1

Lab Documentation.(Available in computerised form)

Spectroscopy of Flames;Luminescence spectra of reactive intermediates

Ágúst Kvaran*, Árni Hr. Haraldsson, and Thorsteinn I. SigfussonScience Institute, University of Iceland, Dunhaga 3, 107 Reykjavík, Iceland

CONTENT:

THE SCOPE OF THE EXPERIMENTMAIN DIRECTIONS FOR THE STUDENTSEXPERIMENTAL SETUP AND PROCEDURERESULTSTHEORY AND DATA ANALYSISCONCLUSIVE REMARKSLTTERATURE CITEDAPPENDIXES

A. ExperimentalA1. Monochromator specifications:A2. Integration circuit ; pulse integrator

B. Conventional spectra analysisB1. Birge Sponer extrapolation curves / plots [<∆ ν v,v+1 > vs v+1] forC 2 (d-a) and line fits for i) a-state and ii) d-state.B2. Table and plot of ∆ ν J´´,J´´+1 vs J for rotational analysis of CH(B-X)

C. Other Things

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THE SCOPE OF THE EXPERIMENT

Vibrational and rotational structure of UV-Vis luminescence spectra due toelectronic transitions in the reactive intermediates, C2, CH and OH, formed in excited statesin flames of burning natural gas (propane or butane), are recorded by a conventionalspectroscopic technique. i) Electronic and ii) vibrational molecular parameters are derivedby Birge Sponer analysis and Franck-Condon factor calculations while iii) rotationalparameters are obtained either by a conventional analysis technique or specta simulations.iv) The vibrational structure analyses serve the purpose to demonstrate the Franck-Condonprinciple.

MAIN DIRECTIONS FOR THE STUDENTS

In an oxygen rich flame of a propane gas (“gas of the house”), luminescence from numberof reactive intermediates, due to electronic transitions (C2(d->a), CH(A->X and B->X)and OH(A->X)) is observed (see fig. 1) (1). In this experiment, vibrational and rotationalstructures of some electronic spectra will be studied.

550500450400350300

λ/ nm

C2(d( 3Πg)->a(3Πu ) )

CH(B( 2Σ -)->X(2Π))

CH(A( 2∆ )->X(

2Π))

OH(A-X), [CH(C-X)]

Fig.1, Kvaran et al.

Figure 1 . Emission spectrum of oxygen rich propane gas flame from a gas burner. Emission from the flamesource upwards (about 2 cm) is recorded. Molecular emissions observed are indicated.

1. Preparation work / equipment handling : Measure signal from a selected molecularspecies (chosen wavelength) (see Fig. 1) in order to optimize signal intensity. Optimize theintensity by adjusting:

i) Flame position with respect to the monochromator entrance slit (emphasizerecording the region closest to the flame source)ii) Flame composition (use oxygen rich flame / blue colored flame)iii) Slit widths near 50 µm (try 30 - 100 µm)iv) PMT / detector power supply (try: 1 - 1.2 kV); (see fig. 2)

2. C 2 (d->a) vibrational structure (1-4).2.1 Record the C2(d->a) spectrum using medium resolution:

Spectral range: 460 - 560 nm (see Fig. 1).

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Scan speed: 2- 4 nm/minSlit width: 50 - 100 µm

2.2 Analyse the spectrum by2.2.1 Birge Sponer extrapolation (5-7)

Derive vibrational parameters (ωe´, ωexe´, ωe´´ and ωexe´´) andelectronic energy difference values (E e´ - Ee´´) (1)

2.2.2 Franck-Condon-Factor (FCF) simulation calculations (5,8)Discuss how (relative) signal intensities depend on i)transition probabilities (FCF), ii) temperature and iii) detectorwavelength dependent response.

Mono-chromator

PMT

computer

entrance slit

gasflow

oxygenflow

gasburner

"innerflame"

"outerflame"

powersupply

Monochromatorcontrol unit

Fig. 2. Equipments

3) CH(B->X) rotational structure (1,3,4,9).3.1 Record the CH(B->X) spectrum in high resolution:

Spectral range: 386 - 404 nm (see Fig. 1)Scan speed: 1 nm/minSlit width: 50 µm

3.2 Analyse the spectrum by a “conventional rotational analysis method” (1)Derive the first order rotational constant (B v´) for the B(2Σ-) state and assignrotational peaks of the spectrum. Make use of necessary known parameters for theground state (X) (4).

4) CH(A->X) (1,3,4,9).4.1 Record the CH(A-X) spectrum in high resolution, spectral range: 415 - 440 nm4.2 Analyse the spectrum by simulation calculations

Derive relevant spectroscopic parameters (use known parameters from theliterature as starting values(4))Interpret the structure of the spectrum.

