Issue 
A&A
Volume 509, January 2010



Article Number  A1  
Number of page(s)  5  
Section  Atomic, molecular, and nuclear data  
DOI  https://doi.org/10.1051/00046361/200913057  
Published online  12 January 2010 
Rotational spectra of CF^{+} and CF^{+}: accurate rest frequencies and spectroscopic parameters
G. Cazzoli^{1}  L. Cludi^{1}  C. Puzzarini^{1}  J. Gauss^{1,2}
1  Dipartimento di Chimica "G. Ciamician", Università di Bologna, via Selmi 2, 40126 Bologna, Italy
2 
Institut für Physikalische Chemie, Universität Mainz, 55099 Mainz, Germany
Received 3 August 2009 / Accepted 2 October 2009
Abstract
Context. The astrophysical relevance of the
fluoromethylidynium ion and its importance for the interstellar
chemistry of fluorine motivated the present laboratory spectroscopic
investigation of both ^{12}CF^{+} and the corresponding ^{13}Ccontaining isotopologue, ^{13}CF^{+}.
Aims. This investigation has been carried out to provide
accurate rest frequencies for future (radioastronomical) observations,
to improve the accuracy of the values for the spectroscopic parameters
available in the literature for CF^{+}, and to provide them for the first time for ^{13}CF^{+}.
Methods. Rotational spectra of CF^{+} and ^{13}CF^{+}
were recorded in the millimeter and submillimeterwave frequency
ranges. Their investigation was supplemented by highlevel
quantumchemical computations using stateoftheart coupledcluster
techniques.
Results. We report the most accurate groundstate rotational parameters available so far for CF^{+} and ^{13}CF^{+}.
Conclusions. The groundstate rotational parameters as well as the rest frequencies of ^{13}CF^{+} will be useful for future observational purposes with the aim of improving the knowledge of fluorine interstellar chemistry.
Key words: molecular data  methods: laboratory  methods: data analysis  techniques: spectroscopic  ISM: molecules  radio lines: ISM
1 Introduction
While hydrogen, carbon, nitrogen, oxygen, silicon, and sulfur are the most abundant elements in the interstellar medium (ISM), about 5% of the 120 molecules detected in the ISM contains less abundant atoms, i.e., fluorine, chlorine, phosphorus, etc. Among the fluorinecontaining molecules, only HF and, very recently, also CF^{+} have been observed. The recent observation of the J = 10, 21, and 32 rotational transitions of CF^{+} toward the Orion Bar region (Neufeld et al. 2006) together with the still very limited knowledge about the interstellar chemistry of fluorine stimulated the present investigation. As ^{13}Ccontaining species are of astrophysical relevance, we decided to further investigate the rotational spectra of ^{12}CF^{+} and to study that of the ^{13}Ccontaining species for the first time.
To the best of our knowledge, the only study concerning the interstellar chemistry of fluorine available in the literature is the one by Neufeld et al. (2005). Their principal conclusion was that hydrogen fluoride is formed rapidly and is the dominant reservoir of fluorine over a wide range of conditions. As a consequence, the reaction of HF with C^{+} might lead to measurable column densities of CF^{+}, and the fluoromethylidynium ion is predicted to be the second most abundant fluorinecontaining molecule in the ISM. This prediction was subsequently confirmed by observations carried out using the IRAM 30 m and APEX 12 m telescopes as reported by Neufeld et al. (2006).
From a spectroscopic point of view, all previous laboratory work was limited to the main isotopic species. The investigation of the pure rotational spectrum was reported in the '80s by Plummer et al. (1986), who recorded the , with J=13, rotational transitions. The rovibrational spectra were studied by Kawaguchi & Hirota (1985), who observed the fundamental band via diode laser spectroscopy, and Gruebele et al. (1986), who investigated the lowest six vibrational hot bands by using velocitymodulation laser spectroscopy.
