Electronic absorption spectrum of a nonlinear carbon chain: trans-C₆H₄⁺

Abstract

The ²B_g–X ²A_u transition of a nonlinear carbon chain trans-C₆H₄⁺, and trans-C₆D₄⁺, has been observed in the gas phase. The spectra were detected in the 580 nm region by direct absorption with a cavity ringdown technique through a supersonic planar discharge. Though the rotational structure is not resolved, the band profiles were analyzed using a “total spectral fitting” procedure using ground-state constants calculated by the CASSCF and CASPT2 methods. The molecular constants in the upper state could thus be determined.

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I Introduction

Nonlinear but planar carbon chains may be important intermediates in flame, plasma and interstellar reactions linking linear chains to polyaromatic hydrocarbons.^1–4 Thus gas-phase high-resolution spectroscopy of such chains is a goal. An electronic transition of H–C≡C–C≡C–CH=CH₂⁺ (hereafter C_s-C₆H₄⁺) was detected in a supersonic planar discharge with cavity ringdown (CRD) spectroscopy in the 604 nm region,¹ and that of the related chains C₄H₄⁺ and C₈H₄⁺ around 512 and 710 nm.² Other isomers are also of interest, e.g. cis- and trans-H–C≡C–CH=CH–C≡C–H⁺ (hereafter cis-C₆H₄⁺ and trans-C₆H₄⁺). The gas-phase electronic spectra of the nonlinear carbon chains are as well of relevance for comparison with the diffuse interstellar bands (DIBs).

The electronic spectra of two C₆H₄⁺ isomers were observed after a mass-selective deposition in a 6 K neon matrix.¹ Concurrently the 609 nm absorption of the ²A″–X ²A″ origin transition for C_s-C₆H₄⁺ could be detected in the gas phase by CRD spectroscopy and two further bands of this system by a high-resolution CW-CRD approach.³ A strong absorption band at 585.3 nm in the neon matrix was expected to belong to another isomer of C₆H₄⁺. This lies near the wavelength for the ²B_g–X ²A_u transition of trans-C₆H₄⁺ according to the He I photoelectron spectrum of trans-3-hexen-1,5-diyne.⁴ In the present work the observation of this band in the gas phase is reported. An analysis of the rotational profiles in conjunction with theoretical calculations by a method called “total spectral fitting”⁵ produces spectroscopic constants for trans-C₆H₄⁺.

II Experimental

The main features of the experiment have been described.^6,7 The gas phase measurements used a cavity ringdown spectrometer sampling a supersonic planar plasma. A small fraction of light from a pulsed tunable dye laser is coupled into an optical cavity comprising two highly reflective mirrors (R > 99.99%). The fraction of light leaking out of the cavity shows a first-order exponential decay, exp(−t/τ). The ringdown time, τ, reflects the absorption coefficient.⁸ The spectrum is recorded by measuring τ as function of the laser wavelength. The ∼0.05 cm⁻¹ laser linewidth was attained with an intracavity etalon, and the spectrum was calibrated by a wavemeter.

A number of improvements have been made. (1) In the previous setup, ringdown profiles obtained at 30 Hz were averaged by an oscilloscope.⁷ Gate A set at the beginning, and B at 2–3τ of the decay curve, were used to determine the exponential waveform, while a third gate C was used for background subtraction. The ringdown time τ is approximated by τ = (I_B − I_C)/(I_A − I_C), where I_X (X = A, B and C) is the intensity at the gates. In the new setup, τ is determined by fitting the whole ringdown curve for each laser pulse with a least-square method, and 60 values of τ are obtained each second. (2) τ Values obtained from low intensity signals or with large fitting error are eliminated. Additionally the data of an individual measurement are not used if the value is 1.5 times outside the standard deviation. Thus in all about 20% of the obtained τ data are rejected. (3) In order to have a flat base line without interference effects, which vary with highest frequency in the cavity, the discharge and gas jet are run at 30 Hz whereas the laser at 60 Hz. Normal ringdown τ_n with discharge and gas jet, or with an empty cavity τ_e is alternately measured, i.e. τ (= τ_n − τ_e). 45 Ringdown events (including rejected ones) for τ_n and τ_e are integrated for 1500 ms to give a point in the spectrum because this produced the highest S/N ratio. When one scans at wavelengths shorter than 400 nm, refraction of laser light by the gas pulse is not negligible. Then the gas jet is also run at 60 Hz, but τ_e is obtained without the discharge. To execute the above three improvements, an analog digital converter card (1.25 MHz, 12-bit) is used to measure the ringdown curve instead of the oscilloscope (300 MHz 8 bit). As a result the signal-to-noise ratio was increased by three in the same integration time by the improvements (1) and (2), and the base line in the spectrum was flattened by 3. The achieved sensitivity was of order 10⁻⁷ to 10⁻⁸ cm⁻¹.

