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Almost free methyl top internal rotation: Rotational spectrum of 2-butynoic acid
Journal of Molecular Spectroscopy 267 (2011) 186–190
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Journal of Molecular Spectroscopy journal homepage: www.elsevier.com/locate/jms
Almost free methyl top internal rotation: Rotational spectrum of 2-butynoic acid Vadim Ilyushin a,⇑, Roberto Rizzato b, Luca Evangelisti b, Gang Feng b, Assimo Maris b, Sonia Melandri b, Walther Caminati b a b
Institute of Radio Astronomy of NASU, Chervonopraporna Street 4, 61002 Kharkov, Ukraine Dipartimento di Chimica ‘‘G. Ciamician’’ dell’ Università, Via Selmi 2, I-40126 Bologna, Italy
a r t i c l e
i n f o
Article history: Available online 29 March 2011 Keywords: Rotational spectroscopy Internal rotation Large amplitude motion Potential energy surface Pulsed jet Carboxylic acid
a b s t r a c t The rotational spectrum of 2-butynoic acid was measured by pulsed supersonic-jet Fourier transform microwave spectroscopy in the frequency range from 6 to 18 GHz. Rotational lines have been measured for the m = 0 and m = 1 torsional states and analyzed using the rho-axis-method. The features of the spectrum illustrate the pattern for an almost free internal rotation of the terminal methyl group that is characterized by a very low barrier V3 = 1.0090(4) cm1. The results are compared with the supporting ab initio calculations for this molecule. Ó 2011 Elsevier Inc. All rights reserved.
1. Introduction Conformational equilibria of carboxylic acids and their dimers have recently acquired new interest. The aim of the studies is observing and determining the potential energy surface for the concerted proton exchange between the monomers, which could be an important phenomenon in the interaction between amino acids. Intermolecular and intramolecular proton exchanges often serve as triggers for more extensive chemical or conformational changes in molecules, and systems that exhibit such phenomena are therefore of interest for molecular dynamics and biochemistry. The 1:1 adduct between a carboxylic acid with a triple CAC bond (propiolic acid) and formic acid was investigated by Daly et al. [1]. Such a heterodimer is quite similar to the formic acid dimer, which was studied extensively because of its concerted double proton tunneling phenomenon (see Ref. [2] and references therein). In their work [1] the authors observed a splitting of the rotational lines attributable to a proton transfer between the two moieties. Therefore complexes of this kind between carboxylic acids and formic acid seem to be very good candidates for observing the proton tunneling splitting. Heterodimers with 2-butynoic acid should also supply important information on proton transfer processes, and with the aim of pursuing this kind of research in the future, we report here an analysis of the rotational spectrum of the 2-butynoic acid monomer since not even the rotational spectrum of the monomer is available in the literature.
⇑ Corresponding author. Fax: +380 57 706 1415. E-mail address: [email protected] (V. Ilyushin). 0022-2852/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2011.03.028
Internal large amplitude motions, such as the internal rotation of a methyl group, can complicate the rotational spectrum of carboxylic acids and their dimers. Acetic acid for example has quite a low barrier to internal rotation (V3 = 170 cm1 [3]), as has also trifluoroacetic acid (V3 = 241 cm1 [4]). Complexation of acetic acid with one or two water molecules [5] or with CF3COOH [6] lowers the barrier to internal rotation to V3 = 138, 118 and 97 cm1, respectively. The considerable decrease of V3 with respect to the value for isolated CH3COOH in the hydrated species and in the heterodimers was interpreted by Howard and collaborators in terms of correlation with the strength of hydrogen-bonding in the complexes [5]. It would be of interest to know how complexation will affect the barrier to internal rotation in 2-butynoic acid, since this molecule is expected to have a very low barrier to internal rotation. As was demonstrated by Olson and Papousek in their infrared work on dimethylacetylene [7], the methyl group experiences nearly free internal rotation when it is attached to a triple C„C bond. The upper limit for the barrier to internal rotation estimated semi-quantitatively in this study for dimethylacetylene [7] is 4 cm1. Our current study shows that 2-butynoic acid has a barrier of about 1 cm1. In this paper we report the results of our pulsed supersonic-jet microwave Fourier transform study of the 2-butynoic acid (CH3AC„CACOOH) spectrum in the frequency range from 6 to 18 GHz. Frequencies of the rotational lines have been measured for the m = 0 and m = 1 torsional states of the molecule. The 2-butynoic acid spectrum is analysed using the well-established rho-axis-method (RAM), which has achieved experimental accuracy (or almost so) for several internal rotation molecules
V. Ilyushin et al. / Journal of Molecular Spectroscopy 267 (2011) 186–190
including acetic acid [3] and a molecule, acetamide [8], with a very low barrier to internal rotation (V3 25 cm1). In the present study a fit within experimental accuracy has also been achieved for the 2-butynoic acid spectrum, giving the lowest barrier height ever analyzed with an RAM Hamiltonian, V3 = 1.0090(4) cm1. 2. Experimental details The sample of 2-butynoic acid was purchased from Aldrich and used without further purification. The rotational spectrum of 2butynoic acid was measured in the 6–18 GHz frequency range using a COBRA-type [9] pulsed supersonic-jet Fourier-transform microwave (FTMW) spectrometer described elsewhere [10] and updated with the FTMW++ set of programs [11]. Helium at a pressure of 2 bar was flowed over a sample of 2-butynoic acid heated to about 350 K and the resulting mixture was expanded through a solenoid valve (General Valve, Series 9, nozzle diameter 0.5 mm) into the Fabry–Pérot cavity. The frequencies were determined after Fourier transformation of the 8 k data points contained in the time domain signal, recorded with 100 ns sample intervals. Each rotational transition is split by the Doppler effect due to the molecular beam expansion in the coaxial arrangement of the supersonic jet and resonator axes. The rest frequency is calculated as the arithmetic mean of the frequencies of the Doppler components. The estimated accuracy of frequency measurements is better than 3 kHz and lines separated by more than 7 kHz are resolvable.
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ric in the group G6 are allowed. Such an approach provides much higher flexibility in testing and fitting different Hamiltonian terms than the BELGI code which has a fixed set of Hamiltonian terms [18]. Readers are encouraged to look at Section 3 of Ref. [16] for more details on the structure of the computer program. In the process of spectrum analysis the question of labeling the torsional states has arisen. It is well known that the internal rotation of a methyl top attached to some molecular frame should be treated as an anharmonic vibrational motion well below the top of the barrier to internal rotation, and as a nearly free internal rotation motion well above the top of the barrier. Therefore a harmonic oscillator vibrational quantum number vt is not well defined for levels above the barrier and a free-rotor quantum number m is not well defined for levels below the barrier. The vt labeling assumes that the spacings between degenerate and nondegenerate levels of the torsional Hamiltonian associated with given vt are much smaller than those between levels with different vt [19]. Since this was true for the majority of molecules with a threefold barrier treated up to now by microwave spectroscopy the harmonic oscillator vibrational quantum number vt was traditionally used to label torsional states in the case of a threefold barrier. In the present case we deal with an extremely low threefold barrier where the E component of the ground torsional state already lies well above the barrier, and where the free-rotor quantum number m should be more appropriate. So we decided to use m quantum number for labeling torsional states in the fit of the 2-butynoic acid spectrum.
