Carbon Monoxide Flame Bands BY R. N. DIXON Dept. of Chemistry The University Sheffield 10 Received 1st January 1963 The carbon monoxide flame bands have been photographed at high dispersion. The bands in the wavelength region 3100-3900 8 show a regular pattern. This is interpreted in terms of emission from a BZ level of bent C02 to high vibrational levels of the linear ground state the vibrational pattern being complicated by the effects of Fenni resonance. The upper state has an energy of about 46,700 cm-1 above the lowest level of the ground state and an equilibrium angle of 1 2 3 f 3 O . The rotational structure breaks off from which it is deduced that the upper state is probably 1B2. The light emission from the combustion of carbon monoxide has been the subject of numerous investigations.The spectrum consists of a complex series of narrow bands overlaid by a characterless emission that appears continuous at moderate resolution. The relative intensities of the two spectra vary with experi-mental conditions and the bands are favoured by low temperature and pressure. The complexity of the banded spectrum rules out a diatomic molecule as the emitter. Gaydon 1 has reviewed the subject and it is now generally accepted that the bands arise from the chemiluminescent reaction of carbon monoxide and oxygen atoms. However there has been no direct proof of this suggestion neither is there agreement over the nature of the electronic states of CO2 involved in the transition. This paper gives an interpretation of a high-resolution spectrum of the bands photographed using an afterglow source.EXPERIMENTAL Commercial carbon dioxide was partially dissociated in a Wood’s tube drawing an 8.c. current of 1.2 A at 2.5 kV. The electrodes were water-cooled aluminium alloy. The effluent from the discharge was pumped by a 150 l./min rotary pump through a light trap and down an afterglow tube 3 m long and 2 cm diam. A pale blue-grey glow filled the body of the tube and at the highest powers available a thin straw-coloured glow was seen on the wall of the tube. When viewed through a direct-vision spectroscope light could be seen throughout the whole of the visible range of the spectrum. The afterglow stretched a considerable distance down the tube and at a pressure of 1 mmHg the gas was still glowing as it entered the pump.The tube acted as a light pipe and the emission through the quartz end window was sufficiently intense to give a good photograph of the carbon monoxide flame bands with 5 min exposure on Ilford Zenith Astronomical plates using a Hilger small quartz spectrograph with a slit-width of 25p. The appearance of the spec-trum was very similar to that described by Hornbeck and Herman,2 who used a cool flame, and showed a system of partially resolved bands extending from the 3064A OH band to the long wavelength limit of the plates at about 48OOA. A plane mirror mounted inside the pump-end of the tube perpendicular to the tube length was found to increase the light output by about one-half. The maximum light output with the power available was obtained with a pressure of 5 mm Hg.The spectrum was then photographed in the second order of a 15,000 line/inch concave grating spectrograph. Exposure times of several days were required. Since the material sputtered from the electrodes slowly poisoned the glassware the discharge tube was cleaned with 4 % HF solution every 12 h and the afterglow tube every 2 days. The best plates 10 106 CARBON MONOXIDE FLAME BANDS were taken with an exposure time of 5 days using a slit-width of 35p and pre-exposed Kodak OaO plates. Instability in the temperature and pressure in the spectrograph over such Iong periods resulted in a slight blurring of the focus and the best resolution obtained was about 0-5 cm-1. Wavelengths were measured on a photoelectric comparator with reference to an iron hollow cathode lamp using the M.I.T.Wavelength tables 3 and the vacuum corrections of Edlen.4 RESULTS The high-resolution photographs of the carbon monoxide flame bands show a large number of narrow bands and close groups of lines every few A apart. The intensity distribution in the 3064A OH band