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On the c3Π (v = 0) state of carbon monoxide
Journal of Molecular Spectroscopy 234 (2005) 75–83 www.elsevier.com/locate/jms
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 2005 Available 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 was jointly analysed with the perturbing k3P (v = 2) state and data from the c3P–X1R+ (0–0) transition and 3A band system were included. It is shown that the available data are consistent with the c3P (v = 0) state having near HundÕs case b coupling with a spin–orbit constant of A = 0.45 ± 0.02 cm1, a homogeneous perturbation with the k3P (v = 2) state, and K-type doubling arising predominantly from its interaction 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 monoxide has been the subject of a number of spectroscopic studies. It was first observed in UV emission as the upper state of the 3A band system (c3P–a3P (0–v00 )) [1–6]. These emission bands are fairly complex with a possible 27 parity doubled rotational branches, although not all have sufficient intensity to be observed, and are overlapped with bands of the fourth positive system (A1P–X1R+ emission bands). Hence, many of the rotational lines are congested and difficult to identify. Ginter and Tilford [2] through the analysis of these bands were first to identify K-type doubling within the c3P state and noted a moderate perturbation on the rotational levels giving rise to an anomalous negative sign for the centrifugal distortion constant. Rytel and co-workers [3–5] further analysed these bands and identified the perturbing state as a valence 3P state at lower energy. This perturbing state has since been identified as the k3P (v = 2)
*
Fax: +44 121 414 5528. E-mail address: [email protected].
0022-2852/$ - see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2005.08.009
valence state [7–9]. Most recently, Hakalla [10] has extended the analysis of these 3A bands to lower J and to J up to 26. Perturbations were reported for J = 1 and 10 6 J 6 20 for both e and f parity levels and for all three spin substates f1, f2, and f3, and only a partial analysis was given. The c3P (v = 0) state has also been identified in VUV absorption from the X1R+ground state [11,12]. An analysis by Baker et al. [12] indicated that this spin-forbidden band gains its intensity predominantly as a result of an interaction of the c3P (v = 0) state with the C1R+ (v = 0) state, which lies 160 cm1 to lower energy. The c3P– X1R+ (0–0) band had a fairly simple structure consisting of six rotational branches, comprising S-, R-, P-, and O-type branches (DN = ±2,±1) and two overlapping Qtype branches (DN = 0). However, the low J levels of the Q-type branches were not resolved as a result of a band head formation and the P- and O-type branches were overlapped with the strong C1R+–X1R+ (0–0) absorption band. Consequently, only the S- and R-type branches were fairly well determined which yields information for only some of the c3P state spin and parity levels (f3e and f2e in this case [12]). In fact a small doubt remains for the R-type branch assignment (see Table 2 of [12]).
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J. Baker / Journal of Molecular Spectroscopy 234 (2005) 75–83
Dabrowski et al. [13] reported the near infrared c3P– b R (0–0) emission band of carbon monoxide in a radio-frequency discharge. This represents the highest resolution study of the c3P state to date. Despite the high resolution and relatively simple band structure (with nine main rotational branches and additional satellite branches) only a partial analysis of the band was possible as both states were reported as being heavily perturbed, particularly the b state [14]. Effective parameters for both states were given where the analysis was limited to transition lines with N00 < 10. These lines did not appear to be severely perturbed and perturbations were neglected in the analysis. Another study of note was carried out by Klopotek and Vidal [15] in which high-lying excited states of carbon monoxide were examined by means of a twostep excitation from the ground state. That study reported triplet splitting in the c3P state for N = 1–5, but no line positions were given. A triplet splitting corresponding to a spin–orbit constant of A = 1.49 cm1 was reported for one of the parity components while the other parity component was said to be perturbed with a different fine structure splitting. The spectroscopic studies to date leave some uncertainty in the details of the possible perturbations within the c3P (v = 0) state and its molecular constants. In this study, the c3P–b3R+ (0–0) band is reanalysed. The c3P (v = 0) state is jointly analysed with the perturbing k3P (v = 2) state and data from the c3P–X1R+ (0–0) transition and 3A band system are included. Molecular constants and term values are obtained which are consistent with all the available data except for some aspects of the recent study by Hakalla [10]. Fig. 1 shows the RKR potential curves of relevant triplet states considered in this work.
1.1. Analysis and spectroscopic data
3 +
The c3P (v = 0) state was analysed with the perturbing k P (v = 2) state, which causes the apparent anomaly in the sign of the centrifugal distortion constant. Each state was represented by the 3P Hamiltonian of Brown and Merer [16] forming a 6 · 6 Hamiltonian in total. The homogeneous interaction between the two states was represented by the interaction term, Æc3Pi (v = 0)jHjk3Pi (v = 2) æ = W, where i = 0–2 [4,17]. In a previous study, where this interaction was considered, only the fixed molecular constants determined by Mellinger and Vidal were used for the k3P (v = 2) state [12,18]. Term values for the k3P (v = 2) state were derived from the laser-based studies of Mellinger and Vidal [18] and Berden et al. [9]. Mellinger and Vidal [18] reported 27 lines for the k3P (v = 2)–a 0 3R+ (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 0 3R+ (v = 14) state had been initially populated by VUV laser absorption from the ground state. The reported transition energies were converted into k3P (v = 2) term values (referenced to the X1R+ (v = 0, J = 0) level) by making use of the reported energies of the a 0 3R+ (v = 14)–X1R+ (v = 0) transition [19] and the known rotational energy levels of the ground state [20]. This generated 19 unique term values for the k3P (v = 2) state. Berden et al. [9] reported 7 lines for the k3P (v = 2)–a3P (v = 1) transition in a 1 + 1 resonance enhanced ionisation study, with both parity levels of the a3P (v = 1, J = 1, X = 1) state being initially populated. This data generated seven term values six of which can be compared to those derived from Mellinger and VidalÕs work [18,19], where they are found to agree to approximately their combined experimental uncertainties. 3
c 3Π
100000
k 3Π
Energy / cm−1
b 3Σ+ 80000
a´ 3Σ+
60000
X 1Σ + a 3Π 40000 0.5
1
1.5
2
2.5
Internuclear distance / Å Fig. 1. RKR potential energy curves of some of the relevant triplet states considered in this work. The energy origin is taken at the minimum of the X1R+ground state potential.
