Resonant two-photon threshold ionization spectroscopy is employed to determine the ionization energy of C2 to 5 meV precision, about two orders of magnitude more precise than the previously accepted value. Through exploration of the ionization threshold after pumping the 0–3 band of the newly discovered 43Πga3Πu band system of C2, the ionization energy of the lowest rovibronic level of the a3Πu state was determined to be 11.791(5) eV. Accounting for spin-orbit and rotational effects, we calculate that the ionization energy of the forbidden origin of the a3Πu state is 11.790(5) eV, in excellent agreement with quantum thermochemical calculations which give 11.788(10) eV. The experimentally derived ionization energy of X1Σg+ state C2 is 11.866(5) eV.

The carbon dimer is among the most abundant molecules in the known universe, its absorption and emission spectra being displayed in various astrophysical objects including the “Red Rectangle” proto-planetary nebula,1–4 the diffuse interstellar medium,5,6 comets,7–9 and stars,10,11 including our sun.12 The bonding of C2 is also of great interest, with the ground state exhibiting some evidence of a quadruple bond.13,14 This assertion is far from uncontroversial, however.15–18 Arguably, C2 is the longest spectroscopically studied molecule, the Swan bands having first been described by Wollaston in 1802 in his studies on the blue part of a flame.19 Despite this, new electronic states continue to be uncovered, with the 43Πga3Πu transition reported for the first time just last year.20 

While C2 is the smallest carbon cluster identified in astrophysical objects, the fullerenes are now known to pervade the circumstellar regions of young planetary nebulae.21,22 In its ionized state, C60+ has been identified as the carrier of several diffuse interstellar bands.23–25 A detailed understanding of the ionization dynamics of interstellar carbon molecules relies on accurate figures for the ionization energies. For C60 this is accurately known: 7.57(1) eV.26–28 However, and perhaps surprisingly, the figure for dicarbon, C2, has not been experimentally determined to comparable accuracy. The evaluated ionization energy (IE) for dicarbon is 11.4 ± 0.3 eV,29 measured by electron impact, but reports range from 10.9 to 13 eV.30–36 The most reliable report seems to be that of Reid and co-workers who reported 11.4(1) ± 0.30 and 12.3(3) ± 0.30 eV, respectively, for ionization of C2 (X1Σg+) into the lowest 4Σg and 2Πu states.30 

The ground state of C2 is X1Σg+ while that of C2+ is 4Σg. As such, there is no allowed one-electron transition which will result in ground state cations, probably contributing to the difficulty of IE measurement. The lower state of the Swan bands is a3Πu, the zero point energy of which is only 613.650(3) cm−1 (76 meV) above that of the X1Σg+ ground state.37 Dicarbon is readily produced in this metastable state in electrical discharges and other plasmas, and ionization from this state to the cation’s 14Σg state is spin-allowed. Furthermore, the a3Πu state is well described as a single-reference wavefunction, and is thus amenable to theoretical methods such as coupled cluster theory.

Recently, we reported the first resonant ionization spectrum of a3Πu state C2, through its 43Πga3Πu transition.20 Though performed with one colour, introduction of a second ionizing wavelength enables the ionization threshold to be established to few meV precision. In this paper, we report the IE of C2 by spectroscopic means for the first time. We corroborate our results with those of high-level ab initio calculations, both single- (coupled cluster) and multi-reference (MRCI) based methods. The agreement between the determinations firmly places the IE of C2 from the a3Πu state at about 11.79 eV. We discuss the implications of this measurement for thermochemical cycles.

As with our previous contributions to the spectroscopy of C2,20,38–41 the MRCI method42,43 with Davidson’s correction (MRCI+Dav)44,45 was employed to generate the potential energy curves of the 14Σg and a3Πu states. The reference wavefunctions were of the complete active space self-consistent field (CASSCF) type, with a full-valence active space.46,47 The MRCI wavefunctions contain all single and double excitations from the valence space of the reference.

