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Vibrationally excited states of HC5N: millimeter-wave spectroscopy and coupled cluster calculations
Journal of Molecular Spectroscopy 230 (2005) 185–195 www.elsevier.com/locate/jms
Vibrationally excited states of HC5N: millimeter-wave spectroscopy and coupled cluster calculations C. Degli Espostia, L. Bizzocchia,*, P. Botschwinab, K.M.T. Yamadac,1, G. Winnewisserc, S. Thorwirthc,2, P. Fo¨rsterc a b
Dipartimento di Chimica ‘‘G. Ciamician,’’ Universita` di Bologna, Via F. Selmi 2, 40126 Bologna, Italy Institut fu¨r Physikalische Chemie, Universita¨t Go¨ttingen, Tammannstraße 6, D-37077 Go¨ttingen, Germany c I. Physikalisches Institut, Universita¨t zu Ko¨ln, Zu¨lpicherstraße 77, 50937 Cologne, Germany Received 27 September 2004; in revised form 24 November 2004 Available online 7 January 2005
Abstract The rotational spectrum of HC5N has been investigated in the millimeter-wave region, from 60 to 290 GHz, for 15 vibrationally excited states which lie approximately between 500 and 860 cm1, namely (v6 v7 v8 v9 v10 v11) = (000005), (000006), (000007), (000008), (000020), (000030), (001000), (010000), (100000), (000021), (000101), (001001), (010001), (000110), and (001010). Gasphase copyrolysis of pyridine and phosphorus trichloride or, alternatively, a dc discharge in a gaseous mixture of vinyl cyanide and acetylene were used to produce the semi-stable HC5N molecule. A large number of vibrational and rovibrational interactions has been taken into account to fit properly the measured transition frequencies of the states investigated. The most important perturbations are caused by the high-order Coriolis resonances observed between the (v8, v10) and (v8 1, v10 + 2) states, and between the (v7, v10, v11) and (v7 1, v10 + 3, v11 1) states, and by the cubic anharmonic interactions which mix the (v6, v8, v11) states with the (v6 1, v8 + 1, v11 + 1) states, and the (v6, v10) states with the (v6 1, v10 + 2) states. The analysis of the spectra was facilitated by CCSD(T) calculations with the cc-pVQZ basis, which provided accurate predictions of a large variety of spectroscopic constants like harmonic vibrational wavenumbers, vibration–rotation coupling constants, l-type doubling constants, and normal-coordinate cubic force constants. Excellent agreement between experiment and theory was generally observed, even when the experimental data were strongly perturbed by resonance effects. 2004 Elsevier Inc. All rights reserved. Keywords: Rotational spectroscopy; HC5N; Vibrationally excited states; Resonances; CCSD(T) calculations
1. Introduction The first laboratory study of the rotational spectrum of cyanobutadiyne (HC5N) was published by Alexander et al. [1], who recorded the ground-state spectra of eight
*
Corresponding author. Fax: +39 051 2099 456. E-mail address: [email protected] (L. Bizzocchi). 1 Present address: AIST, Tsukuba-West, Onogawa 16-1, 305-8569, Japan. 2 Present address: Department of Engineering and Applied Sciences, Harvard University, Pierce Hall, 29 Oxford St., MA 02138, USA. 0022-2852/$ - see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2004.11.010
isotopomers in the centimeter-wave (cm-wave) region. In the same year, Avery et al. [2] reported the first interstellar detection of this carbon chain in the molecular cloud Sgr B2, where the 10.65 GHz line was observed. Since that time, the number of new HC5N sources and interstellar transitions has regularly increased, leading to the detection of emission lines also in the millimeter-wave (mm-wave) region [3], and for several isotopic species [4,5]. The study of the ground-state rotational spectrum of HC5N was extended to the mm-wave region by Winnewisser et al. [6], and then to the submm-wave region by Bizzocchi et al. [7]. As far as the vibrational spectrum is concerned, m2 and m7 were the only vibra-
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tional bands studied by high-resolution IR spectroscopy [8–10], while among the few ab initio calculations currently available for HC5N in the literature, the coupled cluster calculations of Botschwina et al. [11] are of greatest relevance for the present work, since they provide theoretical estimates of the vibrational energy level structure of this molecule. HC5N has several low-lying bending vibrational states, so that its room-temperature rotational spectrum exhibits a rich pattern of vibrational satellites, which were first analyzed by Hutchinson et al. [12] in the 26– 40 GHz region. Recently, mm-wave lines of vibrationally excited HC5N were also observed in space toward the proto-planetary nebula CRL 618 [13–15], whose thick and dusty molecular envelope is particularly rich of small hydrocarbons, which produce a rather congested mmwave spectrum. These radioastronomical observations stimulated an earlier laboratory work [16], whose objective was a detailed analysis of the mm-wave spectra for the eight excited states of HC5N which approximately lie below 500 cm1, to provide accurate rest frequencies useful for a sure identification of the corresponding radioastronomical lines. The present paper reports on new mm-wave laboratory measurements for 15 further vibrationally excited states of cyanobutadiyne which lie in the energy range 500–860 cm1 above ground, yielding the first identification of the strongly perturbed rotational spectrum of HC5N in the v6 = 1 stretching state. Most of the vibrational states investigated are affected by various vibrational or rovibrational resonances, which produce anomalies in the corresponding spectra, whose analysis was greatly facilitated by the results of CCSD(T) calculations with the cc-pVQZ basis, which provided accurate predictions of a large variety of spectroscopic constants like harmonic vibrational wavenumbers, vibration–rotation coupling constants, l-type doubling constants, and normal-coordinate cubic force constants. Excellent agreement between experiment and theory was generally observed, even when the experimental data were strongly perturbed by resonance effects.
2. Results of coupled cluster calculations The coupled cluster variant CCSD(T) [17] was used in the calculation of a complete cubic force field for HC5N. DunningÕs cc-pVQZ basis [18] was employed which comprises a total of 360 contracted Gaussian-type orbitals (cGTOs). Valence electrons were correlated in the CCSD(T) calculations which were carried out with the MOLPRO2000 suite of programs [19,20]. The full set of quadratic and cubic force constants is provided as electronic Supplementary material. From the CCSD(T) equilibrium structure (see footnote to Table 1), the nuclidic masses and the cubic force field, a variety of spectroscopic constants has been calculated (see Table 1). These include
Table 1 CCSD(T)/cc-pVQZ spectroscopic constants for HC5Na,b x1 (cm1) x2 (cm1) x3 (cm1) x4 (cm1) x5 (cm1) x6 (cm1) x7 (cm1) x8 (cm1) x9 (cm1) x10 (cm1) x11 (cm1) qe7 ðMHzÞ qe8 ðMHzÞ qe9 ðMHzÞ qe10 ðMHzÞ qe11 ðMHzÞ
3451.1 2320.3 2231.5 2096.7 1164.3 609.3 650.5 501.0 462.9 254.0 106.8 0.202 (0.214) 0.304 (0.316) 0.320 (0.329) 0.490 (0.500) 1.125 (1.163)
a1 (MHz) a2 (MHz) a3 (MHz) a4 (MHz) a5 (MHz) a6 (MHz) a7 (MHz) a8 (MHz) a9 (MHz) a10 (MHz) a11 (MHz) q7J (Hz) q8J (Hz) q9J (Hz) q10J (Hz) q11J (Hz)
0.924 4.361 3.323 2.434 3.111 1.150 0.278 1.778 1.594 2.453 2.705 0.012 0.013 0.032 0.176 0.993
(4.366)
(1.061) (0.268) (1.718) (1.593) (2.452) (2.786) (0.019) (0.136) (0.039) (0.173) (1.063)
a ˚ ): re (CH) = 1.06425, Calculated equilibrium bond lengths (A R1e = 1.21236, R2e = 1.37008, R3e = 1.21588, R4e = 1.37550, and R5e (CN) = 1.16480. b Experimental values from the present and earlier works [8,16] in parentheses.
harmonic vibrational wavenumbers (xr), vibration–rotation coupling constants (ar) as obtained by conventional second-order perturbation theory in normal-coordinate space, and l-type doubling constants (qet and qtJ). According to vast experience, the present xr values should be accurate to a few cm1. Those for the stretching vibrations (x1–x6) differ by at most 7 cm1 from the results of previous CCSD(T) calculations with the smaller ccpVTZ basis set [11]. The higher flexibility of the cc-pVQZ basis appears to be more important for the bending vibrations. Here, the differences range from 0.4 to 13.7 cm1, with the maximum deviation occurring for x9. High accuracy in the harmonic wavenumbers of the bending vibrations is crucial in view of the various vibrational or rovibrational resonances occurring in HC5N. The most accurate experimental values for the vibration–rotation coupling and l-type doubling constants published in previous papers [8,16] or determined in the present work (see Section 5) are compared with the corresponding CCSD(T)/cc-pVQZ values in Table 1. Throughout, agreement is very good. As is usually observed for linear molecules, the qet values obtained by perturbation theory are slightly lower than the corresponding experimental values. Among the small qtJ constants, excellent agreement between theory and experiment is noted for q7J, q9J, q10J, and q11J. No proper comparison is possible for q8J since the v8 = 1 state appears to be subject to strong Coriolis resonance interaction (see Section 4.1).
3. Experimental details The excited-state rotational spectra of cyanobutadiyne have been recorded in selected frequency
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regions between 60 and 290 GHz using two similar source-modulation mm-wave spectrometers which operate at Cologne (I. Physikalisches Institut) and Bologna (Dipartimento di Chimica ‘‘G. Ciamician’’), respectively. Some details on the spectrometers can be found in [16]. Here it can be only mentioned that the radiation sources were phase-locked Gunn oscillators with subsequent harmonic generation and the absorption cells were glass tubes sealed by PTFE windows. The signal was demodulated at 2f, thus obtaining the second derivative of the actual spectrum profile. At Cologne the sample was prepared by a dc discharge in a mixture of acrylonitrile (vinyl cyanide) vapor and acetylene gas, followed by purification of the collected discharge products by means of a low temperature distillation [16]. HC5N was instead produced at Bologna by gas-phase copyrolysis (T 1200 C) of pyridine and PCl3 in a flow reactor connected to the absorption cell of the mm-wave spectrometer [7]. In the latter case the HC5N spectra were recorded while pumping continuously the pyrolysis products through the cell.
4. Analysis of the spectra The vibrational levels investigated in the present work are labeled using the contracted notation (v6 v7 v8 v9 v10 v11). We have investigated the mm-wave spectra of HC5N in the (000005), (000006), (000007), (000008), (000020), (000030), (001000), (010000), (100000), (000021), (000101), (001001), (010001), (000110), and (001010) excited states, for which the present CCSD(T)/cc-pVQZ calculations predict vibrational energies ranging from 500 to 860 cm1. The main objective of the present work was the study of states of single and double vibrational excitation, because they provide information on the most significant spectroscopic constants (i.e., vibration–rotation coupling constants, l-type doubling constants, and anharmonicity constants). The complete energy level diagram which includes all the states investigated is shown in Fig. 1. It is based on the theoretical xr values, and shows clearly that, owing to the high density of states, many accidental near-degeneracies occur above 500 cm1. Earlier cm-wave frequency data [12] were available for seven of the states studied, for which we have extended the measurements to a frequency as high as 290 GHz. With the exception of the v6 = 1 state, all the states investigated involve excitation of at least one bending quantum, so that multiplets of rotational lines were usually recorded for each J + 1 ‹ J transition, owing to l-type resonance effects between the different l sublevels. The spectra were analyzed using the formalism originally developed by Yamada and coworkers [21,22] and employed recently to fit the excited-state rotational spectra of the carbon chains HC5P [23] and NC4P [24].