J. Baker / Journal of Molecular Spectroscopy 234 (2005) 75–83
Overall from the two studies 20 unique term values of the k3P (v = 2) state are determined, these are given in Table 1. Dabrowski et al. [13] reported the line positions for the c3P–b3R+ (0–0) band at an estimated resolution of 0.005 cm1 but only analysed the band for N00 < 10 producing ‘‘empirical parameters’’ for the two states. In this study, we focus on the c3P (v = 0) state by assuming the line assignments from their Table 1 and taking upper state combination differences. The c3P–b3R+ (0–0) transition is close to a case (b) to case (b) transition and as a result the strong branches are characterised by DN = ±1, 0, and DS = 0. Satellite branches with DS = ±1 appear only for low J and N and may be difficult to identify. A typographical error was identified and corrected for the Q22(8) line position (8251.523 cm1 rather than 8253.523 cm1) in their Table 1. It is also noted that the R23 (N = 3–6) lines, which were not assigned, would be expected to be overlapped with the P21(N = 3–6) lines. All assigned lines were included in the fit. The line positions of the c–X band (0–0) reported in Baker et al. [12] were also included in the rotational fit. The ground state molecular constants are well known and were derived from [20] (B = 1.9225288 cm1, D = 6.12 · 106 cm1, and H = 5.74 · 1012 cm1 were used). Initially only the SR(J) and RR(J) rotational branches were included which extended the J value coverage for the f3e and f2e upper spin–parity states to J = 22 and 26, respectively. Addition of these lines enabled the term origin T00 to be determined. Afterwards all the line positions given in Table 1 of [12] were included in the fit except for the p P(2) line. Addition of these lines did not significantly change the results. The assignment of the pP(2) line, which terminates on the f2e (J = 1) spin–parity level of the c3P state, was found to be incorrect and removed from the fit. The reason for this error was due to an improper treatment of the eigenvalues arising from the Hamiltonian for Table 1 Term values for the k3P (v = 2) state J
X
Parity
Ref. [18]
Ref. [9]
0 0 1 1 2 2 3 1 2 2 3 4 2 2 3 3 4 4 5 5
0 0 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 2 2 2
f e f e f e f e f e f f f e f e f e f e
91932.32 91931.79 91934.63 91934.16 91939.32 91938.82 91946.31
91932.39
91969.84 91969.78 91977.39 91987.46 91994.94 91994.93 92003.48 92003.47 92014.76 92014.79 92028.83 92028.82
91934.28 91939.38 91938.75 91964.94 91969.88
77
Table 2 Summary of the c3p (v = 0) state J levels used in the molecular fit Spin–parity level
Ref. [13]
Ref. [12]
Ref. [2]
f1e f1f f2e f2f f3e f3f
0–20 0–21 1–20 1–19 2–18 2–19
11–21
6–20 6–20 8–21 8–21 2–18 2–18
2–26 2–22
J < 2 which has since been corrected. The pP(2) line would be expected to be close to and possibly overlapped with the Q-type band head of the c–X band. The estimated errors for the weighted least squares fit analysis were 0.05 cm1 for the upper state combination differences of the c–b (0–0) band [13] and the errors specified in Table 1 of [12] for the c–X (0–0) band. The estimated errors for the term values of the k (v = 2) state were 0.07 cm1 for those derived from Mellinger and Vidal [18] (0.04 cm1 for the k–a 0 transition [18] and 0.05 cm1 for the a 0 –X transition [19]), and 0.11 cm1 for those derived from Berden et al. [9] (0.1 cm1 for the k–a transition and about 0.05 cm1 for the a–X transitions). Finally, data from the 3A band system were included in the analysis by including upper state combination differences derived from Ginter and TilfordÕs reported line positions of the c3P–a3P (0–2) and (0–1) bands [2], making use of the assignments given in Rytel and Rytel [4]. Ginter and TilfordÕs line positions were found to be 0.2 cm1 greater than those reported by Rytel and Rytel [4], but there was no significant offset for the combination differences which agreed to within the combined estimated experimental uncertainties (about 0.3 cm1 for unblended lines). Ginter and TilfordÕs data [2] were used rather than Rytel and RytelÕs [4] data because it extended slightly to higher J. Only data derived from the strongest branches (DJ = ±1 and DR = 0) were included in the analysis, with estimated errors for the combination differences of 0.2–0.6 cm1. Combination differences were excluded if differences greater than 0.45 cm1 existed between the 0–1 and 0–2 bands. This 3A band data did not significantly influence the fit but emphasised the higher J data for the c3P state and was mainly included to check for consistency. The more recent 3A band data from Hakalla [10] will be considered later. Table 2 gives a summary of the rotational levels of the c3P (v = 0) state included in the fit. 2. Results and discussion
91995.00
The results of the analysis are given in Table 3. Column three gives the fitted molecular constants in the absence of the homogeneous interaction between the c3P (v = 0) and k3P (v = 2) states while column four includes the homogeneous interaction and represents the final deperturbed molecular constants. For comparison, column two gives the ‘‘empirical parameters’’ for the c3P (v = 0) state from
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J. Baker / Journal of Molecular Spectroscopy 234 (2005) 75–83
Table 3 Molecular constants of the c3P (v = 0) and k3P (v = 2) statesa Molecular parameter
Previous work
c3P (v = 0) T B D · 106 A k o+p+q p+2q q W
Ref. [13]
k3P (v = 2) T B D · 106 A k c o+p+q r
1.9484(7) 60(6) 1.504(12) 0.064(7) 0.087(7) 0.0209(11) 0.00988(13) Ref. [18] 91959.35(2) 1.2805(16) — 29.953(14) 0.022(11) 0.091(21) 0.252(11)
Without c–k interaction
Final fit
92076.93(4) 1.95895(29) 3.08(53) 1.494(22) 0.106(13) 0.085(11) 0.01857(87) 0.009747(47) 0
92073.16(5) 1.97175(23) 11.76(21) 0.453(18) — 0.0893(41) 0.01969(33) 0.009938(18) 21.08(13)
91959.32(6) 1.2803(33) 9.5 fixed 29.971(32) — 0.084(41) 0.255(32) 0.0891
91963.59(6) 1.2616(13) 9.5 fixed 30.895(20) — 0.062(16) 0.254(12) 0.0339
a All units are in cm1. In the final fit the spin–spin constants, k, of both states could not be determined and so were fixed to zero. r corresponds to the standard deviation in the overall weighted fit. Values between parenthesis are errors, to one standard deviation, in the least significant figure.
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 given by 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 centrifugal distortion constant for the k3P (v = 2) state could not be determined (only data up to J = 5 is available) and was fixed to 9.5 · 106 cm1, similar to that determined for the k3P (v = 3) state [8,9]. Comparisons for the single state fit for the c3P state are in fair agreement with that determined by Dabrowski et al. [13] who only considered the N < 11 levels. The main affect of including all available rotational levels, i.e., extending the analysis to higher J for all parity and spin substates, is to change the values of the rotational constant and the centrifugal distortion constant. The quality of this fit was not particularly accurate over the range of J with an overall standard deviation of the weighted fit of r = 0.089 cm1. When the homogeneous interaction with the k3P state was included an excellent fit of all levels was obtained. The standard deviation of the observed calculated differences was 0.017 cm1 for the c3P (v = 0) state combination differences of Dabrowski et al. [13] (139 combination differences), 0.11 cm1 for the c–X (0–0) line positions [12] (73 line positions), 0.17 cm1 for the c3P (v = 0) state combination differences of Ginter and Tilford [2] (79 combination differences), 0.092 cm1 for the k3P (v = 2) state term values of Berden et al. [9] (7 term values) and 0.057 cm1 for the 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 overall accuracy of the fit is mainly determined by the high-resolution near-IR c–b (0–0) line positions [13], with the c–X data determining the band origin and extending the J level coverage [12]. The Ginter and Tilford 3A band data [2] are essentially superceded by the Dabrowski et al. [13] data but were included mainly to check for consistency. Including the homogeneous interaction results in significant changes to most of the molecular constants except for the K-doubling constants. The deperturbed centrifugal distortion constant of the c3P (v = 2) becomes positive and takes on a more normal value of 11.76 · 106 cm1. In addition, the deperturbed spin–orbit constant of the c3P (v = 2) state is decreased and is less than 0.5 cm1, indicating that some of the apparent spin–orbit splitting is actually due to the unequal shifts of the spin-states arising from the 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 published data. It is noted that Mellinger et al. [21] tabulated the term values for the first 10 levels of this state using the empirical parameters of Dabrowski et al. [13] and using 3A data from Rytel and Rytel [4] and the a3P molecular constants from Effantin et al. [22] to derive the energy with respect to the ground state. Their tabulated values are in agreement with those derived in this study except there is about a 0.2 cm1 difference in absolute energy. Table 4 was used to determine the term values for the b3R+ (v = 0) state, the lower state of the c–b (0–0) emission band, and these are given in Table 5. At this point it is instructive to consider the b3R+ (v = 0) state. Rytel [14] has analysed the (0,1) band of the third positive system (b3R+ fi a3P) of carbon monoxide. The b3R+ state is strongly perturbed by several high lying vibrational levels of the a 0 3R+ valence state and the a 0 3R+ (v = 32) state strongly interacts with the b3R+ (v = 0) state at J 19 (see Fig. 2 of [14] and [23]). Rytel [14] analysed the b–a (0,1) emission band up to J = 40 and although the line positions of the band were not published the molecular parameters for a five state interacting complex (b3R+ (v = 0), a 0 3R+ (v = 31–34)) were given. Taking RytelÕs [14] state-mixing Hamiltonian model and choosing the eigenvalues corresponding to the b3R+ (v = 0) state, these levels can be compared with the term values derived here. The origin of RytelÕs model is the b3R+ fi a3P (0–1) band origin and by adding a fixed energy term of 50187.17 cm1 the rotational term values were found to be coincident to within the respective experimental errors to those given in Table 5 (with an observed calculated standard deviation of 0.06 cm1 for N = 0–17 for all spin components) except for the N = 20 levels where there is about a 0.7 cm1 difference. However, this is where the b3R+ (v 0 = 0) state is most perturbed and it is not clear if this difference is due to the accuracy of the Rytel model or the specific line positions measured by Rytel [14], which were not reported. Fig. 2 compares the term values determined in this study and the term values derived from Rytel [14]. Fig. 3 plots all five