5) Lab report . Write a lab report in a “standard way”:i) Purpose of experiment, ii) Experimental (minimal),iii - iv) Experimental results and analysis (use figures and tables),v) Discussion. vi) Conclusions.

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EXPERIMENTAL SETUP AND PROCEDURE

A flame due to burning of a natural gas (propane), from a gas burner with anoxygen inlet tube (alternatively a Bunsen burner with air inlet) is placed in front of theentrance slit of a scanning monochromator. A suitable photomultiplier tube (PMT) ishooked on to the exit slit and connected to a power supply and a recording device of somesort. A luminescence spectrum is obtained by recording the PMT output signal as afunction of the dispersed wavelength from the monochromator ( Figure 2 ) .

The details of usable experimental setups tested in our laboratory are as follows.

1) Flame: An ordinary glass blower gas burner connected to the chemistry laboratory gassupply (propane) and an ordinary oxygen cylinder was used to produce a steadynonfluctuating flame. Alternatively an ordinary Bunsen burner was used. More stable andlonger flame could be obtained by using the glass blower gas burner. Suitable flame showsa clear blue inner region closest to its origin, surrounded by a fainter blue region whichextends further away from the flame source and gradually becomes more yellow colored.

2) Monochromator : The flame was positioned vertically in front of a 2 cm high entrance slitof a Digikröm DK480 1/2 meter monochromator (CVI Laser Corporation). Themonochromator houses three gratings, one of which has 1200 groves per mm, blased at500 nm and was commonly used. In that case the dispersion is 1.6 nm/mm. Slits weretypically set at 50 µm for recording high resolution (rotational structure) spectra. Both thegrating drive and slit openings were computer controlled. Further specifications about themonochromator are given in Appendix A1.

3) PMT and accessories : Most commonly an EMI 9789 QB PMT was used (alternatively aless sensitive RCA IP28 PMT was used) driven by Brandenburgh, model 475R powersupply set at less than 1200 V. The output from the PMT was fed into a simple homemadeintegration circuit (pulse integrator, see Appendix A2) driven by a ±12 V power supply.

4) Data collection and handling : Voltage outputs from the integrator were fed into apersonal computer (Macintosh SE/30) via an ACSE-12-8 A/D converter hardware boardusing Workbench Mac V3.1 software (Strawberry tree inc.) for sampling and displaying.Typically voltage readings were stored every half-second for 1 nm/min scanning rates,used to record high-resolution spectra. Afterwards spectra were loaded into the data-handling program, IGOR (WaveMetrics), for analysis, manipulations and graphic display.

Gas and oxygen (or air) inlet flows were regulated and optimized in terms of maximumsignal intensities and minimum fluctuations.

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RESULTS

The spectrum was found to change rather sharply in structure as the flame wasmoved up and down with respect to the monochromator entrance slit. The molecularspectra, due to the emission from the flame source upwards (2 cm), shown on Figure 1 ,show the transitions, C2(d(3Πg)->a(3Πu)), CH(A(2∆)->X(2Π) and B(2Σ-)-> X(2Π)) and

OH(A(2Σ+)->X(2Π)), while a spectrum due to the emission above the “inner flame” (seeabove) is dominantly due to the OH(A->X) transition (4,10).

22x103 2 12 01 91 8ν / cm-1

<- v´=0 v´´=0v´´=1<- v´=1

v´´=012

<- v´=2

<- v´=4

<- v´=3

v´´=1

v´´=2

v´´=3

23

4

5

x6

FCF x Nv´

<- v´=0

<- v´=1

<- v´=2

<- v´=3

<- v´=4

Figure 3 . Spectrum due to the C2(d(3Πg)->a(3Πu)) transition in an oxygen rich propane gas flame.Vibrational quantum numbers of band heads are indicated on top. Calculated band origins (band intensitiesvs positions) are shown at the bottom for T = 3000 K (flame temperature) as bars. Spectroscopic parametersused in the calculations are from reference (4) and listed in Table II.

The C2(d(3Πg)->a(3Πu)) spectrum is shown more clearly on Figure 3 afterconverting to a wavenumber x-axis scale (spectral range 17800 - 22200 cm-1 / 450 - 560nm). Large number of (v´,v´´) transitions are identified by comparing experimental peakpositions and wavenumber values for vibrational transitions calculated by use of knownvibrational (ωe, ωexe) and electronic (Te) parameters for the two electronic statesinvolved(4). Closer inspection of the band structure shows clear band heads and rotationalstructures in the band wings that degrade to the blue. Band head values are listed in Table I .

