Laboratory rotational spectrum of acrylic acid and its isotopologues in the 6–18.5 GHz and 52–74.4 GHz frequency ranges

Journal of Molecular Spectroscopy 295 (2014) 37–43

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Laboratory rotational spectrum of acrylic acid and its isotopologues in the 6–18.5 GHz and 52–74.4 GHz frequency ranges C. Calabrese a, A. Vigorito a, G. Feng a,1, L.B. Favero b, A. Maris a,⇑, S. Melandri a, W.D. Geppert c, W. Caminati a a b c

Department of Chemistry, University of Bologna, Via Selmi 2, I-40126 Bologna, Italy Istituto per lo Studio dei Materiali Nanostrutturati, CNR, Via Gobetti 101, I-40129 Bologna, Italy Department of Physics, Stockholm University, Albanova University Center, SE-106 91 Stockolm, Sweden

a r t i c l e

i n f o

Article history: Received 25 October 2013 In revised form 7 November 2013 Available online 21 November 2013 Keywords: Acrylic acid Molecular structure Rotational spectroscopy Supersonic expansion spectroscopy Quantum mechanical calculations Molecule detection in space Astrochemistry

a b s t r a c t In order to facilitate the detection of acrylic acid in space, for which a possible mechanism of formation is proposed, we extended the measurements of the rotational spectrum of this molecule to the 6–18.5 GHz (time domain Fourier transform) and 52–74.4 GHz (frequency domain) ranges in supersonic expansions. 77 new lines were assigned to the s-cis conformer and 83 new lines to the s-trans conformer. In addition, the rotational spectra of the three single 13C isotopologues have been measured in natural abundance for both conformers. High resolution measurements of the carboxylic deuterated isotopologues allowed for the determination of the deuterium nuclear quadrupole coupling constants. All the spectroscopic experimental parameters were compared to the ones obtained with quantum chemical methods at the MP2(fc)/aug-cc-pVTZ and B3LYP/aug-cc-pVTZ levels of calculation. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction Several polyatomic organic molecules have been observed in the interstellar medium (ISM) or circumstellar envelopes (see for example the Cologne Database for Molecular Spectroscopy available at the web site http://www.astro.uni-koeln.de/cdms/molecules [1] and the NIST Database of Rest Frequencies for Observed Interstellar Molecular Microwave Transitions available at the website http:// www.nist.gov/pml/data/micro/index.cfm [2]). They are especially abundant in star-forming and protostellar regions. The elevated temperature encountered in these objects leads to massive evaporation of molecules that had been frozen out on icy dust grains, which triggers an involved chemistry. In these regions, also larger molecular entities can be generated through photo-induced grain-surface chemistry on the ice layers covering the grains [3]. Many more complex organic species are thus expected to be detected thanks to new telescopes. Submillimeter observatories such as the Atacama Large Millimeter Array (ALMA), the Stratospheric Observatory for Infrared Astronomy (SOFIA), and the recent Herschel Space Observatory

⇑ Corresponding author. Fax: +39 051 2099456. E-mail address: [email protected] (A. Maris). Permanent address: State Key Laboratory of Molecular Reaction Dynamics, Institute of Chemistry, Chinese Academy of Sciences, No. 2 North 1st Street, ZhongGuanCun, Beijing 100190, PR China. 1

0022-2852/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jms.2013.11.003

(HSO) which have been and will be providing observational data with unprecedented spectral sensitivity, signal-to-noise ratio and spatial resolution. Among the observed organic molecules, the two smallest carboxylic acids, formic (HACOOH) [4] and acetic acid (CH3ACOOH) [5], and two substituted propenes, acrylonitrile (CH2@CHACN) [6] and acrolein (CH2@CHACHO) [7] have been detected. Acrylic acid (CH2@CHACOOH, 2-propenoic acid), indicated hereafter as AA, is the smallest carboxylic acid containing a carbon–carbon double bond, and its search in space with rotational spectroscopy looks promising. A possible formation pathway of acrylic acid in methane and carbon dioxide containing interstellar ices could be:

H þ CO2 ! HOCO

ð1Þ

C2 H3 þ HOCO ! C2 H3 COOH

ð2Þ

An analogue formation mechanism has been invoked for production of acetic acid in an irradiated binary mixture of carbon dioxide and methane in a respective experimental study [8]. In addition, a line of the vinyl radical (C2H3) was detected by infrared spectroscopy of a methane ice that had been irradiated at 10 K with energetic electrons [9]. As mentioned, any acrylic acid present on the surface or inside the ice layer covering interstellar grains in dark clouds could be desorbed in protostellar regions during the warm-up phase occurring in the course of star formation. So far,

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C. Calabrese et al. / Journal of Molecular Spectroscopy 295 (2014) 37–43

H7 H8

H7

C2

O5

C1

C3

H9

O4

H8 H6

a

C2

O4

C1

C3

H9

O5

a

H6

b

b

s-cis

s-trans

The predicted rotational spectra of the two conformers of AA are reported in Fig. 2 at various temperatures. From this figure it can be seen that the conditions of low temperature reached in the jet expansion and found in some regions of interstellar space, allow for the greatest intensity to be observed. Based on these considerations, we report the laboratory rotational spectroscopic studies in supersonic expansions of various isotopologues of AA, including all 13C species observed in natural abundance.

Fig. 1. Sketch and atom numbering of the two forms of AA.

2. Experimental section no feasible gas phase reaction mechanism for the formation of AA has been conceived, so generation of the molecule on icy grain surfaces seems most likely. To the best of our knowledge acrylic acid is not included into standard models for chemical reaction networks in the interstellar medium [10,11]. This is not surprising, since the molecule has neither been observed in this environment yet nor detected in laboratory studies of irradiated interstellar ice analogues. However, the spectroscopic studies in the present paper might allow the discovery of the first unsaturated carbonic acid in the interstellar medium. The rotational spectrum of the AA monomer was first measured by Bolton et al. [12] by static gas waveguide cell microwave spectroscopy in the 18–40 GHz frequency range. They observed two conformers, s-cis and s-trans (see Fig. 1), according to the orientations of the vinyl group with respect to the carbonyl group, the scis conformer being more stable by 0.7 (2) kJ mol1. We went through the microwave spectrum of AA when investigating the rotational spectrum of its dimer, which is polar when it is made by a combination of one s-cis and one s-trans moieties, and displays tunneling splittings related to a concerted double proton transfer motion [13]. In that study, we observed several new transitions of AA, including those of the 13C isotopologue in natural abundance. We realized that new measurements of the rotational spectrum of AA with the microwave spectrometers available in our group (see the details in Section 2) would be useful for a better localization of the radiofrequency signal of AA reaching the earth from space.

A commercial sample of AA was supplied by Aldrich and used without further purification. AA appears as a colorless liquid with melting point of 14 °C, boiling point of 141 °C and vapor pressure of 6.9 kPa at 20 °C. AA deuterated on the carboxylic group was prepared by mixing acrylic acid and D2O. Supersonic-jet Fourier transform microwave (FTMW) [14] measurements in the 6–18.5 GHz frequency range were performed with a COBRA-type [15] spectrometer, described elsewhere [16]. A gas mixture of approximately 2% of acrylic acid in helium at a total pressure of 3  105 Pa was expanded through a solenoid valve (General Valve, series 9, nozzle diameter 0.5 mm) into the Fabry– Pe´rot cavity. The frequencies were determined after Fourier transformation of the 8 k data points time domain signal, recorded with 100 ns sample intervals. Each rotational transition is split by the Doppler effect, enhanced by 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. The estimated rotational temperature is about 1 K. Direct absorption millimeter wave (mmw) measurements in the 52–74.4 GHz frequency range were made with a Stark modulated free-jet spectrometer [17]. A gas mixture of AA (ca. 3.5%) in argon at room temperature was expanded from a pressure of 2  104 Pa to about 0.05 Pa through a nozzle with a 0.3 mm

Fig. 2. Predicted rotational spectra, with maximum absorption coefficients (a/cm1), of the two conformers of AA at different temperatures.

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diameter, achieving a rotational temperature of about 10 K. The estimated accuracy of frequency measurements is better than 50 kHz, and lines separated by more than 300 kHz are resolvable.

