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Perturbations in the 4ν3 level of the A1Au state of acetylene, C2H2
Merer, Anthony J.; Duan, Zicheng; Field, Robert W.; Watson, James K.G.
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Perturbations in the 4n
3
level of the
A
~
1
A
u
state of
acetylene, C
2
H
2
1
Anthony J. Merer, Zicheng Duan, Robert W. Field, and James K.G. Watson
Abstract: Perturbations in the K = 1 and 3 levels of the ~A1Au, 4n3state of acetylene are explained as interactions with
levels of the ~A1Au, 31B4(v3= 1, v4+ v6= 4) polyad. A satisfactory least-squares fit to the perturbed level structure has
been obtained, treating the 4n3state as an asymmetric top perturbed by isolated K = 1 and 3 levels. Accurate deperturbed
rotational constants for the interacting states are presented. PACS No: 33.20.Lg
Re´sume´ : Les perturbations dans les niveaux K = 1 et 3 de l’e´tat ~A1Au, 4v3de l’ace´tyle`ne sont explique´es comme e´tant
des interactions avec le polyade ~A1A
u, 31B4(v3= 1, v4+ v6= 4). Nous obtenons un ajustement satisfaisant par moindres
carre´s pour la structure des niveaux perturbe´s, en traitant l’e´tat 4n3comme une toupie asyme´trique perturbe´e par les
ni-veaux isole´s K = 1 et K = 3. Nous pre´sentons des valeurs pre´cises libres de perturbation des constantes rotationnelles pour les niveaux en interaction.
[Traduit par la Re´daction]
1. Introduction
The ~A1Au state of acetylene is one of the most widely
studied of all excited electronic states of a polyatomic mole-cule. It is important for the information it contains about p– p* excitation of a C-C triple bond, and its value is as an in-termediate in double resonance experiments. A large number of authors have used the ~A1Au state as an intermediate to
gain access to high vibrational levels of the ground state [1–4], to the nonplanar valence states [5], to the Rydberg states [6–8], and to the states of the acetylene cation [9, 10]. Although acetylene is linear in its ground electronic state, it becomes trans-bent in its ~A1A
u state [11, 12]. Seen in
ab-sorption, the ~A ~X transition consists of a long progression in the upper state trans-bending (or ‘‘straightening’’) vibra-tion, n3’, each member of which is the origin of a short
pro-gression in the C-C stretching vibration, n2’ [13, 14]. The
structures of the bands are simple at the long wavelength end of the transition, though the spectrum is crowded because of the presence of many hot bands. The strength of these hot
bands results from the change of molecular shape in the tran-sition, which, according to the Franck–Condon principle, en-hances the vibrational bands from the ground state trans-bending vibration, n4@, and its overtones.
At about 2500 cm–1above the zero-point vibrational level,
the ~A state vibrational levels begin to suffer rotational per-turbations. Among these are some very small perturbations caused by triplet levels, but the most significant interactions are with unseen (Franck–Condon forbidden) levels of the ~A state that involve the low-lying ungerade bending vibrations, n
4’ (torsion, au) and n6’ (in-plane cis-bend, bu). The first
size-able perturbation occurs in the 2131 vibrational level [13],
where the K = 3 stack is almost exactly degenerate with the 3162K= 3 stack, giving rise to two sub-bands, about 6 cm–1
apart. At higher energy is an interesting perturbation affect-ing the 33 (3n
3’) level, where the low-J rotational levels of
the K = 1 stack are doubled [15]. Because of the great inten-sity of the 33
0 band in the Franck–Condon pattern, this
vi-brational level has received considerable attention [16, 17]. It has now been established that the perturbing state, which also has K = 1, belongs to the second-highest of the five members of the v4’ + v6’ = 4 polyad [18], though the
inter-action matrix element is quite small, since the vibrational quantum numbers of the interacting states are very different. This note describes perturbations in the next level of the n
3’ progression, 4n3’. In 1985, Van Craen et al. [14] reported
term values for 4n3’, K’ = 0–3, but were not able to fit them
satisfactorily by least-squares; they noted that the K’ = 1 lev-els were strongly perturbed, giving residuals of up to 1.2 cm–1. Two years ago, we reported experiments using
dif-ferential temperature laser-induced fluorescence to distin-guish overlapping hot bands from cold bands in the spectrum of acetylene [19]. In the course of these experi-ments, spectra were recorded in the region 45 050– 46 310 cm–1, containing sub-bands going to several K stacks
of the 4n3’ level. Although the 4n3’ level was not the original
target of the experiments, it turns out that the new spectra
Received 4 September 2008. Accepted 15 September 2008. Published on the NRC Research Press Web site at cjp.nrc.ca on 17 July 2009.