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\v´´ = 0 1 2 3 4 < ∆ν v ´ , v ´ + 1 >

v´:

0 19380 1620 17760 333

1762 1754 1 7 5 8

1 21142 1628 19514 1593 17921

1729 1719 1 7 2 4

2 21243 1603 19640 1582 18058

1681 1 6 8 1

3 21321 18198

4 21416

< ∆ν v",v"+1> 1 6 2 4 1 5 9 8 1 5 8 2

Table I. Deslandres table of C2(d-a) band heads (ν v´v´´ ; in cm-1). Difference values (∆ν v,v+1) are

written in italic and average difference values (<∆ν v,v+1>) are in bold.

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24.2x103 23.823.623.423.223.022.8

ν / cm-1

<- v´=0

<- v´=1

<- v´=2 v´´=2

v´´=1

v´´=0

calc.(2,2)

CH(A-X)

calc.(1,1)

calc.(0,0)

P

Q

R

Figure 4 . Spectrum due to the CH(A(2∆)->X(2Π)) transition in an oxygen rich propane gas flame.Vibrational quantum numbers of band heads are indicated on top. Calculated spectral contributions (v´,v´´)for T = 3000 K and 10 cm-1 rotational line bandwiths are shown below. Spectroscopic parameters used inthe calculations are listed in Table IV.

The CH(A(2∆)->X(2Π)) spectrum (22740 - 24200 cm-1/ 413 - 440 nm) is shownon Figure 4 . Based on known spectroscopic parameters(4) the vibrational bands (0,0),(1,1) and (2,2) will overlap in this region as indicated. Assuming thermal distribution theband contributions will vary as (0,0) > (1,1) > (2,2). Hence, the rotational structure wingson either side of the band origins are believed to be dominantly due to the v´=0 -> v´´=0transition. This could be verified by inspection of slight structural changes observed in aless intensive emission spectrum, obtained for colder flame (less oxygen flow).

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25.8x103 25.625.425.225.024.8ν / cm-1

*

2468101214 = J´´

P

Q

R CH(B-X)

Figure 5 . Spectrum due to the CH(B(2Σ-)-> X(2Π)) transition in an oxygen rich propane gas flame.Rotational quantum numbers for P lines (J´= J´´-1 -> J´´ transitions) are indicated on top.

The CH(B(2Σ-)-> X(2Π)) spectrum in the region 24500 - 26000 cm-1 (385 - 408nm) shows sharp bandhead at 25860 cm-1 and rotational line series degrading to the red(see Figure 5 ). Limited informations are available in the litterature on spectroscopicparameters for the B state. The regular structure suggests that it is mainly made of oneband, the (0,0) band being the most probable.

The wavenumber range 34600 - 38000 cm-1 (263 - 289 nm) is dominated by thespectrum due to number of vibrational bands of the OH(A(2Σ+)->X(2Π)) transition, but

indications of CH(C(2Σ+)->X(2Π)) transitions were also found. Hence, these spectra arerather complicated in structure and will not be dealt with here any further.

THEORY AND DATA ANALYSIS

In what follows wavenumber units will be assumed for energies and barexpressions used with symbol letters (11) (i.e. E (cm-1) = E (Joule) / hc, etc.).

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Furthermore, Ee, Ev and EJ will be used to indicate energies (in cm-1) for the electronic,vibrational and rotational contributions respectively (corresponding to the term values, Tel,G and F, frequently used in the litterature (5,12)). In all analysis Morse potentials are used

U (r) = Ee + DEe {1 - exp(-β(r - re))}2 (1)

where DEe is the “potential curve d issociation e nergy”, re is the “equilibrium” internuclear

distance and β is a factor which determines the bond stiffness. Both DEe and β can be

expressed as functions of the vibrational parameters (ωe, ωexe)

DEe = ωe2

4 ωexe (2)

β ω µ= −0.12177DE

/ee

1 (3)

µ is the reduced mass. Figure 6 is a schematic representation, showing symbol definitions,of relevance to the following discussion and analysis.

U´(r)

U´´(r)

EJ´

Ev´

Ee´

Ene

rgy

EJ´´

Ev´´

Ee´´

J´v´

J´´v´´

AB*

AB

r(A-B)

DE´´

νv´J´,v´´J´´ν

v´v´´

Figure 6 . Schematic figure showing potential curves, energy levels, energy notations and transitionsdiscussed in this paper.