The species studied was generated by a discharge through a pulsed jet with the sample in a buffer gas at a backing pressure of several bar in the throat of a 3 cm × 100 μm multilayer slit nozzle geometry. Rotational temperatures of the order 10–40 K are achieved. The nozzle was mounted in an optical cavity where the expansion was intersected a few mm downstream by the light of a tunable pulsed dye laser.

III Results and discussion

An electronic absorption spectrum of C₆H₄⁺ has been measured in a 6 K matrix after codeposition of mass-selected cations with excess of neon.¹ The origin band at 609 nm and two vibronic bands (600 and 591 nm) were assigned to the ²A″–X ²A″ transition of C_s-C₆H₄⁺. A band at 585.3 nm (17081 cm⁻¹) was attributed to another cation isomer. The photoelectron spectrum of trans-3-hexen-1,5-diyne gives the adiabatic ionization energies to the 2a_u(π) and 1b_g(π) states as 9.07 and 11.18 eV.⁴ Thus the ²B_g–X ²A_u transition of trans-C₆H₄⁺ is estimated to lie at 2.11 ± 0.02 eV (588 ± 6 nm), where the 585.3 nm band in the neon matrix lies. The photoelectron spectrum of cis-3-hexen-1,5-diyne has also been reported with adiabatic and vertical ionization energies to the 2b₁(π) and 1a₂(π) states of 9.10 and 11.10 eV.⁴ Hence, the strongest vibronic band of the ²A₂–X ²B₁ transition for cis-C₆H₄⁺ is expected to be around 2.00 eV (620 nm).

The gas-phase spectrum was consequently searched in these regions and a band having P- and R-branches was found at 17 239.3 cm⁻¹ (trace (a) in Fig. 1). The optimized conditions for observation of the band used a mixture of 0.3% C₂H₂ in argon and a −600 V discharge while sampling 1.0–1.5 mm downstream from the slit. A high backing pressure in the gas jet produces this absorption band effectively, but to have a stable discharge 5 bar were used. Under such conditions the intensity of the peak is similar with that of the 12¹₀ vibronic band in the ²A″–X ²A″ transition of C_s-C₆H₄⁺,³ or a quarter of the A ²Π_g–X ²Π_u origin band of HC₆H⁺.⁹ The band lies 159 cm⁻¹ to the red in a neon matrix, comparable to the 114 cm⁻¹ shift in C_s-C₆H₄⁺.¹ When the sample gas was deuterated another band with a similar profile was detected at 17 306.6 cm⁻¹ (trace (a) in Fig. 1). The shift observed on deuteration is 67.3 cm⁻¹, which agrees well with 66.9 cm⁻¹ for the C_s-C₆H₄⁺/C_s-C₆D₄⁺ pair (see Appendix for the details).¹ To confirm whether the 17 239.3 cm⁻¹ band is the origin, the region up to 587 cm⁻¹ in lower frequency was searched. None was found indicating that the detected band is probably the origin. Therefore the 17 239.3 cm⁻¹ band is attributed to the same species and transition as the 585.3 nm band in a neon matrix because of the consistent isotope (67.3 cm⁻¹) and gas-neon shifts (159 cm⁻¹); i.e. it is the origin of the ²B_g–X ²A_u system of trans-C₆H₄⁺.

Fig. 1 Electronic absorption spectra of trans-C₆H₄⁺ and trans-C₆D₄⁺ (traces (a)) measured by cavity ringdown through a slit jet discharge. The simulated spectra are traces (b). Traces (c) are the differences between (a) and (b). The sharp lines in the recordings are absorptions from unidentified small carbon fragments.