Fig. 1. Approximate vibrational energy level diagram of HC5N between 500 and 860 cm1. Solid lines indicate the states for which rotational lines were observed.
Using the simplified notation |l7, l8, l9, l10, l11; kæ for the unsymmetrized basis functions, the diagonal elements of the Hamiltonian matrix are: ^ jl7 ;l8 ;l9 ;l10 ;l11 ;ki hl7 ;l8 ;l9 ;l10 ;l11 ;kjH X X xLðttÞ l2t þ xLðtt0 Þ lt lt0 ¼ Gv þ (
t0 >t¼7;11
t¼7;11
þ Bv þ ( Dv þ
X
d JLðttÞ l2t þ
t¼7;11
X
)
X
) d JLðtt0 Þ lt lt0 fJ ðJ þ 1Þ k 2 g
t0 >t¼7;11
hJLðttÞ l2t fJ ðJ þ 1Þ k 2 g
2
t¼7;11 3
þ H v fJ ðJ þ 1Þ k 2 g ;
ð1Þ
where Gv is the vibrational energy of the state and k = l7 + l8 + l9 + l10 + l11. The off-diagonal rotational l-type doubling terms (Dlt = ±2, Dk = 2) have the general form: ^ jlt ;ki ¼ 1fqt þ qtJ J ðJ þ 1Þg hlt 2;k 2jH 4 ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðvt lt Þðvt lt þ 2Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi fJ ðJ þ 1Þ kðk 1ÞgfJ ðJ þ 1Þ ðk 1Þðk 2Þg; ð2Þ while the off-diagonal vibrational l-type doubling terms (Dlt = ±2, Dlt0 ¼ 2, Dk = 0) are given by the expression:
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^ jlt ; lt0 ; ki ¼ 1frtt0 þ rtt0 J J ðJ þ 1Þg hlt 2; lt0 2; kjH 4 ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðvt lt Þðvt lt þ 2Þðvt0 lt0 þ 2Þðvt0 lt0 Þ:
ð3Þ
The resulting energy matrix is factorized into symmetric and antisymmetric blocks adopting Wang-type linear combinations of wavefunctions [21], so that any sublevel belonging to a given vibrational state can be labeled through its k (or lt) value and by the ‘‘+’’ or ‘‘’’ superscripts which designate the chosen type of symmetrized linear combination of wavefunctions. In addition to the normal l-type resonances, numerous vibrational and rovibrational interactions had to be taken into account to fit properly the measured transition frequencies. The corresponding off-diagonal matrix elements were expressed using the formalism of Okabayashi et al. [25]. Some details dealing with the various resonances analyzed are given in the following subsections. 4.1. The Coriolis resonance between (v8, v10) and (v8 1, v10 + 2) The present CCSD(T) calculations predict 2x10 x8 = 7.0 cm1, and thus a high-order Coriolis resonance between the states (v8, v10) and (v8 1, v10 + 2) may be expected. We observed indeed an anomalous decreasing of the splitting between the two l-doublet lines of the v8 = 1 state starting from the J = 60 ‹ 59 transition, which causes an inversion of the latter components passing from the J = 80 ‹ 79 transition to the J = 82 ‹ 81 transition. This behavior is clearly shown in Fig. 2, where the reduced-frequency plot for the l-doublet of the v8 = 1 state is displayed [mred = mmis/2(J + 1)], and in Fig. 3, where the sequence of transitions corresponding to the inversion of the
Fig. 3. Recordings of the J = 80 ‹ 79, J = 81 ‹ 80, and J = 82 ‹ 81 transitions for the (001000) vibrational state of HC5N (pyrolitic production), which show the inversion of the two l-doublet components.
two components is drawn. This unusual trend of the measured frequencies was explained by considering a high-order Coriolis resonance between the v8 = 1, l8 = 1 state and the v10 = 2, l10 = 0, 2+ states, which are connected by matrix elements with the general form: D E ^ 31 jðv8 þ 1Þl8 1 ; ðv10 2Þl10 ; J ; k 1 vl88 ; vl1010 ; J ; kjH pffiffiffi 2 ¼ C 31a ½ðv8 l8 þ 2Þðv10 l10 Þðv10 l10 Þ1=2 4 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi J ðJ þ 1Þ kðk 1Þ; ð4aÞ D
Fig. 2. Plot of the reduced transition frequencies for the (001000) vibrational state of HC5N. Circles and triangles identify the observed transitions. The anomalous trend exhibited by the l8 = 1 component is clearly apparent.
E ^ 33 jðv8 þ 1Þl8 1 ; ðv10 2Þl10 2 ; J ; k 3 vl88 ; vl1010 ; J ; kjH pffiffiffi 2 1=2 ¼ C 33 ½ðv8 l8 þ 2Þðv10 l10 2Þðv10 l10 Þ 4 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi J ðJ þ 1Þ kðk 1Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi J ðJ þ 1Þ ðk 1Þðk 2Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi J ðJ þ 1Þ ðk 2Þðk 3Þ: ð4bÞ
The same kind of resonance affects also the couples of states (001001)–(000021) and (001010)–(000030). The effects produced by this Coriolis-type interaction are strongly dependent on the Fermi resonance which mixes
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the (v6, v10) states with the (v6 1, v10 + 2) states, because the latter changes appreciably the vibrational energy of the states for which v10 P 2 (see next section). 4.2. The cubic anharmonic resonances coupling (v6, v8, v11) with (v6 1, v8 + 1, v11 + 1), and (v6, v10) with (v6 1, v10 + 2) The present CCSD(T) calculations predict x6 (x8 + x11) = 1.5 cm1 and x6 2x10 = 101.3 cm1, with the corresponding normal-coordinate cubic force constants |/6,8,11| = 5.9 cm1 and |/6,10,10| = 98.1 cm1. One may therefore expect that the v6 = 1 stretching state is considerably mixed with the (001001) and (000020) bending states by Fermi-type resonances, producing a considerable low-frequency displacement of the rotational lines for the 0+ sublevels of both bending states and a parallel high-frequency displacement of the v6 = 1 transitions. The plot of the reduced transition frequencies for the lines of the (001001) and (000020) states is presented in Fig. 4, which shows the anomalous lowfrequency shift exhibited by the curves corresponding to the 0+ sublevels, which are the only ones which can be coupled to the v6 = 1 state. This effect is also shown in Fig. 5, where a 85 MHz long scan including the J = 31 ‹ 30 transitions of the two perturbed bending states is displayed. Accordingly, the v6 = 1 lines were found in correspondence of an effective B constant ca. 1.06 MHz greater than the predicted unperturbed value. These cubic resonances were taken into account through the off-diagonal matrix elements given by: D
E ^ 30 þ H ^ 32 jðv6 þ 1Þ; ðv8 1Þl8 1 ;ðv11 1Þl11 1 ;J ;k v6 ; vl88 ; vl1111 ; J ; kjH pffiffiffi h i 2 ð6;8;11Þ ð6;8;11Þ C 30 þ C 30J J ðJ þ 1Þ ½ðv6 þ 1Þðv8 l8 Þðv11 l11 Þ1=2 ; ¼ 2
ð5aÞ
Fig. 5. Recording of the J = 31 ‹ 30 transitions for six doubly excited vibrational states of HC5N (pyrolitic production), including the (001001) combination and the (000020) overtone which are perturbed by cubic anharmonic resonances.
D
E ^ 30 jðv6 þ 1Þ; ðv10 2Þl10 ; J ; k v6 ; vl1010 ; J ; kjH pffiffiffi ð6;10;10Þ 1=2 ¼ 2C 30 ½ðv6 þ 1Þðv10 l10 Þðv10 þ l10 Þ :
ð5bÞ
The C30 coefficients are related to the corresponding normal-coordinate cubic force constants by the expressions: ðstt0 Þ
/stt0 ¼ 4C 30 ; ðsttÞ
/stt ¼ 8C 30 :
ð6aÞ ð6bÞ
The resonance due to /6,10,10 was also considered in the analysis of the lines measured for the (000021) and (000030) states. For the latter state, the off-diagonal matrix element given by Eq. (5b) is large enough to bring both the perturbed |l10| = 1 components below the corresponding unperturbed |l10| = 3 lines. The assignment previously reported in [12] for the |l10| = 1 components is therefore incorrect, probably because of the presence of lines of the (000012) combination tone [16] appearing close to the hypothetical unperturbed transition frequencies of the v3 = 10, |l10| = 1 doublet. 4.3. The Coriolis resonance between the (010001) and (000030) states
Fig. 4. Plot of the reduced transition frequencies for the (001001) and (000020) vibrational states of HC5N. Open and solid symbols identify the observed transitions for the (001001) combination and the (000020) overtone, respectively. Triangles are used for the sublevels perturbed by cubic anharmonic resonances.
The two k = 2 components of the (010001) bending combination, for which high-resolution IR data were already available [10], show a pronounced perturbation in a narrow J range, indicative of a rovibrational avoided crossing. A similar perturbation, at the same J values, is also exhibited by the two |l10| = 1 components of the v10 = 3 states, so that a high-order Coriolis resonance was assumed between these states. The frequency deviations produced by the resonance in the spectra of both states are displayed in Fig. 6. The off-diagonal matrix elements employed to account for this interaction have the form:
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combination and the v6 = 1 stretching state had to be considered through the following off-diagonal matrix element: D
E ^ 41 jðv6 þ 1Þ;ðv10 2Þl10 2 ;ðv11 1Þl11 1 ; J ; k 1 v6 ; vl1010 ; vl1111 ; J ; kjH ¼ 12C 41b ½ðv6 þ 1Þðv10 l10 2Þðv10 l10 Þðv11 l11 Þ1=2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi J ðJ þ 1Þ kðk 1Þ:
ð8Þ
Furthermore, a weak anharmonic resonance connecting the (001010) bending combination to the v6 = 1 stretching state was included via: D E ^ 30 jðv6 þ 1Þ;ðv8 1Þl8 1 ;ðv10 1Þl10 1 ;J ;k v6 ;vl88 ;vl1010 ;J ;kjH pffiffiffi 2 ð6;8;10Þ 1=2 ¼ C ½ðv6 þ 1Þðv8 l8 Þðv10 l10 Þ ; ð9Þ 2 30
Fig. 6. Plot of the frequency deviations Dm produced by the Coriolis resonance between the (010001) and (000030) vibrational states of HC5N. Triangles identify the observed transitions.
D
E ^ 51 jðv7 þ 1Þl7 1 ; ðv10 3Þl10 1 ; ðv11 þ 1Þl11 1 ;J ;k 1 vl77 ; vl1010 ;vl1111 ; J; kjH pffiffiffi 2 1=2 ¼ C 51a ½ðv7 l7 þ 2Þðv10 l10 Þðv10 l10 Þðv10 l10 2Þðv11 l11 þ 2Þ 8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi J ðJ þ 1Þ kðk 1Þ; ð7aÞ
D
E ^ 53 jðv7 þ 1Þl7 1 ;ðv10 3Þl10 1 ;ðv11 þ 1Þl11 1 ;J ;k 3 vl77 ;vl1010 ;vl1111 ;J; kjH pffiffiffi 2 ¼ C 53 ½ðv7 l7 þ 2Þðv10 l10 Þðv10 l10 Þðv10 l10 2Þðv11 l11 þ 2Þ1=2 8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi JðJ þ 1Þ kðk 1Þ J ðJ þ 1Þ kðk 1Þðk 2Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð7bÞ JðJ þ 1Þ kðk 2Þðk 3Þ:
where the C30 coefficient is related to the corresponding normal-coordinate cubic force constant through Eq. (6a). The effects of a weak resonance were also detected in the spectrum of the v11 = 8 state, but no detailed analysis could be accomplished, and the corresponding leastsquares fit was simply performed by removing the few perturbed lines from the data set. As a consequence of the various resonances taken into account, we found that only seven of the investigated states could be properly analyzed as isolated. These are (v6 v7 v8 v9 v10 v11) = (000005), (000006), (000007), (000008), (010000), (000101), and (000110). The remaining eight states, namely (v6 v7 v8 v9 v10 v11) = (000020), (000030), (001000), (100000), (000021), (001001), (010001), and (001010), were all included within a rather large rovibrational energy matrix, whose offdiagonal elements are given by Eqs. (5a) and (5b) and (7–9). In addition to the investigated states, the (100001) and (100010) states were also included into the matrix, because they are connected to (000021) and (000030) through matrix elements expressed by Eq. (5b). The scheme of rovibrational interactions taken into account for the analysis of the resonance system of HC5N is summarized in Fig. 7.