3. Theoretical model The Hamiltonian used in the present work is the so-called rho-axis-method internal-rotation Hamiltonian which is rather completely described in the works of Kirtman [12], Lees and Baker [13], Herbst et al. [14] and Hougen et al. [15]. In the present study we apply a RAM torsion–rotation program recently developed for molecules with a low internal rotation barrier [16]. This program has two modes: the first one, the so-called V6-mode, is intended for molecules with a C3v top and a C2v frame that possess a sixfold barrier to internal rotation; the second one, the so-called V3-mode, is intended for molecules with a C3v top and a Cs frame that possess a threefold barrier. This program was successfully applied to fit the microwave spectra of molecules with low sixfold barriers, such as toluene [16] (light top) or benzotrifluoride [17] (heavy top). Here we decided to apply this program to the analysis of the spectrum of a molecule with a very low V3 barrier, such as 2-butynoic acid, also in order to test the V3-mode of the new program on a very low V3 barrier problem. The V3-mode follows the procedure realized in the BELGI code (see Ref. [18] for details) with the main difference being the form of presentation of the Hamiltonian terms. In our program we encoded the following general expression for the Hamiltonian:
H ¼ ð1=2Þ
X
h i Bknpqrs0 J 2k J nz J px J qy pra cosð3saÞ þ cosð3saÞpra Jqy J px J nz J 2k
knpqrs
þ ð1=2Þ
X
h i Bknpqr0t J2k J nz J px J qy pra sinð3t aÞ þ sinð3t aÞpra J qy J px J nz J 2k ;
knpqrt
ð1Þ where the Bknpqrst are fitting parameters; pa is the angular momentum conjugate to the internal rotation angle a; Jx, Jy, Jz are projections on the x, y, z axes of the total angular momentum J. In the program, matrix elements are calculated for specific terms in the general expression of Eq. (1), which the user selects via sets of k, n, p, q, r, s, t integer indices in the input file. During input, each set of k, n, p, q, r, s, t integer indices is checked for conformity with time reversal and symmetry requirements. In the V3-mode only terms in the torsion–rotation Hamiltonian that are totally symmet-
3.1. Ab initio calculations The structural parameters of 2-butynoic acid have been optimized by ab initio calculations performed with the G09 suite of programs [20]. The HF, MP2 and B3LYP methods were used with the 6-311G(d,p), 6-311++G(d,p) and 6-311++G(3df,3p) basis sets. The three configurations related to the orientation of the methyl group considered here for 2-butynoic acid are shown in Fig. 1. Two of them, Cs(OH) and Cs(@O) have a Cs symmetry, while C1 does not have symmetry elements. We optimized the structure of each configuration, and subsequently run harmonic frequency calculations. In the C1 structure one of the methyl hydrogen atoms was forced to be orthogonal to the carboxyl group, whereas in the Cs forms one of the methyl hydrogen atoms was forced to be coplanar with the carboxyl group. For each of the optimized geometries the harmonic vibrational frequency values were found to be all positive or all positive except for the one corresponding to the methyl rotation motion. The results are given as Supplementary material. The obtained relative electronic energies among the three forms vary between 0.04 and 1.6 cm1, as a result of the almost flat potential energy surface (PES) for the low barrier to internal rotation of the methyl group. Due to such flatness, it is even difficult to identify which of the forms is a minimum when calculating vibrational frequencies within the harmonic approximation. Whereas we believe that it is rather difficult to obtain an accurate V3 value for such a flat PES it should be noted that the values obtained in our ab initio calculations lie below 1.6 cm1, which is in good correspondence with the V3 value obtained from the fit (see next section). In Table 1 the rotational constants calculated with several theoretical approaches are compared with experimental values obtained in the current study (see next section for details). One can see that for this kind of molecule the best results are obtained with the MP2/6-311++G(3df,3p) combination of method and basis set. Table 2 gives the rotational and centrifugal distortion constants calculated with this method, and Fig. 2 gives the global minimum energy configuration. The structural parameters obtained for
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Cs(OH): minimum
C1: V6
Cs(=O) : V3
Fig. 1. Stationary points along the coordinate describing the internal rotation of the methyl group.
Table 1 Ab initio rotational constantsa of 2-butynoic acid obtained with various methods and basis sets.
a
A (MHz)
B (MHz)
C (MHz)
Experiment
11269.9
1752.1
1529.5
MP2/6-311++G(3df,3p) MP2/6-311++G(d,p) MP2/6-311G(d,p)
11 267 11 167 11 203
1748 1738 1738
1527 1518 1519
B3LYP/6-311++G(3df,3p) B3LYP/6-311++G(d,p) B3LYP/6-311G(d,p)
11 298 11 246 11 261
1762 1756 1756
1538 1533 1534
HF/6-311++G(3df,3p) HF/6-311++G(d,p) HF/6-311G(d,p)
11 739 11 694 11 702
1773 1769 1769
1555 1551 1551
Calculated for Cs(OH) configuration, see Fig.1.
Table 2 MP2/6-311++G(3df,3p) spectroscopic parameters of 2-butynoic acid. A = 11 267 MHz B = 1748 MHz C = 1527 MHz la = 2.03 D lb = 1.39 D
DJ = 0.20 kHz DJK = 9.35 kHz DK = 1.10 kHz d1 = 0.01 kHz d2 = 0.07 kHz
Fig. 2. Global minimum energy configuration of 2-butynoic acid obtained at the MP2/6-311++G(3df,3p) level.
2-butynoic acid at the MP2/6-311++G(3df,3p) level are given in the Supplementary material.