The valence correlated calculations were carried out using the aug-cc-pV6Z basis set of Wilson et al.,48 while the core and core-valence (CV) correlation corrections were computed with the aug-cc-pCVQZ basis of Woon and Dunning,49 as in our previous studies.38,39,41

Scalar relativistic effects were calculated with the Douglas-Kroll Hamiltonian,50–52 employing the quadruple zeta aug-cc-pCVQZ-DK basis set.49,53 These quantum chemical calculations were carried out using the MOLPRO2012.154 programs on the Fujitsu PRIMERGY supercomputer of the National Computational Infrastructure (NCI) of Australia. Vibrational energies and wave functions were obtained by a variational approach, as in our previous work.20,38–41

The ionization energy of C2 has been calculated with the High-accuracy Extrapolated Ab initio Thermochemistry (HEAT) composite approach.55–57 HEAT calculations attempt to accurately estimate the exact electronic energy in the Born-Oppenheimer (BO) approximation based on basis set extrapolation and the use of very highly correlated electronic wavefunctions. In addition to the scalar relativistic contributions that are a part of the BO picture, HEAT also adds a correction for the adiabatic (diagonal Born-Oppenheimer) correction and an anharmonic treatment of zero-point energy. While this class of approaches relies on somewhat empirical procedures for extrapolation and certain additivity assumptions governing the interplay of basis set and correlation effects, it has been amply documented to provide bond energies with sub-kJ mol−1 accuracy. While its use in ionization energy determinations is somewhat less well benchmarked,58 it appears that the performance of the method is at least as good in these cases.

The specific variant of HEAT chosen for use in this work is the HEAT345-(Q) method, which is fully documented in Ref. 57. Briefly, these calculations estimate the CCSD(T) correlation energy by extrapolating results obtained with the aug-cc-pCVXZ (X = T, Q and 5) results in all-electron calculations, while the residual correlation effects are estimated by carrying out CCSDT calculations to determine the intrinsic error in the (T) approximation to T, and then using CCSDT(Q)59 to estimate the small amount of residual correlation energy. In Ref. 57, CCSDT(Q) gave a rms error of 0.35 kJ mol−1 (28 cm−1, 3.5 meV) for the atomization energies of a test suite of 20 small atoms and molecules. A similar uncertainty will be assumed below for the calculations reported here (conservatively 10 meV).

Potential energy curves calculated at the MRCI/aug-cc-pCVQZ level are plotted in Figure 1 for the a3Πu and 43Πg states of C2, and the 14Σg state of C2+. Our best MRCI-based results were obtained at the valence correlated MRCI+Dav/aug-cc-pV6Z level of theory corrected for CV correlation and scalar relativistic effects as described above. This method has been shown previously to reproduce spectroscopic parameters with high accuracy.38,39 At this level, the 14Σg state is calculated to exhibit a slightly longer equilibrium bond length than the lowest triplet state, a3Πu. The calculated re is 2.656 a0 (1.405 Å), which compares very favorably with the 2.655 a0 inferred by an extrapolation of the high resolution rotational constants reported by Oka and co-workers,60 and the linear fit to rotational constants reported by Maier and Rösslein,61 2.652 a0. A fit of the vibrational energies of the first few vibrational levels results in vibrational frequencies and anharmonicities of ωe = 1350.7 cm−1 and ωexe = 12.73 cm−1, in close agreement with the values reported by Maier and Rösslein, 1351.21 cm−1 and 12.06 cm−1, respectively. The calculated levels for the a3Πu state deviate from the experimental levels by a maximum of 1.2 cm−1 up to v = 5, and as such the curve is taken as highly accurate.

FIG. 1.

Potential energy curves of relevant states of C2 and C2+ calculated at the MRCI/aug-cc-pCVQZ level, with variationally calculated vibrational wavefunctions. Inset are cartoons of the leading configurations of the a3Πu and 14Σg states.

FIG. 1.

Potential energy curves of relevant states of C2 and C2+ calculated at the MRCI/aug-cc-pCVQZ level, with variationally calculated vibrational wavefunctions. Inset are cartoons of the leading configurations of the a3Πu and 14Σg states.

Close modal

The accuracy of calculated relative energies of different electronic states, at the MRCI level, was shown by us previously to be in the range of 100-200 cm−1.38,39 In light of the ionization occurring at substantially higher energies (∼95 000 cm−1) than most electronic excitations in our studies, a conservative estimate of the error in the computed ionization energy is ∼300 cm−1 (∼0.04 eV). The zero point corrected ionization energy of C2 in its a3Πu state, as calculated at the MRCI+Dav level of theory, is thus 11.74(4) eV. A breakdown of the contributions to this value is given in Table I. From our previous work,38,39 we calculated the zero-point level of the a3Πu state to lie 705 cm−1 higher in energy than that of the X1Σg+ state. This is higher than the experimentally determined value of 613.650(3) cm−1,37 resulting in a calculated IE for X1Σg+ state C2 of 11.83(4) eV.

TABLE I.

Components of MRCI-based determination of the ionization energy of C2 from its a3Πu state.