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Conventional vibrational and rotational spectra analysis

Vibrational structure analysis; C2(d(3Πg)->a(3Πu))

Conventionally Birge Sponer extrapolation is used to derive vibrational parameters(ωe, ωexe) for the electronic states of concern in UV/Vis spectra of diatomic molecules (5).Energies of vibrational states (Eev = Ee + Ev) can be expressed as functions of thevibrational parameters since

Ev = ωe (v + 1/2) - ωexe (v + 1/2)2 (4)

Spacings between neighbor energy levels (∆Ev,v+1 = Ev+1 - E v), hence spacings betweenvibrational bands (∆ν v,v+1) in vibrational band series, (i.e. vibrational bands for commonvibrational level, either in the lower (v´´) or the upper state (v´)) then are

∆Ev,v+1 = ∆ν v,v+1 = ωe - 2 ωexe (v+1) (5)

Vibrational band head wavenumbers for the C2(d->a) system were read into every otherbox in a spreadsheet (excel) for ∆ν v´,v´+1 and ∆ν v´´,v´´+1 (hence ∆Ev´,v´+1 and ∆Ev´´,v´´+1)evaluations as shown in Table I . Average values were displayed to the right (<∆ν v´,v´+1 >)

and at the bottom (<∆ν v´´,v´´+1 >) of the table, from which, ωe´, ωexe´, ωe´´ and ωexe´´were evaluated by linear least square fit analysis of these values plotted against (v+1) (Eq.5). Furthermore, average value for the difference in the electronic parameters (<E e´ - Ee´´>)was evaluated from all the band head values (νv´,v´´) based on the relationship

E e´ - E e´´ = νv´,v´´ - Ev´+ Ev´´ (6)

The result are listed in Table II along with literature values (4). See also Appendix B1.

Our values from ref. (4)

ωe´ (d(3Πg)) 1798 1788.22

ωexe´ (d(3Πg)) 19.3 16.440

ωe´´ (a(3Πu)) 1643 1641.35

ωexe´´ (a(3Πu)) 10.5 11.67

Ee´ -Ee´´ (Τ´el-Τ´´el)19306 19306.26

Table II. Vibrational and electronic parameters for the d(3Πg) and the a(3Πu) states of C2. Our values were

obtained from conventional spectra analysis described in the text. Literature values are from reference [9].

All values are in cm-1.

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Rotational structure analysis; CH(B(2Σ-)-> X(2Π))

The CH((B(2Σ-)-> X(2Π)) spectrum shown on Figure 5 is believed to bedominantly due to the (0,0) band. Other bands which might appear in this region are the(2,1) band and bands for v´ ≥ 4. The red degradation of the band indicates that therotational constant in the upper state (Bv´=0) is less than the one for the lower state (Bv´´=0),hence a reversed relationship holds for the corresponding average internuclear distances(r´>r´´) (5,13,14). The sharp bandhead at 25860 cm-1 is the R branch while the Q and the Pbranches overlap at lower energy with the P branch dominating in the lowest wavenumberregion. The regular pattern of gradually increasing line spacings between rotational lineson the low energy side of the 25560 cm-1 peak (marked with asterisk on Figure 5 ) suggeststhat the P branch lines stick out in that region suitably to allow a conventional rotationalanalysis.

Wavenumber values for rovibrational lines (νv´J´,v´´J´´ = Ee´ + Ev´ + EJ´ - Ee´´ - Ev´´ -EJ´´) can be expressed in terms of the rotational constants B v´ and B v´´ based on the rigidrotor approximation for the rotational energies

E J = B v J (J+1) (7)hence

E J´ - E J´´ = (J + ∆J)(J + ∆J + 1) B v´ - J(J + 1) B v´´ (8)

for J = J´´ and ∆ J = J´- J´´. This allows evaluation of P, Q and R lines from whichspacings between rotational lines (within a vibrational band) (∆ν J´´, J´´+1 = ν J+1´, J´´+1 - ν J´, J´´)

can be shown to be linear functions of J (i.e. ∆ν J´´, J´´+1 = αJ + β; Table III )

∆ν J´´,J´´+1

Lineseries

∆J =J´- J´´ α β

P -1 2(B v´ - B v´´) -2 B v´´

Q 0 2(B v´ - B v´´) 2(B v´ - B v´´)

R +1 2(B v´ - B v´´) 2(2B v´ - B v´´)

Table III. Spacings between rotational lines (∆ν J´´,J´´+1 = ν J+1´,J´´+1 - ν J´,J´´) for P, Q and R rotational lines.

J´´= J. ∆ν J´´,J´´+1 = αJ + β.