J. Baker / Journal of Molecular Spectroscopy 234 (2005) 75–83
79
Table 4 Term values for the c3P (v = 0) statea J
f1e
f2e
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
92079.63 92080.26 92081.74 92089.28 92100.83 92116.32 92135.74 92159.09 92186.37 92217.58 92252.73 92291.81 92334.82 92381.77 92432.64 92487.43 92546.14 92608.76 92675.29 92745.72 92820.05 92898.26 92980.36 93066.33 93156.17 93249.88 93347.44
92088.14 92088.82 92100.63 92116.29 92135.85 92159.35 92186.79 92218.18 92253.51 92292.80 92336.04 92383.23 92434.36 92489.44 92548.45 92611.40 92678.27 92749.06 92823.76 92902.38 92984.89 93071.31 93161.61 93255.79 93353.85 93455.77
f3e
f1f
f2f
f3f
92100.07 92115.76 92135.30 92158.74 92186.08 92217.34 92252.52 92291.64 92334.67 92381.64 92432.52 92487.33 92546.05 92608.68 92675.22 92745.66 92819.99 92898.21 92980.31 93066.29 93156.13 93249.84 93347.40 93448.81 93554.06
92079.82 92080.35 92081.79 92089.37 92100.98 92116.55 92136.07 92159.53 92186.95 92218.32 92253.65 92292.92 92336.16 92383.34 92434.47 92489.54 92548.55 92611.49 92678.36 92749.15 92823.86 92902.47 92984.98 93071.39 93161.69 93255.87 93353.93
92088.27 92088.84 92100.60 92116.18 92135.65 92159.03 92186.33 92217.56 92252.71 92291.80 92334.82 92381.77 92432.65 92487.44 92546.16 92608.78 92675.31 92745.75 92820.08 92898.30 92980.39 93066.37 93156.21 93249.92 93347.48 93448.89
92100.24 92116.00 92135.64 92159.19 92186.67 92218.09 92253.45 92292.76 92336.02 92383.22 92434.36 92489.45 92548.47 92611.42 92678.29 92749.09 92823.80 92902.41 92984.93 93071.35 93161.65 93255.83 93353.89 93455.81 93561.60
a Determined in this work—see text for further details. Units are in cm1. Estimated error in relative energy 0.05 cm1, and absolute energy 0.15 cm1.
Table 5 Term values for the b3R+ (v = 0) state of COa N
f1f
f2e
f3f
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
83833.43 83837.03 83844.24 83855.09 83869.66 83887.99 83910.14 83936.16 83966.08 83999.90 84037.64 84079.26 84124.77 84174.08 84227.13 84283.96 84343.94 84406.96 84471.96 84536.45 84595.36
83836.94 83844.14 83855.00 83869.57 83887.91 83910.07 83936.11 83966.02 83999.86 84037.59 84079.23 84124.72 84173.93 84227.13 84283.92 84343.91 84406.92 84471.86 84536.28 84595.03
83837.18 83844.30 83855.14 83869.69 83888.02 83910.17 83936.19 83966.11 83999.93 84037.67 84079.30 84124.79 84174.03 84227.23 84283.88 84344.00 84407.05 84472.07 84536.63 84595.77
a Derived from Dabrowski et al.Õs c–b (0–0) line positions, [13], and the fitted c3P term values. Units are in cm1. Estimated error in relative energy 0.05 cm1 and absolute energy 0.15 cm1. See text for further details.
states of RytelÕs model (energy shifted by 50187.17 cm1) showing how successive vibrational levels of the a 0 3R+ state perturb the b3R+ (v = 0) state. The reduced term value plot (Fig. 2) reveals several aspects of the perturbations affecting the b state. In the absence of any perturbation and no centrifugal distortion the reduced term values would form straight lines within the plot while centrifugal distortion causes the lines to curve gently downwards with increasing N(N + 1). Considering Fig. 2 which shows the b3R+ (v = 0) state N levels from 0 to 20, at low N the levels are perturbed upwards in energy, which is due to the homogeneous perturbation with the a 0 3R+ (v = 31) state which lies below the b3R+ (v = 0) state, while at N = 16–20 the levels are shifted downwards which is due to the perturbation with the a 0 3R+ (v = 32) state which lies above the b3R+ (v = 0) state (see Fig. 3). In fact there is a ‘‘crossing’’ (in the diabatic sense) at N = 20 between the f3 and f1 levels of the b3R+ (v = 0) and a 0 3R+ (v = 32) states, respectively. It is noted that the fixed energy term required to bring the calculated term values into coincidence with those derived in this work is very close to the a3P–X1R+ (1–0) band origin as given by Field et al. [24], of 50187.809 cm1. In summary, it is shown that RytelÕs study of the b3R+ state is in excellent agreement with the term values given in
80
J. Baker / Journal of Molecular Spectroscopy 234 (2005) 75–83
T(N) – 1.9088 × N(N+1) / cm − 1
83837 83832 83827 83822 83817 83812 83807 83802 83797 83792
0
5
10
15
20
N(N+1) with N labelling
T(N) / cm−1
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 derived from RytelÕs [14] five state interaction model with 50187.17 cm1 added to bring all the levels in to coincidence—in the diagram these levels have been shifted upwards in energy by 2 cm1 for comparison purposes (dashed lines and solid triangles). All three spin substates (f1, f2, and f3) are plotted but on this energy scale they are not separated.
85500
a´ 3Σ + (v=34)
85000
a´ 3Σ + (v=33)
84500
a´ 3Σ + (v=32) b 3 Σ + (v=0)
84000
a´ 3 Σ + (v=31) 83500 0
5
10
15
20
25
30
N
Fig. 3. Term value plot of the rotational energy levels of the b3R+ (v = 0) state and interacting vibrational levels of the a 0 3R+ state derived from RytelÕs [14] five state interaction model, with 50187.17 cm1 added to reference the levels to the X1R+ (v = 0, J = 0) ground state.
Table 5 and is therefore consistent with the c–b (0–0) line assignments [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 consistent with the double resonance study of Klopotek and Vidal [15]. That study looked at the triplet splitting for the N = 1–5 levels of the c3P state, excited via the a 0 3R+ (v = 14) state, and a spin–orbit constant of A = 1.49 cm1 was reported. However, this fine structure splitting was reported as being dependent on the parity level of the intermediate a 0 3R+ (v = 14) state and it was suggested that one of the parity components of the c state was perturbed. Line positions were not reported so it is
difficult to comment on these specific statements, although it is noted that the value of the ‘‘spin–orbit constant’’ specified is equal to that determined in this study if the homogenous interaction with the k3P (v = 2) state is neglected. Of more interest here is Fig. 12 of [15] which shows 5 transition lines, forming a triplet and a doublet, corresponding to transitions from the f2e (N = 1, J = 1) level of the a 0 3R+ (v = 14) state to the c3P (v = 0) state. Now the figure is not correctly labelled; allowable transitions correspond to OP12(1), PQ12(1), QR12(1), QQ22(1), RR22(1), SR32(1) transitions and so, in terms of increasing energy, the triplet lines 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
doublet to the f2f (J = 1) and f2e (J = 2) levels. The term values of these levels are given in Table 4 and are 92079.63, 92080.35, 92081.74, 92088.27, and 92088.82 cm1, respectively. The relative energy differences 0.078:0.230:0.940: 1.000 match to within the resolution of Fig. 12 in [15] the relative spacing of the lines 0.075(7):0.230(7):0.947(7): 1.000, where the bracketed numbers are estimated errors in the least significant figure. Hence, Klopotek and VidalÕs Fig. 12 supports the low J assignments of the c state. Fig. 4 plots the calculated reduced term values of both the c3P (v = 0) and k3P (v = 2) states. The separation between the states increases with increasing rotational energy as a result of the fairly large difference in their respective
81
rotational constants, where Bk < Bc—see Table 3. Consequently the interaction between the two states decreases 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 the c3P (v = 0) state sublevels into two groups of three at increasing N is due to the rapid change from coupling case a to case b at low N and the K-type doubling arising from the near pure precessional interaction with the 3pr, j3R+ (v = 0) state which occurs at lower energy at T00 = 90833.2 cm1 [2,18]. The effect of the interaction with the j3R+ state which has f1f, f2e, and f3f spin parity components is to raise the energy of the corresponding levels in
92400
T(J) – 1.6 × J(J+1) / cm−1
92300 92200
c3Π(v=0)
f1
f2
f3
92100 92000 91900 91800
k3Π(v=2)
91700
3Π
3Π
3Π
2(f3)
1(f2)
0(f1)
91600
0 5
10
15
20
25
J (J+1) with J labelling Fig. 4. Reduced term value plot showing the calculated e parity levels of the c3P (v = 0) and k3P (v = 2) states.
