In the Laboratory
Spectroscopy of Flames: Luminescence Spectra of Reactive Intermediates
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Ágúst Kvaran,* Árni Hr. Haraldsson, and Thorsteinn I. Sigfusson Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavík, Iceland; *
[email protected] Medium- and high-resolution UV–vis and IR spectroscopy of diatomic molecules are powerful tools to demonstrate how quantum theory can be applied along with experimental data to derive information on structure, dynamics, and energetics of molecules. Furthermore, these are suitable techniques to demonstrate a number of quantum theoretical principles. Thus, medium-resolution visible absorption spectra of I2 (and Br2) have proved to be easy experiments, suitable to derive information on vibrational frequencies, anharmonicities, and vibrational and bond energies for excited electronic states in particular (1–6 ). High-resolution IR spectra of HCl and DCl are suitable to demonstrate the usefulness of the structure of rotational spectra in deriving molecular structure parameters (bond lengths), rotational energetics, and centrifugal distortions of molecular bonds (4–7). Such experiments and data analyses bridge the gap between theoretical principles and a rapidly growing technique of recording informative (super-) high resolution spectra of larger molecules (8). Despite the importance of such spectroscopic techniques only a limited variety of experiments are used for educational purposes, the most common ones being those for I2 and HCl/ DCl. In this paper we describe experimental and analytical methods that serve an analogous purpose. We present an easy and relatively inexpensive method for deriving high-quality spectroscopic data for both excited and ground electronic molecular states of several diatomic molecules. Analysis by conventional quantum theoretical techniques and simple spectral simulations are used to derive information relevant to the electronic, vibrational, and rotational states and the characteristics of transitions involved (Franck–Condon principle). The experiment fits into the final year B.S. degree program in chemistry. Students should have some background in basic quantum chemistry and spectroscopy. The experiment demonstrates basic spectroscopic principles and is of relevance to all major chemistry fields. It is particularly suitable for students emphasizing physical or analytical chemistry. It involves basic fragment units in the burning of organic compounds (CH, C2, OH), and hence is of relevance to organic and environmental chemistry as well. Furthermore, the emphasis laid on the spectroscopy of C2 in a flame, which is believed to be the cornerstone in the building blocks of fullerenes, makes it appropriate for students doing inorganic chemistry majors. Experimental Methods The vibrational and rotational structure of UV–vis luminescence spectra due to electronic transitions in the reactive intermediates C2, CH, and OH formed in excited states in a flame of burning natural gas (propane or butane) are recorded. A hot flame due to burning of the gas, with an oxygen inlet (alternatively a Bunsen burner with large air inlet), is placed in front of the entrance slit of a scanning monochromator. A suitable photomultiplier tube is hooked onto the exit slit and
connected to a power supply and to a recording device of some sort. A luminescence spectrum is obtained by recording the output signal as a function of the dispersed wavelength from the monochromator. The following is one of several usable experimental setups tested in our laboratory. A flame from an ordinary glassblowing burner was situated vertically in front of the entrance slit of a Digikröm DK480 1⁄2-meter monochromator (CVI Laser Corporation). A grating with 1200 grooves per millimeter, blazed at 500 nm, was used. The dispersion in that case was 1.6 nm/mm and the slits were typically set at 50 µm for recording high-resolution (rotational structure) spectra to give 0.08-nm resolution (minimum resolution of about 0.2 nm is desirable). Both the grating drive and the slit openings were computer controlled. Most commonly an EMI 9789 QB PMT (alternatively a RCA IP28 PMT) driven by a Brandenburgh model 475R power supply set at less than 1200 V was used. The output from the PMT was fed into a simple homemade pulse integrator driven by a ±12-V power supply. Voltage outputs were fed into a personal computer (Macintosh SE/30) via an ACSE-12-8 A/D converter hardware board and Workbench Mac V3.1 software (Strawberry Tree, Inc.) for sampling and displaying. Typically voltage readings were stored every half-second for wavelength scanning