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Journal of Molecular Spectroscopy 234 (2005) 75–83

On the c3P (v = 0) state of carbon monoxide

Jacob Baker *

Division of Environmental Health and Risk Management, School of Geography, Earth and Environmental Sciences,

University of Birmingham, Edgbaston, Birmingham, England B15 2TT, UK

Received 16 May 2005; in revised form 1 August 2005Available online 7 October 2005

Abstract

A full analysis of the near infrared c3P–b3R+ (0–0) band is given and term values for both states determined. The c3P (v = 0) state wasjointly analysed with the perturbing k3P (v = 2) state and data from the c3P–X1R+ (0–0) transition and 3A band system were included. Itis shown that the available data are consistent with the c3P (v = 0) state having near Hund�s case b coupling with a spin–orbit constant ofA = 0.45 ± 0.02 cm�1, a homogeneous perturbation with the k3P (v = 2) state, and K-type doubling arising predominantly from its inter-action with the j 3R+ state. A discrepancy with a more recent report of the 3A band system is identified and discussed. The perturbed b3R+

state term values are consistent with a previously reported five state interaction model.� 2005 Elsevier Inc. All rights reserved.

Keyword: Perturbation

1. Introduction

The 3pp, c3P (v = 0) Rydberg state of carbon monox-ide has been the subject of a number of spectroscopicstudies. It was first observed in UV emission as theupper state of the 3A band system (c3P–a3P (0–v00))[1–6]. These emission bands are fairly complex with apossible 27 parity doubled rotational branches, althoughnot all have sufficient intensity to be observed, and areoverlapped with bands of the fourth positive system(A1P–X1R+ emission bands). Hence, many of the rota-tional lines are congested and difficult to identify. Ginterand Tilford [2] through the analysis of these bands werefirst to identify K-type doubling within the c3P state andnoted a moderate perturbation on the rotational levelsgiving rise to an anomalous negative sign for the centrif-ugal distortion constant. Rytel and co-workers [3–5] fur-ther analysed these bands and identified the perturbingstate as a valence 3P state at lower energy. This perturb-ing state has since been identified as the k3P (v = 2)

0022-2852/$ - see front matter � 2005 Elsevier Inc. All rights reserved.

doi:10.1016/j.jms.2005.08.009

* Fax: +44 121 414 5528.E-mail address: j.baker@bham.ac.uk.

valence state [7–9]. Most recently, Hakalla [10] hasextended the analysis of these 3A bands to lower J andto J up to 26. Perturbations were reported for J = 1and 10 6 J 6 20 for both e and f parity levels and forall three spin substates f1, f2, and f3, and only a partialanalysis was given.

The c3P (v = 0) state has also been identified in VUVabsorption from the X1R+ground state [11,12]. Ananalysis by Baker et al. [12] indicated that this spin-forbid-den band gains its intensity predominantly as a result of aninteraction of the c3P (v = 0) state with the C1R+ (v = 0)state, which lies �160 cm�1 to lower energy. The c3P–X1R+ (0–0) band had a fairly simple structure consistingof six rotational branches, comprising S-, R-, P-, andO-type branches (DN = ±2,±1) and two overlapping Q-type branches (DN = 0). However, the low J levels of theQ-type branches were not resolved as a result of a bandhead formation and the P- and O-type branches were over-lapped with the strong C1R+–X1R+ (0–0) absorption band.Consequently, only the S- and R-type branches were fairlywell determined which yields information for only some ofthe c3P state spin and parity levels (f3e and f2e in this case[12]). In fact a small doubt remains for the R-type branchassignment (see Table 2 of [12]).

76 J. Baker / Journal of Molecular Spectroscopy 234 (2005) 75–83

Dabrowski et al. [13] reported the near infrared c3P–b3R+ (0–0) emission band of carbon monoxide in aradio-frequency discharge. This represents the highest res-olution study of the c3P state to date. Despite the highresolution and relatively simple band structure (with ninemain rotational branches and additional satellite branch-es) only a partial analysis of the band was possible asboth states were reported as being heavily perturbed, par-ticularly the b state [14]. Effective parameters for bothstates were given where the analysis was limited to transi-tion lines with N00 < 10. These lines did not appear to beseverely perturbed and perturbations were neglected inthe analysis. Another study of note was carried out byKlopotek and Vidal [15] in which high-lying excited statesof carbon monoxide were examined by means of a two-step excitation from the ground state. That study reportedtriplet splitting in the c3P state for N = 1–5, but no linepositions were given. A triplet splitting corresponding toa spin–orbit constant of A = 1.49 cm�1 was reported forone of the parity components while the other parity com-ponent was said to be perturbed with a different finestructure splitting.