ComponentEnergy (eV)
CASSCF/aug-cc-pV6Z +10.413 
MRCI−CASSCF/aug-cc-pV6Z +1.196 
Dav/aug-cc-pV6Z +0.126 
CV (MRCI+Dav/aug-cc-pCVQZ) +0.025 
Rel (MRCI+Dav/aug-cc-pCVQZ-DK) −0.003 
ZPE −0.019 
Total 11.738 
ComponentEnergy (eV)
CASSCF/aug-cc-pV6Z +10.413 
MRCI−CASSCF/aug-cc-pV6Z +1.196 
Dav/aug-cc-pV6Z +0.126 
CV (MRCI+Dav/aug-cc-pCVQZ) +0.025 
Rel (MRCI+Dav/aug-cc-pCVQZ-DK) −0.003 
ZPE −0.019 
Total 11.738 

The determination of the ionization energy of the a3Πu state by the HEAT procedure is 11.788 eV, which may be broken down into several components, as shown in Table II. The largest components are the SCF energy and the correlation correction calculated at the CBS-CCSD(T) level (345 extrapolation). The correction to the energy for non-perturbative consideration of triple excitations is −19 meV, which is somewhat compensated for perturbative consideration of quadruple excitations, +13 meV. The zero-point correction is calculated to be −17.7 meV, which differs from the experimental value by only +0.3 meV.61,62 It is conservatively estimated that the uncertainty of the HEAT-345(Q) IE is on the order of 10 meV, i.e., IEHEAT−345(Q) = 11.788(10) eV.

TABLE II.

Breakdown of components of the HEAT-345(Q) determination of the IE of a3Πu state C2.

ComponentEnergy (eV)
ΔEHF +10.3919 
ΔECCSD(T) +1.4224 
ΔECCSDT −0.0187 
ΔEHLC +0.0131 
ΔEZPE −0.0177 
ΔErel −0.0029 
ΔEDBOC +0.0003 
Sum 11.7884 
ComponentEnergy (eV)
ΔEHF +10.3919 
ΔECCSD(T) +1.4224 
ΔECCSDT −0.0187 
ΔEHLC +0.0131 
ΔEZPE −0.0177 
ΔErel −0.0029 
ΔEDBOC +0.0003 
Sum 11.7884 

In general, the ionization energy measurement in a resonant ionization experiment is quite straightforward, involving two subsequent laser pulses, excitation and ionization. The key to obtaining clear ionization energy spectra is to excite molecules of interest to an electronic state that is located less than halfway to the ionization energy, which ensures that two-photon absorption events do not generate ions, giving zero one laser baseline. The second laser pulse is shortly thereafter, providing higher energy photons and, ideally, used at low power to minimize two-photon events due to ionization laser alone. Ionization energy spectra are recorded by scanning the second laser and looking for the threshold energy, where the cation signal starts to rise above the zero baseline. The measurement of the ionization energy of the C2 molecule proved to be very challenging due to the fact that the intermediate electronic state is near halfway to the ionization threshold. Also, there are resonant transitions from many excited vibrational states in the a3Πu state, resulting in resonant two-photon ionizing transitions from both lasers in the region of interest.

In the electrical discharge, the C2 molecules are formed in a variety of vibrational states in the a3Πu electronic state. We have successfully identified v″ = 0–6 in the a3Πu ground state, meaning that the second laser alone might generate a non-zero baseline while exciting and ionizing a high vibrational state in a two-photon event. Indeed, while scanning the relevant region with the second laser alone we recorded a one-color spectrum that displayed (1–5) and (0–5) bands of the 43Πga3Πu electronic system (Figure 2, bottom). These observations respectively imply an ionization energy less than 12.0 and 11.8 eV. The fact that in the same experiment we were unable to observe the (0–6) band (final energy 11.6 eV) allowed us to bracket the upper and lower limits of the ionization energy as 11.6 < IE < 11.8 eV. The IE measured via the (0–6) band would potentially be free from excitation-laser only background. Therefore, we searched for it using a second, higher energy laser for ionization. However, it was extremely weak and consequent IE measurements through this band were too noisy to determine a precise threshold. Nevertheless, the two-laser dependent signal allowed us to measure the lifetime of the v = 0 level of the 43Πg electronic state. A lifetime of >100 ns suggested that separating the excitation and ionization lasers in time by 100 ns would remove the one laser background due to excitation only. Using this technique, we were able to perform IE measurements via a strong band, the (0–3) band of the 43Πga3Πu electronic transition.

FIG. 2.

The ion signal as a function of the total energy above the (v = 0) a3Πu state level (top axis), by changing ν̄2 (bottom axis). Inset: Ion signal from the two laser pulses separated in time.

FIG. 2.