rates of 1 nm/min when recording high-resolution spectra. Spectra were loaded into the data-handling program IGOR (WaveMetrics) for analysis, manipulations, and graphic display. Hazards Apart from the usual hazard that can be caused by careless handling of a flame, no significant hazards are related to the procedures involved. Results and Data Analysis Gas and oxygen (or air) inlet flows are regulated and optimized in terms of maximum signal intensities and minimum fluctuations. A suitable flame typically shows a clear blue inner region nearest to its origin, surrounded by a fainter blue region that extends farther away from the flame source and gradually becomes more yellow. The molecular spectra covering the emission from the region above the flame source are shown on Figure 1 (9–13). In the C2(d→a) spectrum a large number of (v′,v′′) transitions are identified (9, 11, 13). Closer inspection of the band structure shows clear band heads and rotational structure in the band wings, which degrade to the blue. The CH(A→X) spectrum (10, 11, 13) is predominantly due to the v′ = 0 → v′′ = 0 transition, with some contribution(s) from the (1,1) and (2,2) transitions, showing rather simple, nearly symmetric rotational structure resembling IR molecular spectra. The CH(B→X) spectrum (10, 11, 13) shows a sharp band
JChemEd.chem.wisc.edu • Vol. 77 No. 10 October 2000 • Journal of Chemical Education
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In the Laboratory
head and rotational line series degrading to the red, made up of one vibrational band. Conventional Vibrational and Rotational Spectra Analysis
Vibrational Structure Analysis: C2 (d→ a) Conventionally the Birge–Sponer extrapolation is used to derive vibrational parameters (ωe, ωexe) for the electronic states of concern (4 ). The spacings between vibrational bands (∆ν¯ v,v+1) in vibrational band series are ∆ν¯ v,v+1 = ωe – 2ωexe(v + 1)
(1)
Band-head wavenumbers can be read into every other box in a spreadsheet for ∆ν¯ v ′, v ′+1 and ∆ν¯ v ′′, v ′′+1 evaluations. Average values are determined, from which ωe′, ωe xe′, ωe′′, and ωe xe′′ can be evaluated by linear least square fit analysis. Furthermore, average – values of the difference in the electronic – parameters (〈 Ee ′ – Ee ′′〉 )can be evaluated from all the bandhead values (ν¯ v ′,v ′′).
Rotational Structure Analysis: CH(B→X) The CH((B(2 Σ ᎑)→X(2Π)) spectrum shown in Figure 2 is predominantly due to the (0,0) band. The rotational lines on the low-energy side of the 25,560 cm᎑1 peak (marked with an asterisk in Fig. 2) are the P branch lines. – ¯ – Wavenumber – – –values–for rovibrational lines (νv ′J ′,v′′J ′′ = Ee ′ + Ev ′ + EJ ′ – Ee ′′ – Ev ′′ –– EJ ′′) can – be expressed in terms of the rotational constants Bv ′ and Bv ′′ based on the rigid rotor approximation – – EJ = Bv J ( J + 1) (2) hence – – – – EJ ′ – EJ ′′ = ( J + ∆J )( J + ∆J + 1) Bv ′ – J ( J + 1)Bv ′′
(3)
for J = J ′′ and ∆J = J ′ – J ′′. This allows evaluation of the P lines, from which the spacings between neighbor lines (∆ν¯ J ′′, J ′′+1 = ν¯ J ′+1,J ′′+1 – ν¯ J ′,J ′′) can be shown to be linear functions of J: – – – ∆ν¯ J ′′, J ′′+1 = 2( Bv ′ – Bv ′′) J – 2Bv ′′ (4)
CH(A(2∆)
X(2Π))
Spacing values for rotational lines in the region 24,800– 25,560 cm᎑1 were evaluated from the spectrum and plotted as a function of integer numbers, n ≥ 0. A slope value of 4.2 cm–᎑1 was derived from a line fit, –to allow determination of Bv ′ – (12.1 cm᎑1) from the known Bv ′′=0 value ( Bv ′′=0 = 14.19 cm᎑1) (13) and the expression for the slope (eq 4). This value (12.1 cm᎑1) can be compared with the Be value for the B( 2Σ ᎑) state, known to be about 12.645 cm᎑1) (13). Furthermore, the minimum integer number (n0) in the ∆ν¯ J ′′, J ′′+1-vs-n plots was varied–to give different intercept values until a value closest to ᎑2Bv ′′ (᎑28.38 cm᎑1) could be obtained. Hence, the P rotational lines could be assigned as J ′′ = n (see Fig. 2). Spectrum Simulations Spectrum simulations are based on comparison of calculated and experimental spectra for different values of spectroscopic parameters until a “good fit” is obtained in terms of positions and intensities of spectral lines or bands. The quality of the fit can be judged either visually (trial-anderror analysis) or more quantitatively by applying least-squares analysis. The spectrum calculations required in the simulation analysis can easily be done by a number of software packages, such as spreadsheet programs (e.g. Excel) or data-handling software of various kinds (e.g. IGOR). Computer codes for IGOR are available for interested readers on request from the corresponding author (Á.K.).