In this case, the mixing of states produced by the resonance enabled also the detection of several interstate transitions.
5. Experimental results
4.4. Further weak resonances
5.1. The isolated states
The vibrational and rovibrational resonances previously discussed produce anomalies in the spectral patterns which are recognizable even before any detailed analysis of the measured frequencies is performed. In addition, during the fitting procedures we found that two further weak resonances must be taken into account in order to fit the measured transition frequencies within the experimental accuracy (ca. 15 kHz). First, a high-order Coriolis resonance between the (000021) bending
Transition frequencies for the fundamental bending state v7 = 1 and for the overtone bending states v11 = 5–8 had been already measured in the frequency range 26–40 GHz [12]. In addition, high-resolution IR data were also available for the m7 fundamental band [10]. The measurements for the bending state v7 = 1 have been extended up to 270 GHz, reaching a J value as high as 100, and they have been analyzed through Eqs. (1) and (2) (having k = l7), fitting the rotational
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For the overtone bending states v11 = 5–8 we have extended the measurements up to 105 GHz, reaching J values as high as 38. The spectra have been analyzed using Eqs. (1) and (2), having k = l11. Since the off-diagonal matrix element given by Eq. (2) gives a first-order contribution to the rotational energy only when l11 = ± 1 (degenerate l-sublevels), the constants q11 and q11J were fitted for the states with odd values of v11, but they were constrained to interpolated or extrapolated values for the states with even values of v11. Accurate determinations of the xL(11,11) and dJL(11,11) constants have been obtained for each state investigated. The results of the least-squares fits performed for these overtone bending states are collected in columns 2–5 of Table 2. The change of the rotational constant B produced by progressive excitation of the v11 vibrational mode can be expressed using the formula: DBðv11 Þ ¼ Bðv11 Þ Bðv11 1Þ ¼ a11 þ c11;11 ð2v11 þ 1Þ;
Fig. 7. Vibrational energy level diagram for the resonance system of HC5N. Thin arrows indicate the vibrational and rovibrational interactions taken into account. Large arrows indicate the vibrational energy displacements produced by Fermi-type resonances.
constant B, the quartic centrifugal distortion constant D and the l-type doubling parameters q7 and q7J. The sextic distortion constant H was held fixed at the value of 1.635 lHz previously determined for the ground state of HC5N [7]. This constraint was systematically adopted for all the spectra analyzed. The results of the leastsquares fit are listed in the first numerical column of Table 2. They agree very well with earlier results obtained by FTIR spectroscopy [10].
ð10Þ
where a11 actually includes also all high-order vibration– rotation interaction constants of the type cr11 (r = 1, 2, . . . , 10). The experimental results of the present work and of [16] make it possible to calculate DB (v11) values from v11 = 1 to v11 = 8, which satisfy well Eq. (10). A linear regression analysis of the experimental data yields c11,11 = 4.115 ± 0.023 kHz. No previous spectroscopic information was instead available for the (000101) and (000110) bending combinations, whose rotational spectra have been assigned for the first time in the frequency range 80–190 GHz. No anomaly was observed in the recorded quadruplets of lines, which were simply analyzed taking into account the usual rotational and vibrational l-type resonances. The qt constants involved in the off-diagonal matrix elements were generally held fixed at the values determined for the singly excited bending states [16], but we found useful to release q11 in the (000101) combination to improve slightly the quality of the fit. The change observed
Table 2 Spectroscopic constants determined for the (010000), (000005), (000006), (000007), and (000008) states of HC5N (010000)
(000005)
(000006)
(000007)
(000008)
Bv (MHz) av (MHz) Dv (Hz) xL(11,11) (GHz) dJL(11,11) (kHz) qt (MHz) qtJ (Hz) r (kHz)
1331.600997(28) 0.2683 30.1349(20) — — 0.213887(55) 0.0187(39) 12.4
1345.342260(69) — 38.192(30) 6.23004(70) 3.3951(21) 1.182729(68) 1.171(30) 8.8
1348.168400(99) — 39.738(42) 6.21159(20) 3.4068(15) 1.187578a 1.150a 11.2
1351.00339(11) — 41.507(48) 6.19112(53) 3.4191(13) 1.192427(96) 1.128(41) 12.3
1353.84661(13) — 43.245(59) 6.17228(28) 3.4300(11) 1.197276a 1.106a 17.0
No. of lines J range
68 10–100
67 13–37
63 13–37
67 13–37
60 13–37
Standard errors in units of the last digit are given in parentheses for the fitted parameters. a Fixed in the analysis.
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Table 3 Spectroscopic constants determined for the (000101) and (000110) states of HC5N (000101)
(000110)
Bv (MHz) Dv (Hz)
1335.716874(28) 32.0761(41)
1335.381480(45) 31.0373(62)
xL(9t) (GHz) dJL(9t) (kHz) dJL(11,11) (kHz)
7.5873(18) 6.889(44) 3.3047a
13.243(20) 6.787(49) —
r9t (GHz) r9tJ (kHz)
7.3226(23) 8.360(23)
22.177(40) 0.530(35)
q9 (MHz) q9J (Hz) qt (MHz) qtJ (Hz)
0.328526a 0.0393a 1.16564(14) 1.0629a
0.328526a 0.0393a 0.500190a 0.1734a
r (kHz) No. of lines J range
9.1 63 30–70
13.9 61 30–70
Standard errors in units of the last digit are given in parentheses for the fitted parameters. a Fixed in the analysis.
is less than 1%, as expected for a normal vibrational dependence of the qt constants. The results of these least-squares fits are collected in Table 3. The complete set of transition frequencies analyzed for the isolated states is provided as electronic Supplementary material. 5.2. The resonance system Taking into account the off-diagonal matrix elements corresponding to Eqs. (5a) and (5b) and (7–9), an
infinitely large rovibrational energy matrix is produced. The eigenvalues necessary to analyze the spectra of the states investigated were calculated by diagonalization of a truncated matrix which includes the eight vibrational states for which resonance effects were experimentally observed, plus the two states (100001) and (100010), for which no line was recorded. The inclusion of further vibrational states connected by the abovementioned off-diagonal terms did not improve significantly the results. Since most of the vibrational states considered produce several substates because of different k and lt values, 17 · 17 (e symmetry) and 15 · 15 (f symmetry) rovibrational energy matrices were actually diagonalized for each J value to obtain the required eigenvalues. The vibrational energies Gv of the resonant states were generally held fixed at the values calculated by means of the theoretical xr constants, but when nearly degenerate states were considered, the corresponding Gv values were also optimized. More than 600 transition frequencies were simultaneously analyzed fitting independently a total number of 57 parameters. Many other spectroscopic constants were held fixed at values derived from states of lower vibrational excitation. The standard deviation of the least-squares fit was 11.3 kHz. The spectroscopic constants determined or assumed for each vibrational state of the resonance system are reported in Tables 4 and 5. The values obtained for the coefficients included in the off-diagonal elements are listed in Table 6, where a simplified notation is employed to identify the interacting states. The complete set of transition frequencies analyzed for the resonance system is provided as electronic Supplementary material.
Table 4 Spectroscopic constants determined for the (001000), (000020), (001001), (100000), and (000021) resonant states of HC5N (001000)
(000020)
(001001)
(100000)
(000021)
Gv (cm1) Bv (MHz) av (MHz) Dv (Hz)
502.7540(22) 1333.051138(27) 1.7185 30.0644(76)
508.0a 1336.255431(44) — 31.545(12)
608.985(45) 1335.84602(12) — 31.859(16)
609.3a 1330.27109(88) 1.0614 30.100(74)
614.524(39) 1339.05616(22) — 33.072(38)
xL(11,11) (GHz) xL(10,10) (GHz) xL(t,11) (GHz) dJL(11,11) (kHz) dJL(t,11) (kHz) hJL(10,10) (Hz)
— — — — — —
— 23.29(11) — — — 0.0467(35)
6.3139a — 6.799(54) 3.3047a 1.40(11) —
— — — — — —
6.3139a 23.29a 7.256(16) 3.3047a 4.12(12) 0.0467a
rt,11 (GHz) rt,11J (kHz)
— —
— —
6.16(11) 0.0a
— —
3.657(92) 1.301a
q11 (MHz) q11J (Hz) qt (MHz) qtJ (Hz)
— — 0.316154(59) 0.136(10)
— — 0.51122a 0.1734a
1.15926(41) 1.0629a 0.316154a 0.136a
— — — —
1.19104(72) 1.0629a 0.51122a 0.1734a
No. of lines J range
81 10–107
84 30–107
69 30–70
16 30–70
74 28–42
Standard errors in units of the last digit are given in parentheses for the fitted parameters. a Fixed in the analysis.
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193
Table 5 Spectroscopic constants determined for the (100001), (010001), (001010), (000030), and (100010) resonant states of HC5N (100001) 1
b
(010001)
(001010) b
(000030) a
(100010)
Gv (cm ) Bv (MHz) Dv (Hz)
715.824 1333.0566a 31.643a
750.550(36) 1334.385776(27) 31.6406(42)
756.754 1335.47596(71) 30.662(13)
762.0 1338.746514(53) 31.903(30)
863.3a 1332.7232a 30.753a
xL(11,11) (GHz) xL(10,10) (GHz) xL(tt 0 ) (GHz) dJL(11,11) (kHz) dJL(tt 0 ) (kHz) hJL(10,10) (Hz)
6.3139a — — 3.3047a — —
6.3139a — 7.5928(77) 3.3047a 0.454(42) —
— 23.29a 7.649(39) — 35.713(63) —
— 23.29a — — — 0.1233(36)
— 23.29a — — — —
rtt 0 (GHz) rtt 0 J (kHz)
— —
0.7000(38) 1.946(20)
2.03(10) 0.0a
— —
— —
q11 (MHz) q11J (Hz) q10 (MHz) q10J (Hz) qt (MHz) qtJ (Hz)
1.162898a 1.0629a — — — —
1.16631(71) 1.0629a — — 0.213887a 0.0187a
— — 0.500190a 0.1734a 0.316154a 0.136a
— — 0.522251(27) 0.1734a — —
— — 0.500190a 0.1734a — —
No. of lines J range
— —
118 30–70
75 30–70
89 30–70
— —
Standard errors in units of the last digit are given in parentheses for the fitted parameters. a Fixed in the analysis. b Adjusted by fixing energy differences. See text.