Table 2 Spectroscopic constants (S-reduction, Ir representation) of s-cis and s-trans AA. s-cis A (MHz) B (MHz) C (MHz) DJ (kHz) DJK (kHz) DK (kHz) d1 (kHz) d2 (kHz) Nb rc (kHz)

3. Quantum chemical methods Ab initio and density functional theory (DFT) [18] calculations were performed employing the Gaussian09 suite of programs [19]. Electron correlation was taken into consideration in the ab initio calculations using Møller–Plesset second-order perturbation theory (MP2) [20], and frozen core (fc) approximation. Becke’s three-parameter hybrid functional [21] employing the Lee, Yang, and Parr correlation functional (B3LYP) [22] was employed in the DFT calculations. Peterson and Dunning’s [23] correlation-consistent triple-wave basis set augmented with diffuse functions, augcc-pVTZ, was employed. The default convergence criteria of Gaussian09 were used in the computations and geometry optimizations were always followed by the evaluation of the Hessian matrix in order to test the nature of the found stationary point. The selected MP2 and B3LYP levels of calculation are among the most widely used for the prediction of molecular properties, thus it is of interest to compare the results of the two methods with the corresponding experimental results. The large aug-cc-pVTZ basis set could be used with a standard workstation because of the small dimension of the investigated molecule (9 atoms, 38 electrons). The calculated geometries are given in the electronic supplementary material, whereas the essential spectroscopic parameters are reported in Table 1.

4. Results and discussion 4.1. Rotational spectra Additional measurements with respect to those reported by Bolton et al. [12], were easily performed for the parent species, based on their rotational constants. For the s-cis conformer 11 and 66 new transitions have been measured in the microwave and millimeter wave regions respectively. In the same two regions, for the s-trans, 16 and 67 transitions were detected. The rotational quantum numbers of the measured transitions, given in the elec-

Table 1 Theoretical rotational constants, quartic centrifugal distortion constants, dipole moment components, and deuterium nuclear quadruple coupling constants of the s-cis and s-trans conformers of AA.

A (MHz) B (MHz) C (MHz) DJ (kHz) DJK (kHz) DK (kHz) d1 (kHz) d2 (kHz) la (D) lb (D) vaaa (MHz) vbba (MHz) vcca  vzzb (MHz) vaba (MHz) vxxb (MHz) vyyb (MHz) a

MP2/aug-cc-pVTZ

B3LYP/aug-cc-pVTZ

s-cis

s-trans

s-cis

s-trans

11019.8 4274.5 3079.9 0.655 5.217 4.283 0.226 0.073 0.56 1.37 0.166 0.002 0.164 0.201 0.295 0.134

10749.1 4397.3 3120.7 0.673 5.333 3.973 0.241 0.081 1.74 1.09 0.271 0.106 0.165 0.110 0.296 0.134

11110.4 4245.4 3071.7 0.648 5.240 4.397 0.221 0.071 0.68 1.47 0.172 0.011 0.161 0.194 0.299 0.136

10745.4 4382.1 3112.7 0.676 5.425 3.725 0.242 0.082 1.89 1.20 0.268 0.106 0.162 0.107 0.301 0.136

Principal Inertial Axes System tensor’s nuclear quadrupole coupling elements. Principal electric field gradient Axes System tensor’s nuclear quadrupole coupling elements. b

a b c

11078.8724(17) 4251.9706(5) 3073.3980(5) 0.641(4) 5.19(3) 4.42(7) 0.218(2) 0.072(1) 106 33

s-trans a

10716.2013(13) 4388.3005(5) 3114.3123(5) 0.66(5) 5.46(3) 3.61(8) 0.230(3) 0.088(2) 113 38

Errors in parenthesis are expressed in units of the last digit. Number of fitted lines, including transition frequencies from Ref. [12]. Standard deviation of the fit.