The ion signal as a function of the total energy above the (v = 0) a3Πu state level (top axis), by changing ν̄2 (bottom axis). Inset: Ion signal from the two laser pulses separated in time.

Close modal

Since there have been multiple reports of the C2 ionization energy, quoting a range of numbers with various precision, as a starting point we decided to use the value of 11.5 eV. This dictated the choice of the laser dyes used. We employed two Nd-YAG lasers (355 nm) pumping two Sirah dye lasers operating on Exalite 428 and Coumarin 460 dyes, frequency-doubled, to reach combined energy of >11.5 eV.

We recorded photo-ionization spectra in our previously described apparatus,20 which is a resonance-enhanced multiphoton ionization spectrometer consisting of two differentially pumped vacuum chambers. In the first chamber, C2 molecules were generated in a pulsed discharge nozzle which admitted high pressure argon (6 bars) containing room-temperature vapor-pressure of toluene into the first chamber. A 200 μs electrical pulse was applied to the outer electrode with a 300 Ω ballast resistor. The products of the (2 kV) electrical discharge were supersonically cooled, and the coldest part of the beam was admitted to the second chamber through a 2 mm skimmer. In the second chamber, the C2 molecules were subjected to two laser pulses. The first, ν̄1, excited the recently described 43Πga3Πu excitation of C2, generating ions. A second, 100 ns-delayed laser pulse, ν̄2, ionizes remaining population in the 43Πg state. A static electric field of ∼160 V/cm served to accelerate the two ion-packets towards the multichannel plate of a Wiley-McLaren time-of-flight mass spectrometer. The two ionizing laser pulses thus generated two temporally separated signals on the detector corresponding to m/z 24 (see inset, Figure 2). Without temporal separation, the signal-to-noise was found to be significantly smaller. The photon energy of the second laser was tuned from below to above the IE of the lower quantum state of the C2 molecules that were selected by the first laser pulse. The two-laser dependent signal of the second ion-packet thus generates the ionization efficiency spectrum.

The 2-colour photoionization efficiency spectrum, as a function of ν̄2, measured by pumping the Q(2) line of the F1 component of the (0–3) band of the 43Πga3Πu system of C2 at 213.965 nm (vacuum), is shown in Figure 2. The intermediate level has J = 2 and Ω = 2, meaning that it exhibits minimal rotational energy of the nuclear framework. As such, transitions from this state to the 14Σu state of the cation are expected to access the lowest-energy eigenstates. Therefore, the observed ionization threshold should coincide with the ionization energy.

The observation of ion signal occurs at a combined energy (the two photons plus the initial C2 energy) between 11.75 eV and 11.80 eV (top axis, Figure 2). There is clearly a structure in the ionization curve above the ionization threshold, which we attribute to transitions to the auto-ionizing v = 1 levels of Rydberg series converging to the 14Σg state, as also seen in Be2.63 

The vibrational wave functions in the a3Πu, 43Πg, and 14Σg electronic states (shown in Figure 1) clearly indicate that the vertical transition from the (v = 0) level of the 43Πg state to the ionized 14Σg state is to v > 0. As such, transitions to the autoionizing Rydberg series converging on (v = 1) of the 14Σg state are stronger than the direct transitions to the (v=0)14Σg continuum. The different equilibrium bond lengths of the a3Πu, 43Πg, and 14Σg states of C2 are rationalized in terms of their qualitative bond orders. The a3Πu state has a leading valence σg2σu2πu3σg1 configuration, and a bond order of 2. As discussed previously,20 the 43Πg state has a bond order of 1. The σg2σu2πu2σg1 configuration of the 14Σg state results in a bond order of 1.5.

There is also a signal generated by ν̄2 alone, indicated by the lower trace in Figure 2. Some of this structure is assigned in the figure. While one-colour signal due to ν̄1 is minimized due to the temporal displacement of the laser pulses, some signal is unavoidable. However, it can be subtracted from the two-colour signal, and this trace is plotted in Figure 3, where the abscissa is given by

IE=hcν̄1+ν̄2+ν̄a3Πg(v=3,J=2,Ω=2)e,
(1)

where ν̄1=46736.6 cm−1, ν̄a3Πu(v=3,J=2,Ω=2)=4774.2 cm−1 is the energy above the origin of the v = 0 level (see inset in Figure 3).62 

FIG. 3.

The ionization efficiency measured at an applied field of 200 V with background due to ν̄2-only signal subtracted. Inset: Diagram of the energy of the initial state of the IE determination relative to the a3Πu state origin.

FIG. 3.