Vibrational Structure Analysis: C2 (d→ a) Vibrational band positions (i.e. band origins, ν¯v°′, v ′′) are calculated from the energy difference in the vibrational states for zero rotational energies determined by the vibrational parameters involved. The intensity of a vibrational band (Iv ′,v ′′), in the first approximation, is proportional to the Franck–Condon factor (FCF) and the population in the emitting vibrational state (Nv ′): Iv ′,v ′′ = K × FCF × Nv ′
where K is a constant. Nv ′ is based on the Boltzmann distribution for the flame temperature. The vibrational wave
14 C2(d(3Πg)
(5)
12
10
8
6
4
2
= J''
a(3Πu))
OH(A−X), [CH(C−X)]
*
Q R
CH(B-X) CH(B(2Σ −)
300
350
X(2Π))
400
P
450
500
550
λ / nm Figure 1. Emission spectrum of oxygen-rich propane gas flame from a gas burner. Emission from the flame source upward (about 2 cm) is recorded. The observed molecular emissions are indicated.
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24.8
25.0
25.2
ν / cm
25.4
25.6
25.8x103
−1
Figure 2. Emission due to the CH(B(2 Σ ᎑)→X(2 Π)) transition in an oxygen-rich propane gas flame. Rotational quantum numbers for P lines (J ′ = J ′′ – 1 → J ′′ transitions) are indicated at the top.
Journal of Chemical Education • Vol. 77 No. 10 October 2000 • JChemEd.chem.wisc.edu
In the Laboratory
functions needed to evaluate the FCF can be evaluated either directly from known analytical expressions derived by solving the radial Schrödinger equation for Morse potentials (14, 15), or by numerical methods (16, 17 ). Calculation of line positions and intensities based on these methods requires knowledge of vibrational parameters, electronic energy difference values, and flame temperature. By varying the temperature in the calculation procedure and using derived (see above) or literature values of spectroscopic parameters (13), calculated spectra suitable for visual comparison with the observed spectra can be obtained.