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Spacing values for rotational lines in the region 24800 - 25560 cm-1 were evaluatedfrom the spectrum and plotted as a function of integer numbers, n ≥ 0. Slope value (α =4.2 cm-1) was derived from a line fit, to allow determination of B v´ (12.1 cm-1) from

known B v´´=0 value (B v´´=0 = 14.19 cm-1 derived from the Be and αe parameters for theground state(4,12)) by using the expression for the slope of the P serie line ( Table III ) .This value (12.1 cm-1) can be compared with the Be value for the (B(2Σ-)) state known inthe literature to be about 12.645 cm-1 (4). Furthermore, the minimum integer number (no)

in the “∆ν J´´, J´´+1 vs n plots” was varied to give different intercept values (β) until a value

closest to β = -2 B v´´ (- 28.38 cm-1) was obtained. Hence, the P- rotational lines could beassigned as J´´ = n (see Figure 5 ). See also Appendix B2.

Spectra simulations

Spectra simulations are based on comparison of calculated and experimental spectrafor different values of spectroscopic parameters in the calculations until reasonableagreement (“good fit”) is obtained in terms of positions and intensities of spectra lines orbands. The quality of the fit can either be judged visually (“trial and error analysis”) ormore quantitatively by applying least square analysis. The spectra calculations required inthe simulation analysis described below can easily be done by number of different softwarepackages, such as spreadsheet programs or data handling software of some kind. In ourlaboratory, formulas for evaluating line positions and intensities were written by studentsas MACRO´s in the data handling software package IGOR, which allowed fast calculationsand simultaneous display of calculated end experimental spectra. The MACRO proceduresare available on request from the correspondent author (Á.K.). Below a description ofprocedures and examples of analysis of vibrational and rotational structures of flamespectra will be given.

Vibrational structure analysis; C2(d(3Πg)->a(3Πu))

Vibrational band positions (i.e. band origins, νov´,v´´) can be calculated from the

energy difference in the vibrational states for zero rotational energies (νov´,v´´ = Ee´ + Ev´ -

Ee´´ - Ev´´) for the Ev ´s expressed by Eq. (4) to obtain function of the vibrational parameters

involved (ωe´, ωexe´, ωe´´ ωexe´´).

νov´,v´´ = Ee´ - Ee´´ + {ωe´(v´+ 1/2) - ωexe´(v´+ 1/2)2} -

{ ωe´´(v´´+ 1/2) - ωexe´´(v´´+ 1/2)2} (9)

Intensity of a vibrational band (Iv´v´´), in first approximation, is proportional to theFranck-Condon factor (FCF) and the population in the emitting vibrational state (Nv´) (i.e.Iv´v´´ = K x FCF x Nv´; K is a constant), where

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FCF = ψv´(r)ψv´´(r) dr2

(10)

andNv´ = Nv´=0 exp(-{Ev´ - Ev´=0}hc/kBT) (11)

ψv´ and ψv´´ are normalized vibrational wavefunctions, h is Plancks constant, c is speed oflight, kB is the Boltzmann constant and T is the flame temperature. The vibrationalwavefunctions could either be evaluated directly from known analytical expressions derivedby solving the radial Schrödinger equation for the Morse potentials (15,16) or by numericalmethods. In our laboratory numerical integration of the Schrödinger equation by a videlyused method, described by Cooley (17) and summarized by Cashion (18), is used. Inprinciple it involves determination of ψv and Ev values which satisfy the Schrödinger

equation (ΗΗ ψv =Ev ψv), where ΗΗ is the Hamilton operator for the Morse potential. This isfollowed by summing up product values for the wavefunctions evaluated in small radialsteps (typically dr ~ ∆r = 0.05Å) to derive the FCF´s (Eq. 10).

Calculations of line positions and intensities based on the above-mentionedmethods, thus, require knowledge (input values) of vibrational parameters (ωe´, ωexe´,

ωe´´ ωexe´´), electronic energy difference values (E e´ - E e´´), flame temperature (T) as well

as the reduced mass of the molecule (µ). Typically FCF´s were calculated for onevibrational line series (v´ = constant) at a time to obtain positions of bands and relativestrengths of these within each band series (variables: ωe´, ωexe´, ωe´´ ωexe´´ and E e´ - Ee´´). Afterwards the FCF´s were multiplied (weighted) with population values (Nv´; Eq. 11;variable: T) and scaled (factor K) for visual comparison of the calculated and experimentalspectra. Results for analysis of the C2(d(3Πg)->a(3Πu)) spectrum are shown on Figure 3 .Parameters used in the calculation are from reference (4) (see Table II) , T = 3000 K andµ(C2) = 6.000000 g mol-1.