The spectroscopic studies to date leave some uncertain-ty in the details of the possible perturbations within thec3P (v = 0) state and its molecular constants. In thisstudy, the c3P–b3R+ (0–0) band is reanalysed. The c3P(v = 0) state is jointly analysed with the perturbingk3P (v = 2) state and data from the c3P–X1R+ (0–0)transition and 3A band system are included. Molecularconstants and term values are obtained which are consis-tent with all the available data except for some aspects ofthe recent study by Hakalla [10]. Fig. 1 shows the RKRpotential curves of relevant triplet states considered inthis work.

Internuclear

En

erg

y /

cm−1

a 3Π

a´ 3Σ+

c 3Π

b 3Σ+

40000

60000

80000

100000

0.5 1

Internuclear

En

erg

y /

cm−1

a 3Π

a´ 3Σ+

c 3Π

b 3Σ+

Fig. 1. RKR potential energy curves of some of the relevant triplet states coX1R+ground state potential.

1.1. Analysis and spectroscopic data

The c3P (v = 0) state was analysed with the perturbingk3P (v = 2) state, which causes the apparent anomaly inthe sign of the centrifugal distortion constant. Each statewas represented by the 3P Hamiltonian of Brown andMerer [16] forming a 6 · 6 Hamiltonian in total. The homo-geneous interaction between the two states was representedby the interaction term, Æc3Pi (v = 0)jHjk3Pi (v = 2) æ = W,where i = 0–2 [4,17]. In a previous study, where this interac-tion was considered, only the fixed molecular constantsdetermined by Mellinger and Vidal were used for the k3P(v = 2) state [12,18].

Term values for the k3P (v = 2) state were derived fromthe laser-based studies of Mellinger and Vidal [18] and Ber-den et al. [9]. Mellinger and Vidal [18] reported 27 lines forthe k3P (v = 2)–a 03R+ (v = 14) transition (the k3P (v = 2)state had been labelled the (v = 1) state in this study—see[9]), where individual rotational levels of the a 03R+

(v = 14) state had been initially populated by VUV laserabsorption from the ground state. The reported transitionenergies were converted into k3P (v = 2) term values (refer-enced to the X1R+ (v = 0,J = 0) level) by making use of thereported energies of the a 03R+ (v = 14)–X1R+ (v = 0) tran-sition [19] and the known rotational energy levels of theground state [20]. This generated 19 unique term valuesfor the k3P (v = 2) state. Berden et al. [9] reported 7 linesfor the k3P (v = 2)–a3P (v = 1) transition in a 1 + 1 reso-nance enhanced ionisation study, with both parity levelsof the a3P (v = 1, J = 1, X = 1) state being initially popu-lated. This data generated seven term values six of whichcan be compared to those derived from Mellinger andVidal�s work [18,19], where they are found to agree toapproximately their combined experimental uncertainties.

distance / Å

X 1Σ+

k 3Π

1.5 2 2.5

distance / Å

X 1Σ+

k 3Π

nsidered in this work. The energy origin is taken at the minimum of the

Table 2Summary of the c3p (v = 0) state J levels used in the molecular fit

Spin–parity level Ref. [13] Ref. [12] Ref. [2]

f1e 0–20 11–21 6–20f1f 0–21 6–20f2e 1–20 2–26 8–21f2f 1–19 8–21f3e 2–18 2–22 2–18f3f 2–19 2–18

J. Baker / Journal of Molecular Spectroscopy 234 (2005) 75–83 77

Overall from the two studies 20 unique term values of thek3P (v = 2) state are determined, these are given in Table 1.

Dabrowski et al. [13] reported the line positions for thec3P–b3R+ (0–0) band at an estimated resolution of0.005 cm�1 but only analysed the band for N00 < 10 produc-ing ‘‘empirical parameters’’ for the two states. In this study,we focus on the c3P (v = 0) state by assuming the lineassignments from their Table 1 and taking upper state com-bination differences. The c3P–b3R+ (0–0) transition is closeto a case (b) to case (b) transition and as a result the strongbranches are characterised by DN = ±1, 0, and DS = 0. Sa-tellite branches with DS = ±1 appear only for low J and N

and may be difficult to identify. A typographical error wasidentified and corrected for the Q22(8) line position(8251.523 cm�1 rather than 8253.523 cm�1) in their Table1. It is also noted that the R23 (N = 3–6) lines, which werenot assigned, would be expected to be overlapped with theP21(N = 3–6) lines. All assigned lines were included in the fit.