The experimental values of the a6 and a8 vibration– rotation coupling constants, and of the q8 l-doubling constant agree well with the results of the CCSD(T) calculations (cf. Table 1), and no serious anomaly appears in the Dv and qt constants fitted for the various overtone and combination states involved in the resonance system. This indicates that the main resonance effects
Table 6 Off-diagonal coefficients determined for the resonance system of HC5N Interacting states
Parameters
Fitted values
Units
(v8) (2v10)
C31a C33
33.994(11) 0.793(29)
MHz kHz
(v8 + v11) (2v10 + v11)
C31a C33
33.128(47) 0.22(15)
MHz kHz
(v8 + v10) (3v10)
C31a C33
42.84(84) 0.3476(57)
MHz kHz
(2v10) (v6)
C 30
ð6;10;10Þ
9.2856(17)
cm1
(2v10 + v11) (v6 + v11)
ð6;10;10Þ C 30
9.1836(47)
cm1
(3v10) (v6 + v10)
C 30
ð6;10;10Þ
9.287(15)
cm1
(v6) (v8 + v11)
C 30
ð6;8;11Þ
1.0701(35)
cm1
ð6;8;11Þ C 30J
0.2092(80)
MHz
(v6) (2v10 + v11)
C41b
12.35(31)
MHz
(v6) (v8 + v10)
ð6;8;10Þ C 30
4.520(11)
cm1
(v7 + v11) (3v10)
C51a C53
0.140097(55) 0.474979(62)
MHz kHz
Standard errors in units of the last digit are given in parentheses for the fitted parameters.
have been well treated, even if the presence of small residual perturbations is revealed by the high value obtained for q8J and by the large difference which exists between the hJL(10,10) values fitted for the v10 = 2 and v10 = 3 states, respectively. It is, however, to remark that these high-order parameters give contributions to the transition frequencies which never exceed 1.7 MHz in the J range investigated. Differently from the v7 = 1 state, the parameters obtained for the (010001) bending combination show small discrepancies in comparison with earlier FTIR spectroscopy results [10]. This is probably due to the fact that the weak high-order Coriolis resonance existing between the (010001) and (000030) states was neglected in [10]. Table 7 shows the comparison between the Gv values calculated through the theoretical xr constants and those corresponding to the best fit of the experimental data. The optimized set of unperturbed vibrational energies was obtained assuming the CCSD(T) values of x6 and x10 to fix the energies of the states in which only v6 and v10 are excited, and also to fix the energy differences between the states (100001) and (000021), and between the states (001010) and (001000), while the energies of the (001000), (001001), (000021), and (010001) states were freely adjusted in the least-squares procedure. Inspection of Table 7 shows that the largest discrepancy between fitted and theoretically computed vibrational terms concerns the (010001) combination, the difference being 6.8 cm1, but it is to be noted that this value is close to the difference which exists between the experimental band origin of the m7 band (642.1 cm1
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C. Degli Esposti et al. / Journal of Molecular Spectroscopy 230 (2005) 185–195
from [10]) and the theoretical value of x7 (650.5 cm1 from Table 1). This slight discrepancy could be explained by the presence of an anharmonic interaction between the v7 = 1 state and the near by (100001) state, which pushes down the v7 = 1 level, but the small theoretical value of the /6,7,11 cubic force constant (2.5 cm1) does not support this interpretation. On the other hand the rovibrational parameters derived treating the (010000) bending state as isolated do not show any evidence of perturbations, making unlikely the existence of significantly strong high-order interactions. No restrictive hypothesis about the energy of the v11 = 1 state was made within the best-estimates set, but making the appropriate differences between fitted vibrational terms (including also the m7 band origin [10]) it is possible to calculate this energy by three independent ways, which yield the values of 106.2, 106.5, and 108.3 cm1, respectively, all of which are close to the CCSD(T)/ccpVQZ value of x11 = 106.8 cm1. From the fitted C30 coefficients it is possible to derive the values of the corresponding normal-coordinate cubic force constants, which are |/6,10,10| = 74.3 cm1, |/6,8,11| = 4.27 cm1, and |/6,8,10| = 18.1 cm1. These experimental results are consistent with the corresponding CCSD(T) values of 98.1, 5.9, and 17.2 cm1, respectively.
tionally excited states of this molecule [16]. The present paper extends the study of the mm-wave spectra of HC5N to 15 further vibrational states which approximately lie between 500 and 860 cm1 above ground, where the high density of states produces numerous accidental near-degeneracies which cause anomalies in the observed spectra. Their assignment and analysis have been facilitated by accurate theoretical predictions for vibrational energies, cubic normal-coordinate force constants, and various vibration–rotation coupling parameters. Novel determinations of the a6 vibration– rotation coupling constant of the lowest-energy stretching state, and of the xL(10,10), xL(9,11), xL(9,10), xL(8,11), and xL(8,10) anharmonicity constants have been obtained from the analysis of the measured transition frequencies. In addition to the normal l-type resonances, a large number of vibrational and rovibrational interactions have been taken into account to fit properly the measured transition frequencies. As already observed in HC5P [23] and NC4P [24], also in HC5N the lowest-energy stretching state is perturbed by strong anharmonic resonances which produce a very small effective value for the a6 vibration–rotation coupling constant, pushing the rotational lines of the v6 = 1 state quite far from the expected, unperturbed positions. The rotational and centrifugal distortion constants fitted for the observed overtone and combination states are generally in excellent agreement with the values which is possible to extrapolate from the singly excited bending states, thus supporting the reliability of the analyses performed, as the good agreement between experimental and theoretical results also demonstrates. Although the vibrational states investigated in the present work are less likely observable in space than those of lower excitation [16], an accurate knowledge of their rotational spectra is anyway useful to avoid misassignments of the radio lines observed in very congested regions. For example, some mm-wave lines detected towards CRL 618 have been tentatively assigned to the v10 = 3, |l10| = 1 doublet of HC5N [13] using predictions extrapolated from earlier cm-wave measurements [12], but the present investigation establishes that the v10 = 3, |l10| = 1 lines undergo a large frequency displacement because of Fermi resonance effects, and a different assignment must be therefore proposed for the observed features.
6. Conclusions
Acknowledgments
Millimeter-wave transitions in low-lying excited vibrational states of HC5N have been recently detected in the C-rich proto-planetary nebula CRL 618 [13–15]. These observations stimulated an earlier laboratory work which provided very accurate rest frequencies and spectroscopic constants for the eight lowest vibra-
C.D.E. and L.B. gratefully acknowledge financial support from MIUR and from the University of Bologna (Funds for Selected Research Topics). Thanks are due to the Fonds der Chemischen Industrie for providing support to P.B. The work at Cologne has been supported by the Deutsche Forschungsgemeinschaft
Table 7 Comparison between experimentally adjusted and theoretical (harmonic approximation) vibrational energies of HC5N
(001000) (000020) (001001) (100000) (000021) (100001) (010001) (001010) (000030) (100010)
Unperturbed energies
Anharmonic resonance shiftsa
Ab initiob
502.754c 508.0d 608.985c 609.3d 614.524c 715.82e 750.550c 756.75e 762.0c 863.3c
— 6.424 0.609 6.476 6.318 6.233 — 0.568 12.161 12.117
501.0 508.0 607.0 609.3 614.8 716.1 757.3 755.0 762.0 863.3
a
The negative sign indicates that the level is pushed down by the resonance. b Calculated using the xr constants of Table 1. c Fitted. d Constrained to the ab initio values. e Adjusted by fixing energy differences. See text.
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through Grant SFB 494 and by additional funding from the Minisitry of Science and Technology of the State Nordrhein-Westfalen.
Appendix A. Supplementary data Supplementary data for this article are available on ScienceDirect (www.sciencedirect.com) and as part of the Ohio State University Molecular Spectroscopy Archives (http://msa.lib.ohio-state.edu/jmsa_hp.htm).
References [1] A.J. Alexander, H.W. Kroto, D.R.M. Walton, J. Mol. Spectrosc. 62 (1976) 175–180. [2] L.W. Avery, N.W. Broten, J.M. MacLeod, T. Oka, H.W. Kroto, Astrophys. J. 200 (1976) L173–L175. [3] G. Winnewisser, C.M. Walmsley, Astrophys. Space Sci. 65 (1979) 83–93. [4] J.M. MacLeod, L.W. Avery, N.W. Broten, Astrophys. J. 251 (1981) L33–L36. [5] S. Takano, H. Suzuki, M. Ohishi, S. Ishikawa, N. Kaifu, Y. Hirahara, A. Masuda, Astrophys. J. 361 (1990) L15–L18. [6] G. Winnewisser, M. Winnewisser, J.J. Christiansen, Astron. Astrophys. 109 (1982) 141–144. [7] L. Bizzocchi, C. Degli Esposti, P. Botschwina, J. Mol. Spectrosc. 225 (2004) 145–151. [8] K.M.T. Yamada, G. Winnewisser, Z. Naturforsch. 36a (1981) 1052–1056. [9] K.M.T. Yamada, G. Winnewisser, Z. Naturforsch. A 40 (1981) 476–478.
195
[10] S. Haas, G. Winnewisser, K.M.T. Yamada, Can. J. Phys. 72 (1994) 1165–1178. ¨ . Heyl, M. Oswald, T. Hirano, Spectrochim. [11] P. Botschwina, A Acta Part A 53 (1997) 1079–1090. [12] M. Hutchinson, H.W. Kroto, D.R.M. Walton, J. Mol. Spectrosc. 82 (1980) 394–410. [13] J. Cernicharo, A.M. Heras, J.R. Pardo, A.G.G.M. Tielens, M. Guelin, E. Dartois, R. Neri, L.B.F.M. Waters, Astrophys. J. 546 (2001) L127–L130. [14] S. Thorwirth, Ph.D. thesis, Universita¨t zu Ko¨ln, 2001. [15] F. Wyrowski, P. Schilke, S. Thorwirth, K.M. Menten, G. Winnewisser, Astrophys. J. 586 (2003) 344–355. [16] K.M.T. Yamada, C. Degli Esposti, P. Botschwina, P. Fo¨rster, L. Bizzocchi, S. Thorwirth, G. Winnewisser, Astron. Astrophys. 425 (2004) 767–772. [17] K. Raghavachari, G.W. Trucks, J.A. Pople, M. Head-Gordon, Chem. Phys. Lett. 157 (1989) 479–483. [18] T.H. Dunning Jr., J. Chem. Phys. 90 (1989) 1007–1023. [19] H.-J. Werner, P.J. Knowles, with contributions from R.D. Amos, A. Bernhardsson, A. Berning, P. Celani, D.L. Cooper, M.J.O. Deegan, A.J. Dobbyn, F. Eckert, C. Hampel, G. Hetzer, T. Korona, R. Lindh, A.W. Lloyd, S.J. McNicholas, F.R. Manby, W. Meyer, M.E. Mura, A. Nicklass, P. Palmieri, P. Pulay, R. Pitzer, G. Rauhut, M. Schu¨tz, H. Stoll, J. Stone, R. Tarroni, T. Thorsteinsson, MOLPRO2000. [20] C. Hampel, K.A. Peterson, H.-J. Werner, Chem. Phys. Lett. 190 (1992) 1–12. [21] K.M.T. Yamada, F.W. Birss, M.R. Aliev, J. Mol. Spectrosc. 112 (1985) 347–356. [22] M. Niedenhoff, K.M.T. Yamada, J. Mol. Spectrosc. 157 (1993) 182–197. [23] L. Bizzocchi, C. Degli Esposti, P. Botschwina, Phys. Chem. Chem. Phys. 5 (2003) 4090–4095. [24] L. Bizzocchi, C. Degli Esposti, P. Botschwina, Phys. Chem. Chem. Phys. 6 (2004) 46–50. [25] T. Okabayashi, K. Tanaka, T. Tanaka, J. Mol. Spectrosc. 195 (1999) 22–42.