The expected region of the most intense vibronic band in the ²A₂–X ²B₁ transition of cis-C₆H₄⁺ was searched for, but no band was detected. Neither it is apparent in the neon-matrix absorption spectrum.

There are two possible reaction schemes to produce nonlinear C₆H₄⁺ (Scheme 1). One is to produce polyacetylene from three acetylene molecules and the other is by joining an ethylene and two acetylene molecules. When ethylene was added to the mixture of acetylene in argon, the intensities of both the C_s-C₆H₄⁺ and trans-C₆H₄⁺ bands clearly decrease. If the latter route is important, ethylene should enhance the production of all the C₆H₄⁺ isomers. In contrast, the former pathway would be disturbed by ethylene. Thus the production route of nonlinear C₆H₄⁺ in the discharge appears to be via polyacetylene formation.

Scheme 1

A: Theoretical calculations

Although the observed band is attributed to trans-C₆H₄⁺, the profile is not similar to that of C_s-C₆H₄⁺ studied previously.¹ In the rotational profile of C_s-C₆H₄⁺, the R-branch is stronger than P due to ΔA (= A′ − A″) > 0 and Δ(B + C)/2 < 0. In the case of trans-C₆H₄⁺, ΔA and Δ(B + C)/2 are small and have inverted signs because both branches are symmetric and R is slightly weaker than P. In order to analyze the rotational profiles, theoretical calculations on the C₆H₄⁺ isomers and rotational profile fits were carried out.

Ab initio computations used the MOLPRO 2002.3 package.¹⁰ The adiabatic transition energies of the ²A″–X ²A″ system and molecular structures of both states for C_s-C₆H₄⁺ were reported using the CASSCF method^11,12 with a cc-pVTZ basis set where all 10π orbitals were included in the active space 6a″ and 4a′, and the results were in good agreement with the experiment.³ Subsequently the molecular structures of cis- and trans-C₆H₄⁺ in the excited and ground states were calculated using the same method (Table 1). The geometry in the ground state of trans-C₆H₄⁺ is shown in Fig. 2. The excited and ground-state rotational constants of trans-C₆H₄⁺ are not significantly different i.e. ΔA ∼ 0 and Δ(B + C)/2 ∼ 0, consistent with the estimated differences from the analysis of the rotational profile (vide infra).

Fig. 2 Calculated molecular structure (in Å and °) in the ground state of trans-C₆H₄⁺ using CASSCF/cc-pVTZ assuming a C_2h symmetry. The horizontal and vertical dotted lines indicate the a- and b-axes.

Table 1 Calculated molecular constants of the C₆H₄⁺ isomers (cm⁻¹)^a

	C s-C6H4^+ ^b	cis-C6H4^+	trans-C6H4^+
Ground state	^2A″	^2B1	^2Au
A″	1.271	0.241	1.473	1.029^c
B″	0.0466	0.0858	0.0495	0.0451^c
C″	0.0450	0.0632	0.0479	0.0432^c
½(B″ + C″)	0.0458	0.0745	0.0487	0.0442^c

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Excited state	^2A″	^2A2	^2Bg
a Calculated with CASSCF/cc-pVTZ. b Ref. 3. c For the deuterated species using the same molecular structure. d Calculated with CASPT2/cc-pVTZ.
ΔA	0.080	−0.031	0.046	0.0259^c
Δ½(B + C)	−0.0011	0.0078	−0.0010	−0.0009^c
ΔEadiabatic/eV	2.18	2.20	2.40
		1.85^d	1.96^d
Oscillator strength	0.087	0.076	0.140

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The adiabatic transition energies of the ²A₂–X ²B₁ and ²B_g–X ²A_u systems for cis- and trans-C₆H₄⁺ are calculated 2.20 and 2.40 eV using the CASSCF method, higher than the experimental values ∼1.90⁴ and 2.14 eV. A multireference perturbation theory CASPT2^13,14 gave the values 1.85 and 1.96 eV. The optimized molecular structures were similar to those obtained from CASSCF. Additionally, the calculated transition energy of another isomer (H–C≡C–)₂C=CH₂ is sufficiently low to rule it out as a carrier of the observed band.