The line positions of the c–X band (0–0) reported inBaker et al. [12] were also included in the rotational fit.The ground state molecular constants are well knownand were derived from [20] (B = 1.9225288 cm�1,D = 6.12 · 10�6 cm�1, and H = 5.74 · 10�12 cm�1 wereused). Initially only the SR(J) and RR(J) rotational branch-es were included which extended the J value coverage forthe f3e and f2e upper spin–parity states to J = 22 and 26,respectively. Addition of these lines enabled the term originT00 to be determined. Afterwards all the line positions giv-en in Table 1 of [12] were included in the fit except for thepP(2) line. Addition of these lines did not significantlychange the results. The assignment of the pP(2) line, whichterminates on the f2e (J = 1) spin–parity level of the c3Pstate, was found to be incorrect and removed from thefit. The reason for this error was due to an improper treat-ment of the eigenvalues arising from the Hamiltonian for

Table 1Term values for the k3P (v = 2) state

J X Parity Ref. [18] Ref. [9]

0 0 f 91932.32 91932.390 0 e 91931.791 0 f 91934.631 0 e 91934.16 91934.282 0 f 91939.32 91939.382 0 e 91938.82 91938.753 0 f 91946.311 1 e 91964.942 1 f 91969.84 91969.882 1 e 91969.783 1 f 91977.394 1 f 91987.462 2 f 91994.94 91995.002 2 e 91994.933 2 f 92003.483 2 e 92003.474 2 f 92014.764 2 e 92014.795 2 f 92028.835 2 e 92028.82

J < 2 which has since been corrected. The pP(2) line wouldbe expected to be close to and possibly overlapped with theQ-type band head of the c–X band.

The estimated errors for the weighted least squares fitanalysis were 0.05 cm�1 for the upper state combinationdifferences of the c–b (0–0) band [13] and the errors speci-fied in Table 1 of [12] for the c–X (0–0) band. The estimatederrors for the term values of the k (v = 2) state were0.07 cm�1 for those derived from Mellinger and Vidal[18] (0.04 cm�1 for the k–a 0 transition [18] and 0.05 cm�1

for the a 0–X transition [19]), and 0.11 cm�1 for those de-rived from Berden et al. [9] (0.1 cm�1 for the k–a transitionand about 0.05 cm�1 for the a–X transitions).

Finally, data from the 3A band system were includedin the analysis by including upper state combination dif-ferences derived from Ginter and Tilford�s reported linepositions of the c3P–a3P (0–2) and (0–1) bands [2], mak-ing use of the assignments given in Rytel and Rytel [4].Ginter and Tilford�s line positions were found to be� 0.2 cm�1 greater than those reported by Rytel and Ry-tel [4], but there was no significant offset for the combina-tion differences which agreed to within the combinedestimated experimental uncertainties (about 0.3 cm�1 forunblended lines). Ginter and Tilford�s data [2] were usedrather than Rytel and Rytel�s [4] data because it extendedslightly to higher J. Only data derived from the strongestbranches (DJ = ±1 and DR = 0) were included in theanalysis, with estimated errors for the combination differ-ences of 0.2–0.6 cm�1. Combination differences wereexcluded if differences greater than 0.45 cm�1 existed be-tween the 0–1 and 0–2 bands. This 3A band data didnot significantly influence the fit but emphasised the high-er J data for the c3P state and was mainly included tocheck for consistency. The more recent 3A band datafrom Hakalla [10] will be considered later. Table 2 givesa summary of the rotational levels of the c3P (v = 0) stateincluded in the fit.

2. Results and discussion

The results of the analysis are given in Table 3. Columnthree gives the fitted molecular constants in the absence ofthe homogeneous interaction between the c3P (v = 0) andk3P (v = 2) states while column four includes the homoge-neous interaction and represents the final deperturbedmolecular constants. For comparison, column two givesthe ‘‘empirical parameters’’ for the c3P (v = 0) state from

Table 3Molecular constants of the c3P (v = 0) and k3P (v = 2) statesa

Molecular parameter Previous work Without c–kinteraction

Final fit

c3P (v = 0) Ref. [13]T 92076.93(4) 92073.16(5)B 1.9484(7) 1.95895(29) 1.97175(23)D · 106 �60(6) �3.08(53) 11.76(21)A 1.504(12) 1.494(22) 0.453(18)k 0.064(7) 0.106(13) —o + p + q 0.087(7) 0.085(11) 0.0893(41)p+2q 0.0209(11) 0.01857(87) 0.01969(33)q 0.00988(13) 0.009747(47) 0.009938(18)W 0 21.08(13)

k3P (v = 2) Ref. [18]T 91959.35(2) 91959.32(6) 91963.59(6)B 1.2805(16) 1.2803(33) 1.2616(13)D · 106 — 9.5 fixed 9.5 fixedA 29.953(14) 29.971(32) 30.895(20)k 0.022(11) — —c �0.091(21) �0.084(41) 0.062(16)o + p + q �0.252(11) 0.255(32) 0.254(12)r 0.0891 0.0339

a All units are in cm�1. In the final fit the spin–spin constants, k, of bothstates could not be determined and so were fixed to zero. r corresponds tothe standard deviation in the overall weighted fit. Values betweenparenthesis are errors, to one standard deviation, in the least significantfigure.

78 J. Baker / Journal of Molecular Spectroscopy 234 (2005) 75–83

Dabrowski et al. [13] and the single state fit for the k3P(v = 2) state given by Mellinger and Vidal [18].