Rotational structure analysis; CH(A(2∆)->X(2Π))

The rovibrational line positions (νv´J´,v´´J´´) are calculated from the vibrational bandorigins (Eq. 9) and the rotational energy differences (νv´J´,v´´J´´ = νo

v´,v´´ +{EJ´ - EJ´´}) byadding a second term to the rotational energy expression in Eq. 7 (D v J

2(J+1)2) to representcentrifugal distortion

EJ´ - EJ´´ = (J + ∆J)(J + ∆J + 1) B v´ - J(J + 1) B v´´

- (J + ∆J)2 (J + ∆J + 1)2D v´ + J2(J+1)2D v´´ (12)

where J = J´´ and ∆J = J´-J´´.

The Intensity of a rovibrational line (Iv´J´,v´´J´´) is proportional to a product of the linestrength, S Λ´J´, Λ´´J´´, the population in the emitting rotational state (N J´) as well as the v´,v´´ dependent terms, FCF and Nv´ mentioned before (i.e. Iv´J´,v´´J´´ = K x S Λ´J´, Λ´´J´´ x N J´

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x {FCF x Nv´}; K is a constant). The line strengths (S Λ´J´, Λ´´J´´) are given as functions of

the quantum numbers J´, J´´, Λ´ and Λ´´ by the Hönl-London formulas (see page 208 inreference (12)) and

NJ´ = NJ´=0 (2J´+1) exp(-EJ´ hc/kBT) (13)

See equations 10 and 11 for FCF and Nv´.

Finally, rotational line shapes are assumed to be and displayed as Gaussian-shapedfunctions for a chosen bandwidth of same value for all rotational lines within a vibrationalband.

Full spectra calculations of line positions and intensities of rovibrational spectrarequire the same informations as those needed to calculate the vibrational structurementioned above (i.e. ωe´, ωexe´, ωe´´ ωexe´´, E e´ - E e´´, T and µ) as well as informationson rotational constants (B v´ ,D v´,B v´´,D v´´) and orbital electronic angular momentum

quantum numbers (Λ´ and Λ´´). In order to view (calculate) the rotational structure spectrawithin a single vibrational band only (IJ´, J´´), calculations of the v´, v´´ dependent terms(FCF and Nv´) could be omitted (i.e. IJ´, J´´ = K´ x S Λ´J´, Λ´´J´´ x N J´ ; K´ = constant).Further simplification of the calculation could be achieved by evaluating relative linepositions (ν J´, J´´ = EJ´ - EJ´´), corresponding to setting the band origin to zero. Such spectra

(i.e. IJ´, J´´ vs ν J´, J´´) can be calculated without knowledge of the vibrational parameters (ωe´,

ωexe´, ωe´´ ωexe´´) and the electronic energy differences (Ee´ - Ee´´). In the simulationprocedure rotational constants could either be treated as variables or calculated from knownequilibrium rotational constants (Be, α e, De) in a standard way (12).

A(2∆) X(2Π)

Λ 2 1

E e (Te) (cm-1) 23189.8 0

ωe(cm-1) 2930.7 2858.5

ωexe(cm-1) 96.65 63.02

Be(cm-1) 14.934 14.457

αe(cm-1) 0.697 0.534

De(10-4cm-1) 15.4 14.5

Bv=0(cm-1) 14.5855 14.19

Bv=1(cm-1) 13.8885 13.656

Bv=2(cm-1) 13.1915 13.122

Table IV . Orbital angular momentum quantum numbers, electronic, vibrational and rotational parameters

for CH, A(2∆) and X(

2Π) states from reference (4).

15

Figure 4 shows the calculated rotational structure bands, (0,0), (1,1) and (2,2) forCH(A(2∆)->X(2Π)) along with the experimental spectrum. Parameters used in the

calculations are from reference (4), (see Table IV) . Furthermore T is 3000 K, µ(CH) is0.92974056 g mol-1and bandwidths of rotational lines are 10 cm-1. The simulation allowsthe following interpretations. i) The sharp peak at 23174 cm-1 is due to the Q branch of the(2,2) band. ii) The strongest peak at 23242 cm-1 is made of Q branches both from (0,0)and (1,1). iii) The rotational structure on the high-energy side of the 23242 cm-1 peakmainly consists of rotational lines from (0,0) and (1,1), which superimpose in the region23330 - 23775 cm-1, but are separated above 23775 cm-1. iv) The shape of the vibrationalbands change from slight blue degradation (0,0) to a near symmetric shape (2,2) as therotational constants (Bv´ , Bv´´) (hence the average internuclear distances (rv´, r v´´)) for v´=v´´ gradually resemble each other.