In the present work, the experimental investigation is supported by highlevel quantumchemical calculations at the coupledcluster level (for a recent review, see Bartlett & Musia 2007). The purpose of these calculations is mainly to obtain reliable predictions for the relevant spectroscopic parameters for the ^{13}Ccontaining isotopologue of CF^{+}. In a further step, the computational results are also used for the determination of the BornOppenheimer breakdown parameters for the rotational constant of the fluoromethylidynium ion. To achieve sufficient accuracy in the theoretical treatment, coupledcluster methods up to pentuple excitations are used in our calculations together with an adequate treatment of core correlation, extrapolation to the basisset limit and consideration of zeropoint vibrational corrections as well as the electronic contribution to the rotational constants. Previous, presumably less accurate theoretical studies of CF^{+} have been reported by Peterson and coworkers using fourthorder MøllerPlesset perturbation theory (Peterson et al. 1987) and multireference configurationinteraction techniques (Peterson et al. 1990).
2 Methodology
The fluoromethylidynium ion has been investigated by means of rotational spectroscopy and quantum chemistry with the aim of obtaining accurate spectroscopic parameters. In the following sections the relevant experimental and theoretical details are given.
2.1 Experimental details
A frequency modulated computercontrolled spectrometer, equipped with a liquid heliumcooled InSb detector, was used to record the rotational spectra. The millimeter and submillimeterwave sources employed are frequency multipliers driven by Gunn diode oscillators. The measurements were carried out in the 190600 GHz frequency range with the source phaselocked to a rubidium frequency standard, and the frequency modulation obtained by sinewave modulating the 75 MHz local oscillator of the synchronization loop. The detector output is processed by means of a lockin amplifier tuned at twice the modulation frequency so that practically the recorded profile is the second derivative of the natural line profile. A detailed description of the spectrometer can be found in Cazzoli & Dore (1990).
Samples of CF^{+} and ^{13}CF^{+} were prepared directly inside the absorption cell starting from a mixture of either H_{2} and CF_{4} or H_{2} and ^{13}CF_{4} (99% in ^{13}C), respectively, approximately in the ratio 1:1 and by applying a DC discharge (2600 V, 15 mA). Measurements were performed in a continuous flow of gas, maintained by a diffusion pump, in order to constantly provide fresh precursor gases and to remove the final discharge products. It was found to be necessary to apply a magnetic field of about 350 G in order to detect the rotational spectra of the cations under consideration. By applying discharge and magnetic field, it is observed that the total pressure decreases from the initial value of 50 mTorr down to 35 mTorr (effect already observed in Plummer et al. 1986). The recording of the spectra was performed as soon as stationarity in the discharge conditions was reached. Since no rotational parameters were available for the ^{13}Ccontaining species, quantumchemically calculated values of the relevant spectroscopic parameters were used to predict rotational transition frequencies. The latter have been further improved by empirically scaling, thereby using the available literature data for CF^{+}(Plummer et al. 1986).
The , with J=14, rotational transitions of CF^{+} and the , with J=1, 35, rotational transitions of ^{13}CF^{+} have been recorded with an accuracy of about 50 kHz.
2.2 Dunham fit and BornOppenheimer breakdown
In a Dunhamtype fit for the analysis of the data (Dunham
1932), a potential function of the form:
is employed, where )/ and a_{0}, a_{1}, ... are the potential constants. The vibrorotational transition frequencies are fitted to the socalled Dunham expression:
with Y_{l,m} as the actual Dunham parameters as well as J and v representing the rotational and vibrational quantum numbers, respectively.
Watson showed that the Dunham parameters Y_{l,m} for different
isotopologues can be expressed to a good approximation in terms of
the isotopically invariant parameters U_{l,m},
and
(Watson 1973; Watson 1980):
where M_{A} and M_{B} denote the atomic masses and is the reduced mass. In Eq. (3), the first term in parentheses gives the BO contribution, while the second and third ones are the socalled BO breakdown terms. Consequently, the parameters and are usually referred to as BO breakdown parameters. We focus our attention on the Y_{0,1}parameter which corresponds to the equilibrium rotational constant and can be expressed as:
In Eq. (4), and are the adiabatic and equilibrium bond distance (with ), respectively, and and are the electron and proton mass, respectively. The expression also involves the rotational g factor and the socalled Dunham corrections . This correction as well as the adiabatic (given by the second term of Eq. (4)) and nonadiabatic (given by the third term of Eq. (4)) corrections can be evaluated via quantum chemistry. We refer the interested reader to Gauss & Puzzarini (2009) for details. A slight modification of the presented theory, however, is required in the case of ions with charge number C (see, for instance, Odashima 2006). Instead of the reduced mass , the chargemodified reduced mass
(5) 
needs to be used when applying Eq. (3) for the determination of the parameters U_{l,m}, and .