corresponds to a low rotational tem-perature. The most striking feature of the spectrum is the occurrence of two types of pairs of strong violet degraded bands in the wavelength range 3100-3900 A. One such type has a spacing between heads of 30-40cm-1 and the shorter wavelength head is the stronger in each pair; the other type has a spacing between heads of 60-80 cm-1 and the longer wavelength head is the stronger in each pair and shows a splitting of 2-3 cm-1 (see plate 1).These features may be arranged in series of up to 5 members of similar type with a spacing of -300 cm-1 and the complete spectrum shows an alternation of series of narrow pairs and series of wide pairs. At longer wavelengths than 3900 A this regularity is no longer obvious. DISCUSSION Recent measurements 59 6 on the kinetics of the reaction between carbon monoxide and oxygen atoms suggest a mechanism : CO('C*)+ 0(3P)+ M-*CO,*+M (1) with an activation energy of 4-10 kcal/mole. The dissociation energy Dg of the ground state of C02 to ground state CO and 0 is 5.435 eV.7 Since the shortest wavelength bands lie at about 3100A (4 eV) this mechanism requires that the lower state of the emission lies no higher than 2 eV above the ground state. Mole-cular orbital considerations predict 8 * 9 that the lowest excited states of C02 should be 1B2 and 1Az states at about 5 eV and 3B2 and 3A2 states at about 4 eV in all of which the molecule will be bent.(Following Mulliken's recommendations 10 for the axes of C2v molecules a vector parallel to the 0-0 distance has species b2.) No experimental evidence has been found for any electronic absorption of C02 at longer wavelengths than 2500A (5 eV) even with absorption paths as great as 280 m atm.11 It is therefore concluded that the bands must arise from transitions from a bent upper state to high vibrational levels of the linear ground state the extensive wavelength range of the spectrum being the result of the change in geometry. A bent COz molecule with an angle greater than about 110" will be a slightly asymmetric prolate top with the top axis parallel to the 0-0 distance.The rota-tional levels will therefore be closely approximated by -F(J K ) = BJ(J+ 1) +(A-@K2; = 3(B+ C). (2) The asymmetric top splitting of the double degeneracy of levels with K>O will be greatest for K = 1. The zero nuclear spin of 160 atoms will result in the existence of only one of the levels for each J and K but this will alternate between the upper and lower levels of the K doublets for increasing J and constant K. The rotational levels of the linear ground state are given by F(J) = BJ(J+I). (3 PLATE 1.-The carbon monoxide flame bands. (a) and (b) the assignment of quantum numbers 2v1+u2 and n to series spectrum ; (c) a typical section of the spectrum at longer wavelengths R .N. DIXON 107 The bending vibration v2 is doubly degenerate and levels with v2>0 may possess angular momentum Zh12n about the molecular axis where I = 02 212-2 * 1 or 0. There is a strong Fermi resonance between v2 and the symmetric stretching vibration vl due to the near equality of v1 and 2v2 and this results in a separation of levels differing in I which are degenerate in a harmonic approximation. The close pairs of bands in the spectrum may thus be identified with sub-bands differing in K (K EZ). Since the spacing in the pairs is not constant and no constant combination differences can be found in the spectrum it is concluded that the transitions are of type a (parallel in the limiting symmetric top). The single-headed appearance of most of the bands is in keeping with the low relative intensity of the Q branch in parallel bands with low values of K.The pairs of bands are assigned as follows. (i) Narrow pairs spacing 30-40 cm-1. Sub-bands with K = 0 (longer wave-length) and K = 2 (shorter wavelength and stronger on account of the double de-generacy of levels with K>O). These will be referred to as Z and A bands, respectively. Sub-bands with K = 1 (longer wavelength, the splitting of -2 cm-1 being mainly asymmetric top splitting of the upper state rotational levels) and K = 3 (weaker shorter wavelength band). These will be referred to