Infrared Emission Spectrum of the Hydroxyl Radical A Novel Experiment in Molecular Spectroscopy Giles Henderson, Chun-Sheng KO and Tsao-Chin Huang Eastern Illinois University, Charleston. IL 61920
Students are usually exposed to vibrational-rotational absorption spectra in undergraduate physical chemistry. Laboratorv"exneriments tvoicallv introduce the effects of vibra. .. tional-rotational coupling and nuclear isotopes in addition to the usual snectrosconic and notential narameters (1-4). Hvdrogen hatdes are dften employed aAamples because they are vapors a t room temperature and, due to their unusually small amount of inertia, their rotational fine structure is easily resolved (5). In some experiments, students use isotopic substitution to determine the molecular structure of simple linear polyatomic molecules (6). Although infrared spectrometers are used extensively throughout chemistry curricula, students probably never observe infrared emission. In this paper we describe a rather novel experiment in which parameters derived from arecent a b initio potential (7) are used to calculate vibrational-rotational energy levels and then construct a "stick spectrum'' for the overtone emission of the hydroxyl radical. This exercise immediately reveals several interesting and unusual spectral phenomena including band beads much like those observed in vibronic spectra and "spin-orbital" multiplets due to the radicals unpaired electron, similar to the well known doublets observed in the atomicspectra of alkali metals. Students then use their results to desien " an exneriment to observe the soectra in the laboratory using an oxy-acetylene torch as a source and a conventional double beam absorotion soectrometer sliabtlv modified to observe emission. ~~
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Ab-lnitlo Spectrum Shih-I Chu and co-workers (7) have used the configuration interaction (CI) method to obtain theoretical Born-Oppenbeimer electronic wavefunctions and to determine the dependence of the hydroxyl radicals 2n electronic ground state energy on interatomic distance. This a b initio potential (see Fig. 1) may he used with numerical methods (8)to determine vibrational wavefunctions, eigenvalues, and rotational constants. Spectroscopic constants can then be obtained for this potential by a least squares fit of the vibrational eigenvalues to eqn. (1)
where G ( u ) is the vibrational energy in cm-' units for the u vibrational quantum level. The parameters we and w,~, are the vibrational frequency and anharmonicity constant, respectively. These results are given in Table 1. The rotational levels of a free radical exhibit snlittines " due to the magnetic coupling of molecular rotation with electron snin and. to a smaller extent. with electronic orbital motion. These magnetic moment components are vectors which are colinear with corresponding angular momentum vectors, N, S and L, respectively. Their mutual interactions may be represented with vector models corresponding to the various Hunds coupling cases (9) (see Fig. 2). A rigorous expression for rotational terms includes the effects of centrifugal distortion and the coupling of molecular rotation with electronic orbital motion (N.L) which give rise to so-called A-type doubling in addition to the spin-rotation interaction (S.N). However, splittings due to A-type doubling
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Figure 1. Ab initio potential curve and lower vibrational levels fw me X*T stale 0 overtone and 3 1 hot band transitions 01 OH. k this experiment, the 2 am Observed.
Table 1.
o.
(cm-') W.X. (cm-') 8. (cm-'1 re (A1 a. (cm-') A (cm-')
Molecular Constants tor the 2~ State of OH ab inilio (7. 13)
Experimental
Literature ( 10)
3713.0 83.2 18.87 0.9742 0.68 141.4
3732 i 8 84 i 2 19i1 0.97 i .02 0.6 i .I
3737.76 84.887 18.911 0.96966 0.7242 139.21 0.275"
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are small, less than 1cm-', and can only be experimentally observed under high resolution (10). Simple perturbation theory may be used to describe the effects of spin-rotation interactions in 2n molecules (11,12) and gives the following rotational term expression F(J) = B,[(J + ' 1 ~ ) ~A2]i '/z[A(A - 419,)
+ 4B3J + %)2]1"
(2)
where B, is the rotational constant, see eqn. (3), J is the rotational quantum number, A corresponds to the component of orbital angular momentum along the molecular axis, and A is the spin-orbital coupling constant.