2.3 Quantumchemical details
Quantumchemical calculations were performed with the twofold aim of predicting the unknown spectroscopic parameters of ^{13}CF^{+} and of determining the BO breakdown parameters for the rotational constant of CF^{+} as discussed above.
Most calculations that are reported here were performed at the coupledcluster (CC) level of theory (Bartlett & Musia 2007) employing the CC singles and doubles (CCSD) approximation (Purvis & Bartlett 1982) augmented by a perturbative treatment of triple excitations (CCSD(T)) (Raghavachari et al. 1989). The full CC singles, doubles and triples (CCSDT) (Noga & Bartlett 1987; Watts & Bartlett 1993), the CC singles, doubles, triples and quadruples (CCSDTQ), as well as the singles, doubles, triples, quadruples, pentuples (CCSDTQP) (Kállay & Surján 2001) models were used in a few additional calculations.
The calculations were performed using the following correlationconsistent basis sets: the valence ccpVnZ ( , T) basis sets (Dunning 1989) and the corevalence ccpCVnZ ( 6) basis (Dunning 1989; Woon & Dunning 1995). The frozencore (fc) approximation, i.e., consideration of electron correlation of the valence electrons only, has been adopted in conjunction with the former basis sets, and, to account for corecorrelation effects, computations correlating all electrons were carried out with the ccpCVnZ sets.
All quantumchemical computations reported here were carried out with the CF OUR program package (2009), except those including higher than triple excitations which were performed with the MRCC package (2001) by Kállay which has been interfaced to CF OUR.
To predict the rotational spectrum of ^{13}CF^{+}, the vibrational
groundstate rotational constant was computed using an approach
similar to the one proposed and thoroughly tested in Puzzarini et al. (2008). This scheme makes use of an additivity scheme for the various electroncorrelation
contributions, employs extrapolation techniques to reach the
basisset limit, and considers additional zeropoint vibrational and
electronic contributions. The starting level in this scheme is
CCSD(T) in conjunction with basis sets up to sextuplezeta quality.
To estimate the CCSD(T) basisset limit, extrapolation techniques
(Feller 1993; Helgaker et al. 1997) are applied at
the gradient level within the geometry optimization (Heckert et al.
2006). Corecorrelation effects are already included at
this level by basing this step on allelectron CCSD(T) calculations
and the corepolarized ccpCVnZ sets. Higherorder correlation
effects are considered via frozencore CCSDT/ccpVTZ,
CCSDTQ/ccpVDZ, and CCSDTQP/ccpVDZ calculations with the
corresponding corrections again included at the gradient level. On
the whole, this composite level to obtain the best estimate for the
equilibrium structure and also the equilibrium rotational constant
is best characterized as
where CCSD(T)/ccpCVZ denotes the extrapolation to the basisset limit, and T, Q, and P denote the full triples, quadruples and pentuples corrections, respectively.
The final prediction of the groundstate rotational constant
B_{0} necessitates the additional computation of the vibrational and electronic
contributions:
(6) 
The first of these two contributions requires the evaluation of the harmonic and anharmonic force field to compute the vibrationrotation interaction constant via vibrational secondorder perturbation theory (for details, see Mills 1972). The required force field calculations were carried out at the CCSD(T)/ccpCVQZ level of theory. The second contribution is closely related to the rotational g tensor (see Puzzarini et al. 2008) which can be computed using analytic second derivatives as described in Gauss et al. (1996) and Gauss et al. (2007). It was evaluated in the present work at the CCSD(T)/ccpCVQZ level using the corresponding structure.
To complete our prediction, quartic and sextic centrifugal distortion constants were derived from the available harmonic and cubic force fields.
To evaluate the BO breakdown parameters, as explained in Gauss &
Puzzarini (2009), we need theoretical values for ,
,
g and
.