tronic supplementary material, are: 0 6 J 6 11 and 0 6 K1 6 5/7 (s-cis/s-trans). Global fittings of all available data were done with Pickett’s SPFIT program [24], using a semi-rigid rotor Hamiltonian (HR) in the S-reduction and Ir representation [25]. Our data allowed for a considerable improvement of the fittings, and the full sets of quartic centrifugal distortion terms could be determined for both conformers. The obtained parameters are listed in Table 2. Comparing the data in Table 1 and Table 2, one can note that the maximum discrepancy with both sets of calculated values of the rotational constants (Table 1) is less than 1%, in spite of the different meanings of the experimental (r0) and theoretical (re) of the two sets of data. For the remaining physical properties, the two methods provide different accuracies. When comparing the calculated values of the dipole moment components to the experimental ones (lscis ¼ 0:56 ð10Þ, lbscis ¼ 1:35 ð5Þ, ls-trans ¼ 1:70 ð4Þ and a a ls-trans ¼ 1:10 ð5Þ D, [12]), we can see that the ab initio method is b more successful in reproducing them. The difference between the MP2 and B3LYP computed quartic centrifugal distortion constants is below 3% except for the DK values of s-trans (7%). For s-cis the predicted centrifugal distortion constants are closer to the experimental ones than those of s-trans, and a general better performance of B3LYP emerges. The rotational spectra of the three mono-substituted 13C species, observed in natural abundance, have been assigned for both conformers. The transition frequencies (given in the electronic supplementary material) were fitted while keeping the values of the centrifugal distortion constants fixed to those of the corresponding parent species. The obtained values of the rotational constants are listed in Table 3. Additional measurements on the OD enriched deuterated isotopologues were also performed in the microwave band. The deuterium nucleus has a non-zero quadrupole moment, which interacts with the electric field gradient (EFG) created by the rest of molecular charges. This interaction leads to the coupling between the D nuclear spin (I = 1) angular momentum and the overall rotational angular momentum, giving rise to a hyperfine structure observed in the rotational spectrum. For each conformer, eight rotational transitions lines showing a hyperfine structure were observed. All the measured quadrupole coupling hyperfine components were fitted together with the unresolved transition lines reported in Ref. [12] using the semi-rigid rotor Hamiltonian (HR) supplemented with a HQ term to account for the nuclear quadrupole coupling contribution [26]. The Hamiltonian was set up in the coupled basis set I + J = F and diagonalized in blocks of F. The energy levels involved in each transition are thus labeled with the quantum numbers J, K1, K+1, F. All five quartic centrifugal distortion constants and the diagonal components of the deuterium quadrupole coupling tensor in the Principal Inertial Axes System (PAS; a, b, c axes) were determined

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Table 3 Spectroscopic constants (S-reduction, Ir representation) of the 13C isotopologues of scis and s-trans AA. Centrifugal distortion constants have been fixed to the values of the corresponding parent species. 13

a b c

13

C1

C2

13

C3

(1) s-cis A (MHz) B (MHz) C (MHz) Nb rc (kHz)

11078.684(3)a 4113.518(1) 3000.393(1) 9 4

10978.665(3) 4226.0140(7) 3052.1499(9) 9 3

11078.488(3) 4245.6530(7) 3070.0689(9) 9 1

(2) s-trans A (MHz) B (MHz) C (MHz) Nb rc (kHz)

10715.400(3) 4245.731(2) 3041.762(1) 6 2

10615.882 (3) 4360.491(2) 3091.858(1) 8 4

10715.267(3) 4379.112(3) 3109.605(2) 7 2

Errors in parenthesis are expressed in units of the last digit. Number of fitted lines, including transition frequencies from Ref. [12]. Standard deviation of the fit.

for the first time and the rotational constants were improved. The centrifugal distortion constants of the vibrational ground state were used to improve the fit of the first CAC torsion excited state of s-cis and s-trans as described below for the parent species. The results are shown in Table 4. The MP2 and B3LYP computed PAS deuterium nuclear quadrupole coupling tensors are very similar to each other and close to the experimental tensor: the calculated vaa are higher (about 0.03 MHz) than the experimental ones, although they remain within the error, whereas the calculated vbb  vcc values are quite similar to the experimental ones. In order to make comparisons with data on other molecules it is useful to diagonalize the PAS tensor to obtain the Principal Electric Field Gradient Axis System (PEFG; x, y, z axes) tensor. AA being a planar molecule, the z axes is coincident with the c rotational axis and perpendicular to the plane of the molecule, and there is only one non-zero diagonal element (vab). The vab term is related to the relative orientation of the a, b axes with respect the x, y axes by the equation: tan(2h) = 2vab/(vaa  vbb), where h is the rotation angle between the a and the x axis. Although we could not determine the experimental vab value, we know that the vxx component

Table 4 Spectroscopic constants (S-reduction, Ir representation) of the ground state and one skeletal vibrational satellite of the OD isotopologues of s-cis and s-trans AA.