as II and @ bands respectively. Since the bands are degraded to the violet B'>B". For an angle of 120" this requires that the upper-state bond-length shall not be more than 0.15 A longer than that in the ground state.It is now necessary to enquire into the nature of the spacing of -300 cm-1 between members of the series of similar bands. The vibrational levels of C02 have been extensively studied by Courtoy.12 For each " polyad " of levels that are nearly degenerate in the harmonic approximation and have constant values of I u3 and (2111 + 02) the splitting between levels increases almost linearly with (201 + 02). Extrapolation of this behaviour suggested that a splitting of -300 cm-1 would be expected for levels with (2ul+u2) = 20. Courtoy has shown that the levels with ( 2 ~ + 212) up to 8 are represented within the experimental error by using a diagonal energy level expression : (ii) Wide pairs spacing 60-80 cm-1.G,(u1 212 213 1) = 1345.0401+ 667.25212 +2361.7103 - 3.63~ +3*44tl,tl2 - 19.280103 -0.63521; - 12.510~0 - 12.5603 +0*130; -0.080f0 +O-O211~11~21~ +O*Olt.$ - 0 * 0 7 ~ ~ +0*015~ +0*07O1V$ + 0 * 0 1 0 2 ~ ~ +0*775Z2. (4) The Fermi resonance is then evaluated using off-diagonal matrix elements of the anharmonicity : W(V~ 212 03 2; 01 -1 02 +2 03 I ) = (51*31-0*1501 - 0 4 1 ~ 2 - 0*7803)$[(0 + 2) 2- Z']'U~. ( 5) The calculation of the energy levels is carried out by diagonalizing a square matrix of order [ul+ 1 +$(vz- Z)] for each polyad. A programme was therefore prepared to evaluate the energies of levels with high values of (2211 +uz) using the Manchester University Mercury Computer. A trial run for (201 + 212) = 20 gave a maximum separation of E:g" levels of 296 cm-1.The calculations were then extended to give energies of all the levels with 20<(2ul+v2)<30 03 = 0 and 0<1<4. A portion of these calculations is illustrated in fig. 1 108 CARBON MONOXIDE FLAME BANDS This method of calculation is subject to two sources of error. (i) The extrapolation of a series of vibrational levels of low quantum number to give levels of high quantum number is an unreliable procedure in any molecule. In this case it may be justified by the small values of the cubic coefficients in eqn. (4), and the fact that the highest calculated energy levels are at about 45 % of the energy of the first (spin-forbidden) dissociation process and have bending vibrational amplitudes of about 60”. 1 I - I a3 22 24 2e (2Vl +v2) FIG.1 .-A portion of the calculated array of vibrational levels for the ground state of C02 v3 = 0 2 ~ 1 + ~ 2 = 20. . . 26 Z = 0 2 4. z=o 1 = 2 - 1 = 4 (ii) The theoretical expressions on which eqn. (4) and ( 5 ) are based are derived using second-order perturbation theory to evaluate the anharmonic mixing of levels which differ in the value of (2ul+212).13 The values of the appropriate matrix elements have been estimated by substituting Courtoy’s data 12 for the vibration-rotation interaction constants in Dennison’s equations,l3 and it was found that this approximation is no longer strictly valid. In addition it is seen from fig. 1 that the resonance leads to an overlapping of polyads which differ in the value of (201 +u$. However preliminary estimates of the accuracy of the calculations indicate that the calculated energy level scheme is not seriously in error.In particular the separation of neighbouring levels which differ only in 2 which is as small as 10 cm-1 in some cases is thought to be quite accurate R. N. D ~ x O N 109 All the strong bands between 3100 and 3900A and most of the weak bands, may be explained with the aid of these calculated lower state vibrational levels if it is assumed that all the transitions arise from the various rotational levels of one upper state vibrational level of species B2. In particular the following details of the pattern of bands is reproduced. (a) The separation of the levels in a polyad is greatest between the two highest levels and each interval is 25-30 em-1 less than the next highest interval for levels in the upper half of the polyad.