Hill: New York, 1972. 10. Steeitwieser.A.. Jr. Moleculnr OrbitolTheory for Or@& Chomiats:Wiiey:NewYork,

1967

York. 1965. 12. A SERAPHIM program for simulating and plotting Ilmt derivative ESR spectra far

simole radicals is "ESR-SIM" bv McKelvev. R. D. J. Chem.Edue. 1987.64.4974198. rhli IHI-PC pr~nram ran a ~ ~ ; lupd i g e n a r a ~ -exp*r,men~~:. ~ n r n .inn E5H mnrumm r nor avadshlc

13 A-I I~I SFHAPIIIM lvr(lrdn1 r, r IIII. k-I h I O ~ l t l ~ 1 1 I ~ l i o n 8 0 n ~ n IR\I.PCfor ~ ~ ~ 0 2 1 atvm m. I ~ C ~ ~ S . .nc~rdlnp N and o atom.. ir .-HUCKBI." by M~K.IV.Y. H I ) J Cham. Educ. 1981.64.49749S,

..mw..,A", A""".

17. Vincow,G.;FraenkeI.O.K. J.Chem.Phya 1961.34,1S35-1S43

266 Journal of Chemical Education