(1) Ground states A (MHz) B (MHz) C (MHz) DJ (kHz) DJK (kHz) d1 (kHz) d2 (kHz) vaa (MHz) vbb  vcc (MHz) Nb rc (kHz)

s-cis

s-trans

11068.1926(29)a 4075.5343(12) 2979.5056(10) 0.60(7) 5.1(3) 0.164(9) 0.077(7) 0.148(6) 0.156(18) 38 39

10242.1235(20) 4307.8658(16) 3033.3858(10) 0.76(7) 5.3(3) 0.26(6) 0.07(3) 0.237(5) 0.051(10) 39 29

(2) v = 1 (skeletal torsion) states A (MHz) 10992.582(9) B (MHz) 4074.064(5) C (MHz) 2986.896(5) Nb 12 rc (kHz) 78

roughly lies along the OD bond, so an estimation value of h corresponds to the angle formed by the OD bond and the a axis. Using the \(OD, a) angles derived from the r0 structure (34° and 13.5° for s-cis and s-trans, respectively) we diagonalized the PAS nuclear quadrupole coupling tensor obtaining the so called bond axis system quadrupole coupling constants reported in Table 5. These values for s-cis and s-trans are very similar to each other, as predicted by theoretical calculations, and to those of formic acid [27]. In the previous paper on AA [12], the rotational spectra of four vibrational excited states relative to the CAC torsion were assigned. In spite of the fact that in the supersonic expansions we could not observe these vibrational satellites, we could improve the corresponding fits introducing the centrifugal distortion constants, fixed to the corresponding ground state values. The new values of the rotational constants are given in Table 6. 4.2. Semi-experimental equilibrium rotational constants By applying perturbation theory to the molecular vibration– rotation Hamiltonian expressed in normal coordinates, the vibrational dependency of the rotational constants A, B, C (Bi) of the vth vibrational state can be expressed by as expansion in powers of (v + ½) [29]: h i Biv ¼ Bie  RQ aiQ ðv Q þ dQ =2Þ  RQ 0 PQ ciQ ðv Q þ dQ =2ÞciQ 0 ðv Q 0 þ dQ 0 =2Þ þ   ð3Þ

where the sums run over all normal modes Q, ‘‘i’’ refers to the principal axis, ‘‘dQ’’ is the degeneracy of the Qth vibrational mode, aiQ and ciQ denote, respectively, the linear and the quadratic vibration–rotation interaction constants corresponding to the Qth mode and the ith inertial axis. Applying the vibrational second-order perturbation theory (VPT2), only the linear term is retained:

Table 5 Experimental deuterium nuclear quadrupole coupling tensor elements in the bond axis system of s-cis and s-trans AA, formic acida and water.b

s-cis s-trans H-COODa D2Ob a b

b c

vzz  vcc (MHz)

0.12 0.11 0.124 0.1333 (1)

0.15 (1) 0.144 (8) 0.148 (2) 0.1748 (2)

Ref. [27]. Ref. [28].

(1) s-cis A (MHz) B (MHz) C (MHz) Nb rc (kHz)

v=1

v=2

v=3

v=4

11007.459(6)a 4249.657(3) 3080.979(3) 19 36

10943.031(6) 4247.460(3) 3087.916(3) 17 57

10883.784(7) 4245.337(3) 3094.425(3) 12 46

10828.646(9) 4243.231(4) 3100.639(4) 10 108

10602.860(9) 4381.613(3) 3129.449(3) 11 50

10552.34(1) 4378.046(4) 3136.381(3) 9 143

10504.1(4) 4374.47(1) 3142.923(9) 4 106

(2) s-trans A (MHz) 10657.462(6) B (MHz) 4385.007(3) C (MHz) 3122.119(3) Nb 13 rc (kHz) 69

10191.2(4) 4303.880(9) 3040.76(1) 5 42

Errors in parenthesis are expressed in units of the last digit. Number of fitted lines, including transition frequencies from Ref. [12]. Standard deviation of the fit.

vyy (MHz)

0.27 0.26 0.272 0.309 (1)

Table 6 Spectroscopic constants (S-reduction, Ir representation) of the vibrational satellites of s-cis and s-trans AA.

a a

vxx (MHz)

b c

Errors in parenthesis are expressed in units of the last digit. Number of fitted lines, including transition frequencies from Ref. [12]. Standard deviation of the fit.