(b) The maximum separation in each polyad increases by 15-20 cm-1 with an increase of 2 in (2vl+ 4. (c) The alternation of series of narrow and wide pairs of bands is associated with even and odd values of (2211 + 24. The nature of this patttern of levels makes possible the assignment of vibrational quantum numbers to the bands. This has been done by fitting the calculations to the experimental pattern for the shortest wavelength bands which involve the lowest value of (2ul+ 02). The comparison is given in tables 1 and 2. Since the harmonic quantum numbers 01 and 112 are meaningless for such strong Fermi resonance the levels are labelled by the value of (2vl+ 112) and a running number n that has the 201 +v2 22 22 22 24 24 24 24 26 26 26 26 26 28 28 28 28 2 V l + v2 23 23 23 25 25 25 25 25 27 27 27 27 27 29 2 3 4 1 2 3 4 1 2 3 4 5 2 3 4 5 3 1,011 -6 3 1,300-6 31,558-4 29,211.7 29,533-5 29,833-7 30,108.0 27,716.5 28,051-7 28 3 65.9 28,6584 28,927-9 26,567-5 26,8951 27,200.8 27,48 5.2 15,674.8 15,388-1 15,122.8 17,4703 17,155.4 16,858-3 16,580.7 18,961.5 18,638-6 18,332.4 18,044.3 17,776.3 20,123.5 19,809-6 19,s 12-5 19,233-8 TABLE THE ASSIGNMENT OF rI BAND-HEADS n Yobs.(cm-9 G&* (cm-1) 2 3 4 1 2 3 4 5 1 2 3 4 5 5 30,279-5 30,572-9 30,844-3 28,4703 28,799-2 29,107.0 29,393-2 29,656-1 26,973.8 27,317.4 27,637.0 27,937.1 28,2159 26,770.0 16,411.5 16,118.8 15,846-0 18,213.3 17,893.7 17,591.3 17,307.5 17,043.9 19,704.8 19,378.1 19,067.4 18,773-9 18,499.1 19,959.9 Y + G" (cm-1) 46,686.4 46,688.7 46,68 1 a 2 46,682.2 46,68869 46.692.0 46,688-7 46,678-0 46,690.3 46,698.3 46,702.7 46,704-2 46,69 1-0 46,704-7 46,713-3 46,7 19.0 Y + G" (cm-1) 46,691-0 46,691.7 46,690.3 46,68 3 * 8 46,692.9 46,698-3 46,700-7 46,700.0 46,678-6 46,695-5 46,704.4 46,711.0 46,715.0 46,729-110 CARBON MONOXIDE FLAME BANDS value 1 for the upper level in each polyad.This vibrational assignment is not unique. The values of (2ul+v2) cannot be reduced unless the energy level cal-culations are considerably in error since the chosen numbering assigns some bands to the uppermost levels of polyads.However all the bands could have (2ul+272) increased by 4 with a corresponding increase of 1 in n. The chosen numbering gives vo = 46,700k 20 cm-1. It is difficult to estimate the probable error in the calculations, but this might be several hundred cm-1. The lack of exact agreement between cal-culation and experiment indicates that the calculations are not completely reliable. The upper level therefore lies 8 & 1 kcal/mole higher than the energy of CO(lC+) + Further justification for the above model may be found in the intensity distribu-tion. The Frank-Condon principle predicts a long progression in the bending vibration for a transition from a bent upper state to a linear lower state.Fermi resonance will complicate this distribution. The wave-functions of the polyad of X levels with (2vl+272) = 8 have been calculated with the approximation that all anharmonic effects have been neglected except the Fermi resonance and with 01 = 2w2. From the form of these functions it is possible to generalize the highest level of each polyad corresponds to a classical motion with a turning point at which the molecule is bent with elongated bonds; the lowest level has a turning point at which the molecule is bent with contracted bonds; and the intermediate levels are intermediate in character. The observation that the bands involve only the upper levels in each polyad indicates that the excited state equilibrium bond length is greater than that in the ground state.The frequency difference between adjacent-X and A bands is the sum of the upper state rotational energy difference 4(A’-B‘) and the separation of the lower levels. The calculations show that this lower state separation is -10 cm-1 and the upper-state difference is therefore the greater part of the observed spacing. Thus we can use the expression : to give a good estimate of (A’ -3’). A similar expression will give 8(A’ - B’) frem the observed spacing of Il and bands. The values of 4(A’-B’) and 8(A’-B’) calculated in this way are given in tables 3 and 4. The consistency of the various o(3~). 4(A’ - B’) = AvobS(A - C) - AG&,,(C -A) ( 6 ) I TABLE THE DETERMINATION OF (A’-) FROM THE SPACING OF PAIRS OF AND A BAND-HEADS 2 U l + 02 n Avobs.