Vibrationally excited states of HC5N: millimeter-wave spectroscopy and coupled cluster calculations C. Degli Espostia, L. Bizzocchia,*, P. Botschwinab, K.M.T. Yamadac,1, G. Winnewisserc, S. Thorwirthc,2, P. Fo¨rsterc a b
Dipartimento di Chimica ‘‘G. Ciamician,’’ Universita` di Bologna, Via F. Selmi 2, 40126 Bologna, Italy Institut fu¨r Physikalische Chemie, Universita¨t Go¨ttingen, Tammannstraße 6, D-37077 Go¨ttingen, Germany c I. Physikalisches Institut, Universita¨t zu Ko¨ln, Zu¨lpicherstraße 77, 50937 Cologne, Germany Received 27 September 2004; in revised form 24 November 2004 Available online 7 January 2005
Abstract The rotational spectrum of HC5N has been investigated in the millimeter-wave region, from 60 to 290 GHz, for 15 vibrationally excited states which lie approximately between 500 and 860 cm1, namely (v6 v7 v8 v9 v10 v11) = (000005), (000006), (000007), (000008), (000020), (000030), (001000), (010000), (100000), (000021), (000101), (001001), (010001), (000110), and (001010). Gasphase copyrolysis of pyridine and phosphorus trichloride or, alternatively, a dc discharge in a gaseous mixture of vinyl cyanide and acetylene were used to produce the semi-stable HC5N molecule. A large number of vibrational and rovibrational interactions has been taken into account to fit properly the measured transition frequencies of the states investigated. The most important perturbations are caused by the high-order Coriolis resonances observed between the (v8, v10) and (v8 1, v10 + 2) states, and between the (v7, v10, v11) and (v7 1, v10 + 3, v11 1) states, and by the cubic anharmonic interactions which mix the (v6, v8, v11) states with the (v6 1, v8 + 1, v11 + 1) states, and the (v6, v10) states with the (v6 1, v10 + 2) states. The analysis of the spectra was facilitated by CCSD(T) calculations with the cc-pVQZ basis, which provided accurate predictions of a large variety of spectroscopic constants like harmonic vibrational wavenumbers, vibration–rotation coupling constants, l-type doubling constants, and normal-coordinate cubic force constants. Excellent agreement between experiment and theory was generally observed, even when the experimental data were strongly perturbed by resonance effects. 2004 Elsevier Inc. All rights reserved. Keywords: Rotational spectroscopy; HC5N; Vibrationally excited states; Resonances; CCSD(T) calculations
1. Introduction The first laboratory study of the rotational spectrum of cyanobutadiyne (HC5N) was published by Alexander et al. [1], who recorded the ground-state spectra of eight
*
Corresponding author. Fax: +39 051 2099 456. E-mail address: [email protected] (L. Bizzocchi). 1 Present address: AIST, Tsukuba-West, Onogawa 16-1, 305-8569, Japan. 2 Present address: Department of Engineering and Applied Sciences, Harvard University, Pierce Hall, 29 Oxford St., MA 02138, USA. 0022-2852/$ - see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2004.11.010
isotopomers in the centimeter-wave (cm-wave) region. In the same year, Avery et al. [2] reported the first interstellar detection of this carbon chain in the molecular cloud Sgr B2, where the 10.65 GHz line was observed. Since that time, the number of new HC5N sources and interstellar transitions has regularly increased, leading to the detection of emission lines also in the millimeter-wave (mm-wave) region [3], and for several isotopic species [4,5]. The study of the ground-state rotational spectrum of HC5N was extended to the mm-wave region by Winnewisser et al. [6], and then to the submm-wave region by Bizzocchi et al. [7]. As far as the vibrational spectrum is concerned, m2 and m7 were the only vibra-
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tional bands studied by high-resolution IR spectroscopy [8–10], while among the few ab initio calculations currently available for HC5N in the literature, the coupled cluster calculations of Botschwina et al. [11] are of greatest relevance for the present work, since they provide theoretical estimates of the vibrational energy level structure of this molecule. HC5N has several low-lying bending vibrational states, so that its room-temperature rotational spectrum exhibits a rich pattern of vibrational satellites, which were first analyzed by Hutchinson et al. [12] in the 26– 40 GHz region. Recently, mm-wave lines of vibrationally excited HC5N were also observed in space toward the proto-planetary nebula CRL 618 [13–15], whose thick and dusty molecular envelope is particularly rich of small hydrocarbons, which produce a rather congested mmwave spectrum. These radioastronomical observations stimulated an earlier laboratory work [16], whose objective was a detailed analysis of the mm-wave spectra for the eight excited states of HC5N which approximately lie below 500 cm1, to provide accurate rest frequencies useful for a sure identification of the corresponding radioastronomical lines. The present paper reports on new mm-wave laboratory measurements for 15 further vibrationally excited states of cyanobutadiyne which lie in the energy range 500–860 cm1 above ground, yielding the first identification of the strongly perturbed rotational spectrum of HC5N in the v6 = 1 stretching state. Most of the vibrational states investigated are affected by various vibrational or rovibrational resonances, which produce anomalies in the corresponding spectra, whose analysis was greatly facilitated by the results of CCSD(T) calculations with the cc-pVQZ basis, which provided accurate predictions of a large variety of spectroscopic constants like harmonic vibrational wavenumbers, vibration–rotation coupling constants, l-type doubling constants, and normal-coordinate cubic force constants. Excellent agreement between experiment and theory was generally observed, even when the experimental data were strongly perturbed by resonance effects.
2. Results of coupled cluster calculations The coupled cluster variant CCSD(T) [17] was used in the calculation of a complete cubic force field for HC5N. DunningÕs cc-pVQZ basis [18] was employed which comprises a total of 360 contracted Gaussian-type orbitals (cGTOs). Valence electrons were correlated in the CCSD(T) calculations which were carried out with the MOLPRO2000 suite of programs [19,20]. The full set of quadratic and cubic force constants is provided as electronic Supplementary material. From the CCSD(T) equilibrium structure (see footnote to Table 1), the nuclidic masses and the cubic force field, a variety of spectroscopic constants has been calculated (see Table 1). These include
Table 1 CCSD(T)/cc-pVQZ spectroscopic constants for HC5Na,b x1 (cm1) x2 (cm1) x3 (cm1) x4 (cm1) x5 (cm1) x6 (cm1) x7 (cm1) x8 (cm1) x9 (cm1) x10 (cm1) x11 (cm1) qe7 ðMHzÞ qe8 ðMHzÞ qe9 ðMHzÞ qe10 ðMHzÞ qe11 ðMHzÞ
3451.1 2320.3 2231.5 2096.7 1164.3 609.3 650.5 501.0 462.9 254.0 106.8 0.202 (0.214) 0.304 (0.316) 0.320 (0.329) 0.490 (0.500) 1.125 (1.163)
a1 (MHz) a2 (MHz) a3 (MHz) a4 (MHz) a5 (MHz) a6 (MHz) a7 (MHz) a8 (MHz) a9 (MHz) a10 (MHz) a11 (MHz) q7J (Hz) q8J (Hz) q9J (Hz) q10J (Hz) q11J (Hz)
0.924 4.361 3.323 2.434 3.111 1.150 0.278 1.778 1.594 2.453 2.705 0.012 0.013 0.032 0.176 0.993
(4.366)
(1.061) (0.268) (1.718) (1.593) (2.452) (2.786) (0.019) (0.136) (0.039) (0.173) (1.063)
a ˚ ): re (CH) = 1.06425, Calculated equilibrium bond lengths (A R1e = 1.21236, R2e = 1.37008, R3e = 1.21588, R4e = 1.37550, and R5e (CN) = 1.16480. b Experimental values from the present and earlier works [8,16] in parentheses.
harmonic vibrational wavenumbers (xr), vibration–rotation coupling constants (ar) as obtained by conventional second-order perturbation theory in normal-coordinate space, and l-type doubling constants (qet and qtJ). According to vast experience, the present xr values should be accurate to a few cm1. Those for the stretching vibrations (x1–x6) differ by at most 7 cm1 from the results of previous CCSD(T) calculations with the smaller ccpVTZ basis set [11]. The higher flexibility of the cc-pVQZ basis appears to be more important for the bending vibrations. Here, the differences range from 0.4 to 13.7 cm1, with the maximum deviation occurring for x9. High accuracy in the harmonic wavenumbers of the bending vibrations is crucial in view of the various vibrational or rovibrational resonances occurring in HC5N. The most accurate experimental values for the vibration–rotation coupling and l-type doubling constants published in previous papers [8,16] or determined in the present work (see Section 5) are compared with the corresponding CCSD(T)/cc-pVQZ values in Table 1. Throughout, agreement is very good. As is usually observed for linear molecules, the qet values obtained by perturbation theory are slightly lower than the corresponding experimental values. Among the small qtJ constants, excellent agreement between theory and experiment is noted for q7J, q9J, q10J, and q11J. No proper comparison is possible for q8J since the v8 = 1 state appears to be subject to strong Coriolis resonance interaction (see Section 4.1).
3. Experimental details The excited-state rotational spectra of cyanobutadiyne have been recorded in selected frequency
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regions between 60 and 290 GHz using two similar source-modulation mm-wave spectrometers which operate at Cologne (I. Physikalisches Institut) and Bologna (Dipartimento di Chimica ‘‘G. Ciamician’’), respectively. Some details on the spectrometers can be found in [16]. Here it can be only mentioned that the radiation sources were phase-locked Gunn oscillators with subsequent harmonic generation and the absorption cells were glass tubes sealed by PTFE windows. The signal was demodulated at 2f, thus obtaining the second derivative of the actual spectrum profile. At Cologne the sample was prepared by a dc discharge in a mixture of acrylonitrile (vinyl cyanide) vapor and acetylene gas, followed by purification of the collected discharge products by means of a low temperature distillation [16]. HC5N was instead produced at Bologna by gas-phase copyrolysis (T 1200 C) of pyridine and PCl3 in a flow reactor connected to the absorption cell of the mm-wave spectrometer [7]. In the latter case the HC5N spectra were recorded while pumping continuously the pyrolysis products through the cell.
4. Analysis of the spectra The vibrational levels investigated in the present work are labeled using the contracted notation (v6 v7 v8 v9 v10 v11). We have investigated the mm-wave spectra of HC5N in the (000005), (000006), (000007), (000008), (000020), (000030), (001000), (010000), (100000), (000021), (000101), (001001), (010001), (000110), and (001010) excited states, for which the present CCSD(T)/cc-pVQZ calculations predict vibrational energies ranging from 500 to 860 cm1. The main objective of the present work was the study of states of single and double vibrational excitation, because they provide information on the most significant spectroscopic constants (i.e., vibration–rotation coupling constants, l-type doubling constants, and anharmonicity constants). The complete energy level diagram which includes all the states investigated is shown in Fig. 1. It is based on the theoretical xr values, and shows clearly that, owing to the high density of states, many accidental near-degeneracies occur above 500 cm1. Earlier cm-wave frequency data [12] were available for seven of the states studied, for which we have extended the measurements to a frequency as high as 290 GHz. With the exception of the v6 = 1 state, all the states investigated involve excitation of at least one bending quantum, so that multiplets of rotational lines were usually recorded for each J + 1 ‹ J transition, owing to l-type resonance effects between the different l sublevels. The spectra were analyzed using the formalism originally developed by Yamada and coworkers [21,22] and employed recently to fit the excited-state rotational spectra of the carbon chains HC5P [23] and NC4P [24].