CONCLUDING REMARKS

Oxygen rich propane gas flame proves to be rich in vibrational androtational spectra structure. Medium high-resolution emission spectra can be used todemonstrate a number of basic principles in quantum chemistry and spectroscopy, relevantto electronic- vibrational- and rotational- structure of molecules as well as transitionprobabilities. Thus the large number of observed bandheads in the C2(d-a) spectrum makesit useful for analysis by the Birge-Sponer extrapolation method. The relatively simpleCH(B-X) band spectrum makes it suitable for conventional rotational analysis.Furthermore the C2(d-a) band spectrum is ideal for comparison with Franck-Condon factorcalculations for simple potential curves to demonstrate its principle and to interpret thevibrational structure. Simple simulation calculations can be performed to show that theCH(A-X) spectrum is made of overlapping rotational series of (v´,v´´) bands for v´= v´´(v´= 0,1,2). Observed trends in structural changes as v´ and v´´ increase can be interpretedin terms of characteristics in potential curves involved.

In this paper, only few examples of possible data analysis of the flame spectra havebeen demonstrated. The individual analysis methods described can be used more widely forthe different spectra systems observed. Furthermore, by adding number of different gases,either through the third inlet tube in a burner or simply along with the air in a Bunsenburner we found large variety of different molecular spectra, suitable for similar purpose asdescribed above(19).

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APPENDICES

A. Experimental

A1. Monochromator specifications:

Digikröm DK480 1/2 meter monochromator (CVI Laser Corporation) / Triple gratingTurret 1/2 meter monochromator, DK 480T.

wavelength drive.............. worm and wheel with computer control.wavelength precision......... >0.007nmwavelength accuracy......... ± 0.007 nmscan speed..................... 1 - 1200 nm/min.slits............................. computer controlled

- width: 10µm - 2000 µm- height: 2mm - 20 mm

• width: 50µm and height : 20 mm most commonly used.

gratings:

no. ruling peak Range(g/mm) (nm) (nm)

1 2400 250 180-6802 1200 500 330-15003 600 1200 800-3000

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A2. integration circuit ; pulse integrator

18

B. Conventional spectra analysis

B1. Birge Sponer extrapolation curves / plots [<∆ ν v,v+1 > vs v+1] forC 2 (d-a) and line fits for i) a-state and ii) d-state.

1 6 2 0

1 6 1 0

1 6 0 0

1 5 9 0

3.02 .52 .01 .51 .0

14.7.´98, C2•CurveFit line da /X=vp1 y= K0+K1*x K0= 1654;K1= -25;V_chisq= 54; V_npnts= 3; V_numNaNs= 0; V_numINFs= 0; V_siga= 11.225; V_sigb= 5.19615; V_q= 1; V_Rab= -0.130938; V_Pr= -0.979076;

Point da.x da.d

0 0 1 6 2 41 1 1 5 9 82 2 1 5 8 2

1740

1720

1700

3.02.52.01.51.0

14.7.´98 C2,•CurveFit line dd /X=vp1 y= K0+K1*x K0= 1808.67;K1= -42.5;V_chisq= 0.166667; V_npnts= 3; V_numNaNs= 0; V_numINFs= 0; V_siga= 0.62361; V_sigb= 0.288675; V_q= 1; V_Rab= -2.35689; V_Pr= -0.999977;

Point dd.x dd.d

0 0 1 7 5 81 1 1 7 2 42 2 1 6 8 1

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B2. table and plot of ∆ ν J´´,J´´+1 vs J for rotational analysis of CH(B-X)

- 8 0

- 7 0

- 6 0

- 5 0

- 4 0

∆νJ´

´,J´´

+1

12108642

J (=J´´)

CH(B-X), rotational analysisCurveFit line dn /X=n /D fit_dn= W_coef[0]+W_coef[1]*x W_coef={-29.809,-4.1822} V_chisq= 112.377; V_npnts= 12; V_numNaNs= 0; V_numINFs= 0; V_q= 1; V_Rab= -0.0651121; V_Pr= -0.978265; W_sigma={2.31,0.28}

Point dn n

0 - 3 7 . 7 21 - 3 7 . 7 32 - 4 5 . 2 43 - 5 1 54 - 5 8 . 6 65 - 6 3 . 6 76 - 6 3 . 6 87 - 7 0 . 7 98 - 7 3 . 8 1 09 - 6 9 . 7 1 1

1 0 - 7 9 . 6 1 21 1 - 8 2 . 9 1 3

C. Other things

-which are made available to the instructors are:

•reference list on supplimentary material / text (enclosed*)