The first of these
quantities, ,
is defined via the minimum of the BO potential,
while the second is the minimum of the potential in the adiabatic
approximation for which the potential is given by the sum of the BO
potential and the diagonal BO correction (DBOC). The determination
of
was performed as explained above and involves extrapolation
to the complete basis set limit, corecorrelation effects, and
higher excitation. In a second step the adiabatic distance
was obtained by augmenting the previously obtained
value with
the shift due to the DBOC computed at the CCSD/ccpVTZ level. The
geometry optimization including DBOC was performed using numerically
evaluated forces. The rotational g factor was computed in the
third step as already discussed. Finally, to evaluate the Dunham
correction, the potential given in Eq. (1) and thus the
corresponding potential constants are required. They are obtained by
calculating a suitable number (in the present case 30) of energy
points around .
Those were computed at the CCSD(T)/ccpCV5Z
level. The Dunham correction is then given by (Watson 1973;
Dunham 1932)
(7) 
With the Dunham coefficients Y_{0,1} computed via Eq. (4) for ^{12}C^{19}F^{+}, ^{13}C^{19}F^{+}, ^{12}C^{18}F^{+}, and ^{13}C^{18}F^{+}, it is then possible via a leastsquares fit using Eq. (3) to determine the carbon and fluorine BO breakdown parameters.
3 Results and discussion
The measured frequencies of the (J=14) rotational transitions of CF^{+} and the (J=1, 35) rotational transitions of ^{13}CF^{+} are given in Table 1. The values reported were obtained as averages of several sets of measurements, and for all of them the standard deviation is well within the given uncertainty of 50 kHz. For predictive purpose, in Table 1 the calculated frequencies, together with their estimated accuracy, based on the fit described below are also reported. Figure 1 shows the J = 4 3 rotational transition for both CF^{+} and ^{13}CF^{+} and provides an example of the signaltonoise (S/N) ratio obtained in our measurements. The worse S/N ratio observed for the ^{13}Ccontaining species is due to the shorter averaging time employed, a choice made in order to preserve the ^{13}CF_{4}sample as much as possible.
Table 1: (with J''=07) rotational transitions (MHz) and, for measured frequencies, corresponding observedcalculated (oc) differences (kHz) for CF^{+} and ^{13}CF^{+} together with the determined spectroscopic parameters. The latter are compared with the theoretical values as well as previous literature data.
Figure 1: The 3 rotational transition of ^{13}CF^{+} and CF^{+}. The poorer S/N ratio for the ^{13}Ccontaining species is due to a shorter averaging time. 

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To determine the rotational parameters, the transition frequencies were included in a leastsquares fit in which each line is weighted proportionally to the inverse square of its experimental uncertainty. This fit was carried out with Pickett's SPCAT/SPFIT program (Pickett 1991). The four transitions observed for each isotopic species allow us to determine the rotational constant B_{0}and the quartic centrifugal distortion constant D_{0}. The results are collected in Table 1, where they are compared to literature and theoretical data. We note that the residuals from the fit, i.e., the differences between observed and calculated values, are small and actually smaller than the ascribed uncertainties in the measured frequencies. In comparison with the results of Plummer et al. (1986), we note that their quartic centrifugaldistortion constant D_{0} does not agree with our value within the given uncertainties, while the vibrational groundstate rotational constants agree within the given error bars. As we have observed one more transition, higher in frequency, than Plummer et al. (1986) and our fit reproduces observed frequencies well within the stated uncertainty, we consider our results more reliable. Concerning the comparison with the results from the analysis of the rovibrational spectra (Kawaguchi & Hirota 1985; Gruebele et al. 1986), the larger accuracy in determining the vibrational groundstate rotational constant by means of microwave spectroscopy is evident. When comparing to the quantumchemical results, a good agreement with the experimental data for CF^{+} is noted. Detailed analysis reveals that corecorrelation effects contribute about 250 MHz to the rotational constant of CF^{+}, that corrections due to the full treatment of triples via CCSDT amount to about 20 MHz, and that the corrections due to quadruple and pentuple excitations are of the order of 40 and 15 MHz, respectively. The overall accuracy of our best theoretical estimate for the rotational constant of CF^{+} can be thus estimated as roughly 2030 MHz. The computed spectroscopic parameters are therefore clearly able to guide observation of the spectrum of ^{13}CF^{+}. Furthermore, the computations confirm that the sextic centrifugaldistortion constant is very small and therefore barely determinable (i.e., rotational transitions with J > 1015 are required).