Fig. 1. Approximate vibrational energy level diagram of HC5N between 500 and 860 cm1. Solid lines indicate the states for which rotational lines were observed.
Using the simplified notation |l7, l8, l9, l10, l11; kæ for the unsymmetrized basis functions, the diagonal elements of the Hamiltonian matrix are: ^ jl7 ;l8 ;l9 ;l10 ;l11 ;ki hl7 ;l8 ;l9 ;l10 ;l11 ;kjH X X xLðttÞ l2t þ xLðtt0 Þ lt lt0 ¼ Gv þ (
t0 >t¼7;11
t¼7;11
þ Bv þ ( Dv þ
X
d JLðttÞ l2t þ
t¼7;11
X
)
X
) d JLðtt0 Þ lt lt0 fJ ðJ þ 1Þ k 2 g
t0 >t¼7;11
hJLðttÞ l2t fJ ðJ þ 1Þ k 2 g
2
t¼7;11 3
þ H v fJ ðJ þ 1Þ k 2 g ;
ð1Þ
where Gv is the vibrational energy of the state and k = l7 + l8 + l9 + l10 + l11. The off-diagonal rotational l-type doubling terms (Dlt = ±2, Dk = 2) have the general form: ^ jlt ;ki ¼ 1fqt þ qtJ J ðJ þ 1Þg hlt 2;k 2jH 4 ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðvt lt Þðvt lt þ 2Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi fJ ðJ þ 1Þ kðk 1ÞgfJ ðJ þ 1Þ ðk 1Þðk 2Þg; ð2Þ while the off-diagonal vibrational l-type doubling terms (Dlt = ±2, Dlt0 ¼ 2, Dk = 0) are given by the expression:
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^ jlt ; lt0 ; ki ¼ 1frtt0 þ rtt0 J J ðJ þ 1Þg hlt 2; lt0 2; kjH 4 ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðvt lt Þðvt lt þ 2Þðvt0 lt0 þ 2Þðvt0 lt0 Þ:
ð3Þ
The resulting energy matrix is factorized into symmetric and antisymmetric blocks adopting Wang-type linear combinations of wavefunctions [21], so that any sublevel belonging to a given vibrational state can be labeled through its k (or lt) value and by the ‘‘+’’ or ‘‘’’ superscripts which designate the chosen type of symmetrized linear combination of wavefunctions. In addition to the normal l-type resonances, numerous vibrational and rovibrational interactions had to be taken into account to fit properly the measured transition frequencies. The corresponding off-diagonal matrix elements were expressed using the formalism of Okabayashi et al. [25]. Some details dealing with the various resonances analyzed are given in the following subsections. 4.1. The Coriolis resonance between (v8, v10) and (v8 1, v10 + 2) The present CCSD(T) calculations predict 2x10 x8 = 7.0 cm1, and thus a high-order Coriolis resonance between the states (v8, v10) and (v8 1, v10 + 2) may be expected. We observed indeed an anomalous decreasing of the splitting between the two l-doublet lines of the v8 = 1 state starting from the J = 60 ‹ 59 transition, which causes an inversion of the latter components passing from the J = 80 ‹ 79 transition to the J = 82 ‹ 81 transition. This behavior is clearly shown in Fig. 2, where the reduced-frequency plot for the l-doublet of the v8 = 1 state is displayed [mred = mmis/2(J + 1)], and in Fig. 3, where the sequence of transitions corresponding to the inversion of the
Fig. 3. Recordings of the J = 80 ‹ 79, J = 81 ‹ 80, and J = 82 ‹ 81 transitions for the (001000) vibrational state of HC5N (pyrolitic production), which show the inversion of the two l-doublet components.
two components is drawn. This unusual trend of the measured frequencies was explained by considering a high-order Coriolis resonance between the v8 = 1, l8 = 1 state and the v10 = 2, l10 = 0, 2+ states, which are connected by matrix elements with the general form: D E ^ 31 jðv8 þ 1Þl8 1 ; ðv10 2Þl10 ; J ; k 1 vl88 ; vl1010 ; J ; kjH pffiffiffi 2 ¼ C 31a ½ðv8 l8 þ 2Þðv10 l10 Þðv10 l10 Þ1=2 4 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi J ðJ þ 1Þ kðk 1Þ; ð4aÞ D
Fig. 2. Plot of the reduced transition frequencies for the (001000) vibrational state of HC5N. Circles and triangles identify the observed transitions. The anomalous trend exhibited by the l8 = 1 component is clearly apparent.
E ^ 33 jðv8 þ 1Þl8 1 ; ðv10 2Þl10 2 ; J ; k 3 vl88 ; vl1010 ; J ; kjH pffiffiffi 2 1=2 ¼ C 33 ½ðv8 l8 þ 2Þðv10 l10 2Þðv10 l10 Þ 4 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi J ðJ þ 1Þ kðk 1Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi J ðJ þ 1Þ ðk 1Þðk 2Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi J ðJ þ 1Þ ðk 2Þðk 3Þ: ð4bÞ
The same kind of resonance affects also the couples of states (001001)–(000021) and (001010)–(000030). The effects produced by this Coriolis-type interaction are strongly dependent on the Fermi resonance which mixes
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the (v6, v10) states with the (v6 1, v10 + 2) states, because the latter changes appreciably the vibrational energy of the states for which v10 P 2 (see next section). 4.2. The cubic anharmonic resonances coupling (v6, v8, v11) with (v6 1, v8 + 1, v11 + 1), and (v6, v10) with (v6 1, v10 + 2) The present CCSD(T) calculations predict x6 (x8 + x11) = 1.5 cm1 and x6 2x10 = 101.3 cm1, with the corresponding normal-coordinate cubic force constants |/6,8,11| = 5.9 cm1 and |/6,10,10| = 98.1 cm1. One may therefore expect that the v6 = 1 stretching state is considerably mixed with the (001001) and (000020) bending states by Fermi-type resonances, producing a considerable low-frequency displacement of the rotational lines for the 0+ sublevels of both bending states and a parallel high-frequency displacement of the v6 = 1 transitions. The plot of the reduced transition frequencies for the lines of the (001001) and (000020) states is presented in Fig. 4, which shows the anomalous lowfrequency shift exhibited by the curves corresponding to the 0+ sublevels, which are the only ones which can be coupled to the v6 = 1 state. This effect is also shown in Fig. 5, where a 85 MHz long scan including the J = 31 ‹ 30 transitions of the two perturbed bending states is displayed. Accordingly, the v6 = 1 lines were found in correspondence of an effective B constant ca. 1.06 MHz greater than the predicted unperturbed value. These cubic resonances were taken into account through the off-diagonal matrix elements given by: D
E ^ 30 þ H ^ 32 jðv6 þ 1Þ; ðv8 1Þl8 1 ;ðv11 1Þl11 1 ;J ;k v6 ; vl88 ; vl1111 ; J ; kjH pffiffiffi h i 2 ð6;8;11Þ ð6;8;11Þ C 30 þ C 30J J ðJ þ 1Þ ½ðv6 þ 1Þðv8 l8 Þðv11 l11 Þ1=2 ; ¼ 2
ð5aÞ
Fig. 5. Recording of the J = 31 ‹ 30 transitions for six doubly excited vibrational states of HC5N (pyrolitic production), including the (001001) combination and the (000020) overtone which are perturbed by cubic anharmonic resonances.
D
E ^ 30 jðv6 þ 1Þ; ðv10 2Þl10 ; J ; k v6 ; vl1010 ; J ; kjH pffiffiffi ð6;10;10Þ 1=2 ¼ 2C 30 ½ðv6 þ 1Þðv10 l10 Þðv10 þ l10 Þ :
ð5bÞ
The C30 coefficients are related to the corresponding normal-coordinate cubic force constants by the expressions: ðstt0 Þ
/stt0 ¼ 4C 30 ; ðsttÞ
/stt ¼ 8C 30 :
ð6aÞ ð6bÞ
The resonance due to /6,10,10 was also considered in the analysis of the lines measured for the (000021) and (000030) states. For the latter state, the off-diagonal matrix element given by Eq. (5b) is large enough to bring both the perturbed |l10| = 1 components below the corresponding unperturbed |l10| = 3 lines. The assignment previously reported in [12] for the |l10| = 1 components is therefore incorrect, probably because of the presence of lines of the (000012) combination tone [16] appearing close to the hypothetical unperturbed transition frequencies of the v3 = 10, |l10| = 1 doublet. 4.3. The Coriolis resonance between the (010001) and (000030) states
Fig. 4. Plot of the reduced transition frequencies for the (001001) and (000020) vibrational states of HC5N. Open and solid symbols identify the observed transitions for the (001001) combination and the (000020) overtone, respectively. Triangles are used for the sublevels perturbed by cubic anharmonic resonances.
The two k = 2 components of the (010001) bending combination, for which high-resolution IR data were already available [10], show a pronounced perturbation in a narrow J range, indicative of a rovibrational avoided crossing. A similar perturbation, at the same J values, is also exhibited by the two |l10| = 1 components of the v10 = 3 states, so that a high-order Coriolis resonance was assumed between these states. The frequency deviations produced by the resonance in the spectra of both states are displayed in Fig. 6. The off-diagonal matrix elements employed to account for this interaction have the form:
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combination and the v6 = 1 stretching state had to be considered through the following off-diagonal matrix element: D
E ^ 41 jðv6 þ 1Þ;ðv10 2Þl10 2 ;ðv11 1Þl11 1 ; J ; k 1 v6 ; vl1010 ; vl1111 ; J ; kjH ¼ 12C 41b ½ðv6 þ 1Þðv10 l10 2Þðv10 l10 Þðv11 l11 Þ1=2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi J ðJ þ 1Þ kðk 1Þ:
ð8Þ
Furthermore, a weak anharmonic resonance connecting the (001010) bending combination to the v6 = 1 stretching state was included via: D E ^ 30 jðv6 þ 1Þ;ðv8 1Þl8 1 ;ðv10 1Þl10 1 ;J ;k v6 ;vl88 ;vl1010 ;J ;kjH pffiffiffi 2 ð6;8;10Þ 1=2 ¼ C ½ðv6 þ 1Þðv8 l8 Þðv10 l10 Þ ; ð9Þ 2 30
Fig. 6. Plot of the frequency deviations Dm produced by the Coriolis resonance between the (010001) and (000030) vibrational states of HC5N. Triangles identify the observed transitions.
D
E ^ 51 jðv7 þ 1Þl7 1 ; ðv10 3Þl10 1 ; ðv11 þ 1Þl11 1 ;J ;k 1 vl77 ; vl1010 ;vl1111 ; J; kjH pffiffiffi 2 1=2 ¼ C 51a ½ðv7 l7 þ 2Þðv10 l10 Þðv10 l10 Þðv10 l10 2Þðv11 l11 þ 2Þ 8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi J ðJ þ 1Þ kðk 1Þ; ð7aÞ
D
E ^ 53 jðv7 þ 1Þl7 1 ;ðv10 3Þl10 1 ;ðv11 þ 1Þl11 1 ;J ;k 3 vl77 ;vl1010 ;vl1111 ;J; kjH pffiffiffi 2 ¼ C 53 ½ðv7 l7 þ 2Þðv10 l10 Þðv10 l10 Þðv10 l10 2Þðv11 l11 þ 2Þ1=2 8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi JðJ þ 1Þ kðk 1Þ J ðJ þ 1Þ kðk 1Þðk 2Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð7bÞ JðJ þ 1Þ kðk 2Þðk 3Þ:
where the C30 coefficient is related to the corresponding normal-coordinate cubic force constant through Eq. (6a). The effects of a weak resonance were also detected in the spectrum of the v11 = 8 state, but no detailed analysis could be accomplished, and the corresponding leastsquares fit was simply performed by removing the few perturbed lines from the data set. As a consequence of the various resonances taken into account, we found that only seven of the investigated states could be properly analyzed as isolated. These are (v6 v7 v8 v9 v10 v11) = (000005), (000006), (000007), (000008), (010000), (000101), and (000110). The remaining eight states, namely (v6 v7 v8 v9 v10 v11) = (000020), (000030), (001000), (100000), (000021), (001001), (010001), and (001010), were all included within a rather large rovibrational energy matrix, whose offdiagonal elements are given by Eqs. (5a) and (5b) and (7–9). In addition to the investigated states, the (100001) and (100010) states were also included into the matrix, because they are connected to (000021) and (000030) through matrix elements expressed by Eq. (5b). The scheme of rovibrational interactions taken into account for the analysis of the resonance system of HC5N is summarized in Fig. 7.