The individual fit for the k state is similar to that givenby Mellinger and Vidal [18] except that k, the spin splitting,could not be determined and was fixed to zero and(o + p + q) is positive rather than negative. The centrifugaldistortion constant for the k3P (v = 2) state could not bedetermined (only data up to J = 5 is available) and wasfixed to 9.5 · 10�6 cm�1, similar to that determined forthe k3P (v = 3) state [8,9]. Comparisons for the single statefit for the c3P state are in fair agreement with that deter-mined by Dabrowski et al. [13] who only considered theN < 11 levels. The main affect of including all availablerotational levels, i.e., extending the analysis to higher J

for all parity and spin substates, is to change the valuesof the rotational constant and the centrifugal distortionconstant. The quality of this fit was not particularly accu-rate over the range of J with an overall standard deviationof the weighted fit of r = 0.089 cm�1.

When the homogeneous interaction with the k3P statewas included an excellent fit of all levels was obtained.The standard deviation of the observed � calculated differ-ences was 0.017 cm�1 for the c3P (v = 0) state combinationdifferences of Dabrowski et al. [13] (139 combination differ-ences), 0.11 cm�1 for the c–X (0–0) line positions [12] (73line positions), 0.17 cm�1 for the c3P (v = 0) state combina-tion differences of Ginter and Tilford [2] (79 combinationdifferences), 0.092 cm�1 for the k3P (v = 2) state term val-ues of Berden et al. [9] (7 term values) and 0.057 cm�1 forthe k3P (v = 2) state term values of Mellinger and Vidal[18] (19 term values). These standard deviations essentially

lie within the respective experimental errors. The overallaccuracy of the fit is mainly determined by the high-resolu-tion near-IR c–b (0–0) line positions [13], with the c–X datadetermining the band origin and extending the J level cov-erage [12]. The Ginter and Tilford 3A band data [2] areessentially superceded by the Dabrowski et al. [13] databut were included mainly to check for consistency.

Including the homogeneous interaction results in signif-icant changes to most of the molecular constants except forthe K-doubling constants. The deperturbed centrifugal dis-tortion constant of the c3P (v = 2) becomes positive andtakes on a more normal value of 11.76 · 10�6 cm�1. Inaddition, the deperturbed spin–orbit constant of the c3P(v = 2) state is decreased and is less than 0.5 cm�1, indicat-ing that some of the apparent spin–orbit splitting is actual-ly due to the unequal shifts of the spin-states arising fromthe homogeneous interaction with the k state.

Table 4 gives the calculated term values for the c3P(v = 0) state, which is our best fit of the available publisheddata. It is noted that Mellinger et al. [21] tabulated the termvalues for the first 10 levels of this state using the empiricalparameters of Dabrowski et al. [13] and using 3A data fromRytel and Rytel [4] and the a3P molecular constants fromEffantin et al. [22] to derive the energy with respect to theground state. Their tabulated values are in agreement withthose derived in this study except there is about a 0.2 cm�1

difference in absolute energy. Table 4 was used to deter-mine the term values for the b3R+ (v = 0) state, the lowerstate of the c–b (0–0) emission band, and these are givenin Table 5. At this point it is instructive to consider theb3R+ (v = 0) state.

Rytel [14] has analysed the (0,1) band of the third posi-tive system (b3R+ fi a3P) of carbon monoxide. The b3R+

state is strongly perturbed by several high lying vibrationallevels of the a 03R+ valence state and the a 03R+ (v = 32) statestrongly interacts with the b3R+ (v = 0) state at J � 19 (seeFig. 2 of [14] and [23]). Rytel [14] analysed the b–a (0,1)emission band up to J = 40 and although the line positionsof the band were not published the molecular parametersfor a five state interacting complex (b3R+ (v = 0), a 03R+

(v = 31–34)) were given. Taking Rytel�s [14] state-mixingHamiltonian model and choosing the eigenvalues corre-sponding to the b3R+ (v = 0) state, these levels can be com-pared with the term values derived here. The origin ofRytel�s model is the b3R+ fi a3P (0–1) band origin andby adding a fixed energy term of 50187.17 cm�1 the rota-tional term values were found to be coincident to withinthe respective experimental errors to those given in Table5 (with an observed � calculated standard deviation of0.06 cm�1 for N = 0–17 for all spin components) exceptfor the N = 20 levels where there is about a 0.7 cm�1 differ-ence. However, this is where the b3R+ (v 0 = 0) state is mostperturbed and it is not clear if this difference is due to theaccuracy of the Rytel model or the specific line positionsmeasured by Rytel [14], which were not reported. Fig. 2compares the term values determined in this study andthe term values derived from Rytel [14]. Fig. 3 plots all five