B: Rotational profile analysis

Generally to determine spectroscopic constants from a rotationally resolved spectrum one executes three steps: measurement of the line frequencies, assignment and a least-square fitting. If the rotational structure is not resolved, this method cannot be applied. Molecular constants could be determined by trial and error via a visual check between the observed and simulated rotational profiles. However to obtain significant molecular constants, a least-square fitting procedure called “total spectrum fitting” (TSF)⁵ is used. This method compares the observed and simulated rotational profiles in order to infer the molecular constants. A rotationally non-resolved spectrum for CN⁵ and partially resolved ones for I₂¹⁵ were analyzed by the TSF method, as well as a profile of a DIB assuming the carrier is a linear molecule.¹⁶

We have used the TSF method to analyze the profiles of the observed bands under the assumption that a spectrum of an asymmetric top molecule is characterized only by the following parameters: rotational constants A, B, C in both states, transition frequency, temperature, spin statistical weights, a FWHM of Lorentzian line shape, an amplitude and base line bias (the slope was corrected before the analysis). The minimized quantity was the sum of the weighted, squared differences between the observed and calculated spectral points. The calculations require partial derivatives with respect to the adjustable parameters; these were estimated numerically from the spectra simulated for slightly altered values.

Lines beyond J = 35 become vanishingly weak in the spectrum of C₆H₄⁺ around 10 K, but ones through to J = 50 were included in the simulations. Sharp absorption lines apparent in the spectra (Fig. 1) due to unidentified small carbon fragments were treated with zero-weight. The FWHM of Lorentzian line shape was assumed to be 0.10 cm⁻¹ because the rotational structure is not resolved. Rotational constants in the ground state were fixed to the calculated ones, and temperatures of 18 and 20 K were used for C₆H₄⁺ and C₆D₄⁺, respectively. These temperatures gave the minimal rms in the least-square fitting. ΔA and Δ(B + C)/2 the transition frequency T₀₀ were the free parameters in the fitting. When the ground-state rotational constants of trans-C₆H₄⁺ were used in the fits, the determined ΔA and Δ(B + C)/2 agreed with the calculated ones within the error limiting although the signs are opposite and the rotational profiles are well reproduced (traces (b) in Fig. 1). The molecular constants in the excited state determined are listed in Table 2. There are non-random deviations (prominent in traces (c)) at the intermediate regions between the P- and R-branches at 17 239.5 cm⁻¹ for trans-C₆H₄⁺ and at 17 306.7 cm⁻¹ for trans-C₆D₄⁺, because the temperature distribution in the slit jet discharge does not fit exactly to a single Boltzmann distribution.

Table 2 Experimental molecular constants of trans-C₆H₄⁺ and trans-C₆D₄^+ a

State		trans-C6H4^+	trans-C6D4^+
a Values in parentheses denote the standard deviation and apply to the last digits. Rms values in both fittings are about 3% of the heights of the band profiles. b Fixed to the calculated values of the trans-isomer with the CASSCF method as given in Table 1. c Errors were determined by a least-square fit at the fixed temperature. However, values correlate with temperature, and thus the effective accuracy should be taken as several % of the given value. d The error is from the least-squares fit, but the real uncertainty is 0.02 cm^−1 due to the calibration. e Fixed.
X ^2Au	A″	1.473^b	1.029^b
	B″	0.0495^b	0.0451^b
	C″	0.0479^b	0.0432^b
	½(B″ + C″)	0.0487^b	0.0442^b
^2Bg	ΔA	−0.0360(2)^c	−0.0166(2)^c
	Δ½(B + C)	0.000 35(2)^c	0.000 30(2)^c
	T 00	17 239.401(2)^d	17 306.483(2)^d
	T/K	18^e	20^e

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If the lineshape would be 0.05 cm⁻¹ (the laser bandwidth used), the rotational lines of P- and R-branches would be seen, which is not the case. Thus we took the narrowest lineshape 0.1 cm⁻¹ which produced a non-resolved profile in the simulation. With 0.1 cm⁻¹ lineshape the lifetime broadening would be 0.04 cm⁻¹ after subtracting the laser bandwidth (0.05 cm⁻¹) and the Doppler contribution (0.01 cm⁻¹ as observed directly in the study of C_s-C₆H₄⁺)³. The lifetime in the excited state of this molecule can thus be estimated as 0.13 ns.