In this case, the mixing of states produced by the resonance enabled also the detection of several interstate transitions.
5. Experimental results
4.4. Further weak resonances
5.1. The isolated states
The vibrational and rovibrational resonances previously discussed produce anomalies in the spectral patterns which are recognizable even before any detailed analysis of the measured frequencies is performed. In addition, during the fitting procedures we found that two further weak resonances must be taken into account in order to fit the measured transition frequencies within the experimental accuracy (ca. 15 kHz). First, a high-order Coriolis resonance between the (000021) bending
Transition frequencies for the fundamental bending state v7 = 1 and for the overtone bending states v11 = 5–8 had been already measured in the frequency range 26–40 GHz [12]. In addition, high-resolution IR data were also available for the m7 fundamental band [10]. The measurements for the bending state v7 = 1 have been extended up to 270 GHz, reaching a J value as high as 100, and they have been analyzed through Eqs. (1) and (2) (having k = l7), fitting the rotational
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191
For the overtone bending states v11 = 5–8 we have extended the measurements up to 105 GHz, reaching J values as high as 38. The spectra have been analyzed using Eqs. (1) and (2), having k = l11. Since the off-diagonal matrix element given by Eq. (2) gives a first-order contribution to the rotational energy only when l11 = ± 1 (degenerate l-sublevels), the constants q11 and q11J were fitted for the states with odd values of v11, but they were constrained to interpolated or extrapolated values for the states with even values of v11. Accurate determinations of the xL(11,11) and dJL(11,11) constants have been obtained for each state investigated. The results of the least-squares fits performed for these overtone bending states are collected in columns 2–5 of Table 2. The change of the rotational constant B produced by progressive excitation of the v11 vibrational mode can be expressed using the formula: DBðv11 Þ ¼ Bðv11 Þ Bðv11 1Þ ¼ a11 þ c11;11 ð2v11 þ 1Þ;
Fig. 7. Vibrational energy level diagram for the resonance system of HC5N. Thin arrows indicate the vibrational and rovibrational interactions taken into account. Large arrows indicate the vibrational energy displacements produced by Fermi-type resonances.
constant B, the quartic centrifugal distortion constant D and the l-type doubling parameters q7 and q7J. The sextic distortion constant H was held fixed at the value of 1.635 lHz previously determined for the ground state of HC5N [7]. This constraint was systematically adopted for all the spectra analyzed. The results of the leastsquares fit are listed in the first numerical column of Table 2. They agree very well with earlier results obtained by FTIR spectroscopy [10].
ð10Þ
where a11 actually includes also all high-order vibration– rotation interaction constants of the type cr11 (r = 1, 2, . . . , 10). The experimental results of the present work and of [16] make it possible to calculate DB (v11) values from v11 = 1 to v11 = 8, which satisfy well Eq. (10). A linear regression analysis of the experimental data yields c11,11 = 4.115 ± 0.023 kHz. No previous spectroscopic information was instead available for the (000101) and (000110) bending combinations, whose rotational spectra have been assigned for the first time in the frequency range 80–190 GHz. No anomaly was observed in the recorded quadruplets of lines, which were simply analyzed taking into account the usual rotational and vibrational l-type resonances. The qt constants involved in the off-diagonal matrix elements were generally held fixed at the values determined for the singly excited bending states [16], but we found useful to release q11 in the (000101) combination to improve slightly the quality of the fit. The change observed
Table 2 Spectroscopic constants determined for the (010000), (000005), (000006), (000007), and (000008) states of HC5N (010000)
(000005)
(000006)
(000007)
(000008)
Bv (MHz) av (MHz) Dv (Hz) xL(11,11) (GHz) dJL(11,11) (kHz) qt (MHz) qtJ (Hz) r (kHz)
1331.600997(28) 0.2683 30.1349(20) — — 0.213887(55) 0.0187(39) 12.4
1345.342260(69) — 38.192(30) 6.23004(70) 3.3951(21) 1.182729(68) 1.171(30) 8.8
1348.168400(99) — 39.738(42) 6.21159(20) 3.4068(15) 1.187578a 1.150a 11.2
1351.00339(11) — 41.507(48) 6.19112(53) 3.4191(13) 1.192427(96) 1.128(41) 12.3
1353.84661(13) — 43.245(59) 6.17228(28) 3.4300(11) 1.197276a 1.106a 17.0
No. of lines J range
68 10–100
67 13–37
63 13–37
67 13–37
60 13–37
Standard errors in units of the last digit are given in parentheses for the fitted parameters. a Fixed in the analysis.
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Table 3 Spectroscopic constants determined for the (000101) and (000110) states of HC5N (000101)
(000110)
Bv (MHz) Dv (Hz)
1335.716874(28) 32.0761(41)
1335.381480(45) 31.0373(62)
xL(9t) (GHz) dJL(9t) (kHz) dJL(11,11) (kHz)
7.5873(18) 6.889(44) 3.3047a
13.243(20) 6.787(49) —
r9t (GHz) r9tJ (kHz)
7.3226(23) 8.360(23)
22.177(40) 0.530(35)
q9 (MHz) q9J (Hz) qt (MHz) qtJ (Hz)
0.328526a 0.0393a 1.16564(14) 1.0629a
0.328526a 0.0393a 0.500190a 0.1734a
r (kHz) No. of lines J range
9.1 63 30–70
13.9 61 30–70
Standard errors in units of the last digit are given in parentheses for the fitted parameters. a Fixed in the analysis.
is less than 1%, as expected for a normal vibrational dependence of the qt constants. The results of these least-squares fits are collected in Table 3. The complete set of transition frequencies analyzed for the isolated states is provided as electronic Supplementary material. 5.2. The resonance system Taking into account the off-diagonal matrix elements corresponding to Eqs. (5a) and (5b) and (7–9), an
infinitely large rovibrational energy matrix is produced. The eigenvalues necessary to analyze the spectra of the states investigated were calculated by diagonalization of a truncated matrix which includes the eight vibrational states for which resonance effects were experimentally observed, plus the two states (100001) and (100010), for which no line was recorded. The inclusion of further vibrational states connected by the abovementioned off-diagonal terms did not improve significantly the results. Since most of the vibrational states considered produce several substates because of different k and lt values, 17 · 17 (e symmetry) and 15 · 15 (f symmetry) rovibrational energy matrices were actually diagonalized for each J value to obtain the required eigenvalues. The vibrational energies Gv of the resonant states were generally held fixed at the values calculated by means of the theoretical xr constants, but when nearly degenerate states were considered, the corresponding Gv values were also optimized. More than 600 transition frequencies were simultaneously analyzed fitting independently a total number of 57 parameters. Many other spectroscopic constants were held fixed at values derived from states of lower vibrational excitation. The standard deviation of the least-squares fit was 11.3 kHz. The spectroscopic constants determined or assumed for each vibrational state of the resonance system are reported in Tables 4 and 5. The values obtained for the coefficients included in the off-diagonal elements are listed in Table 6, where a simplified notation is employed to identify the interacting states. The complete set of transition frequencies analyzed for the resonance system is provided as electronic Supplementary material.
Table 4 Spectroscopic constants determined for the (001000), (000020), (001001), (100000), and (000021) resonant states of HC5N (001000)
(000020)
(001001)
(100000)
(000021)
Gv (cm1) Bv (MHz) av (MHz) Dv (Hz)
502.7540(22) 1333.051138(27) 1.7185 30.0644(76)
508.0a 1336.255431(44) — 31.545(12)
608.985(45) 1335.84602(12) — 31.859(16)
609.3a 1330.27109(88) 1.0614 30.100(74)
614.524(39) 1339.05616(22) — 33.072(38)
xL(11,11) (GHz) xL(10,10) (GHz) xL(t,11) (GHz) dJL(11,11) (kHz) dJL(t,11) (kHz) hJL(10,10) (Hz)
— — — — — —
— 23.29(11) — — — 0.0467(35)
6.3139a — 6.799(54) 3.3047a 1.40(11) —
— — — — — —
6.3139a 23.29a 7.256(16) 3.3047a 4.12(12) 0.0467a
rt,11 (GHz) rt,11J (kHz)
— —
— —
6.16(11) 0.0a
— —
3.657(92) 1.301a
q11 (MHz) q11J (Hz) qt (MHz) qtJ (Hz)
— — 0.316154(59) 0.136(10)
— — 0.51122a 0.1734a
1.15926(41) 1.0629a 0.316154a 0.136a
— — — —
1.19104(72) 1.0629a 0.51122a 0.1734a
No. of lines J range
81 10–107
84 30–107
69 30–70
16 30–70
74 28–42
Standard errors in units of the last digit are given in parentheses for the fitted parameters. a Fixed in the analysis.
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Table 5 Spectroscopic constants determined for the (100001), (010001), (001010), (000030), and (100010) resonant states of HC5N (100001) 1
b
(010001)
(001010) b
(000030) a
(100010)
Gv (cm ) Bv (MHz) Dv (Hz)
715.824 1333.0566a 31.643a
750.550(36) 1334.385776(27) 31.6406(42)
756.754 1335.47596(71) 30.662(13)
762.0 1338.746514(53) 31.903(30)
863.3a 1332.7232a 30.753a
xL(11,11) (GHz) xL(10,10) (GHz) xL(tt 0 ) (GHz) dJL(11,11) (kHz) dJL(tt 0 ) (kHz) hJL(10,10) (Hz)
6.3139a — — 3.3047a — —
6.3139a — 7.5928(77) 3.3047a 0.454(42) —
— 23.29a 7.649(39) — 35.713(63) —
— 23.29a — — — 0.1233(36)
— 23.29a — — — —
rtt 0 (GHz) rtt 0 J (kHz)
— —
0.7000(38) 1.946(20)
2.03(10) 0.0a
— —
— —
q11 (MHz) q11J (Hz) q10 (MHz) q10J (Hz) qt (MHz) qtJ (Hz)
1.162898a 1.0629a — — — —
1.16631(71) 1.0629a — — 0.213887a 0.0187a
— — 0.500190a 0.1734a 0.316154a 0.136a
— — 0.522251(27) 0.1734a — —
— — 0.500190a 0.1734a — —
No. of lines J range
— —
118 30–70
75 30–70
89 30–70
— —
Standard errors in units of the last digit are given in parentheses for the fitted parameters. a Fixed in the analysis. b Adjusted by fixing energy differences. See text.