Rotational Structure Analysis: CH(A→X) Rovibrational line positions (ν¯ v ′J ′, v ′′J ′′) are calculated from the vibrational band origins and the rotational energy differences. The intensity of rovibrational lines (I v ′J ′, v ′′J ′′) is proportional to a product of the line strength, SΛ′J ′, Λ′′J ′′ (18), the population in the emitting rotational state (NJ ′), and the v ′,v ′′dependent terms FCF and Nv ′ : I v ′J ′, v ′′J ′′ = K × SΛ′J ′, Λ′′J ′′ × NJ ′ × (FCF × Nv ′)
(6)
where K is a constant. Finally, the rotational line shapes are assumed to be and are displayed as Gaussian-shaped functions for a chosen bandwidth. The same value for the bandwidth was used for all rotational lines within a vibrational band. In fitting the spectrum, rotational parameters of the states involved are needed. These can be either treated as variables in the simulation procedure or calculated from known equilibrium rotational constants (13) in a standard way (18). Final Remarks The experiment can help the students to learn the following. Emission spectroscopic technique; that is, how a luminescence spectrum can be resolved. Equipment units are basic and the combination of units is logical: a monochromator for light resolving, photomultiplier tube for detecting, and a computer for displaying and handling data. Molecular spectroscopy principles. The experiment shows how UV–vis spectroscopy of molecules involves electronic, vibrational, and rotational structure due to corresponding transitions. The vibrational structure analysis demonstrates the Franck–Condon principle. Methods of detailed spectra analysis. Both conventional and simulation analysis techniques are used. Conventional methods are particularly suitable for demonstrating the link between quantum chemistry and spectroscopy. The student will learn to analyze spectra by use of formulas based on fundamental approaches such as the rigid-rotor approximation and the Morse potential. The computer simulation methods are not just “black-box” methods! Intensity analysis of electronic spectra requires distinguishing between the effects of transition probabilities based on the Franck–Condon principle and
population distributions determined by the Boltzmann distribution for the flame temperature. Simulation of rotationally structured spectra shows how internuclear distances affect spectrum structure and gives meaning to commonly used expressions like “blue or red degradation of spectra bands”. We suggest that the experiment be performed either with the conventional analysis only or with both conventional and simulation techniques. Approximately two afternoons’ work should be allowed for the former, whereas three afternoons’ work may be required for the latter, assuming the necessary simulation programs to be available. Acknowledgments We are grateful for financial support from the Students’ Innovation Fund. We would like to thank Sæberg Sigursson for his contribution to recording spectra and Jón Ásgeirsson for helping with developing simulation programs. W
Supplemental Material
Supplemental material for this article is available in this issue of JCE Online, where the laboratory procedures and data analysis are explained in detail. Literature Cited 1. Stafford, F. E. J. Chem. Educ. 1962, 39, 626–629. 2. McNaught, I. J. J. Chem. Educ. 1980, 57, 101–103. 3. Sime, R. J. Physical Chemistry: Methods, Techniques, and Experiments; Saunders: Philadelphia, PA, 1990; pp 660–668. 4. Shoemaker, D. P.; Garland, C. W.; Nibler, J. W. Experiments in Physical Chemistry, 6th ed.; McGraw-Hill: New York, 1996; pp 397, 425. 5. Matthews, G. P. Experimental Physical Chemistry; Oxford University Press: Oxford, 1985; pp 220, 253. 6. Atkins, P. W. Physical Chemistry, 6th ed.; Oxford University Press: New York, 1998; Chapters 16, 17. 7. Ganapathisubramanian, N. J. Chem. Educ. 1993, 70, 1035. 8. Hollas, M. High Resolution Spectroscopy, 2nd ed.; Wiley-VCH: New York, 1998. 9. Landsverk, O. G. Physic. Rev. 1939, 56, 769. 10. Gerö, L. Z. Phys. 1941, 118, 27. 11. Bleekrode, R.; Nieuwpoort, W. C. J. Chem. Phys. 1965, 43, 3680. 12. Krishnamachari, S. L. N. G.; Broida, H. P. J. Chem. Phys. 1961, 34, 1709. 13. Hüber, K. P.; Herzberg, G. Constants of Diatomic Molecules; Van Nostrand-Reinhold: New York, 1979. 14. Morse, P. M. Phys. Rev. 1929, 34, 57–64. 15. Vasan, V. S.; Cross, R. J. J. Chem. Phys. 1983, 78, 3869–3871. 16. Cooley, J. W. Math. Computation 1961, 15, 363–374. 17. Cashion, J. K. J. Chem. Phys. 1963, 39, 1872–1877. 18. Herzberg, G. Molecular Spectra and Molecular Structure: I. Spectra of Diatomic Molecules, 2nd ed.; Van Nostrand Reinhold: New York, 1950; pp 106–107.
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