4. Rotational spectra Preliminary calculations of the spectrum using a Watson type Hamiltonian were based on the ab initio values of the spectroscopic constants listed in Table 2. We searched first for la-R-type transitions, which were expected to be more intense than the lb-type
ones. Lines corresponding to m = 0 torsional state with Ka = 0–2, and with J ranging from 2 to 3 were easily identified and assigned. As can be seen in Fig. 3, where a portion of the broad band spectrum with the 30,3 20,2 and 31,3 21,2 rotational transitions is shown, the m = 0 – m = 1 splitting in Ka = 0 la-R-type transitions is rather small. This gave us an opportunity to start identification of the m = 1 transitions of 2-butynoic acid. First we tried to apply the Combined Axis Method (CAM) (XIAM program [21]) which allowed to predict m = 1 la-R-type transitions quite well (but not btype m = 1 transitions). However the fit of the la-R-type transitions for m = 1 was not satisfactory. Next we tried to apply the perturbative Principal Axis Method (PAM) [18] with the ‘‘Coriolis like’’ term DaJa and its J and K dependence to analysis of m = 1 state. Here we were able to get a satisfactory fit of the m = 1 la-R-type transitions, but again we failed with this method to assign any b-type m = 1 transitions. Therefore from this point forward we used the RAM Hamiltonian model which appeared to be successful in analysis of the 2-butynoic acid spectrum. Using the RAM Hamiltonian we were able to extend considerably the spectral assignment, up to a total of 43 m = 0 and 46 m = 1 transitions. Measured transition frequencies and their assignments are given in Supplementary material with this paper. The Hamiltonian model includes 16 terms with one fixed parameter. The resulting parameter values obtained from the fit of the 89 line frequencies are reported in Table 3. The root mean square (rms) deviation of 2.6 kHz obtained in our analysis is below experimental accuracy of the measurements. Separate rms deviations for the m = 0 and m = 1 states are equal (2.6 kHz). Since we fit both states simultaneously, this demonstrates that RAM provides a similar quality of fit for both the nondegenerate and degenerate symmetry species. In the course of our fitting attempts we tested the quartic centrifugal distortion part of the RAM Hamiltonian both in the form of A- and S-reductions (the asymmetry parameter of 2-butynoic acid 0.95). It appeared that in both cases practically the same rms deviation of the fit may be obtained but the S-reduction gives a less correlated set of RAM Hamiltonian parameters. In the case of A-reduction the main correlation was observed between the dK fPa ; P2b P 2c g and (qbc/2)fP a ; P 2b P 2c gpa terms. When dKfPa; P2b P2c g is replaced by d2 ðJ 4þ þ J 4 Þ, which corresponds to replacing A-reduction by S-reduction, the overall correlation of the parameter set is reduced significantly (the condition number for the least square matrix was improved almost by two orders of magnitude). Omission of the (qbc/2){Pa ; P2b P 2c }pa term in the A-reduction fit led to analogous improvement in the condition number for the least square matrix but resulted in an increased rms deviation of the fit (3.54 kHz). Therefore in the final fit we adopted the S-reduction form of the quartic centrifugal distortion part of the RAM Hamiltonian. Since there were only rotational transitions belonging to the m = 0 and m = 1 states (belonging only to the ground torsional state in vt terminology) it was not possible due to high correlation to
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189
Fig. 3. A portion of the spectrum of 2-butynoic acid showing the m = 0 and m = 1 components of the 30,3 20,2 and 31,3 21,2 rotational transitions. Each rotational transition is split by the Doppler effect due to the molecular beam expansion in the coaxial arrangement of the supersonic jet and resonator axes.
Table 3 Torsion–rotation parameters from the fit of transitions involving m = 0 and m = 1 torsional energy levels of 2-butynoic acid CH3AC„CACOOH. Parametera (units)
Operatorb
Value 1.00900(42)c 5.66d
q
(½)(1 cos3a) p2a paJa
A (MHz)
J2a
0.071528698(37) 11269.90006(66)
B (MHz)
J2b
1752.18588(15)
C (MHz)
J2c (JaJb + JbJa) J4
1
V3 (cm ) F (cm1)
Dab (MHz) DJ (kHz) DJK (kHz)
J2 J2a
1529.58083(15) 16.1845(48) 0.0440(17) 11.351(11)
DK (kHz)
J4a
2.65(21)
d1 (kHz)
2J2(J 2b J2c )
0.01200(65)
d2 (kHz)e
J4þ þ J 4
0.0154(19)
FJ (kHz)
p2a J2
37.255(96)
qbc (kHz) qJ (kHz) qK (kHz)
(½){Ja,(J2b J 2c )}pa paJaJ2
0.748(63)
Nf rms (kHz)
paJ3a
35.204(36) 15.05(74) 89 2.6
a
Parameter nomenclature based on the subscript procedures of [22]. {A,B} = AB + BA. The product of the parameter and operator from a given row represents the term used in the RAM Hamiltonian, except for F, q, and A, B, C which occur in the Hamiltonian in the form F(pa qJa)2 + (½)(B + C)J2 + (A (½)(B + C))J 2a + (½)(B C)(J2b J 2c ). c Statistical uncertainties are shown as one standard uncertainty in the last two digits. d Fixed, see text. e In the fit the J 4þ þ J4 operator was represented as 2(J 4b þ J4c 3fJ2b ; J 2c g 5J 2a þ 2J 2 ). f Number of lines in the fit. b
vary the principal torsional parameters F, V3 and q at the same time. Usually in such cases the F parameter is fixed at some value that corresponds to an acceptable value for the moment of inertia of the methyl top Ia. In order to choose an appropriate value of Ia in the case of 2-butynoic acid we made a small survey of the Ia values obtained for other molecules with internal rotation and of the cor-
respondence between experimental values obtained from the fit and ab initio values calculated at the MP2/6-311++G(3df,3p) level. According to Lin and Swalen [19] we can easily recalculate an Ia value from either the q or the F parameter (see Eqs. 2–25, 2–30 of Ref. [19]). The values recalculated from q and from F differ slightly due to structural distortions during the internal rotation process. In Table 4 we compare the experimentally obtained Ia values with ab initio values for several molecules: acetic acid [3], acetamide [8], methanol [22], methyl carbamate [23], acetaldehyde [24]. As it is seen from Table 4 the MP2/6-311++G(3df,3p) values for Ia are always lower than those obtained from experiment via an RAM Hamiltonian fit. Therefore, although the MP2/6311++G(3df,3p) value obtained for 2-butynoic acid was 3.145 uÅ2 we decided to use F = 5.66 cm1, which corresponds to Ia 3.21 uÅ2, in our final fit. In such a way we used an Ia value that corresponds to the average of the experimental Ia values considered in Table 4.
5. Discussion It is well known that even second order parameters in the RAM Hamiltonian may change well above stated confidence intervals when the dataset is augmented by new measurements and new higher order torsion–rotation perturbation terms are added to the model. Therefore the rather limited amount of experimental data available (m = 0,1 states only, Jmax = 10, K max ¼ 4) as well as a the possibility to fit these data satisfactorily with slightly different sets of the rotation–torsion perturbation RAM Hamiltonian terms brings up the question of estimating more reliable bounds for the V3 = 1.0090(4) cm1 value than those provided by the confidence interval. One possible source of error is the choice of the fixed value of F discussed above. If we take, for example, F = 5.76 cm1, which corresponds to the Ia value obtained from ab initio calculations, then we will get V3 = 1.03618 cm1. Variation of the F value from F = 5.51 cm1 to F = 5.84 cm1 (corresponding to variation of Ia from 3.10 uÅ2 to 3.30 uÅ2) gives a variation in V3 from V3 = 0.96868 cm1 to V3 = 1.05808 cm1. Also we have run several
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Table 4 Comparison between experimental and calculated Ia/uÅ2 values of several molecules with methyl group internal rotation.