92080
T(N) – 1.96 × N(N+1) / c m−1
92079
f1f
f2e
f3f
92078
92077
92076
f1e f2f
92075
f3e
92074
0 5
10
15
20
25
N(N+1) with N labelling Fig. 5. Reduced term value plot showing the c3P state (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 evident in Fig. 5. Also evident is the shifting to higher energy of the low N levels, particularly the N < 12 levels, due to the homogeneous interaction with the k3P state. This interaction contributes to the apparent spin–orbit splitting of the c3P 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 reduced term values of Fig. 5 curve downwards in energy with increasing N, which can be explained by centrifugal distortion. The current analysis is consistent with both Ginter and TilfordÕs [2] and Rytel and RytelÕs [4] published line positions of the 3A bands, taking into account the experimental resolution and overlap of lines. Hakalla [10] reanalysed the c3P–a3P (0–2) and (0–3) 3A emission bands of 12C16O in a study that extended the work of Rytel and Rytel [4]. Line positions for 18 doubled branches were given for each band and the P- and Rbranches corresponding to DR = 0 transitions were extended to J 0 = 24 and 26, respectively. It was reported that the c3P (v = 0) state of 12C16O was perturbed, with the strongest perturbation in the J = 1 and 10 6 J 6 20 levels for all spin-substates and parity levels and only a partial analysis was given. An attempt was made to incorporate HakallaÕs data [10] into the current molecular fit by taking upper state combination differences of the reported c–a (0–2) and (0–3) bands of 12C16O. The upper state combination differences from both bands were similar and generally lay within the experimental error, which we estimate to be about 0.15 cm1. When trying to merge this data it was found that the c3P state levels from J = 19–26 diverged from the fit for all spin
and parity levels. This discrepancy is shown in Fig. 6, which compares the calculated c3P term values of Table 4 (solid curves and filled circles) with the term values derived from HakallaÕs work [10] (dashed curves and open circles). Term values from HakallaÕs work were determined by adding the corresponding a3P (v = 3) rotational term values to the reported c3P–a3P (0–3) line positions. The rotational term values of the a3P (v = 3) state were derived from the molecular parameters and Hamiltonian given by Field et al. [24], which are estimated to be accurate to within about 0.02 cm1. Fig. 6 shows reasonable agreement for term values corresponding to N < 20 with differences of less than 0.3 cm1 (except for some of the lowest J levels). However, there is an increasing discrepancy for HakallaÕs N > 19 levels, where all spin–parity levels on the reduced term value plot curve upwards with increasing N. This data for N > 19 in our fit is dominated by data from the sR and R R branches of the c–X (0–0) band, which extends to N = 26 the f2e levels and to N = 23 the f3e levels. However, there is also some data from Dabrowski et al. [13] (up to N = 20) and Ginter and Tilford [12] (up to N = 21) in which the beginning of the discrepancy is noticeable. The reason for the discrepancy is unclear. The Hakalla data [10] would imply another homogeneous interaction with a 3 P state at lower energy. However, the effect of the k3P (v = 2) state has already been taken into account and the next 3P state is the k3P (v = 3) state at higher energy and would give rise to a downward energy shift rather than an upward shift. The perturbations that Hakalla [10] reports for the c3P (v = 0) state of 12C16O are also reported in the same J levels for the 13C16O and 14C16O isotopomers and for the reported c3P (v = 1) state of the 12C16O and 13C16O isotopomers
T(N) – 1.96 × N(N+1) / cm−1
92086
92084
92082
f1f
f2e
f3f
92080
92078
92076
f1e f2f
f3e
92074
0 5
10
15
20
25
N(N+1) with N labelling abelling Fig. 6. Reduced term value plot showing the c3P state (v = 0) rotational levels derived in this study (solid curves and filled circles—only the data included in the fit (see Table 2) are plotted here) and those derived from Hakalla [10] (dashed curves and open circles). Notice the deviation at N P 19. All six spin–parity sublevels are plotted but on this energy scale the (f1f, f2e, and f3f) and (f1e, f2f, and f3e) subgroups are not clearly separated at least for medium to high N.
J. Baker / Journal of Molecular Spectroscopy 234 (2005) 75–83
(see for example Fig. 1 of [10]). However, significant changes in the J-dependence of a perturbation might be expected as a result of isotopic and in particular vibrational energy shifts. It seems possible that due to the highly congested nature of the 3A bands that misassignment of lines beyond N = 19 could have occurred and this may explain HakallaÕs observations. 3. Conclusion A full reanalysis of the near infrared c3P–b3R+ (0–0) band is given and term values for all spin and parity components of the c3P (v = 0) state was determined down to their lowest J values. The c3P (v = 0) state was jointly analysed with the perturbing k3P (v = 2) state and data from the c3P–X1R+ (0–0) transition and 3A band system were included. Molecular constants and term values are obtained which are consistent with all the available data except for some aspects of the recent 3A band study by Hakalla [10]. The results show that the available data are entirely consistent with the c3P (v = 0) state having near HundÕs case b coupling and very weak spin–orbit coupling with A = 0.45 ± 0.02 cm1. The state is also characterised by a homogeneous perturbation with the k3P (v = 2) state that shifts to higher energy the low J levels compared to the higher levels and K-type doubling arising predominantly from its interaction with the j3R+ state. The term values of the perturbed b3R+ Rydberg state, that forms the lower state of the c–b (0–0) band, were found to be in close agreement with RytelÕs five state interaction model.