• copies of papers listed in above mentioned reference list (not included here)

• copies of student lab reports (´97-´98) (in Icelandic; not included here)

• catalogues for all equipments: i) Monochromator, ii) PMT, iii) PMT power supply, iv)hardware card for signal entrance to computer, v) software for data sampling and storing,vi) software for data manipulation. (not included here)

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* Reference list for instructors:

a) given to the students

1 Á. Kvaran, Á. H. Haraldsson, and T. I. Sigfusson J. Chem. Educ. 2000, 77,1345-1347.2 K. P. Hüber and G. Herzberg Constants of Diatomic Molecules Van Nostrand-Reinhold, New York, 1979.3 D. P. Shoemaker, C. W. Garland, and J. W. Nibler Experiments in PhysicalChemistry, 6 ed. McGraw-Hill, 1996.4 R. J. Sime Physical Chemistry; Methods, Techniques, and Experiments SaundersCollege Publishing, 1990.5 G. P. Matthews Experimental Physical Chemistry Oxford University Press,Oxford, 1985.6 P. W. Atkins Physical Chemistry, 6 ed. Oxford University Press, Oxford, 1998.

b) Supplimentary reference list:

ref: content:

7 E.H. Fink and K.H. Welge J. Chem. Phys. spectra of CH and1967, 46(11), 4315. C28 H. Okabe Photochemistry of small Molecules spectra informat-Wiley-Interscience, 1978. on CH, C2 and

OH9 William C. Gardiner, Jr. The Chemistry of FlamesScientific American 1982, 246(2), 86.10 O. G. Landsverk Physic. Rev. 1939, 56, 769. original paper on

C2(d-a)11 L. Gerö Z. Physik 1941, 118, 27. original paper on

CH12 R. Bleekrode and W. C. Nieuwpoort J. Chem. Phys. emission spectra1965, 43, 3680. of C2 and CH in

flames

13 J. W. Cooley Math. Computation 1961, XV, 363-374. Numerical analysis14 J. K. Cashion J. Chem. Phys. 1963, 39, 1872-1877. of Schrödinger eq.

15 Ágúst Kvaran, Huasheng Wang, Jón Ásgerisson RotationalJ. Mol. Spectrosc. 1994, 163, 541-558. structure analysis16 Ágúst Kvaran, Huasheng Wang, Gísli Hólmar RotationalJóhannesson J. Phys. Chem. 1995, 99, 4451-4457. structure analysis

21

Literature Cited:

1 Á. Kvaran, Á. H. Haraldsson, and T. I. Sigfusson J. Chem. Educ. 2000, 77,1345-1347.2 O. G. Landsverk Physic. Rev. 1939, 56, 769.3 R. Bleekrode and W. C. Nieuwpoort J. Chem. Phys. 1965, 43, 3680.4 K. P. Hüber and G. Herzberg Constants of Diatomic Molecules Van Nostrand-Reinhold, New York, 1979.5 D. P. Shoemaker, C. W. Garland, and J. W. Nibler Experiments in PhysicalChemistry, 6 ed. McGraw-Hill, 1996; pages 397 and 425.6 R. J. Sime Physical Chemistry; Methods, Techniques, and Experiments SaundersCollege Publishing, 1990; pages 660 - 668.7 G. P. Matthews Experimental Physical Chemistry Oxford University Press,Oxford, 1985; pages 220 and 253.8 P. W. Atkins Physical Chemistry, 6 ed. Oxford University Press, Oxford, 1998;Chapters 16 and 17.9 L. Gerö Z. Physik 1941, 118, 27.10 H. Okabe Photochemistry of small Molecules Wiley-Interscience, 1978.11 D. A. McQuarrie Quantum Chemistry Oxford University Press, 1983; pages 17 -19.12 G. Herzberg Molecular Spectra and Molecular Structure; I. Spectra of DiatomicMolecules, 2nd ed. Van Nostrand Reinhold Company, New York, 1950.13 C. N. Banwell and E. M. McCash Fundamentals of Molecular Spectroscopy, 4 ed.1994; page 173.14 M. Hollas High Resolution Spectroscopy, 2nd ed. Wiley-VCH, 1998.15 P. M. Morse Physical Review 1929, 34, 57- 64.16 V. S. Vasan and R. J. Cross J. Chem. Phys. 1983, 78, 3869 - 3871.17 J. W. Cooley Math. Computation 1961, XV, 363-374.18 J. K. Cashion J. Chem. Phys. 1963, 39, 1872-1877.19 T. I. Sigfusson, S. Sigurdsson, and Á. Kvaran to be published.