a
Molecule
Formula
From q valuea
From F valuea
MP2 6-311++G(3df,3p)
2-butynoic acid Methanol [22] Acetaldehyde [24] Acetamide [8] Acetic acid [3] Methyl carbamate [23]
CH3AC„CACOOH CH3AOH CH3ACHO CH3ACONH2 CH3ACOOH CH3AOACONH2
3.21 3.19 3.20 3.21 3.22
3.21 3.19 3.22 3.23 3.18
3.145 3.134 3.157 3.141 3.152 3.194
see Eqs. 2–25, 2–30 of Lin and Swalen [19].
trial fits where we add to the current model different 4th order torsion–rotation perturbation terms. The resulting V3 values from these trial fits are the following (with the parameter added to the model given in the parentheses): 1.0566 cm1 (V3K), 1.0372 cm1 (qm), 0.9834 cm1 (Fab), 1.0606 cm1 (Fm), 0.9824 cm1 (FK), 1.00946 cm1 (DabJ), 1.00928 cm1 (qab), 1.00934 cm1 (DabK) (parameter nomenclature based on the subscript procedures of [22]). Two more trial fits were undertaken with a fixed V6 term added to the model in order to test for possible truncation error in the potential function expansion V(a) = ½V3(1 cos3a) + ½V6(1 cos6a) + . . . As said above, it was not possible to fit all second order torsional parameters F, V3 and q. Also, even with a fixed F, it was not possible to fit the V6 term. It is well known that errors due to truncation of the expansion are usually accumulated in the last used term of the expansion. In our case this is the V3 term and therefore it was of interest to investigate whether it can be significantly contaminated by truncation error. It should be noted that for the example molecules in Table 4 the V6 values vary from 0.58 cm1 in methyl carbamate [23] to 12.0 cm1 in acetaldehyde [24], and in acetamide [8] the ratio between second and first terms in expansion is V6/V3 0.4). Therefore we used V6 = ±0.5 cm1 (i.e. approximately half of the value obtained for 2-butynoic acid) in the trial fits (the value was fixed) and obtained values for the barrier height of V3 = 1.006 cm1 (V6 = 0.5 cm1) and V3 = 1.01092 cm1 (V6 = 0.5 cm1). This means that fixing V6 to zero should not significantly affect the value of V3 obtained from the fit. All these tests show that the value obtained for the barrier height for 2-butynoic acid is rather accurate despite the limited amount of data available. Certainly the confidence interval obtained from the least square fit is an overoptimistic estimate of the accuracy, but with high probability the bounds for the retrieved V3 value may be taken to be ±0.05 cm1 after model errors are taken into account. 6. Conclusions In this study we report the results of the first investigation of the rotational spectrum of 2-butynoic acid. The spectrum was analyzed by using the RAM Hamiltonian and a fit within experimental error has been obtained for 43 m = 0 and 46 m = 1 transitions with a model including 16 parameters. To our knowledge this is the lowest threefold internal rotation barrier ever analyzed with the RAM Hamiltonian and the obtained rms deviation of 2.6 kHz says that the method successfully passed this test. Finally the structural parameters of 2-butynoic acid have been obtained through ab initio calculations, where good correspondence between calculated and experimental values for the rotational constants support our current analysis of the 2-butynoic acid spectrum.
Acknowledgments We thank the University of Bologna and MIUR (PRIN08, Project KJX4SN_001) for financial support. G. Feng acknowledges the program of China scholarship council (CSC). The authors also wish to thank Dr. Jon T. Hougen for helpful scientific discussion and comments on the English. 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://library.osu.edu/sites/ msa/jmsa_hp.htm). Supplementary data associated with this article can be found, in the online version, at doi:10.1016/ j.jms.2011.03.028. References [1] M. Daly, P.R. Bunker, S.G. Kukolich, J. Chem. Phys. 132 (2010) 201101. [2] O. Birer, M. Havenith, Annu. Rev. Phys. Chem. 60 (2009) 263–275. [3] V.V. Ilyushin, E.A. Alekseev, S.F. Dyubko, I. Kleiner, J. Mol. Spectrosc. 220 (2003) 170–186. [4] V.M. Stolwijk, B.P. van Eijck, J. Mol. Spectrosc. 113 (1985) 196–207. [5] B. Ouyang, B.J. Howard, Phys. Chem. Chem. Phys. 11 (2009) 366–373. [6] L. Martinache, W. Kresa, M. Wegener, U. Vonmont, A. Bauder, Chem. Phys. 148 (1990) 129–140. [7] W.B. Olson, D. Papousek, J. Mol. Spectrosc. 37 (1971) 527–534. [8] V.V. Ilyushin, E.A. Alekseev, S.F. Dyubko, I. Kleiner, J.T. Hougen, J. Mol. Spectrosc. 227 (2004) 115–139. [9] (a) J.-U. Grabow, W. Stahl, Z. Naturforsch A. 45 (1990) 1043; (b) J.-U.Grabow, doctoral thesis, Christian-Albrechts-Universität zu Kiel, Kiel, 1992; (c) J.-U. Grabow, W. Stahl, H. Dreizler, Rev. Sci. Instrum. 67 (1996) 4072. [10] W. Caminati, A. Millemaggi, J.L. Alonso, A. Lesarri, J.C. Lopez, S. Mata, Chem. Phys. Letters 392 (2004) 1–6. [11] J. Grabow, Habilitationsschrift, Universität Hannover, Hannover 2004; http:// www.pci.uni-hannover.de/lgpca/spectroscopy/ftmw. [12] B. Kirtman, J. Chem. Phys. 37 (1962) 2516–2539. [13] R.M. Lees, J.G. Baker, J. Chem. Phys. 48 (1968) 5299–5318. [14] E. Herbst, J.K. Messer, F.C. De Lucia, P. Helminger, J. Mol. Spectrosc. 108 (1984) 42–57. [15] J.T. Hougen, I. Kleiner, M. Godefroid, J. Mol. Spectrosc. 163 (1994) 559–586. [16] V.V. Ilyushin, Z. Kisiel, L. Pszczólkowski, H. Mäder, J.T. Hougen, J. Mol. Spectrosc. 259 (2010) 26–38. [17] V.V. Ilyushin, L.B. Favero, W. Caminati, J.-U. Grabow, ChemPhysChem 11 (2010) 2589–2593. [18] I. Kleiner, J. Mol. Spectrosc. 260 (2010) 1–18. [19] C.C. Lin, J.D. Swalen, Rev. Mod. Phys. 31 (1959) 841–892. [20] M.J. Frisch et al., Gaussian 09, Revision A.02, Gaussian, Inc., Wallingford CT, 2009. [21] H. Hartwig, H. Dreizler, Z. Naturforsch. 51a (1996) 923–932. [22] Li-Hong Xu, J. Fisher, R.M. Lees, H.Y. Shi, J.T. Hougen, J.C. Pearson, B.J. Drouin, G.A. Blake, R. Braakman, J. Mol. Spectrosc. 251 (2008) 305–313. [23] V. Ilyushin, E. Alekseev, J. Demaison, I. Kleiner, J. Mol. Spectrosc. 240 (2006) 127–132. [24] I. Kleiner, J.T. Hougen, J.-U. Grabow, S.P. Belov, M.Yu. Tretyakov, J. Cosléou, J. Mol. Spectrosc. 179 (1996) 41–60.