83
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
R. Schmid, L. Gero¨, Nature 139 (1937) 928. M.L. Ginter, S.G. Tilford, J. Mol. Spectrosc. 31 (1969) 292–307. T. Siwiec-Rytel, J. Mol. Spectrosc. 97 (1983) 234–243. T. Rytel, M. Rytel, Acta Phys. Hung. 55 (1984) 69–84. T. Rytel, M. Rytel, Acta Phys. Hung. 59 (1986) 355–369. R. Hakalla, R. Kepa, M. Rytel, M. Zachwieja, J. Mol. Spectrosc. 197 (1999) 199–211. J. Baker, J.L. Lemaire, S. Couris, A. Vient, D. Malmasson, F. Rostas, Chem. Phys. 178 (1993) 569–579. J. Baker, F. Launay, J. Mol. Spectrosc. 165 (1994) 75–87. G. Berden, R.T. Jongma, D. Van der Zande, G. Meijer, J. Chem. Phys. 107 (1997) 8303–8310. R. Hakalla, J. Mol. Spectrosc. 209 (2001) 71–80. S.G. Tilford, J. Chem. Phys. 50 (1969) 3126–3127. J. Baker, F. Launay, M. Eidelsberg, F. Rostas, J. Mol. Spectrosc. 203 (2000) 314–319. I. Dabrowski, M. Vervloet, D.-C. Wang, Can. J. Phys. 65 (1987) 1171–1177. T. Rytel, J. Mol. Spectrosc. 145 (1991) 420–428. P. Klopotek, C.R. Vidal, J. Opt. Soc. Am. B. 2 (1985) 869–876. J.M. Brown, A.J. Merer, J. Mol. Spectrosc. 74 (1979) 488–494. H. Lefebvre-Brion, R.W. Field, Perturbations in the Spectra of Diatomic Molecules, Academic Press, Orlando, 1986. A. Mellinger, C.R. Vidal, J. Chem. Phys. 101 (1994) 104–110. T. Sykora, C.R. Vidal, J. Chem. Phys. 108 (1998) 6320–6330. G. Guelachvili, D. De Villeneuve, R. Farrenq, W. Urban, J. Verges, J. Mol. Spectrosc. 98 (1983) 64–79. A. Mellinger, E.G. Rohwer, C.R. Vidal, J. Mol. Spectrosc. 206 (2001) 126–134. C. Effantin, F. Michaud, F. Roux, J. DÕIncan, J. Verges, J. Mol. Spectrosc. 92 (1982) 349–362. G. Zikratov, D.W. Setser, N. Sadeghi, J. Chem. Phys. 112 (2000) 10845– 10857. R.W. Field, S.G. Tilford, R.A. Howard, J.D. Simmons, J. Mol. Spectrosc. 44 (1972) 347–382.
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 2005 Available 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 was jointly analysed with the perturbing k3P (v = 2) state and data from the c3P–X1R+ (0–0) transition and 3A band system were included. It is shown that the available data are consistent with the c3P (v = 0) state having near HundÕs case b coupling with a spin–orbit constant of A = 0.45 ± 0.02 cm1, a homogeneous perturbation with the k3P (v = 2) state, and K-type doubling arising predominantly from its interaction 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 monoxide has been the subject of a number of spectroscopic studies. It was first observed in UV emission as the upper state of the 3A band system (c3P–a3P (0–v00 )) [1–6]. These emission bands are fairly complex with a possible 27 parity doubled rotational branches, although not all have sufficient intensity to be observed, and are overlapped with bands of the fourth positive system (A1P–X1R+ emission bands). Hence, many of the rotational lines are congested and difficult to identify. Ginter and Tilford [2] through the analysis of these bands were first to identify K-type doubling within the c3P state and noted a moderate perturbation on the rotational levels giving rise to an anomalous negative sign for the centrifugal distortion constant. Rytel and co-workers [3–5] further analysed these bands and identified the perturbing state as a valence 3P state at lower energy. This perturbing state has since been identified as the k3P (v = 2)
*
Fax: +44 121 414 5528. E-mail address: [email protected].
0022-2852/$ - see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2005.08.009
valence state [7–9]. Most recently, Hakalla [10] has extended the analysis of these 3A bands to lower J and to J up to 26. Perturbations were reported for J = 1 and 10 6 J 6 20 for both e and f parity levels and for all three spin substates f1, f2, and f3, and only a partial analysis was given. The c3P (v = 0) state has also been identified in VUV absorption from the X1R+ground state [11,12]. An analysis by Baker et al. [12] indicated that this spin-forbidden band gains its intensity predominantly as a result of an interaction of the c3P (v = 0) state with the C1R+ (v = 0) state, which lies 160 cm1 to lower energy. The c3P– X1R+ (0–0) band had a fairly simple structure consisting of six rotational branches, comprising S-, R-, P-, and O-type branches (DN = ±2,±1) and two overlapping Qtype branches (DN = 0). However, the low J levels of the Q-type branches were not resolved as a result of a band head formation and the P- and O-type branches were overlapped with the strong C1R+–X1R+ (0–0) absorption band. Consequently, only the S- and R-type branches were fairly well determined which yields information for only some of the c3P state spin and parity levels (f3e and f2e in this case [12]). In fact a small doubt remains for the R-type branch assignment (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– b R (0–0) emission band of carbon monoxide in a radio-frequency discharge. This represents the highest resolution study of the c3P state to date. Despite the high resolution and relatively simple band structure (with nine main rotational branches and additional satellite branches) only a partial analysis of the band was possible as both states were reported as being heavily perturbed, particularly the b state [14]. Effective parameters for both states were given where the analysis was limited to transition lines with N00 < 10. These lines did not appear to be severely perturbed and perturbations were neglected in the analysis. Another study of note was carried out by Klopotek and Vidal [15] in which high-lying excited states of carbon monoxide were examined by means of a twostep excitation from the ground state. That study reported triplet splitting in the c3P state for N = 1–5, but no line positions were given. A triplet splitting corresponding to a spin–orbit constant of A = 1.49 cm1 was reported for one of the parity components while the other parity component was said to be perturbed with a different fine structure splitting. The spectroscopic studies to date leave some uncertainty in the details of the possible perturbations within the c3P (v = 0) state and its molecular constants. In this study, the c3P–b3R+ (0–0) band is reanalysed. The c3P (v = 0) state is jointly analysed with the perturbing k3P (v = 2) state and data from the c3P–X1R+ (0–0) transition and 3A band system are included. Molecular constants and term values are obtained which are consistent with all the available data except for some aspects of the recent study by Hakalla [10]. Fig. 1 shows the RKR potential curves of relevant triplet states considered in this work.
1.1. Analysis and spectroscopic data
3 +
The c3P (v = 0) state was analysed with the perturbing k P (v = 2) state, which causes the apparent anomaly in the sign of the centrifugal distortion constant. Each state was represented by the 3P Hamiltonian of Brown and Merer [16] forming a 6 · 6 Hamiltonian in total. The homogeneous interaction between the two states was represented by the interaction term, Æc3Pi (v = 0)jHjk3Pi (v = 2) æ = W, where i = 0–2 [4,17]. In a previous study, where this interaction was considered, only the fixed molecular constants determined by Mellinger and Vidal were used for the k3P (v = 2) state [12,18]. Term values for the k3P (v = 2) state were derived from the laser-based studies of Mellinger and Vidal [18] and Berden et al. [9]. Mellinger and Vidal [18] reported 27 lines for the k3P (v = 2)–a 0 3R+ (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 0 3R+ (v = 14) state had been initially populated by VUV laser absorption from the ground state. The reported transition energies were converted into k3P (v = 2) term values (referenced to the X1R+ (v = 0, J = 0) level) by making use of the reported energies of the a 0 3R+ (v = 14)–X1R+ (v = 0) transition [19] and the known rotational energy levels of the ground state [20]. This generated 19 unique term values for the k3P (v = 2) state. Berden et al. [9] reported 7 lines for the k3P (v = 2)–a3P (v = 1) transition in a 1 + 1 resonance enhanced ionisation study, with both parity levels of the a3P (v = 1, J = 1, X = 1) state being initially populated. This data generated seven term values six of which can be compared to those derived from Mellinger and VidalÕs work [18,19], where they are found to agree to approximately their combined experimental uncertainties. 3
c 3Π
100000
k 3Π
Energy / cm−1
b 3Σ+ 80000
a´ 3Σ+
60000
X 1Σ + a 3Π 40000 0.5
1
1.5
2
2.5
Internuclear distance / Å Fig. 1. RKR potential energy curves of some of the relevant triplet states considered in this work. The energy origin is taken at the minimum of the X1R+ground state potential.