Table 4Term values for the c3P (v = 0) statea

J f1e f2e f3e f1f f2f f3f

0 92079.63 92079.821 92080.26 92088.14 92080.35 92088.272 92081.74 92088.82 92100.07 92081.79 92088.84 92100.243 92089.28 92100.63 92115.76 92089.37 92100.60 92116.004 92100.83 92116.29 92135.30 92100.98 92116.18 92135.645 92116.32 92135.85 92158.74 92116.55 92135.65 92159.196 92135.74 92159.35 92186.08 92136.07 92159.03 92186.677 92159.09 92186.79 92217.34 92159.53 92186.33 92218.098 92186.37 92218.18 92252.52 92186.95 92217.56 92253.459 92217.58 92253.51 92291.64 92218.32 92252.71 92292.7610 92252.73 92292.80 92334.67 92253.65 92291.80 92336.0211 92291.81 92336.04 92381.64 92292.92 92334.82 92383.2212 92334.82 92383.23 92432.52 92336.16 92381.77 92434.3613 92381.77 92434.36 92487.33 92383.34 92432.65 92489.4514 92432.64 92489.44 92546.05 92434.47 92487.44 92548.4715 92487.43 92548.45 92608.68 92489.54 92546.16 92611.4216 92546.14 92611.40 92675.22 92548.55 92608.78 92678.2917 92608.76 92678.27 92745.66 92611.49 92675.31 92749.0918 92675.29 92749.06 92819.99 92678.36 92745.75 92823.8019 92745.72 92823.76 92898.21 92749.15 92820.08 92902.4120 92820.05 92902.38 92980.31 92823.86 92898.30 92984.9321 92898.26 92984.89 93066.29 92902.47 92980.39 93071.3522 92980.36 93071.31 93156.13 92984.98 93066.37 93161.6523 93066.33 93161.61 93249.84 93071.39 93156.21 93255.8324 93156.17 93255.79 93347.40 93161.69 93249.92 93353.8925 93249.88 93353.85 93448.81 93255.87 93347.48 93455.8126 93347.44 93455.77 93554.06 93353.93 93448.89 93561.60

a Determined in this work—see text for further details. Units are in cm�1. Estimated error in relative energy �0.05 cm�1, and absolute energy� 0.15 cm�1.

Table 5Term values for the b3R+ (v = 0) state of COa

N f1f f2e f3f

0 83833.431 83837.03 83836.94 83837.182 83844.24 83844.14 83844.303 83855.09 83855.00 83855.144 83869.66 83869.57 83869.695 83887.99 83887.91 83888.026 83910.14 83910.07 83910.177 83936.16 83936.11 83936.198 83966.08 83966.02 83966.119 83999.90 83999.86 83999.9310 84037.64 84037.59 84037.6711 84079.26 84079.23 84079.3012 84124.77 84124.72 84124.7913 84174.08 84173.93 84174.0314 84227.13 84227.13 84227.2315 84283.96 84283.92 84283.8816 84343.94 84343.91 84344.0017 84406.96 84406.92 84407.0518 84471.96 84471.86 84472.0719 84536.45 84536.28 84536.6320 84595.36 84595.03 84595.77

a Derived from Dabrowski et al.�s c–b (0–0) line positions, [13], and thefitted c3P term values. Units are in cm�1. Estimated error in relativeenergy � 0.05 cm�1 and absolute energy � 0.15 cm�1. See text for furtherdetails.

J. Baker / Journal of Molecular Spectroscopy 234 (2005) 75–83 79

states of Rytel�s model (energy shifted by 50187.17 cm�1)showing how successive vibrational levels of the a 03R+ stateperturb the b3R+ (v = 0) state.

The reduced term value plot (Fig. 2) reveals several as-pects of the perturbations affecting the b state. In the ab-sence of any perturbation and no centrifugal distortionthe reduced term values would form straight lines withinthe plot while centrifugal distortion causes the lines tocurve gently downwards with increasing N(N + 1). Consid-ering Fig. 2 which shows the b3R+ (v = 0) state N levelsfrom 0 to 20, at low N the levels are perturbed upwardsin energy, which is due to the homogeneous perturbationwith the a 03R+ (v = 31) state which lies below the b3R+

(v = 0) state, while at N = 16–20 the levels are shifteddownwards which is due to the perturbation with thea 03R+ (v = 32) state which lies above the b3R+ (v = 0) state(see Fig. 3). In fact there is a ‘‘crossing’’ (in the diabaticsense) at N = 20 between the f3 and f1 levels of the b3R+

(v = 0) and a 03R+ (v = 32) states, respectively.It is noted that the fixed energy term required to bring

the calculated term values into coincidence with those de-rived in this work is very close to the a3P–X1R+ (1–0) bandorigin as given by Field et al. [24], of 50187.809 cm�1. Insummary, it is shown that Rytel�s study of the b3R+ stateis in excellent agreement with the term values given in

20151050N(N+1) with N labelling

T(N

) –

1.90

88

×N

(N+

1) /

cm

−1

83792

83797

83802

83807

83812

83817

83822

83827

83832

83837

N(N+1) with N labelling

T(N

) –

1.90

88

×N

(N+

1) /

cm

−1

83817

Fig. 2. Reduced term value plot showing the b3R+ (v = 0) state rotational energy levels derived in this study (solid curves and circles) and those derivedfrom Rytel�s [14] five state interaction model with 50187.17 cm�1 added to bring all the levels in to coincidence—in the diagram these levels have beenshifted upwards in energy by 2 cm�1 for comparison purposes (dashed lines and solid triangles). All three spin substates (f1, f2, and f3) are plotted but onthis energy scale they are not separated.