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Almost free methyl top internal rotation: Rotational spectrum of 2-butynoic acid Vadim Ilyushin a,⇑, Roberto Rizzato b, Luca Evangelisti b, Gang Feng b, Assimo Maris b, Sonia Melandri b, Walther Caminati b a b
Institute of Radio Astronomy of NASU, Chervonopraporna Street 4, 61002 Kharkov, Ukraine Dipartimento di Chimica ‘‘G. Ciamician’’ dell’ Università, Via Selmi 2, I-40126 Bologna, Italy
a r t i c l e
i n f o
Article history: Available online 29 March 2011 Keywords: Rotational spectroscopy Internal rotation Large amplitude motion Potential energy surface Pulsed jet Carboxylic acid
a b s t r a c t The rotational spectrum of 2-butynoic acid was measured by pulsed supersonic-jet Fourier transform microwave spectroscopy in the frequency range from 6 to 18 GHz. Rotational lines have been measured for the m = 0 and m = 1 torsional states and analyzed using the rho-axis-method. The features of the spectrum illustrate the pattern for an almost free internal rotation of the terminal methyl group that is characterized by a very low barrier V3 = 1.0090(4) cm1. The results are compared with the supporting ab initio calculations for this molecule. Ó 2011 Elsevier Inc. All rights reserved.
1. Introduction Conformational equilibria of carboxylic acids and their dimers have recently acquired new interest. The aim of the studies is observing and determining the potential energy surface for the concerted proton exchange between the monomers, which could be an important phenomenon in the interaction between amino acids. Intermolecular and intramolecular proton exchanges often serve as triggers for more extensive chemical or conformational changes in molecules, and systems that exhibit such phenomena are therefore of interest for molecular dynamics and biochemistry. The 1:1 adduct between a carboxylic acid with a triple CAC bond (propiolic acid) and formic acid was investigated by Daly et al. [1]. Such a heterodimer is quite similar to the formic acid dimer, which was studied extensively because of its concerted double proton tunneling phenomenon (see Ref. [2] and references therein). In their work [1] the authors observed a splitting of the rotational lines attributable to a proton transfer between the two moieties. Therefore complexes of this kind between carboxylic acids and formic acid seem to be very good candidates for observing the proton tunneling splitting. Heterodimers with 2-butynoic acid should also supply important information on proton transfer processes, and with the aim of pursuing this kind of research in the future, we report here an analysis of the rotational spectrum of the 2-butynoic acid monomer since not even the rotational spectrum of the monomer is available in the literature.
⇑ Corresponding author. Fax: +380 57 706 1415. E-mail address: [email protected] (V. Ilyushin). 0022-2852/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2011.03.028
Internal large amplitude motions, such as the internal rotation of a methyl group, can complicate the rotational spectrum of carboxylic acids and their dimers. Acetic acid for example has quite a low barrier to internal rotation (V3 = 170 cm1 [3]), as has also trifluoroacetic acid (V3 = 241 cm1 [4]). Complexation of acetic acid with one or two water molecules [5] or with CF3COOH [6] lowers the barrier to internal rotation to V3 = 138, 118 and 97 cm1, respectively. The considerable decrease of V3 with respect to the value for isolated CH3COOH in the hydrated species and in the heterodimers was interpreted by Howard and collaborators in terms of correlation with the strength of hydrogen-bonding in the complexes [5]. It would be of interest to know how complexation will affect the barrier to internal rotation in 2-butynoic acid, since this molecule is expected to have a very low barrier to internal rotation. As was demonstrated by Olson and Papousek in their infrared work on dimethylacetylene [7], the methyl group experiences nearly free internal rotation when it is attached to a triple C„C bond. The upper limit for the barrier to internal rotation estimated semi-quantitatively in this study for dimethylacetylene [7] is 4 cm1. Our current study shows that 2-butynoic acid has a barrier of about 1 cm1. In this paper we report the results of our pulsed supersonic-jet microwave Fourier transform study of the 2-butynoic acid (CH3AC„CACOOH) spectrum in the frequency range from 6 to 18 GHz. Frequencies of the rotational lines have been measured for the m = 0 and m = 1 torsional states of the molecule. The 2-butynoic acid spectrum is analysed using the well-established rho-axis-method (RAM), which has achieved experimental accuracy (or almost so) for several internal rotation molecules
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including acetic acid [3] and a molecule, acetamide [8], with a very low barrier to internal rotation (V3 25 cm1). In the present study a fit within experimental accuracy has also been achieved for the 2-butynoic acid spectrum, giving the lowest barrier height ever analyzed with an RAM Hamiltonian, V3 = 1.0090(4) cm1. 2. Experimental details The sample of 2-butynoic acid was purchased from Aldrich and used without further purification. The rotational spectrum of 2butynoic acid was measured in the 6–18 GHz frequency range using a COBRA-type [9] pulsed supersonic-jet Fourier-transform microwave (FTMW) spectrometer described elsewhere [10] and updated with the FTMW++ set of programs [11]. Helium at a pressure of 2 bar was flowed over a sample of 2-butynoic acid heated to about 350 K and the resulting mixture was expanded through a solenoid valve (General Valve, Series 9, nozzle diameter 0.5 mm) into the Fabry–Pérot cavity. The frequencies were determined after Fourier transformation of the 8 k data points contained in the time domain signal, recorded with 100 ns sample intervals. Each rotational transition is split by the Doppler effect due to the molecular beam expansion in the coaxial arrangement of the supersonic jet and resonator axes. The rest frequency is calculated as the arithmetic mean of the frequencies of the Doppler components. The estimated accuracy of frequency measurements is better than 3 kHz and lines separated by more than 7 kHz are resolvable.
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ric in the group G6 are allowed. Such an approach provides much higher flexibility in testing and fitting different Hamiltonian terms than the BELGI code which has a fixed set of Hamiltonian terms [18]. Readers are encouraged to look at Section 3 of Ref. [16] for more details on the structure of the computer program. In the process of spectrum analysis the question of labeling the torsional states has arisen. It is well known that the internal rotation of a methyl top attached to some molecular frame should be treated as an anharmonic vibrational motion well below the top of the barrier to internal rotation, and as a nearly free internal rotation motion well above the top of the barrier. Therefore a harmonic oscillator vibrational quantum number vt is not well defined for levels above the barrier and a free-rotor quantum number m is not well defined for levels below the barrier. The vt labeling assumes that the spacings between degenerate and nondegenerate levels of the torsional Hamiltonian associated with given vt are much smaller than those between levels with different vt [19]. Since this was true for the majority of molecules with a threefold barrier treated up to now by microwave spectroscopy the harmonic oscillator vibrational quantum number vt was traditionally used to label torsional states in the case of a threefold barrier. In the present case we deal with an extremely low threefold barrier where the E component of the ground torsional state already lies well above the barrier, and where the free-rotor quantum number m should be more appropriate. So we decided to use m quantum number for labeling torsional states in the fit of the 2-butynoic acid spectrum.