In a second step of the analysis, our frequency values for the main isotopic species were fitted together with those for the fundamental band by Kawaguchi & Hirota (1985) and those for the lowest six vibrational hot bands by Gruebele et al. (1986) to the Dunham expression given by Eq. (2). The results are reported in Table 2, where they are compared with the previously reported parameters by Gruebele et al. (1986). However, it should be noted here that the fits performed in the present study and the one reported by Gruebele et al. (1986) are somewhat different. While we fitted the available frequency values directly to Eq. (2), Gruebele et al. fitted their frequency data to a Dunham expansion of the vibrorotational energies in terms of the equilibrium rotational constant , the harmonic frequency and the first six potential coefficients a_{1} ... a_{6} of Eq. (1). They then used these equilibrium parameters to determine the Dunham coefficients reported in Table 2 by means of the expressions given in Dunham (1932). From the comparison it is apparent that, for the parameters we found determinable in the Dunham analysis, our results agree well with those by Gruebele et al. (1986). On the other hand, we found that the parameters Y_{3,1}, Y_{2,2}, Y_{0,3}, and Y_{1,3} are not determinable from the fit. Furthermore, the value reported by Gruebele et al. (1986) for the latter coefficient seems to be too large, as Y_{1,3} is larger than the Y_{0,3} parameter.
Table 2: Dunham coefficients for ^{12}CF^{+}.
As mentioned in the computational detail section, the BO breakdown parameters for the rotational constant were determined based on quantumchemical calculations. The results are reported in Table 3. There, the various individual contributions, namely , and , are also collected. With respect to the experiment, unfortunately the lack of data for ^{13}CF^{+} in vibrationally excited states prevented their experimental determination.
4 Conclusion
Measurements of the rotational spectra of CF^{+} and ^{13}CF^{+}, carried out in the 190600 GHz frequency range, allowed us to report improved values for the B_{0} and D_{0} parameters of the main isotopic species and to provide for the first time spectroscopic parameters for the ^{13}Ccontaining isotopologue. Since both isotopic species are of astrophysical relevance, the rest frequencies obtained in the present investigation as well as those predicted from our results will be useful for future observational purposes aiming at an improved understanding of the interstellar chemistry of fluorine.
Table 3: Summary of the theoretical analysis of the BO breakdown in CF^{+}. The equilibrium BO rotational constants are reported together with adiabatic, nonadiabatic, and Dunham corrections for the four considered isotopologues of CF^{+} as well as the Dunham coefficients Y_{0,1} (all values in MHz), the BO bond distance (in Å), and the dimensionless BO breakdown parameters. For computational details, see text.
AcknowledgementsThis work has been supported by ``PRIN 2007'' funds (project ``Trasferimenti di energia, carica e molecole in sistemi complessi'') and by University of Bologna (RFO funds) as well as in Mainz by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie.
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All Tables
Table 1: (with J''=07) rotational transitions (MHz) and, for measured frequencies, corresponding observedcalculated (oc) differences (kHz) for CF^{+} and ^{13}CF^{+} together with the determined spectroscopic parameters. The latter are compared with the theoretical values as well as previous literature data.
Table 2: Dunham coefficients for ^{12}CF^{+}.
Table 3: Summary of the theoretical analysis of the BO breakdown in CF^{+}. The equilibrium BO rotational constants are reported together with adiabatic, nonadiabatic, and Dunham corrections for the four considered isotopologues of CF^{+} as well as the Dunham coefficients Y_{0,1} (all values in MHz), the BO bond distance (in Å), and the dimensionless BO breakdown parameters. For computational details, see text.
All Figures
Figure 1: The 3 rotational transition of ^{13}CF^{+} and CF^{+}. The poorer S/N ratio for the ^{13}Ccontaining species is due to a shorter averaging time. 

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