J. Baker / Journal of Molecular Spectroscopy 234 (2005) 75–83
Overall from the two studies 20 unique term values of the k3P (v = 2) state are determined, these are given in Table 1. Dabrowski et al. [13] reported the line positions for the c3P–b3R+ (0–0) band at an estimated resolution of 0.005 cm1 but only analysed the band for N00 < 10 producing ‘‘empirical parameters’’ for the two states. In this study, we focus on the c3P (v = 0) state by assuming the line assignments from their Table 1 and taking upper state combination differences. The c3P–b3R+ (0–0) transition is close to a case (b) to case (b) transition and as a result the strong branches are characterised by DN = ±1, 0, and DS = 0. Satellite branches with DS = ±1 appear only for low J and N and may be difficult to identify. A typographical error was identified and corrected for the Q22(8) line position (8251.523 cm1 rather than 8253.523 cm1) in their Table 1. It is also noted that the R23 (N = 3–6) lines, which were not assigned, would be expected to be overlapped with the P21(N = 3–6) lines. All assigned lines were included in the fit. The line positions of the c–X band (0–0) reported in Baker et al. [12] were also included in the rotational fit. The ground state molecular constants are well known and were derived from [20] (B = 1.9225288 cm1, D = 6.12 · 106 cm1, and H = 5.74 · 1012 cm1 were used). Initially only the SR(J) and RR(J) rotational branches were included which extended the J value coverage for the f3e and f2e upper spin–parity states to J = 22 and 26, respectively. Addition of these lines enabled the term origin T00 to be determined. Afterwards all the line positions given in Table 1 of [12] were included in the fit except for the p P(2) line. Addition of these lines did not significantly change the results. The assignment of the pP(2) line, which terminates on the f2e (J = 1) spin–parity level of the c3P state, was found to be incorrect and removed from the fit. The reason for this error was due to an improper treatment of the eigenvalues arising from the Hamiltonian for Table 1 Term values for the k3P (v = 2) state J
X
Parity
Ref. [18]
Ref. [9]
0 0 1 1 2 2 3 1 2 2 3 4 2 2 3 3 4 4 5 5
0 0 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 2 2 2
f e f e f e f e f e f f f e f e f e f e
91932.32 91931.79 91934.63 91934.16 91939.32 91938.82 91946.31
91932.39
91969.84 91969.78 91977.39 91987.46 91994.94 91994.93 92003.48 92003.47 92014.76 92014.79 92028.83 92028.82
91934.28 91939.38 91938.75 91964.94 91969.88
77
Table 2 Summary of the c3p (v = 0) state J levels used in the molecular fit Spin–parity level
Ref. [13]
Ref. [12]
Ref. [2]
f1e f1f f2e f2f f3e f3f
0–20 0–21 1–20 1–19 2–18 2–19
11–21
6–20 6–20 8–21 8–21 2–18 2–18
2–26 2–22
J < 2 which has since been corrected. The pP(2) line would be expected to be close to and possibly overlapped with the Q-type band head of the c–X band. The estimated errors for the weighted least squares fit analysis were 0.05 cm1 for the upper state combination differences of the c–b (0–0) band [13] and the errors specified in Table 1 of [12] for the c–X (0–0) band. The estimated errors for the term values of the k (v = 2) state were 0.07 cm1 for those derived from Mellinger and Vidal [18] (0.04 cm1 for the k–a 0 transition [18] and 0.05 cm1 for the a 0 –X transition [19]), and 0.11 cm1 for those derived from Berden et al. [9] (0.1 cm1 for the k–a transition and about 0.05 cm1 for the a–X transitions). Finally, data from the 3A band system were included in the analysis by including upper state combination differences derived from Ginter and TilfordÕs reported line positions of the c3P–a3P (0–2) and (0–1) bands [2], making use of the assignments given in Rytel and Rytel [4]. Ginter and TilfordÕs line positions were found to be 0.2 cm1 greater than those reported by Rytel and Rytel [4], but there was no significant offset for the combination differences which agreed to within the combined estimated experimental uncertainties (about 0.3 cm1 for unblended lines). Ginter and TilfordÕs data [2] were used rather than Rytel and RytelÕs [4] data because it extended slightly to higher J. Only data derived from the strongest branches (DJ = ±1 and DR = 0) were included in the analysis, with estimated errors for the combination differences of 0.2–0.6 cm1. Combination differences were excluded if differences greater than 0.45 cm1 existed between the 0–1 and 0–2 bands. This 3A band data did not significantly influence the fit but emphasised the higher J data for the c3P state and was mainly included to check for consistency. The more recent 3A band data from Hakalla [10] will be considered later. Table 2 gives a summary of the rotational levels of the c3P (v = 0) state included in the fit. 2. Results and discussion
91995.00
The results of the analysis are given in Table 3. Column three gives the fitted molecular constants in the absence of the homogeneous interaction between the c3P (v = 0) and k3P (v = 2) states while column four includes the homogeneous interaction and represents the final deperturbed molecular constants. For comparison, column two gives the ‘‘empirical parameters’’ for the c3P (v = 0) state from
78
J. Baker / Journal of Molecular Spectroscopy 234 (2005) 75–83
Table 3 Molecular constants of the c3P (v = 0) and k3P (v = 2) statesa Molecular parameter
Previous work
c3P (v = 0) T B D · 106 A k o+p+q p+2q q W
Ref. [13]
k3P (v = 2) T B D · 106 A k c o+p+q r
1.9484(7) 60(6) 1.504(12) 0.064(7) 0.087(7) 0.0209(11) 0.00988(13) Ref. [18] 91959.35(2) 1.2805(16) — 29.953(14) 0.022(11) 0.091(21) 0.252(11)
Without c–k interaction
Final fit
92076.93(4) 1.95895(29) 3.08(53) 1.494(22) 0.106(13) 0.085(11) 0.01857(87) 0.009747(47) 0
92073.16(5) 1.97175(23) 11.76(21) 0.453(18) — 0.0893(41) 0.01969(33) 0.009938(18) 21.08(13)
91959.32(6) 1.2803(33) 9.5 fixed 29.971(32) — 0.084(41) 0.255(32) 0.0891
91963.59(6) 1.2616(13) 9.5 fixed 30.895(20) — 0.062(16) 0.254(12) 0.0339
a All units are in cm1. In the final fit the spin–spin constants, k, of both states could not be determined and so were fixed to zero. r corresponds to the standard deviation in the overall weighted fit. Values between parenthesis are errors, to one standard deviation, in the least significant figure.