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B. = B, - (U %)a, (3) where Be is the equilibrium rotational constant given by eqn. (4) and a. is the vibrational coupling constant. Volume 59 Number 8
August 1982
883
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Fimre 2. .~ case b. The anoular momenta cornDonenta are reo- H u n t s couolino resented oy rectors. N due lo molecu ar rotation: A due lo me component of elecvon c orotal motion aoout interatornlc axis 1.1 = 1 tar n states);S dm to electron spin K = N + A and J gwes thc total angLlar momentLm. K + S. ~
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where h is Planck's constant, p is the reduced mass, re is the equilibrium bond length, and c is the speed of light. Walker and Richards 1131 have used the Dirac Hamiltonian with Hartree-Fock wavefunctions to calculate an ab initio value of the snin-orbital counline constant for the 211 state of the hydroxyl~adical: A = i41.lcm-1. These theoretical parameters. summarized in Table 2.. mav .now bv used with eans. (11-14) calcualte calculate the vibrational-rotational en& levels:
td
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r ( v J ) = G(v) F ( J )
(5)
Students are reauired to obtain these narameters from the primary literatuie and to use a FORTRAN program to calculate the energies. CALCOMI'graphics are used to plot the theoretical stick spectrum for the overtone emission transitions u' -* v" = 2 Oand 3 I in accordance with theselection rules A J = i 1. We elected to study the overtone bands since, in practice, the 1 -- 0 prinriplr band of OH is overlapped seriously by strong emission features from H20and CO?. Although Q-branch components due to AJ = U are in general allowed in the spertra of radicals, they are very weak (14) and are neglected in this calculation. Relative line strengths are approximated a i proportional to if%nd Boltzman j~opulationsof the excited states (1.5) assuming a temoerature of 3110 O K for an oxv-acetvlene flame (/fib. . . An example of a calculated ypectrum is given in the lower section oiFieure 3. The intense 2 0 overtone band exhibits a n open, wei-resolved P-branch consisting of "spin-orbital a t values. e doublets" which are assianed with a ~ ~ r o ~ r iK" Each individual component correspondsto = K" f '/a The unassigned R-branch in the short wavelength region contains many closely spaced lines with a distinct band head at approximately 1399 nm. Although quadratic convergence of rotational lines due to vibrational-rotational coupling is commonplace in the IR spectra of diatomics, it is rare that band heads are observed; In this case involving a Au = -2 overtone transition, the convergence rate is anomalously large since the potential is very anharmonic and gives an expectation value of the interatomic distance squared for the v = 2
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Journal of Chemical Education
Figure 3. A comparison of the experimentally observed ir emission spectrum of OH (upper figure)with a theoretical stick specnum calculated from the a6 inifio x Z rpotential (lowerfigure)and a stick spectrum calculated fromthe experimemal parameters (cent&figure).The experimemal specburn was obtained wim a Beckman Acta M-IV spectrometer using an oxy-acehliene welding torch as an emission source. which is much larger than for u = 0, and, therefore, Bz is much smaller than Bo. This unusual difference in the mamitude of the rotational constants of the excited and gro;~nd state species in combination with the population of high K' rotational levels due to the high flame temperature rrst~ltsin the rapid convergence of the rutational lines, ultimately doubling I "hothack on themselves formine" a "band head."The 9 band" series can be clearly seen as a weak system underlying 0 principleseries. The 3 1 P-branch features are the 2 assigned with K" values and the R-branch band head is observed around 1470 nm. Students find the comparison of the ab initio spectrum with experimental spectra very instructive, particularly in resolving assignment difficulties.
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Experimental The ab initio spectrum calculated above suggests scanning the near ir from about 1385to 1685 nm to observe the overtone bands of the hydroxyl radical. Although most undergraduate facilities have spectrometersthat cover this region, most instruments are designed to operate in a double-beam,absorptionmode. In our own case,-students use an Acta M-IV. An oxy-acetylene welding torch equipped with a small no. AAO (0.020 in. i.d.1 tio is used as a source. Students should be reminded of the flammahil&yof acetylene and of the appropriate precautions in igniting and using a high temperature torch. The sample compartment door is removed and the torch is located such that the flame is centered in the "sample beam" of the cell compartment (see Fig. 4). A small exhaust hood should be placed above the sample compartment and burner. It may also he desirable to fabricate a simple chimney with an appropriate window opening facing the entrance slit. These precautions will insure flame stability oreknition build uo of acetvlene and minimize the oossihilitv of anv.. .. i n rhr iprrtnmrtbr. The n'orrnal sarnplc heam is t,lnrkrd w u h the chirnnry t,r nn lRhl rurnputrr card. The iustrument i i tuned I*,a strung emisr~onfmture, and the flame mixture and pwsition optimized. The relative instrument response may beenhanced by partial attenuation of the reference beam with a second IBM card. We find
Figure 4 An oxy-acetylenewelding torch is introduced into the sample beam of (he cell companment a1 a near-lr. double beam recordmg specDometer.The %ampleoeam fromme specvamelers inernal soJce'sobstr~nedandthe mtensity of the referencebeam is anenualed with an ociuler card of adjustable elevation.
Figure 5. Spanroscopic parameters forthe xZshydroxyl radical are obtained by a least-squaresfit of model transition lrequencies (solid curves1to the observed spectra: A represents 2 0: 0 represents 3 1.