The ionization efficiency measured at an applied field of 200 V with background due to ν̄2-only signal subtracted. Inset: Diagram of the energy of the initial state of the IE determination relative to the a3Πu state origin.

Close modal

To determine the background level, we analyzed the relatively steady portion of the signal up to 11.779 eV, and marked the ±2σ range as a grey band. The ion signal remains within the grey band up to about 11.779 eV, and is sustainably in excess of this threshold above 11.782 eV. We estimate that the threshold is no lower than 11.779 eV under the employed static field and thus estimate that the IE is 11.782(3) eV at a 200 V applied extraction potential.

However, the ionization energy is depressed in a static electric field. For hydrogen atoms, ignoring tunneling, the decrement is ΔIE=2E (in atomic units). In previous studies of more complex molecules, we determined a correction factor at a 200 V applied potential of +7(1) meV. For the hydrogen atom (ignoring tunneling) the correction factor for our apparatus is calculated to be +9.8 meV. Attempts to measure the IE depression as a function of applied voltage were unsuccessful. Instead, we take a conservative approach and increase the lower end of our confidence interval by 6 meV, and the upper end by 10 meV. This results in an estimate of IE = 11.790(5) eV from the a3Πu state (relative to v = 0 origin) and 11.866(5) from the ground X1Σg+ state. The IE of the lowest rovibronic level of the a3Πu state is 11.791(5) eV (J = 2, F1). The experimental uncertainty overlaps comfortably with that of the HEAT-345(Q) calculations, as illustrated by dark grey bars in Figure 3. The IEs directly determined by experiment and theory in this work are summarized in Table III.

TABLE III.

Theoretical and experimental IEs of a3Πu state C2.

MethodIE (eV)
MRCI/aug-cc-pV6Z+CV+rel. 11.74(4) 
HEAT345-(Q) 11.788(10) 
Experiment 11.791(5) 
MethodIE (eV)
MRCI/aug-cc-pV6Z+CV+rel. 11.74(4) 
HEAT345-(Q) 11.788(10) 
Experiment 11.791(5) 

The ionization energy of a molecule is a fundamental quantity which is often involved in thermochemical cycles aimed at determining parameters such as bond energies and proton affinities.64,65

The bond dissociation energy (BDE) of acetylene (HCCH → H + CCH) was determined by Mordaunt et al. to be 46 074 ± 8 cm−1, or 5.7124(10) eV.66 The BDE of the CCH radical (CCH → H + CC) is reported by Ruscic to be 4.8958(27) eV, with the BDE of acetylene listed as 5.7114 eV.67 So, reaction of HCCH to C2 + 2H requires 10.6073(28) eV.

Using the present result, we therefore expect an appearance energy for the HCCH to C2++2H channel to be 22.462(5) eV. This is close to, but slightly below, the value determined by Plessis and Marmet, 22.60(12) eV.31 The same authors determined an appearance energy of 18.16(5) eV for the channel to H2. This should be closer to 17.985 eV, given an H2 bond energy of 4.478 eV.68 The lower thresholds determined here highlight the difficulty in determining threshold energies in electron impact experiments.

From the ionization energy of CCH (11.61(7) eV),69 one can determine that the 0 K proton affinity of C2 is 6.87(7) eV, and that the bond dissociation energy for the CCH+ cation (to yield C2++H) is 5.14(7) eV. The BDE of the C2+ cation itself is determined to be 5.639(5) eV if we take the BDE of C2 from the Active Thermochemical Tables (ATcT), i.e., 6.245 eV.70 

The ionization energy of C2 was determined to 5 meV precision by resonant two-photon threshold ionization spectroscopy, nearly two orders of magnitude more precise than the previously accepted value. The value determined for the ground electronic state is 11.866(5) eV and that determined for the lowest triplet rovibronic level, a3Πu, is 11.791(5) eV, which is in excellent agreement with quantum thermochemical calculations using the HEAT345-(Q) procedure. The bond dissociation energy of the C2+ cation is thus determined to be 5.639(5) eV.

This research was supported under Australian Research Councils Discovery Projects funding scheme DP120102559). T.W.S. acknowledges the Australian Research Council for a Future Fellowship (No. FT130100177). We acknowledge the computational resource provided by the Australian Government through Intersect Australia Ltd under the National Computational Merit Allocation Scheme. J.F.S. was supported by the U.S. Department of Energy Office of Science, Basic Energy Sciences [Award No. DE-FG02-07ER1588] and the Robert A. Welch Foundation of Houston, TX (Grant No. F-1283). We thank a referee for detailed comments that helped us to improve the presentation.

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