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 given by 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 centrifugal distortion constant for the k3P (v = 2) state could not be determined (only data up to J = 5 is available) and was fixed to 9.5 · 106 cm1, similar to that determined for the k3P (v = 3) state [8,9]. Comparisons for the single state fit for the c3P state are in fair agreement with that determined by Dabrowski et al. [13] who only considered the N < 11 levels. The main affect of including all available rotational levels, i.e., extending the analysis to higher J for all parity and spin substates, is to change the values of the rotational constant and the centrifugal distortion constant. The quality of this fit was not particularly accurate over the range of J with an overall standard deviation of the weighted fit of r = 0.089 cm1. When the homogeneous interaction with the k3P state was included an excellent fit of all levels was obtained. The standard deviation of the observed calculated differences was 0.017 cm1 for the c3P (v = 0) state combination differences of Dabrowski et al. [13] (139 combination differences), 0.11 cm1 for the c–X (0–0) line positions [12] (73 line positions), 0.17 cm1 for the c3P (v = 0) state combination differences of Ginter and Tilford [2] (79 combination differences), 0.092 cm1 for the k3P (v = 2) state term values of Berden et al. [9] (7 term values) and 0.057 cm1 for the 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 overall accuracy of the fit is mainly determined by the high-resolution near-IR c–b (0–0) line positions [13], with the c–X data determining the band origin and extending the J level coverage [12]. The Ginter and Tilford 3A band data [2] are essentially superceded by the Dabrowski et al. [13] data but were included mainly to check for consistency. Including the homogeneous interaction results in significant changes to most of the molecular constants except for the K-doubling constants. The deperturbed centrifugal distortion constant of the c3P (v = 2) becomes positive and takes on a more normal value of 11.76 · 106 cm1. In addition, the deperturbed spin–orbit constant of the c3P (v = 2) state is decreased and is less than 0.5 cm1, indicating that some of the apparent spin–orbit splitting is actually due to the unequal shifts of the spin-states arising from the 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 published data. It is noted that Mellinger et al. [21] tabulated the term values for the first 10 levels of this state using the empirical parameters of Dabrowski et al. [13] and using 3A data from Rytel and Rytel [4] and the a3P molecular constants from Effantin et al. [22] to derive the energy with respect to the ground state. Their tabulated values are in agreement with those derived in this study except there is about a 0.2 cm1 difference in absolute energy. Table 4 was used to determine the term values for the b3R+ (v = 0) state, the lower state of the c–b (0–0) emission band, and these are given in Table 5. At this point it is instructive to consider the b3R+ (v = 0) state. Rytel [14] has analysed the (0,1) band of the third positive system (b3R+ fi a3P) of carbon monoxide. The b3R+ state is strongly perturbed by several high lying vibrational levels of the a 0 3R+ valence state and the a 0 3R+ (v = 32) state strongly interacts with the b3R+ (v = 0) state at J 19 (see Fig. 2 of [14] and [23]). Rytel [14] analysed the b–a (0,1) emission band up to J = 40 and although the line positions of the band were not published the molecular parameters for a five state interacting complex (b3R+ (v = 0), a 0 3R+ (v = 31–34)) were given. Taking RytelÕs [14] state-mixing Hamiltonian model and choosing the eigenvalues corresponding to the b3R+ (v = 0) state, these levels can be compared with the term values derived here. The origin of RytelÕs model is the b3R+ fi a3P (0–1) band origin and by adding a fixed energy term of 50187.17 cm1 the rotational term values were found to be coincident to within the respective experimental errors to those given in Table 5 (with an observed calculated standard deviation of 0.06 cm1 for N = 0–17 for all spin components) except for the N = 20 levels where there is about a 0.7 cm1 difference. However, this is where the b3R+ (v 0 = 0) state is most perturbed and it is not clear if this difference is due to the accuracy of the Rytel model or the specific line positions measured by Rytel [14], which were not reported. Fig. 2 compares the term values determined in this study and the term values derived from Rytel [14]. Fig. 3 plots all five
J. Baker / Journal of Molecular Spectroscopy 234 (2005) 75–83
79
Table 4 Term values for the c3P (v = 0) statea J
f1e
f2e
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
92079.63 92080.26 92081.74 92089.28 92100.83 92116.32 92135.74 92159.09 92186.37 92217.58 92252.73 92291.81 92334.82 92381.77 92432.64 92487.43 92546.14 92608.76 92675.29 92745.72 92820.05 92898.26 92980.36 93066.33 93156.17 93249.88 93347.44
92088.14 92088.82 92100.63 92116.29 92135.85 92159.35 92186.79 92218.18 92253.51 92292.80 92336.04 92383.23 92434.36 92489.44 92548.45 92611.40 92678.27 92749.06 92823.76 92902.38 92984.89 93071.31 93161.61 93255.79 93353.85 93455.77
f3e
f1f
f2f
f3f
92100.07 92115.76 92135.30 92158.74 92186.08 92217.34 92252.52 92291.64 92334.67 92381.64 92432.52 92487.33 92546.05 92608.68 92675.22 92745.66 92819.99 92898.21 92980.31 93066.29 93156.13 93249.84 93347.40 93448.81 93554.06
92079.82 92080.35 92081.79 92089.37 92100.98 92116.55 92136.07 92159.53 92186.95 92218.32 92253.65 92292.92 92336.16 92383.34 92434.47 92489.54 92548.55 92611.49 92678.36 92749.15 92823.86 92902.47 92984.98 93071.39 93161.69 93255.87 93353.93
92088.27 92088.84 92100.60 92116.18 92135.65 92159.03 92186.33 92217.56 92252.71 92291.80 92334.82 92381.77 92432.65 92487.44 92546.16 92608.78 92675.31 92745.75 92820.08 92898.30 92980.39 93066.37 93156.21 93249.92 93347.48 93448.89
92100.24 92116.00 92135.64 92159.19 92186.67 92218.09 92253.45 92292.76 92336.02 92383.22 92434.36 92489.45 92548.47 92611.42 92678.29 92749.09 92823.80 92902.41 92984.93 93071.35 93161.65 93255.83 93353.89 93455.81 93561.60
a Determined in this work—see text for further details. Units are in cm1. Estimated error in relative energy 0.05 cm1, and absolute energy 0.15 cm1.
Table 5 Term values for the b3R+ (v = 0) state of COa N
f1f
f2e
f3f
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
83833.43 83837.03 83844.24 83855.09 83869.66 83887.99 83910.14 83936.16 83966.08 83999.90 84037.64 84079.26 84124.77 84174.08 84227.13 84283.96 84343.94 84406.96 84471.96 84536.45 84595.36
83836.94 83844.14 83855.00 83869.57 83887.91 83910.07 83936.11 83966.02 83999.86 84037.59 84079.23 84124.72 84173.93 84227.13 84283.92 84343.91 84406.92 84471.86 84536.28 84595.03
83837.18 83844.30 83855.14 83869.69 83888.02 83910.17 83936.19 83966.11 83999.93 84037.67 84079.30 84124.79 84174.03 84227.23 84283.88 84344.00 84407.05 84472.07 84536.63 84595.77
a Derived from Dabrowski et al.Õs c–b (0–0) line positions, [13], and the fitted c3P term values. Units are in cm1. Estimated error in relative energy 0.05 cm1 and absolute energy 0.15 cm1. See text for further details.
states of RytelÕs model (energy shifted by 50187.17 cm1) showing how successive vibrational levels of the a 0 3R+ state perturb the b3R+ (v = 0) state. The reduced term value plot (Fig. 2) reveals several aspects of the perturbations affecting the b state. In the absence of any perturbation and no centrifugal distortion the reduced term values would form straight lines within the plot while centrifugal distortion causes the lines to curve gently downwards with increasing N(N + 1). Considering Fig. 2 which shows the b3R+ (v = 0) state N levels from 0 to 20, at low N the levels are perturbed upwards in energy, which is due to the homogeneous perturbation with the a 0 3R+ (v = 31) state which lies below the b3R+ (v = 0) state, while at N = 16–20 the levels are shifted downwards which is due to the perturbation with the a 0 3R+ (v = 32) state which lies above the b3R+ (v = 0) state (see Fig. 3). In fact there is a ‘‘crossing’’ (in the diabatic sense) at N = 20 between the f3 and f1 levels of the b3R+ (v = 0) and a 0 3R+ (v = 32) states, respectively. It is noted that the fixed energy term required to bring the calculated term values into coincidence with those derived in this work is very close to the a3P–X1R+ (1–0) band origin as given by Field et al. [24], of 50187.809 cm1. In summary, it is shown that RytelÕs study of the b3R+ state is in excellent agreement with the term values given in
80
J. Baker / Journal of Molecular Spectroscopy 234 (2005) 75–83
T(N) – 1.9088 × N(N+1) / cm − 1
83837 83832 83827 83822 83817 83812 83807 83802 83797 83792
0
5
10
15
20
N(N+1) with N labelling
T(N) / cm−1
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 derived from RytelÕs [14] five state interaction model with 50187.17 cm1 added to bring all the levels in to coincidence—in the diagram these levels have been shifted upwards in energy by 2 cm1 for comparison purposes (dashed lines and solid triangles). All three spin substates (f1, f2, and f3) are plotted but on this energy scale they are not separated.
85500
a´ 3Σ + (v=34)
85000
a´ 3Σ + (v=33)
84500
a´ 3Σ + (v=32) b 3 Σ + (v=0)
84000
a´ 3 Σ + (v=31) 83500 0
5
10
15
20
25
30
N
Fig. 3. Term value plot of the rotational energy levels of the b3R+ (v = 0) state and interacting vibrational levels of the a 0 3R+ state derived from RytelÕs [14] five state interaction model, with 50187.17 cm1 added to reference the levels to the X1R+ (v = 0, J = 0) ground state.