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Table 2. Observed P-Branch Llnes In Overtone Bands of OH ICr
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2 0 Band V[P(PII(em-')
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3 1 Band v[P(K"II(em-')
inteeer M values in which M = -K" for P-branch components and-M = K" 1 for R-branch components. This co&ention along with eqn. (I), (3), and (6) may now he used to obtain a general expression for the frequency of the rotational features in cm-' units:
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that lab jacks are particularly useful in making fine adjustments in the flame elevation and also in adjusting the reference beam attenuation. In addition,a simple, flat, first surfaced mirror placed behind the flame and oriented to reflect the flame emission onto the monochromator sample beam entrance slit approximately doubles the signal intensity. A typical, medium-resolution emission spectrum is shown in the top of Figure 3. Under normal conditions, our instrument exhibits a resolution of 10 cm-' in this spectral region. This clearly precludes the observation of "soin-orbital" doublets and indeed iustifies the due s to A-type doublingin eqn. neglect of the even ~ n h e r s p l i t t i n ~ 12) nhove. -...~ Although there is gcod agreement with line spnrinp of the nh iniriu and the ~xperimenulspectrum, thew la clearly sxy4emnticred shift d~splaremmtof the cnrirc ab inirio hand with respect t u the exprrimental band. However, a comparison of these spectra is useful in assigning the 2 0 and 3 1P-branch features. A summary of these assignments are given in Table 2.
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Data Analysis In view of the resolution limitations of the laboratory data, we may neglect splittings of the rotational terms due to spin-orbital coupling. Setting the spin-orbital coupling constant A = 0 and replacing J with K = f% we may simplify eqn. (2) F(K) = K(K 1)B, - A2B, (6)
+
where A = 1for the 2?r state of OH. In order to write a sinde equation to describe the transition energies of both the P (k = -1) and R (AK= +1) hranches, we will introduce a set of
Since eqn. (7) is quadratic in M, the spectroscopic constants for each series may be obtained separately by a simple second-order least-squares fit of the observed transition frequencies. The vihrational-rotational coupling constant is obtained from the second-order constant; the equilibrium rotational constant is obtained from the first-order constant; the equilibrium vibrational frequency and the anharmonicity constant are then obtained by simultaneous solution of the zero-order constant for both the 2 0 and 3 1series. The results of this analysis are illustrated in Figure 5 and are compared with the ab initio and literature values (10)in Table 1.
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Discussion The potential parameters and spectroscopic constants ohtained from thisexperiment are in excellent agreement with literature values. These constants may be used to calculate a model stick spectrum and then can he compared directly with the experimrntal spectrum using the same methods and prupam employed for the ah initio spectrum (see Fig. 31.The major discrepancy between these results and the nh initio sDertrum is a svstematic dis~lacementof the band oririn. - This clearly reflects8 smnll errrur in the magnitude of theab in~tro furre constant of the OH bond. The CI Quantum calculation gives a slightly smaller curvature in the-% ground state potential than the true potential, resultina in a slightly lower vibrational frequency. 'However, the ab rnTfio calr&tion gives excellent values for the OH bond lenrth . and rotntional constants. This experiment introduces students to the primary literature of both theoretical and experimental molecular physics and is probably their only contact with ir emission spectroscopy and the spectroscopic properties of free radicals during their undergraduate training. Volume 59 Number 8
August 1982
685
Acknowledgment The authors wish to acknowledee Mr. Dean Dickerson for his assistance in data acquisition &d analysis and the Eastern Illinois Universitv Council on Facultv Research for the financial support o? this study.
Llteralure Clted
p. 247. (31 Salzherg. H. W., Morrow, J. I., Cohen. S. R.,snd Green, M. E., "Physical ChemisVy Lahoratnry. Principles and Erperimente." Macrnillan Publishing Ca., Now York, 1976. p 468. (41 Richards, L.W., J. CHBM.EDUC.,43,552(1%66).
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Journal of Chemical E d u c a t i o n
(51 (61 (71 (81
Stafford, F.E., Holt, C. W.,snd Psulson, G. L., J. CHEM.EDUC.. 40.245 (19631. Richards, L. W., J. CHeM. Eouc., 43,644 (1966). Chu,Shih-1,Yoshimine.M. andLiu,B., J. Cham. Phys.,61,6389 (19741. (a) KO, Chun-Shew "A Numerieal Method for the Solution of the Schrodinger Equation by a Trial Wavefunction Im~rovernentFormula." M S . Theis. Eastern
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(111 Steinfeld, J. I., "Molecules and Radiation." Harper and k o w ~ ~ h & h eN& ~ i , York, 70," " .?Q *. -, * .*". (121 Howon, J.. "The Caleulafion of Rotatianal Energy Levels and Rotational Line Intensities inDisromie Molecules," N.B.S. monograph 115,U.S. Government Printing Office, Washington, D.C.. (June 1970). (131 Wa1ker.T. E.H.snd Richards, W. G.,Phys. Re"., 177,lW (19691. (141 (8) Hill, E. L. and Van Vleek. J. H., Phys. RPU. 32,250 (19281. (b1 Benedict, W. W., Plyler, E. K., and Humphrey, C. J.. J Chem. Phys., 21,398 (1953). (151 Ref. (3J.p. 127. (161 Mavrodinesnu, R.. and Boiteur. H.,"Flame S w t r s a p y , " Wiley. New York. 1965.