A.J. Merer.2Institute of Atomic and Molecular Sciences,
Academia Sinica, Taipei 10617, Taiwan.
Z. Duan3and R.W. Field. Department of Chemistry,
Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
J.K.G. Watson. Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, ON K1A 0R6, Canada.
1This article is part of a Special Issue on Spectroscopy at the
University of New Brunswick in honour of Colan Linton and Ron Lees.
2Corresponding author (e-mail: merer@chem.ubc.ca). 3Present address: 3 Times Square, 8th Floor, New York, NY
10036, USA.
437
allow a more detailed analysis of it, giving evidence for two major avoided crossings that were not noticed in the earlier work. Allowing for these perturbations, the rotational struc-ture can be fitted by least-squares to good accuracy.
2. Results
Figure 1 is a laser-induced fluorescence excitation spec-trum showing the very intense C-axis polarized 4n3’, K’–‘@ =
1–0 sub-band, together with the weaker axis switching-in-duced K’–‘@ = 0–0 sub-band and two underlying combination bands. Examination of the P and R branches of the 1–0 sub-band shows that extra lines with J’ = 14–24 are present. The resulting pattern of energy levels is illustrated in Fig. 2, where the upper asymmetry component of the K = 1 stack shows a clear avoided crossing. There is a similar avoided crossing in the K = 3 stack, where a perturbing level with a slightly larger B value gives many extra lines at low J.
The similarity in the sizes of the perturbations suggests that the perturbing levels are related. At the same time, it is surprising that only these two perturbations are seen. Based on our recent study of the bending overtones of the ~A1Au
state [18], together with unpublished results on various com-bination polyads involving the bending vibrations, we offer the following interpretation. Just as the 3n3’ level is
per-turbed by the v4’+v6’ = 4 (or B4) polyad [15], the 4n3’ level
is perturbed by the 31B4 polyad, though the appearance of
the perturbations is different, since anharmonicity shifts the interacting levels to different relative positions.
The bending overtone polyads of the ~A1Au state, such as
B4, have highly unusual structures [18]. The two
fundamen-tals, n4’ and n6’, are nearly degenerate, with wavenumbers of
764.9 and 768.3 cm–1, respectively [16]. They correlate with
the n5@ (pu) cis-bending vibration of the linear molecule,
which possesses a vibrational angular momentum. In the bent molecule, the vibrational angular momentum operator acts between the two vibrations, giving rise to strong Coriolis coupling and Darling–Dennison resonance. The effect is that the five K’ = 0 levels of the B4polyad are spread over an
en-ergy range of about 200 cm–1, while for K’ = 0 the usual
asymmetric top patterns break down completely and can only be predicted by detailed calculations.
Enough of the K-structure of the 31B2 and 31B3 polyads
has been identified in our unpublished jet-cooled
laser-in-Fig. 1. Laser-induced fluorescence excitation spectrum of C2H2near 46 250 cm–1, showing the 340, K’–‘@ = 1–0 and 0–0 sub-bands of the
~ A1Au ~X
1
Sþ
g transition at a temperature of about 08C. The branches are labeled by subscripts indicating the values of K’ – ‘’’. Two weaker
K’ – ‘@ = 1–0 bands belonging to combination levels involving the low-lying bending vibrations are also marked; the notation B means v4+v6.