The experimental values of the a6 and a8 vibration– rotation coupling constants, and of the q8 l-doubling constant agree well with the results of the CCSD(T) calculations (cf. Table 1), and no serious anomaly appears in the Dv and qt constants fitted for the various overtone and combination states involved in the resonance system. This indicates that the main resonance effects
Table 6 Off-diagonal coefficients determined for the resonance system of HC5N Interacting states
Parameters
Fitted values
Units
(v8) (2v10)
C31a C33
33.994(11) 0.793(29)
MHz kHz
(v8 + v11) (2v10 + v11)
C31a C33
33.128(47) 0.22(15)
MHz kHz
(v8 + v10) (3v10)
C31a C33
42.84(84) 0.3476(57)
MHz kHz
(2v10) (v6)
C 30
ð6;10;10Þ
9.2856(17)
cm1
(2v10 + v11) (v6 + v11)
ð6;10;10Þ C 30
9.1836(47)
cm1
(3v10) (v6 + v10)
C 30
ð6;10;10Þ
9.287(15)
cm1
(v6) (v8 + v11)
C 30
ð6;8;11Þ
1.0701(35)
cm1
ð6;8;11Þ C 30J
0.2092(80)
MHz
(v6) (2v10 + v11)
C41b
12.35(31)
MHz
(v6) (v8 + v10)
ð6;8;10Þ C 30
4.520(11)
cm1
(v7 + v11) (3v10)
C51a C53
0.140097(55) 0.474979(62)
MHz kHz
Standard errors in units of the last digit are given in parentheses for the fitted parameters.
have been well treated, even if the presence of small residual perturbations is revealed by the high value obtained for q8J and by the large difference which exists between the hJL(10,10) values fitted for the v10 = 2 and v10 = 3 states, respectively. It is, however, to remark that these high-order parameters give contributions to the transition frequencies which never exceed 1.7 MHz in the J range investigated. Differently from the v7 = 1 state, the parameters obtained for the (010001) bending combination show small discrepancies in comparison with earlier FTIR spectroscopy results [10]. This is probably due to the fact that the weak high-order Coriolis resonance existing between the (010001) and (000030) states was neglected in [10]. Table 7 shows the comparison between the Gv values calculated through the theoretical xr constants and those corresponding to the best fit of the experimental data. The optimized set of unperturbed vibrational energies was obtained assuming the CCSD(T) values of x6 and x10 to fix the energies of the states in which only v6 and v10 are excited, and also to fix the energy differences between the states (100001) and (000021), and between the states (001010) and (001000), while the energies of the (001000), (001001), (000021), and (010001) states were freely adjusted in the least-squares procedure. Inspection of Table 7 shows that the largest discrepancy between fitted and theoretically computed vibrational terms concerns the (010001) combination, the difference being 6.8 cm1, but it is to be noted that this value is close to the difference which exists between the experimental band origin of the m7 band (642.1 cm1
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from [10]) and the theoretical value of x7 (650.5 cm1 from Table 1). This slight discrepancy could be explained by the presence of an anharmonic interaction between the v7 = 1 state and the near by (100001) state, which pushes down the v7 = 1 level, but the small theoretical value of the /6,7,11 cubic force constant (2.5 cm1) does not support this interpretation. On the other hand the rovibrational parameters derived treating the (010000) bending state as isolated do not show any evidence of perturbations, making unlikely the existence of significantly strong high-order interactions. No restrictive hypothesis about the energy of the v11 = 1 state was made within the best-estimates set, but making the appropriate differences between fitted vibrational terms (including also the m7 band origin [10]) it is possible to calculate this energy by three independent ways, which yield the values of 106.2, 106.5, and 108.3 cm1, respectively, all of which are close to the CCSD(T)/ccpVQZ value of x11 = 106.8 cm1. From the fitted C30 coefficients it is possible to derive the values of the corresponding normal-coordinate cubic force constants, which are |/6,10,10| = 74.3 cm1, |/6,8,11| = 4.27 cm1, and |/6,8,10| = 18.1 cm1. These experimental results are consistent with the corresponding CCSD(T) values of 98.1, 5.9, and 17.2 cm1, respectively.
tionally excited states of this molecule [16]. The present paper extends the study of the mm-wave spectra of HC5N to 15 further vibrational states which approximately lie between 500 and 860 cm1 above ground, where the high density of states produces numerous accidental near-degeneracies which cause anomalies in the observed spectra. Their assignment and analysis have been facilitated by accurate theoretical predictions for vibrational energies, cubic normal-coordinate force constants, and various vibration–rotation coupling parameters. Novel determinations of the a6 vibration– rotation coupling constant of the lowest-energy stretching state, and of the xL(10,10), xL(9,11), xL(9,10), xL(8,11), and xL(8,10) anharmonicity constants have been obtained from the analysis of the measured transition frequencies. In addition to the normal l-type resonances, a large number of vibrational and rovibrational interactions have been taken into account to fit properly the measured transition frequencies. As already observed in HC5P [23] and NC4P [24], also in HC5N the lowest-energy stretching state is perturbed by strong anharmonic resonances which produce a very small effective value for the a6 vibration–rotation coupling constant, pushing the rotational lines of the v6 = 1 state quite far from the expected, unperturbed positions. The rotational and centrifugal distortion constants fitted for the observed overtone and combination states are generally in excellent agreement with the values which is possible to extrapolate from the singly excited bending states, thus supporting the reliability of the analyses performed, as the good agreement between experimental and theoretical results also demonstrates. Although the vibrational states investigated in the present work are less likely observable in space than those of lower excitation [16], an accurate knowledge of their rotational spectra is anyway useful to avoid misassignments of the radio lines observed in very congested regions. For example, some mm-wave lines detected towards CRL 618 have been tentatively assigned to the v10 = 3, |l10| = 1 doublet of HC5N [13] using predictions extrapolated from earlier cm-wave measurements [12], but the present investigation establishes that the v10 = 3, |l10| = 1 lines undergo a large frequency displacement because of Fermi resonance effects, and a different assignment must be therefore proposed for the observed features.
6. Conclusions
Acknowledgments
Millimeter-wave transitions in low-lying excited vibrational states of HC5N have been recently detected in the C-rich proto-planetary nebula CRL 618 [13–15]. These observations stimulated an earlier laboratory work which provided very accurate rest frequencies and spectroscopic constants for the eight lowest vibra-
C.D.E. and L.B. gratefully acknowledge financial support from MIUR and from the University of Bologna (Funds for Selected Research Topics). Thanks are due to the Fonds der Chemischen Industrie for providing support to P.B. The work at Cologne has been supported by the Deutsche Forschungsgemeinschaft
Table 7 Comparison between experimentally adjusted and theoretical (harmonic approximation) vibrational energies of HC5N
(001000) (000020) (001001) (100000) (000021) (100001) (010001) (001010) (000030) (100010)
Unperturbed energies
Anharmonic resonance shiftsa
Ab initiob
502.754c 508.0d 608.985c 609.3d 614.524c 715.82e 750.550c 756.75e 762.0c 863.3c
— 6.424 0.609 6.476 6.318 6.233 — 0.568 12.161 12.117
501.0 508.0 607.0 609.3 614.8 716.1 757.3 755.0 762.0 863.3
a
The negative sign indicates that the level is pushed down by the resonance. b Calculated using the xr constants of Table 1. c Fitted. d Constrained to the ab initio values. e Adjusted by fixing energy differences. See text.
C. Degli Esposti et al. / Journal of Molecular Spectroscopy 230 (2005) 185–195
through Grant SFB 494 and by additional funding from the Minisitry of Science and Technology of the State Nordrhein-Westfalen.
Appendix A. Supplementary data Supplementary data for this article are available on ScienceDirect (www.sciencedirect.com) and as part of the Ohio State University Molecular Spectroscopy Archives (http://msa.lib.ohio-state.edu/jmsa_hp.htm).
References [1] A.J. Alexander, H.W. Kroto, D.R.M. Walton, J. Mol. Spectrosc. 62 (1976) 175–180. [2] L.W. Avery, N.W. Broten, J.M. MacLeod, T. Oka, H.W. Kroto, Astrophys. J. 200 (1976) L173–L175. [3] G. Winnewisser, C.M. Walmsley, Astrophys. Space Sci. 65 (1979) 83–93. [4] J.M. MacLeod, L.W. Avery, N.W. Broten, Astrophys. J. 251 (1981) L33–L36. [5] S. Takano, H. Suzuki, M. Ohishi, S. Ishikawa, N. Kaifu, Y. Hirahara, A. Masuda, Astrophys. J. 361 (1990) L15–L18. [6] G. Winnewisser, M. Winnewisser, J.J. Christiansen, Astron. Astrophys. 109 (1982) 141–144. [7] L. Bizzocchi, C. Degli Esposti, P. Botschwina, J. Mol. Spectrosc. 225 (2004) 145–151. [8] K.M.T. Yamada, G. Winnewisser, Z. Naturforsch. 36a (1981) 1052–1056. [9] K.M.T. Yamada, G. Winnewisser, Z. Naturforsch. A 40 (1981) 476–478.
195
[10] S. Haas, G. Winnewisser, K.M.T. Yamada, Can. J. Phys. 72 (1994) 1165–1178. ¨ . Heyl, M. Oswald, T. Hirano, Spectrochim. [11] P. Botschwina, A Acta Part A 53 (1997) 1079–1090. [12] M. Hutchinson, H.W. Kroto, D.R.M. Walton, J. Mol. Spectrosc. 82 (1980) 394–410. [13] J. Cernicharo, A.M. Heras, J.R. Pardo, A.G.G.M. Tielens, M. Guelin, E. Dartois, R. Neri, L.B.F.M. Waters, Astrophys. J. 546 (2001) L127–L130. [14] S. Thorwirth, Ph.D. thesis, Universita¨t zu Ko¨ln, 2001. [15] F. Wyrowski, P. Schilke, S. Thorwirth, K.M. Menten, G. Winnewisser, Astrophys. J. 586 (2003) 344–355. [16] K.M.T. Yamada, C. Degli Esposti, P. Botschwina, P. Fo¨rster, L. Bizzocchi, S. Thorwirth, G. Winnewisser, Astron. Astrophys. 425 (2004) 767–772. [17] K. Raghavachari, G.W. Trucks, J.A. Pople, M. Head-Gordon, Chem. Phys. Lett. 157 (1989) 479–483. [18] T.H. Dunning Jr., J. Chem. Phys. 90 (1989) 1007–1023. [19] H.-J. Werner, P.J. Knowles, with contributions from R.D. Amos, A. Bernhardsson, A. Berning, P. Celani, D.L. Cooper, M.J.O. Deegan, A.J. Dobbyn, F. Eckert, C. Hampel, G. Hetzer, T. Korona, R. Lindh, A.W. Lloyd, S.J. McNicholas, F.R. Manby, W. Meyer, M.E. Mura, A. Nicklass, P. Palmieri, P. Pulay, R. Pitzer, G. Rauhut, M. Schu¨tz, H. Stoll, J. Stone, R. Tarroni, T. Thorsteinsson, MOLPRO2000. [20] C. Hampel, K.A. Peterson, H.-J. Werner, Chem. Phys. Lett. 190 (1992) 1–12. [21] K.M.T. Yamada, F.W. Birss, M.R. Aliev, J. Mol. Spectrosc. 112 (1985) 347–356. [22] M. Niedenhoff, K.M.T. Yamada, J. Mol. Spectrosc. 157 (1993) 182–197. [23] L. Bizzocchi, C. Degli Esposti, P. Botschwina, Phys. Chem. Chem. Phys. 5 (2003) 4090–4095. [24] L. Bizzocchi, C. Degli Esposti, P. Botschwina, Phys. Chem. Chem. Phys. 6 (2004) 46–50. [25] T. Okabayashi, K. Tanaka, T. Tanaka, J. Mol. Spectrosc. 195 (1999) 22–42.