3. Theoretical model The Hamiltonian used in the present work is the so-called rho-axis-method internal-rotation Hamiltonian which is rather completely described in the works of Kirtman [12], Lees and Baker [13], Herbst et al. [14] and Hougen et al. [15]. In the present study we apply a RAM torsion–rotation program recently developed for molecules with a low internal rotation barrier [16]. This program has two modes: the first one, the so-called V6-mode, is intended for molecules with a C3v top and a C2v frame that possess a sixfold barrier to internal rotation; the second one, the so-called V3-mode, is intended for molecules with a C3v top and a Cs frame that possess a threefold barrier. This program was successfully applied to fit the microwave spectra of molecules with low sixfold barriers, such as toluene [16] (light top) or benzotrifluoride [17] (heavy top). Here we decided to apply this program to the analysis of the spectrum of a molecule with a very low V3 barrier, such as 2-butynoic acid, also in order to test the V3-mode of the new program on a very low V3 barrier problem. The V3-mode follows the procedure realized in the BELGI code (see Ref. [18] for details) with the main difference being the form of presentation of the Hamiltonian terms. In our program we encoded the following general expression for the Hamiltonian:
H ¼ ð1=2Þ
X
h i Bknpqrs0 J 2k J nz J px J qy pra cosð3saÞ þ cosð3saÞpra Jqy J px J nz J 2k
knpqrs
þ ð1=2Þ
X
h i Bknpqr0t J2k J nz J px J qy pra sinð3t aÞ þ sinð3t aÞpra J qy J px J nz J 2k ;
knpqrt
ð1Þ where the Bknpqrst are fitting parameters; pa is the angular momentum conjugate to the internal rotation angle a; Jx, Jy, Jz are projections on the x, y, z axes of the total angular momentum J. In the program, matrix elements are calculated for specific terms in the general expression of Eq. (1), which the user selects via sets of k, n, p, q, r, s, t integer indices in the input file. During input, each set of k, n, p, q, r, s, t integer indices is checked for conformity with time reversal and symmetry requirements. In the V3-mode only terms in the torsion–rotation Hamiltonian that are totally symmet-
3.1. Ab initio calculations The structural parameters of 2-butynoic acid have been optimized by ab initio calculations performed with the G09 suite of programs [20]. The HF, MP2 and B3LYP methods were used with the 6-311G(d,p), 6-311++G(d,p) and 6-311++G(3df,3p) basis sets. The three configurations related to the orientation of the methyl group considered here for 2-butynoic acid are shown in Fig. 1. Two of them, Cs(OH) and Cs(@O) have a Cs symmetry, while C1 does not have symmetry elements. We optimized the structure of each configuration, and subsequently run harmonic frequency calculations. In the C1 structure one of the methyl hydrogen atoms was forced to be orthogonal to the carboxyl group, whereas in the Cs forms one of the methyl hydrogen atoms was forced to be coplanar with the carboxyl group. For each of the optimized geometries the harmonic vibrational frequency values were found to be all positive or all positive except for the one corresponding to the methyl rotation motion. The results are given as Supplementary material. The obtained relative electronic energies among the three forms vary between 0.04 and 1.6 cm1, as a result of the almost flat potential energy surface (PES) for the low barrier to internal rotation of the methyl group. Due to such flatness, it is even difficult to identify which of the forms is a minimum when calculating vibrational frequencies within the harmonic approximation. Whereas we believe that it is rather difficult to obtain an accurate V3 value for such a flat PES it should be noted that the values obtained in our ab initio calculations lie below 1.6 cm1, which is in good correspondence with the V3 value obtained from the fit (see next section). In Table 1 the rotational constants calculated with several theoretical approaches are compared with experimental values obtained in the current study (see next section for details). One can see that for this kind of molecule the best results are obtained with the MP2/6-311++G(3df,3p) combination of method and basis set. Table 2 gives the rotational and centrifugal distortion constants calculated with this method, and Fig. 2 gives the global minimum energy configuration. The structural parameters obtained for
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Cs(OH): minimum
C1: V6
Cs(=O) : V3
Fig. 1. Stationary points along the coordinate describing the internal rotation of the methyl group.
Table 1 Ab initio rotational constantsa of 2-butynoic acid obtained with various methods and basis sets.
a
A (MHz)
B (MHz)
C (MHz)
Experiment
11269.9
1752.1
1529.5
MP2/6-311++G(3df,3p) MP2/6-311++G(d,p) MP2/6-311G(d,p)
11 267 11 167 11 203
1748 1738 1738
1527 1518 1519
B3LYP/6-311++G(3df,3p) B3LYP/6-311++G(d,p) B3LYP/6-311G(d,p)
11 298 11 246 11 261
1762 1756 1756
1538 1533 1534
HF/6-311++G(3df,3p) HF/6-311++G(d,p) HF/6-311G(d,p)
11 739 11 694 11 702
1773 1769 1769
1555 1551 1551
Calculated for Cs(OH) configuration, see Fig.1.
Table 2 MP2/6-311++G(3df,3p) spectroscopic parameters of 2-butynoic acid. A = 11 267 MHz B = 1748 MHz C = 1527 MHz la = 2.03 D lb = 1.39 D
DJ = 0.20 kHz DJK = 9.35 kHz DK = 1.10 kHz d1 = 0.01 kHz d2 = 0.07 kHz
Fig. 2. Global minimum energy configuration of 2-butynoic acid obtained at the MP2/6-311++G(3df,3p) level.
2-butynoic acid at the MP2/6-311++G(3df,3p) level are given in the Supplementary material.