438 Can. J. Phys. Vol. 87, 2009
duced fluorescence experiments for reasonably good predic-tions (±10 cm–1) to be made for the 31B4polyad. Nine of the
15 K’-stacks with K = 0–2 have now been identified, one of which is the K’ = 1 upper state of the sub-band near 46 240 cm–1, shown in Fig. 1. This particular K’ = 1 stack
belongs to the middle of the five vibrational members of the polyad and has nominal Ag vibrational symmetry. The next
higher K’ = 1 stack in order of energy, which has nominal Bgvibrational symmetry, is predicted to lie near 46 284 cm– 1. It appears to be responsible for the perturbation in the
4n3’, K’ = 1 stack. An interesting point is that it is
pre-dicted to have essentially zero asymmetry splitting, because its vibrational wave function is an almost equal mixture of Ag and Bg vibrational basis functions. Significantly, its K’
= 3 stack is predicted to lie near 46 413 cm–1, in the
cor-rect place to perturb the K’ = 3 stack of 4n3’, but its K’ =
0 and 2 stacks are predicted to lie near 46 344 and 46 314 cm–1, respectively, comparatively far from the
cor-responding K’ stacks of 4n3’.
We have therefore modeled the rotational structure of the 4n3’ level as an asymmetric top, perturbed by a K = 1 level
with zero asymmetry splitting and a K = 3 level with a very small asymmetry splitting equal to that of the 4n3’ K = 3
stack. The data set consisted of upper state term values cal-culated from our measurements, supplemented by those of Van Craen et al. [14] for K’ = 2, J > 10, where we have no data, and for levels where the lines in our spectra are blended. These term values, reduced by 1.07(J + 1), are
Fig. 2. Observed term values of the 4n3’ level of C2H2and two perturbing levels belonging to the 31B4polyad, plotted against J(J + 1).
A quantity 1.07J(J + 1) has been subtracted to magnify the scale. Perturbations occur in the K = 1 (upper asymmetry component) and
K= 3 stacks.
Table 1. Rotational constants for the perturbed ~A1A
u, 4n3level of C2H2. 4n3(Zero order) T0 46 270.558±0.041 DJK 0.000 099±0.000 060 A 19.033 8±0.050 6 DJ 0.000 0046±0.000 0005 B 1.131 69±0.000 79 dK 0.001 56±0.000 26 C 1.014 96±0.000 74 dJ 0.000 001 16±0.000 000 42 DK 0.328 8±0.016 4 HK 0.022 1±0.001 2
Perturbing K’ = 1 level from 31B4 a
T0 46 294.485±0.167 B 1.080 65±0.000 44
W(K = 1 / 4n3) 0.565±0.047
Perturbing K’ = 3 level from 31B4 b
T0 46 419.665±0.058 B 1.0814 1±0.000 48
W(K = 3 / 4n3) 0.830±0.029
RMS error = 0.0401 cm–1
Note: Values are in cm–1, and error limits given are three standard deviations.
a
Energy levels taken as E(J) = T0+ BJ(J+1). The interaction matrix element between the K = 1
stacks of 4n3and 3
1B4is written W(K = 1 / 4n 3).
b
Energy levels taken as E(J) = T0+ BJ(J+1) ± 1.2 10
–9J3(J+1)3.
Merer et al. 439
Table 2. Term values for the 4n3’ level of C2H2and their residuals from the least-squares fit of Table 1.
J K= 0f o-c K= 1f o-c K= 1e o-c
Extra
K= 1e o-c K= 2e o-c K= 2f o-c
Lower K= 3f o-c Upper K= 3f o-c Lower K= 3e o-c Upper K= 3e o-c 1 46 272.60 –10 46 290.29 4 46 290.48 12 2 276.97 –3 294.59 15 294.86 9 46 344.99 –0 46 344.97 –2 3 283.35 –8 300.91 20 301.45 8 351.35 –8 351.38 –5 46 432.34 1 46 434.89 3 46 432.34 1 46 434.89 3 4 291.92 –10 309.13 5 310.18 1 359.99 –2 359.97 –5 440.98 1 443.52 7 440.98 1 443.52 7 5 302.59 –15 319.60 7 321.22 5 370.73 –1 370.71 –4 451.78 0 454.22 3 451.78 0 454.22 3 6 315.46 –14 332.15 7 334.40 3 383.59 –2 383.64 –0 464.75 1 467.05 –2 464.75 1 467.03 –4 7 330.58 –1 346.91 20 349.83 6 398.62 –0 398.63 –5 479.86 0 482.05 –5 482.05 –5 8 347.70 –1 a 367.40 4 415.77 –1 415.85 –3 497.17 4 499.30 2 9 366.93 –3 382.22 –1 387.15 0 435.05 –2 435.21 –2 516.49 –8 518.60 –1 518.63 2 10 388.41 8 403.05 –7 409.27 15 456.52 1 456.75 0 538.11 –4 538.11 –4 540.00 –10 11 411.78 –4 426.07 –2 433.35 7 480.10 1 480.44 1 561.91 2 563.66 –8 561.91 2 12 437.45 4 451.15 1 459.73 10 505.83 3 506.27 –0 587.80 3 589.38 –15 587.76 –2 589.52 –2 13 464.95 –16 478.27 0 488.25 9 533.68 3 534.32 3 615.80 0 617.54 5 615.77 –4 617.42 –8 14 494.86 –4 507.45 –3 518.88 2 46 521.52 –3 563.67 4 564.48 –0 645.97 0 647.56 –6 645.99 2 647.67 4 15 526.79 0 538.76 0 551.72 –2 554.00 1 595.79 4 596.88 3 678.26 1 680.04 12 678.32 5 679.94 0 16 560.79 4 572.10 –1 586.72 –5 588.57 –5 630.04 5 631.42 0 712.67 1 714.46 6 712.73 4 714.52 9 17 596.68 –12 607.54 0 623.90 –5 625.48 5 666.39 2 668.10 –4 749.32 13 749.23 –0 18 634.93 3 645.00 –3 663.21 –3 664.48 3 704.92 5 707.05 –1 787.74 –11 787.83 –7 19 675.13 5 684.57 –2 704.60 0 705.75 2 745.55 6 748.10 –7 828.55 –7 828.60 –9 20 717.27 –3 726.36 14 748.04 3 749.32 4 788.24 0 871.48 –3 871.60 –1 21 761.66 8 769.79 –11 793.49 –1 795.04 –2 833.09 –1 836.95 –3 916.51 –2 916.70 4 22 807.92 3 815.52 –13 841.15 4 843.04 0 880.11 2 963.63 –4 963.94 10 23 856.33 8 863.39 –6 890.81 –5 893.17 –1 47 013.00 7 47 013.30 15 24 906.56 –7 913.29 –1 945.41 –6 980.37 –2 25 959.07 3 965.16 –5 26 47 013.52 4 47 019.08 –8 27 069.96 3 075.10 –6 29 188.94 5
Note: Residuals (o-c) are in units of 10–2cm–1.
a
Doubled level: the observed term values are 46362.95 and 46363.84 cm–1.
440 Can. J. Phys. Vol. 87, 2009 Published by NRC Resear ch Press
shown plotted against J(J + 1) in Fig. 2. Not all of these could be included in the final least-squares fit, because there are further small perturbations that we cannot model. Among these are the line doubling at J = 8 of the lower asymmetry component of K’ = 1 and a number of triplet per-turbations, particularly at low J. Triplet perturbations of this type have been discussed in detail by Drabbels et al. [17], Dupre´ et al. [20–22], and Mishra et al. [23] They give rise to unsymmetrical line shapes at our resolution, which can shift the apparent line centers by up to about 0.15 cm–1.
The results of the least-squares fit are given in Table 1, and the residuals are listed in Table 2. The constants for the deperturbed 4n3’ level are consistent with extrapolations
from the lower nn3 levels, other than those for the
centrifu-gal distortion of the K-structure. The large values of DKand
HKshow that the 4n3’ level is already high enough in energy
to feel the effects of the barrier to linearity. As for the per-turbing levels, their effective B values are identical, to within their 3s error limits, which supports the assumption that they belong to the same vibrational polyad. The per-turbed levels show no obviously systematic residuals, and the intensity patterns for the interactions confirm that the se-lection rules are DK = 0.
3. Conclusions
This work has shown that the perturbations noted by Van Craen et al. [14] in the ~A1A
u, 4n3 level of C2H2 can be
ex-plained as interactions with levels of the 31B4 vibrational
polyad. A simple homogeneous interaction mechanism al-lows a satisfactory least-squares fit and provides deperturbed rotational constants for the levels involved.
Acknowledgements
AJM thanks the Natural Sciences and Engineering Re-search Council of Canada for partial support of this work. At MIT the work was supported by DOE grant DE-FG0287ER13671.
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