C: Astrophysical relevance

The short nonlinear carbon chain C₄H₄ was considered as a precursor of polycyclic aromatic hydrocarbons in a circumstellar envelope¹⁷ and chemical reactions to produce large hydrocarbon ions in dense interstellar clouds were considered along the lines C⁺ + C_nH_m → C_n+1H⁺_m−1 + H and C + C_nH⁺_m → C_n+1H⁺_m−1 + H.¹⁸ The optical spectrum obtained for trans-C₆H₄⁺ allows a comparison with the identified DIBs.^19–21 The observed band around 579.9 nm lies near two DIBs reported at 579.7 and 580.08 nm, though the latter is tentative. In order to check whether the frequency differences of the peak positions might be a temperature effect, a comparison was made between an artificial DIB spectrum in the 578.8–581.2 nm range and the simulated trans-C₆H₄⁺ spectrum for low (10 K), intermediate (40 K) and high (150 K) temperature. This is shown in Fig. 3 and it is clear that the absorption band of trans-C₆H₄⁺ does not fit the DIB absorptions at any temperature.

Fig. 3 Diffuse interstellar band absorptions in the 578.9–581.2 nm region (lower trace reproduced from ref. 19) and the simulated trans-C₆H₄⁺ laboratory spectrum at 10, 40 and 150 K (upper traces) with a 0.03 nm resolution. The arrow indicates the position of a tentative DIB at 580.08 nm.

An upper limit for the column density for trans-C₆H₄⁺ in diffuse clouds can be estimated by comparison of the laboratory and DIB data in a similar fashion as before.²² For this it was assumed that a signal to noise ratio of 5 is required for detection of a DIB absorption. The FWHM of the bands is about 0.2 nm, and the sensitivity limit given in ref. 19 for a DIB detection is 0.0002 nm. The oscillator strength of the ²B_g–X ²A_u transition for trans-C₆H₄⁺ obtained theoretically is 0.14 (Table 1). These values then lead to the upper limit for the column density of trans-C₆H₄⁺ in diffuse clouds as 5 × 10¹¹ cm⁻².

The observed electronic absorption of the four nonlinear carbon chains C_s-C_nH₄⁺(n = 4, 6, 8)^1,2 and trans-C₆H₄⁺ in the gas phase have now been compared with DIB data, leading in each case merely to upper limits in their column densities. In future the comparison of laboratory and DIB spectra should be extended to other series of nonlinear carbon chains such as those containing a sulfur or nitrogen atom.

Appendix

In the case of C_s-C₆H₄⁺, five bands were observed using a C₂H₂–C₂D₂ mixture and were assigned to C₆H₄⁺, C₆H₃D⁺, C₆H₂D₂⁺, C₆HD₃⁺ and C₆D₄⁺.¹ The three partially deuterated species C₆H₃D⁺, C₆H₂D₂⁺, C₆HD₃⁺ show only three bands in the low-resolution spectrum separated by ∼15–20 cm⁻¹. Thus the replacement of each successive H by D leads the excitation energy to shift by this amount. The letter three species have four, six, four isomers, respectively, depending on the position of deuteration. The excitation energy thus shifts by only several cm⁻¹ at most for different positions of the D atom in a particular isotopic species, much less than the 15–20 cm⁻¹ overall shift. It is clear that the shift does not have a strong dependence on the position deuterated in the case of nonlinear and non-cyclic C₆H₄⁺. Thus a shift of deuterated trans-C₆H₄⁺ should be approximately equal to that of C_s-one.

On the other hand, a deuteration shift depends on a number of carbons. For example, the shifts of polyacetylene cation H–(C≡C)_n–H⁺ (n = 4, 6, 8, 10) are 18.07, 31.82, 26.34, 20.4 cm⁻¹, respectively, despite the same number of hydrogen atoms.²³ Therefore if the number of carbons is not the same, there is no agreement of the shifts on deuteration, except if by chance. The deuterated shift of trans-C₆H₄⁺ (67.3 cm⁻¹) is in excellent agreement with C_s-C₆H₄⁺ (66.9 cm⁻¹). All the above two support the assignment of the observed band to trans-C₆H₄⁺.

Acknowledgements

This work has been supported by the Swiss National Science Foundation (Project 200020-100019/1).

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