(cm-l) AG”c,lc.(m-9 4 ( ~ - B? (cm-1) 22 22 24 24 24 24 26 26 26 26 26 28 28 2s 28 2 4 1 2 3 4 1 2 3 4 5 2 3 4 5 33.3 41.7 30.5 31.8 34.6 41-0 294 31.1 32.6 35.6 40.5 30.2 31.8 33-4 37.3 13-3 21-2 10-6 12.3 14.8 18-7 9-9 11.5 13.6 16-7 21-9 10.8 12-6 15.2 19.3 20.0 20.5 19.9 19.5 19.8 22.3 19-9 19.6 19.0 18.9 18-6 19.4 19.2 18.2 18. R. N. DIXON 111 TABLE 4.THE DETERMINATION OF (A'-') FROM THE SPACING OF PAIRS OF n AND @ BAND-HEADS * 2Ul +v2 23 23 23 23 25 25 25 25 25 27 27 27 27 27 29 n 1 2 3 4 1 2 3 4 5 1 2 3 4 5 5 (Cm-') 62.7 66.3 71-8 76.0 61.2 64.1 68.2 74.1 83.3 60.2 62-6 65.5 70.2 77.4 72.4 AG"dc (cm-1) 22.7 25.4 30.7 38-7 20.4 23-6 28-1 34.7 45.2 19.3 22- 1 25.9 31-5 39.9 35.8 S(X- B')(cm-1) 40.0 40.9 41-1 37.3 40-8 40.5 40.1 39.4 38-1 40.9 40.5 39.6 38.7 37.5 36.6 * The mean frequency of the double 17 band-heads are used in this calculation.values is extremely good. Since the separation in energy of lower state levels that differ in I is mainly due to the same anharmonic terms that cause the splittings within the polyads and the vibrational structure has been cksely fitted the value of A' should be accurate to within 10 %. Hence (A'-B') = 4-9kO-5 cm-1. If we assume that the upper-state bond length is 0.1 A longer than that in the ground state (the bands are violet degraded hence the increase cannot be more than 0.15 A), corresponding to B' = 0.412 cm-1 then the angle OCO = 123+3".The value of A' indicates that bands should be observable for K up to about 9 if the rotational temperature is close to room temperature. Bands with K = 4 are found at the expected frequencies close to each strong X A pair of bands but no K = 6 bands are found. A narrow group of lines is found at the expected frequencies of K = 5 bands and no K = 7 bands are found. The rotational structure of the upper state must therefore break off at about K = 5. The possible electronic states arising from the combination of ground state CO and 0 into a CO2 molecule of point group C2v are : On simple valence grounds none of these states would be either strongly bonding or strongly antibonding.Hence the stability of the lowest 3A2 and 3B2 states predicted by molecular orbital theory must arise from strong mixing with bound states from the products CO(3II)+O(3P). It would therefore be surprising if the lowest 3B2 state dissociates into ground state products via a potential maximum of 8 kcal/mole. Thus the upper state of the bands is probably 1B2 rather than 3B2, and the breaking-off is due to predissociation by a repulsive triplet state made possible by spin-orbit interaction. Since the 1B2 state arises from the removal of the degeneracy of the TC&~ lAu state of linear C02 on bending the flame bands are thus associated with the absorption spectrum of C02 at about 1500A.9 The straw-coloured glow on the surface of the glass indicates that some excited molecules are formed in a wall reaction. This glow is about 1 mm thick at a pressure of 1 mm Hg and the application of random-walk equations indicates a mean life-time of 3 x 10-4 sec or 4000 collisions. Since this will be a lower limit to the radiative lifetime the straw-coloured glow probably involves an excited triplet state 112 CARBON MONOXIDE FLAME BANDS Thus the emission from the carbon monoxide + oxygen atom reaction would appear to involve both singlet and triplet states. I am indebted to Mr. L. Faine for assistance with the construction of the grating spectrograph and to Mr P. Blundell and Mrs. A. Fairburn for assistance with the calculations. 1 Gaydon The Spectroscopy of Flames (Chapman and Hall London 1953 chap. 6. 2 Hornbeck and Herman Nat. Bur. Stand. circ. 1954,523,9. 3 Harrison M.I.T. Wavelength Tables (Why New York 1939). 4Edlen J. Opt. SOC. Amer. 1953 43 339. 5 Clyne and Thrush Proc. Roy. SOC. A 1962,269,404. 6 Mahan private communication. 7 Rossini Wagman Evans Levine and Jaffe Nat. Bur. Stand. circ. 1952 500. 8 Walsh J. Chem. SOC. 1953,2260. 9 Mulliken Can. J. Chem. 1958 35 10. 10 Mulliken J. Chem. Physics 1955 23 1997. 11 Callomon private communication. 12 Courtoy Can. J. Physics 1957 35 608. 13 Dennjson Rev. Mud. Physics 1940,12 175