4. Rotational spectra Preliminary calculations of the spectrum using a Watson type Hamiltonian were based on the ab initio values of the spectroscopic constants listed in Table 2. We searched first for la-R-type transitions, which were expected to be more intense than the lb-type
ones. Lines corresponding to m = 0 torsional state with Ka = 0–2, and with J ranging from 2 to 3 were easily identified and assigned. As can be seen in Fig. 3, where a portion of the broad band spectrum with the 30,3 20,2 and 31,3 21,2 rotational transitions is shown, the m = 0 – m = 1 splitting in Ka = 0 la-R-type transitions is rather small. This gave us an opportunity to start identification of the m = 1 transitions of 2-butynoic acid. First we tried to apply the Combined Axis Method (CAM) (XIAM program [21]) which allowed to predict m = 1 la-R-type transitions quite well (but not btype m = 1 transitions). However the fit of the la-R-type transitions for m = 1 was not satisfactory. Next we tried to apply the perturbative Principal Axis Method (PAM) [18] with the ‘‘Coriolis like’’ term DaJa and its J and K dependence to analysis of m = 1 state. Here we were able to get a satisfactory fit of the m = 1 la-R-type transitions, but again we failed with this method to assign any b-type m = 1 transitions. Therefore from this point forward we used the RAM Hamiltonian model which appeared to be successful in analysis of the 2-butynoic acid spectrum. Using the RAM Hamiltonian we were able to extend considerably the spectral assignment, up to a total of 43 m = 0 and 46 m = 1 transitions. Measured transition frequencies and their assignments are given in Supplementary material with this paper. The Hamiltonian model includes 16 terms with one fixed parameter. The resulting parameter values obtained from the fit of the 89 line frequencies are reported in Table 3. The root mean square (rms) deviation of 2.6 kHz obtained in our analysis is below experimental accuracy of the measurements. Separate rms deviations for the m = 0 and m = 1 states are equal (2.6 kHz). Since we fit both states simultaneously, this demonstrates that RAM provides a similar quality of fit for both the nondegenerate and degenerate symmetry species. In the course of our fitting attempts we tested the quartic centrifugal distortion part of the RAM Hamiltonian both in the form of A- and S-reductions (the asymmetry parameter of 2-butynoic acid 0.95). It appeared that in both cases practically the same rms deviation of the fit may be obtained but the S-reduction gives a less correlated set of RAM Hamiltonian parameters. In the case of A-reduction the main correlation was observed between the dK fPa ; P2b P 2c g and (qbc/2)fP a ; P 2b P 2c gpa terms. When dKfPa; P2b P2c g is replaced by d2 ðJ 4þ þ J 4 Þ, which corresponds to replacing A-reduction by S-reduction, the overall correlation of the parameter set is reduced significantly (the condition number for the least square matrix was improved almost by two orders of magnitude). Omission of the (qbc/2){Pa ; P2b P 2c }pa term in the A-reduction fit led to analogous improvement in the condition number for the least square matrix but resulted in an increased rms deviation of the fit (3.54 kHz). Therefore in the final fit we adopted the S-reduction form of the quartic centrifugal distortion part of the RAM Hamiltonian. Since there were only rotational transitions belonging to the m = 0 and m = 1 states (belonging only to the ground torsional state in vt terminology) it was not possible due to high correlation to
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Fig. 3. A portion of the spectrum of 2-butynoic acid showing the m = 0 and m = 1 components of the 30,3 20,2 and 31,3 21,2 rotational transitions. Each rotational transition is split by the Doppler effect due to the molecular beam expansion in the coaxial arrangement of the supersonic jet and resonator axes.
Table 3 Torsion–rotation parameters from the fit of transitions involving m = 0 and m = 1 torsional energy levels of 2-butynoic acid CH3AC„CACOOH. Parametera (units)
Operatorb
Value 1.00900(42)c 5.66d
q
(½)(1 cos3a) p2a paJa
A (MHz)
J2a
0.071528698(37) 11269.90006(66)
B (MHz)
J2b
1752.18588(15)
C (MHz)
J2c (JaJb + JbJa) J4
1
V3 (cm ) F (cm1)
Dab (MHz) DJ (kHz) DJK (kHz)
J2 J2a
1529.58083(15) 16.1845(48) 0.0440(17) 11.351(11)
DK (kHz)
J4a
2.65(21)
d1 (kHz)
2J2(J 2b J2c )
0.01200(65)
d2 (kHz)e
J4þ þ J 4
0.0154(19)
FJ (kHz)
p2a J2
37.255(96)
qbc (kHz) qJ (kHz) qK (kHz)
(½){Ja,(J2b J 2c )}pa paJaJ2
0.748(63)
Nf rms (kHz)
paJ3a
35.204(36) 15.05(74) 89 2.6
a
Parameter nomenclature based on the subscript procedures of [22]. {A,B} = AB + BA. The product of the parameter and operator from a given row represents the term used in the RAM Hamiltonian, except for F, q, and A, B, C which occur in the Hamiltonian in the form F(pa qJa)2 + (½)(B + C)J2 + (A (½)(B + C))J 2a + (½)(B C)(J2b J 2c ). c Statistical uncertainties are shown as one standard uncertainty in the last two digits. d Fixed, see text. e In the fit the J 4þ þ J4 operator was represented as 2(J 4b þ J4c 3fJ2b ; J 2c g 5J 2a þ 2J 2 ). f Number of lines in the fit. b
vary the principal torsional parameters F, V3 and q at the same time. Usually in such cases the F parameter is fixed at some value that corresponds to an acceptable value for the moment of inertia of the methyl top Ia. In order to choose an appropriate value of Ia in the case of 2-butynoic acid we made a small survey of the Ia values obtained for other molecules with internal rotation and of the cor-
respondence between experimental values obtained from the fit and ab initio values calculated at the MP2/6-311++G(3df,3p) level. According to Lin and Swalen [19] we can easily recalculate an Ia value from either the q or the F parameter (see Eqs. 2–25, 2–30 of Ref. [19]). The values recalculated from q and from F differ slightly due to structural distortions during the internal rotation process. In Table 4 we compare the experimentally obtained Ia values with ab initio values for several molecules: acetic acid [3], acetamide [8], methanol [22], methyl carbamate [23], acetaldehyde [24]. As it is seen from Table 4 the MP2/6-311++G(3df,3p) values for Ia are always lower than those obtained from experiment via an RAM Hamiltonian fit. Therefore, although the MP2/6311++G(3df,3p) value obtained for 2-butynoic acid was 3.145 uÅ2 we decided to use F = 5.66 cm1, which corresponds to Ia 3.21 uÅ2, in our final fit. In such a way we used an Ia value that corresponds to the average of the experimental Ia values considered in Table 4.
5. Discussion It is well known that even second order parameters in the RAM Hamiltonian may change well above stated confidence intervals when the dataset is augmented by new measurements and new higher order torsion–rotation perturbation terms are added to the model. Therefore the rather limited amount of experimental data available (m = 0,1 states only, Jmax = 10, K max ¼ 4) as well as a the possibility to fit these data satisfactorily with slightly different sets of the rotation–torsion perturbation RAM Hamiltonian terms brings up the question of estimating more reliable bounds for the V3 = 1.0090(4) cm1 value than those provided by the confidence interval. One possible source of error is the choice of the fixed value of F discussed above. If we take, for example, F = 5.76 cm1, which corresponds to the Ia value obtained from ab initio calculations, then we will get V3 = 1.03618 cm1. Variation of the F value from F = 5.51 cm1 to F = 5.84 cm1 (corresponding to variation of Ia from 3.10 uÅ2 to 3.30 uÅ2) gives a variation in V3 from V3 = 0.96868 cm1 to V3 = 1.05808 cm1. Also we have run several
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Table 4 Comparison between experimental and calculated Ia/uÅ2 values of several molecules with methyl group internal rotation.
a
Molecule
Formula
From q valuea
From F valuea
MP2 6-311++G(3df,3p)
2-butynoic acid Methanol [22] Acetaldehyde [24] Acetamide [8] Acetic acid [3] Methyl carbamate [23]
CH3AC„CACOOH CH3AOH CH3ACHO CH3ACONH2 CH3ACOOH CH3AOACONH2
3.21 3.19 3.20 3.21 3.22
3.21 3.19 3.22 3.23 3.18
3.145 3.134 3.157 3.141 3.152 3.194
see Eqs. 2–25, 2–30 of Lin and Swalen [19].