N

T(N

) /

cm

−1

a´ 3Σ+ (v=31)

a´ 3Σ+ (v=32)

a´ 3Σ+ (v=33)

a´ 3Σ+ (v=34)

b 3Σ+ (v=0)

83500

84000

84500

85000

85500

0 5 10 15 20 25 30

T(N

) /

cm

−1

a´ 3Σ+ (v=31)

a´ 3Σ+ (v=32)

a´ 3Σ+ (v=33)

a´ 3Σ+ (v=34)

b 3Σ+ (v=0)

Fig. 3. Term value plot of the rotational energy levels of the b3R+ (v = 0) state and interacting vibrational levels of the a 03R+ state derived from Rytel�s [14]five state interaction model, with 50187.17 cm�1 added to reference the levels to the X1R+ (v = 0, J = 0) ground state.

80 J. Baker / Journal of Molecular Spectroscopy 234 (2005) 75–83

Table 5 and is therefore consistent with the c–b (0–0) lineassignments [13] and c3P state term values of Table 4.We now return our attention back to the c3P state.

The results of this work were also found to be consistentwith the double resonance study of Klopotek and Vidal[15]. That study looked at the triplet splitting for theN = 1–5 levels of the c3P state, excited via the a 03R+

(v = 14) state, and a spin–orbit constant ofA = 1.49 cm�1 was reported. However, this fine structuresplitting was reported as being dependent on the parity le-vel of the intermediate a 0 3R+ (v = 14) state and it wassuggested that one of the parity components of the c statewas perturbed. Line positions were not reported so it is

difficult to comment on these specific statements, althoughit is noted that the value of the ‘‘spin–orbit constant’’ spec-ified is equal to that determined in this study if the homog-enous interaction with the k3P (v = 2) state is neglected. Ofmore interest here is Fig. 12 of [15] which shows 5 transi-tion lines, forming a triplet and a doublet, correspondingto transitions from the f2e (N = 1, J = 1) level of thea 03R+ (v = 14) state to the c3P (v = 0) state. Now the figureis not correctly labelled; allowable transitions correspondto OP12(1),

PQ12(1),QR12(1),

QQ22(1),RR22(1),

SR32(1) tran-sitions and so, in terms of increasing energy, the tripletlines correspond to transitions to the f1e (J = 0), f1f(J = 1), and f1e (J = 2) levels of the c3P state and the

J. Baker / Journal of Molecular Spectroscopy 234 (2005) 75–83 81

doublet to the f2f (J = 1) and f2e (J = 2) levels. The termvalues of these levels are given in Table 4 and are 92079.63,92080.35, 92081.74, 92088.27, and 92088.82 cm�1, respec-tively. The relative energy differences 0.078:0.230:0.940:1.000 match to within the resolution of Fig. 12 in [15] therelative spacing of the lines 0.075(7):0.230(7):0.947(7):1.000, where the bracketed numbers are estimated errors inthe least significant figure. Hence, Klopotek and Vidal�sFig. 12 supports the low J assignments of the c state.

Fig. 4 plots the calculated reduced term values of both thec3P (v = 0) and k3P (v = 2) states. The separation betweenthe states increases with increasing rotational energy as aresult of the fairly large difference in their respective

T(J)

–1.

6×

J(J+

1) /

cm−1

J (J+1)

0 5 10 15

3Π0(f1)

f1f2

f3

c3Π(v=0)

k3Π(v=2)

3Π1(f2)

3Π2(f3)

91600

91700

91800

91900

92000

92100

92200

92300

92400

T(J)

–1.

6×

J(J+

1) /

cm−1

J (J+1)

0 5 10 15

3Π0(f1)

f1f2

f3

c3Π(v=0)

k3Π(v=2)

3Π1(f2)

3Π2(f3)

91600

91700

91800

91900

92100

92200

92300

92400

Fig. 4. Reduced term value plot showing the calculated e

T(N

) –

1.9

6×

N(N

+1)

/ cm

−1

N(N+1)

0 5 10 15

f1ef2f

f3e

f1f

f2e

f3f

92074

92075

92076

92077

92078

92079

92080

T(N

) –

1.9

6×

N(N

+1)

/ cm

−1

N(N+1)