Table 5 and is therefore consistent with the c–b (0–0) line assignments [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 consistent with the double resonance study of Klopotek and Vidal [15]. That study looked at the triplet splitting for the N = 1–5 levels of the c3P state, excited via the a 0 3R+ (v = 14) state, and a spin–orbit constant of A = 1.49 cm1 was reported. However, this fine structure splitting was reported as being dependent on the parity level of the intermediate a 0 3R+ (v = 14) state and it was suggested that one of the parity components of the c state was perturbed. Line positions were not reported so it is
difficult to comment on these specific statements, although it is noted that the value of the ‘‘spin–orbit constant’’ specified is equal to that determined in this study if the homogenous interaction with the k3P (v = 2) state is neglected. Of more interest here is Fig. 12 of [15] which shows 5 transition lines, forming a triplet and a doublet, corresponding to transitions from the f2e (N = 1, J = 1) level of the a 0 3R+ (v = 14) state to the c3P (v = 0) state. Now the figure is not correctly labelled; allowable transitions correspond to OP12(1), PQ12(1), QR12(1), QQ22(1), RR22(1), SR32(1) transitions and so, in terms of increasing energy, the triplet lines 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
doublet to the f2f (J = 1) and f2e (J = 2) levels. The term values of these levels are given in Table 4 and are 92079.63, 92080.35, 92081.74, 92088.27, and 92088.82 cm1, respectively. The relative energy differences 0.078:0.230:0.940: 1.000 match to within the resolution of Fig. 12 in [15] the relative spacing of the lines 0.075(7):0.230(7):0.947(7): 1.000, where the bracketed numbers are estimated errors in the least significant figure. Hence, Klopotek and VidalÕs Fig. 12 supports the low J assignments of the c state. Fig. 4 plots the calculated reduced term values of both the c3P (v = 0) and k3P (v = 2) states. The separation between the states increases with increasing rotational energy as a result of the fairly large difference in their respective
81
rotational constants, where Bk < Bc—see Table 3. Consequently the interaction between the two states decreases 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 the c3P (v = 0) state sublevels into two groups of three at increasing N is due to the rapid change from coupling case a to case b at low N and the K-type doubling arising from the near pure precessional interaction with the 3pr, j3R+ (v = 0) state which occurs at lower energy at T00 = 90833.2 cm1 [2,18]. The effect of the interaction with the j3R+ state which has f1f, f2e, and f3f spin parity components is to raise the energy of the corresponding levels in
92400
T(J) – 1.6 × J(J+1) / cm−1
92300 92200
c3Π(v=0)
f1
f2
f3
92100 92000 91900 91800
k3Π(v=2)
91700
3Π
3Π
3Π
2(f3)
1(f2)
0(f1)
91600
0 5
10
15
20
25
J (J+1) with J labelling Fig. 4. Reduced term value plot showing the calculated e parity levels of the c3P (v = 0) and k3P (v = 2) states.
92080
T(N) – 1.96 × N(N+1) / c m−1
92079
f1f
f2e
f3f
92078
92077
92076
f1e f2f
92075
f3e
92074
0 5
10
15
20
25
N(N+1) with N labelling Fig. 5. Reduced term value plot showing the c3P state (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 evident in Fig. 5. Also evident is the shifting to higher energy of the low N levels, particularly the N < 12 levels, due to the homogeneous interaction with the k3P state. This interaction contributes to the apparent spin–orbit splitting of the c3P 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 reduced term values of Fig. 5 curve downwards in energy with increasing N, which can be explained by centrifugal distortion. The current analysis is consistent with both Ginter and TilfordÕs [2] and Rytel and RytelÕs [4] published line positions of the 3A bands, taking into account the experimental resolution and overlap of lines. Hakalla [10] reanalysed the c3P–a3P (0–2) and (0–3) 3A emission bands of 12C16O in a study that extended the work of Rytel and Rytel [4]. Line positions for 18 doubled branches were given for each band and the P- and Rbranches corresponding to DR = 0 transitions were extended to J 0 = 24 and 26, respectively. It was reported that the c3P (v = 0) state of 12C16O was perturbed, with the strongest perturbation in the J = 1 and 10 6 J 6 20 levels for all spin-substates and parity levels and only a partial analysis was given. An attempt was made to incorporate HakallaÕs data [10] into the current molecular fit by taking upper state combination differences of the reported c–a (0–2) and (0–3) bands of 12C16O. The upper state combination differences from both bands were similar and generally lay within the experimental error, which we estimate to be about 0.15 cm1. When trying to merge this data it was found that the c3P state levels from J = 19–26 diverged from the fit for all spin
and parity levels. This discrepancy is shown in Fig. 6, which compares the calculated c3P term values of Table 4 (solid curves and filled circles) with the term values derived from HakallaÕs work [10] (dashed curves and open circles). Term values from HakallaÕs work were determined by adding the corresponding a3P (v = 3) rotational term values to the reported c3P–a3P (0–3) line positions. The rotational term values of the a3P (v = 3) state were derived from the molecular parameters and Hamiltonian given by Field et al. [24], which are estimated to be accurate to within about 0.02 cm1. Fig. 6 shows reasonable agreement for term values corresponding to N < 20 with differences of less than 0.3 cm1 (except for some of the lowest J levels). However, there is an increasing discrepancy for HakallaÕs N > 19 levels, where all spin–parity levels on the reduced term value plot curve upwards with increasing N. This data for N > 19 in our fit is dominated by data from the sR and R R branches of the c–X (0–0) band, which extends to N = 26 the f2e levels and to N = 23 the f3e levels. However, there is also some data from Dabrowski et al. [13] (up to N = 20) and Ginter and Tilford [12] (up to N = 21) in which the beginning of the discrepancy is noticeable. The reason for the discrepancy is unclear. The Hakalla data [10] would imply another homogeneous interaction with a 3 P state at lower energy. However, the effect of the k3P (v = 2) state has already been taken into account and the next 3P state is the k3P (v = 3) state at higher energy and would give rise to a downward energy shift rather than an upward shift. The perturbations that Hakalla [10] reports for the c3P (v = 0) state of 12C16O are also reported in the same J levels for the 13C16O and 14C16O isotopomers and for the reported c3P (v = 1) state of the 12C16O and 13C16O isotopomers
T(N) – 1.96 × N(N+1) / cm−1
92086
92084
92082
f1f
f2e
f3f
92080
92078
92076
f1e f2f
f3e
92074
0 5
10
15
20
25
N(N+1) with N labelling abelling Fig. 6. Reduced term value plot showing the c3P state (v = 0) rotational levels derived in this study (solid curves and filled circles—only the data included in the fit (see Table 2) are plotted here) and those derived from Hakalla [10] (dashed curves and open circles). Notice the deviation at N P 19. All six spin–parity sublevels are plotted but on this energy scale the (f1f, f2e, and f3f) and (f1e, f2f, and f3e) subgroups are not clearly separated at least for medium to high N.
J. Baker / Journal of Molecular Spectroscopy 234 (2005) 75–83
(see for example Fig. 1 of [10]). However, significant changes in the J-dependence of a perturbation might be expected as a result of isotopic and in particular vibrational energy shifts. It seems possible that due to the highly congested nature of the 3A bands that misassignment of lines beyond N = 19 could have occurred and this may explain HakallaÕs observations. 3. Conclusion A full reanalysis of the near infrared c3P–b3R+ (0–0) band is given and term values for all spin and parity components of the c3P (v = 0) state was determined down to their lowest J values. The c3P (v = 0) state was jointly analysed with the perturbing k3P (v = 2) state and data from the c3P–X1R+ (0–0) transition and 3A band system were included. Molecular constants and term values are obtained which are consistent with all the available data except for some aspects of the recent 3A band study by Hakalla [10]. The results show that the available data are entirely consistent with the c3P (v = 0) state having near HundÕs case b coupling and very weak spin–orbit coupling with A = 0.45 ± 0.02 cm1. The state is also characterised by a homogeneous perturbation with the k3P (v = 2) state that shifts to higher energy the low J levels compared to the higher levels and K-type doubling arising predominantly from its interaction with the j3R+ state. The term values of the perturbed b3R+ Rydberg state, that forms the lower state of the c–b (0–0) band, were found to be in close agreement with RytelÕs five state interaction model.
83
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