trial fits where we add to the current model different 4th order torsion–rotation perturbation terms. The resulting V3 values from these trial fits are the following (with the parameter added to the model given in the parentheses): 1.0566 cm1 (V3K), 1.0372 cm1 (qm), 0.9834 cm1 (Fab), 1.0606 cm1 (Fm), 0.9824 cm1 (FK), 1.00946 cm1 (DabJ), 1.00928 cm1 (qab), 1.00934 cm1 (DabK) (parameter nomenclature based on the subscript procedures of [22]). Two more trial fits were undertaken with a fixed V6 term added to the model in order to test for possible truncation error in the potential function expansion V(a) = ½V3(1 cos3a) + ½V6(1 cos6a) + . . . As said above, it was not possible to fit all second order torsional parameters F, V3 and q. Also, even with a fixed F, it was not possible to fit the V6 term. It is well known that errors due to truncation of the expansion are usually accumulated in the last used term of the expansion. In our case this is the V3 term and therefore it was of interest to investigate whether it can be significantly contaminated by truncation error. It should be noted that for the example molecules in Table 4 the V6 values vary from 0.58 cm1 in methyl carbamate [23] to 12.0 cm1 in acetaldehyde [24], and in acetamide [8] the ratio between second and first terms in expansion is V6/V3 0.4). Therefore we used V6 = ±0.5 cm1 (i.e. approximately half of the value obtained for 2-butynoic acid) in the trial fits (the value was fixed) and obtained values for the barrier height of V3 = 1.006 cm1 (V6 = 0.5 cm1) and V3 = 1.01092 cm1 (V6 = 0.5 cm1). This means that fixing V6 to zero should not significantly affect the value of V3 obtained from the fit. All these tests show that the value obtained for the barrier height for 2-butynoic acid is rather accurate despite the limited amount of data available. Certainly the confidence interval obtained from the least square fit is an overoptimistic estimate of the accuracy, but with high probability the bounds for the retrieved V3 value may be taken to be ±0.05 cm1 after model errors are taken into account. 6. Conclusions In this study we report the results of the first investigation of the rotational spectrum of 2-butynoic acid. The spectrum was analyzed by using the RAM Hamiltonian and a fit within experimental error has been obtained for 43 m = 0 and 46 m = 1 transitions with a model including 16 parameters. To our knowledge this is the lowest threefold internal rotation barrier ever analyzed with the RAM Hamiltonian and the obtained rms deviation of 2.6 kHz says that the method successfully passed this test. Finally the structural parameters of 2-butynoic acid have been obtained through ab initio calculations, where good correspondence between calculated and experimental values for the rotational constants support our current analysis of the 2-butynoic acid spectrum.
Acknowledgments We thank the University of Bologna and MIUR (PRIN08, Project KJX4SN_001) for financial support. G. Feng acknowledges the program of China scholarship council (CSC). The authors also wish to thank Dr. Jon T. Hougen for helpful scientific discussion and comments on the English. 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://library.osu.edu/sites/ msa/jmsa_hp.htm). Supplementary data associated with this article can be found, in the online version, at doi:10.1016/ j.jms.2011.03.028. References [1] M. Daly, P.R. Bunker, S.G. Kukolich, J. Chem. Phys. 132 (2010) 201101. [2] O. Birer, M. Havenith, Annu. Rev. Phys. Chem. 60 (2009) 263–275. [3] V.V. Ilyushin, E.A. Alekseev, S.F. Dyubko, I. Kleiner, J. Mol. Spectrosc. 220 (2003) 170–186. [4] V.M. Stolwijk, B.P. van Eijck, J. Mol. Spectrosc. 113 (1985) 196–207. [5] B. Ouyang, B.J. Howard, Phys. Chem. Chem. Phys. 11 (2009) 366–373. [6] L. Martinache, W. Kresa, M. Wegener, U. Vonmont, A. Bauder, Chem. Phys. 148 (1990) 129–140. [7] W.B. Olson, D. Papousek, J. Mol. Spectrosc. 37 (1971) 527–534. [8] V.V. Ilyushin, E.A. Alekseev, S.F. Dyubko, I. Kleiner, J.T. Hougen, J. Mol. Spectrosc. 227 (2004) 115–139. [9] (a) J.-U. Grabow, W. Stahl, Z. Naturforsch A. 45 (1990) 1043; (b) J.-U.Grabow, doctoral thesis, Christian-Albrechts-Universität zu Kiel, Kiel, 1992; (c) J.-U. Grabow, W. Stahl, H. Dreizler, Rev. Sci. Instrum. 67 (1996) 4072. [10] W. Caminati, A. Millemaggi, J.L. Alonso, A. Lesarri, J.C. Lopez, S. Mata, Chem. Phys. Letters 392 (2004) 1–6. [11] J. Grabow, Habilitationsschrift, Universität Hannover, Hannover 2004; http:// www.pci.uni-hannover.de/lgpca/spectroscopy/ftmw. [12] B. Kirtman, J. Chem. Phys. 37 (1962) 2516–2539. [13] R.M. Lees, J.G. Baker, J. Chem. Phys. 48 (1968) 5299–5318. [14] E. Herbst, J.K. Messer, F.C. De Lucia, P. Helminger, J. Mol. Spectrosc. 108 (1984) 42–57. [15] J.T. Hougen, I. Kleiner, M. Godefroid, J. Mol. Spectrosc. 163 (1994) 559–586. [16] V.V. Ilyushin, Z. Kisiel, L. Pszczólkowski, H. Mäder, J.T. Hougen, J. Mol. Spectrosc. 259 (2010) 26–38. [17] V.V. Ilyushin, L.B. Favero, W. Caminati, J.-U. Grabow, ChemPhysChem 11 (2010) 2589–2593. [18] I. Kleiner, J. Mol. Spectrosc. 260 (2010) 1–18. [19] C.C. Lin, J.D. Swalen, Rev. Mod. Phys. 31 (1959) 841–892. [20] M.J. Frisch et al., Gaussian 09, Revision A.02, Gaussian, Inc., Wallingford CT, 2009. [21] H. Hartwig, H. Dreizler, Z. Naturforsch. 51a (1996) 923–932. [22] Li-Hong Xu, J. Fisher, R.M. Lees, H.Y. Shi, J.T. Hougen, J.C. Pearson, B.J. Drouin, G.A. Blake, R. Braakman, J. Mol. Spectrosc. 251 (2008) 305–313. [23] V. Ilyushin, E. Alekseev, J. Demaison, I. Kleiner, J. Mol. Spectrosc. 240 (2006) 127–132. [24] I. Kleiner, J.T. Hougen, J.-U. Grabow, S.P. Belov, M.Yu. Tretyakov, J. Cosléou, J. Mol. Spectrosc. 179 (1996) 41–60.