0 5 10 15

f1ef2f

f3e

f1f

f2e

f3f

92074

92075

92076

92077

92078

92079

92080

Fig. 5. Reduced term value plot showing the c3P sta

rotational constants, where Bk < Bc—see Table 3.Consequently the interaction between the two statesdecreases with increasing rotational quantum number.Fig. 5 gives the reduced term value plot for the c3P (v = 0)state levels plotted against N(N + 1). The separation of thec3P (v = 0) state sublevels into two groups of three atincreasing N is due to the rapid change from coupling casea to case b at low N and the K-type doubling arising fromthe near pure precessional interaction with the 3pr, j3R+

(v = 0) state which occurs at lower energy atT00 = 90833.2 cm�1 [2,18]. The effect of the interaction withthe j3R+ state which has f1f, f2e, and f3f spin parity compo-nents is to raise the energy of the corresponding levels in

with J labelling

20 25

with J labelling

20 25

parity levels of the c3P (v = 0) and k3P (v = 2) states.

with N labelling

20 25

with N labelling

20 25

te (v = 0) rotational levels derived in this study.

82 J. Baker / Journal of Molecular Spectroscopy 234 (2005) 75–83

the c3P state compared to the f1e, f2f, and f3e levels, as is evi-dent in Fig. 5. Also evident is the shifting to higher energy ofthe low N levels, particularly the N < 12 levels, due to thehomogeneous interaction with the k3P state. This interac-tion contributes to the apparent spin–orbit splitting of thec3P state because the energy separation between the k3P2

and ‘‘c3P2 (f3)’’ levels is less than that between the k3P0

and ‘‘c3P0 (f1)’’ levels—see Fig. 4. At high N the reducedterm values of Fig. 5 curve downwards in energy withincreasing N, which can be explained by centrifugaldistortion.

The current analysis is consistent with both Ginterand Tilford�s [2] and Rytel and Rytel�s [4] published linepositions of the 3A bands, taking into account the exper-imental resolution and overlap of lines. Hakalla [10]reanalysed the c3P–a3P (0–2) and (0–3) 3A emissionbands of 12C16O in a study that extended the work ofRytel and Rytel [4]. Line positions for 18 doubledbranches were given for each band and the P- and R-branches corresponding to DR = 0 transitions wereextended to J 0 = 24 and 26, respectively. It was reportedthat the c3P (v = 0) state of 12C16O was perturbed, withthe strongest perturbation in the J = 1 and 10 6 J 6 20levels for all spin-substates and parity levels and only apartial analysis was given.

An attempt was made to incorporate Hakalla�s data [10]into the current molecular fit by taking upper state combi-nation differences of the reported c–a (0–2) and (0–3) bandsof 12C16O. The upper state combination differences fromboth bands were similar and generally lay within the exper-imental error, which we estimate to be about 0.15 cm�1.When trying to merge this data it was found that the c3Pstate levels from J = 19–26 diverged from the fit for all spin

T(N

) –

1.96

×N

(N+1

) / c

m−1

N(N+1)

0 5 10 15

92074

92076

92078

92080

92082

92084

92086

T(N

) –

1.96

×N

(N+1

) / c

m−1

N(N+1)

0 5 10 15

92074

92076

92080

92082

92084

92086

Fig. 6. Reduced termvalue plot showing the c3P state (v = 0) rotational levels derfit (see Table 2) are plotted here) and those derived from Hakalla [10] (dashed csublevels are plotted but on this energy scale the (f1f, f2e, and f3f) and (f1e, f2f, an

and parity levels. This discrepancy is shown in Fig. 6,which compares the calculated c3P term values of Table4 (solid curves and filled circles) with the term values de-rived from Hakalla�s work [10] (dashed curves and opencircles). Term values from Hakalla�s work were determinedby adding the corresponding a3P (v = 3) rotational termvalues to the reported c3P–a3P (0–3) line positions. Therotational term values of the a3P (v = 3) state were derivedfrom the molecular parameters and Hamiltonian given byField et al. [24], which are estimated to be accurate to with-in about 0.02 cm�1. Fig. 6 shows reasonable agreement forterm values corresponding to N < 20 with differences of lessthan 0.3 cm�1 (except for some of the lowest J levels).However, there is an increasing discrepancy for Hakalla�sN > 19 levels, where all spin–parity levels on the reducedterm value plot curve upwards with increasing N. This datafor N > 19 in our fit is dominated by data from the sR andRR branches of the c–X (0–0) band, which extends toN = 26 the f2e levels and to N = 23 the f3e levels. However,there is also some data from Dabrowski et al. [13] (up toN = 20) and Ginter and Tilford [12] (up to N = 21) inwhich the beginning of the discrepancy is noticeable. Thereason for the discrepancy is unclear. The Hakalla data[10] would imply another homogeneous interaction with a3P state at lower energy. However, the effect of the k3P(v = 2) state has already been taken into account and thenext 3P state is the k3P (v = 3) state at higher energyand would give rise to a downward energy shift rather thanan upward shift.

The perturbations that Hakalla [10] reports for the c3P(v = 0) state of 12C16O are also reported in the same J levelsfor the 13C16O and 14C16O isotopomers and for the report-ed c3P (v = 1) state of the 12C16O and 13C16O isotopomers

with N labelling

20 25

f1ef2f

f3e

f1f

f2e

f3f

with N abelling

20 25

f1ef2f

f3e

f1f

f2e

f3f

ived in this study (solid curves andfilled circles—only thedata included in theurves and open circles). Notice the deviation at NP 19. All six spin–parityd f3e) subgroups are not clearly separated at least for medium to high N.

J. Baker / Journal of Molecular Spectroscopy 234 (2005) 75–83 83

(see for example Fig. 1 of [10]). However, significant chang-es in the J-dependence of a perturbation might be expectedas a result of isotopic and in particular vibrational energyshifts. It seems possible that due to the highly congestednature of the 3A bands that misassignment of lines beyondN = 19 could have occurred and this may explain Hakalla�sobservations.

3. Conclusion

A full reanalysis of the near infrared c3P–b3R+ (0–0)band is given and term values for all spin and parity com-ponents of the c3P (v = 0) state was determined down totheir lowest J values. The c3P (v = 0) state was jointlyanalysed with the perturbing k3P (v = 2) state and datafrom the c3P–X1R+ (0–0) transition and 3A band systemwere included. Molecular constants and term values areobtained which are consistent with all the available dataexcept for some aspects of the recent 3A band study byHakalla [10]. The results show that the available dataare entirely consistent with the c3P (v = 0) state havingnear Hund�s case b coupling and very weak spin–orbitcoupling with A = 0.45 ± 0.02 cm�1. The state is alsocharacterised by a homogeneous perturbation with thek3P (v = 2) state that shifts to higher energy the low J

levels compared to the higher levels and K-type doublingarising predominantly from its interaction with the j3R+

state. The term values of the perturbed b3R+ Rydbergstate, that forms the lower state of the c–b (0–0) band,were found to be in close agreement with Rytel�s five stateinteraction model.

References

[1] R. Schmid, L. Gero, Nature 139 (1937) 928.[2] M.L. Ginter, S.G. Tilford, J. Mol. Spectrosc. 31 (1969) 292–307.[3] T. Siwiec-Rytel, J. Mol. Spectrosc. 97 (1983) 234–243.[4] T. Rytel, M. Rytel, Acta Phys. Hung. 55 (1984) 69–84.[5] T. Rytel, M. Rytel, Acta Phys. Hung. 59 (1986) 355–369.[6] R. Hakalla, R. Kepa, M. Rytel, M. Zachwieja, J. Mol. Spectrosc. 197

(1999) 199–211.[7] J. Baker, J.L. Lemaire, S. Couris, A. Vient, D. Malmasson, F. Rostas,

Chem. Phys. 178 (1993) 569–579.[8] J. Baker, F. Launay, J. Mol. Spectrosc. 165 (1994) 75–87.[9] G. Berden, R.T. Jongma, D. Van der Zande, G. Meijer, J. Chem.

Phys. 107 (1997) 8303–8310.[10] R. Hakalla, J. Mol. Spectrosc. 209 (2001) 71–80.[11] S.G. Tilford, J. Chem. Phys. 50 (1969) 3126–3127.[12] J. Baker, F. Launay, M. Eidelsberg, F. Rostas, J. Mol. Spectrosc. 203

(2000) 314–319.[13] I. Dabrowski, M. Vervloet, D.-C. Wang, Can. J. Phys. 65 (1987)

1171–1177.[14] T. Rytel, J. Mol. Spectrosc. 145 (1991) 420–428.[15] P. Klopotek, C.R. Vidal, J. Opt. Soc. Am. B. 2 (1985) 869–876.[16] J.M. Brown, A.J. Merer, J. Mol. Spectrosc. 74 (1979) 488–494.[17] H. Lefebvre-Brion, R.W. Field, Perturbations in the Spectra of

Diatomic Molecules, Academic Press, Orlando, 1986.[18] A. Mellinger, C.R. Vidal, J. Chem. Phys. 101 (1994) 104–110.[19] T. Sykora, C.R. Vidal, J. Chem. Phys. 108 (1998) 6320–6330.[20] G. Guelachvili, D. De Villeneuve, R. Farrenq, W. Urban, J. Verges, J.

Mol. Spectrosc. 98 (1983) 64–79.[21] A. Mellinger, E.G. Rohwer, C.R. Vidal, J. Mol. Spectrosc. 206 (2001)

126–134.[22] C. Effantin, F. Michaud, F. Roux, J. D�Incan, J. Verges, J. Mol.

Spectrosc. 92 (1982) 349–362.[23] G.Zikratov,D.W.Setser,N.Sadeghi, J.Chem.Phys. 112 (2000) 10845–

10857.[24] R.W. Field, S.G. Tilford, R.A. Howard, J.D. Simmons, J. Mol.

Spectrosc. 44 (1972) 347–382.