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C. Calabrese et al. / Journal of Molecular Spectroscopy 295 (2014) 37–43 Table 7 Experimental and theoretical (B3LYP/aug-cc-pVTZ) vibration–rotation interaction constants (a, c in MHz) of the low frequency CAC torsional vibration of s-cis and strans AA. Exp.

Exp.

B3LYP

i

ais

cis

rms

a0is

ais

s-cis parent

a b c

75.89 2.35 7.92

2.70 0.04 0.23

0.46 0.02 0.06

71.41 2.31 7.58

70.38 2.68 6.83

s-cis OD

a b c

75.60 1.47 7.39

74.98 1.72 6.68

s-trans parent

a b c

58.74 3.29 7.81

59.04 2.58 7.60

s-trans OD

a b c

50.92 3.99 7.37

50.07 3.77 6.87

61.89 3.20 8.19

1.79 0.05 0.21

0.31 0.02 0.01

Table 8 Semi-empirical equilibrium rotational constants. See Fig. 1 for labeling of the atoms. Parent

13

13

13

OD

(1) s-cis Ae (MHz) Be (MHz) Ce (MHz)

11157.7 4281.7 3094.9

11157.7 4142.0 3021.3

11055.3 4255.6 3073.4

11156.4 4275.0 3091.3

11147.4 4103.4 2999.9

(2) s-trans Ae (MHz) Be (MHz) Ce (MHz)

10819.4 4412.8 3134.9

10818.8 4269.3 3061.7

10716.7 4384.8 3112.1

10817.3 4403.4 3130.0

10333.3 4332.6 3053.2

C1

C2

C3

h i Biv ¼ Bie  RQ aiQ ðv Q þ dQ =2Þ

Table 10 Experimental (rs, r es , r0) and theoretical (aug-cc-pVTZ basis set) bond distances and valence angles of in s-cis and s-trans AA. See Fig. 1 for labeling of the atoms. rs

r es

r0

MP2

B3LYP

s-cis C1AC2 (Å) C2AC3 (Å) C1C2C3 (°) O4AH6 (Å)

1.340 1.454 121.0 –

1.334 1.477 120.2 –

1.340(9) 1.486(2) 119.4(5) 0.957(4)

1.3348 1.4790 120.1 0.9702

1.3277 1.4812 121.0 0.9686

s-trans C1AC2 (Å) C2AC3 (Å) C1C2C3 (°) O4AH6 (Å)

1.339 1.484 122.4 –

1.334 1.472 123.6 –

1.325(8) 1.487(4) 123.5(2) 0.958(7)

1.3359 1.4749 123.6 0.9695

1.3287 1.4770 124.5 0.9677

mitted to calculations. The calculated vibration–rotation interaction constants, obtained only at B3LYP/aug-cc-pVTZ level of theory (the MP2 anharmonic calculations were computationally to expensive to be run on our workstation) are reported in the electronic supplementary material, together with the calculated harmonic and anharmonic fundamental frequencies of s-cis and s-trans with the infrared values measured in argon matrix by Kulbida and coworkers [31], and the values for the lowest normal mode, the CAC torsional motion, obtained from relative intensity rotational spectroscopy measurements [12]. For the lowest vibrational mode, the CAC torsion (s), Bolton et al. observed the vibrational progression up to v = 4 for both conformers, and the first excited state of the acidic deuterated forms [12]. This allows for the determination of the corresponding vibration–rotation interaction constants, that can been used as a check to evaluate the reliability of the theoretical values. We fitted the data of s-cis and s-trans to a simplified quadratic equation:

i

ð4Þ

Then, knowing the aiQ terms, from the experimental ground state rotational constants on AA (dQ = 1 for all normal modes), it is possible to estimate the equilibrium rotational constants as:

Bie ¼ Bi0 þ 1=2RQ aiQ

ð5Þ

where the semi-sum of aiQ represents the first order zero-point vibrational correction. The linear vibration–rotation interaction constants, which require harmonic and cubic force-field computations, were calculated by means of the perturbative approach described by Barone [30] and implemented in the Gaussian code [19]. Special care was taken to ensure that the code uses the PAS coordinates of each studied system. Besides the parent species, all the isotopologues of which the ground-state rotational constants are known were sub-

Biv ¼ k  ais ðv s þ 1=2Þ þ cis ðv s þ 1=2Þ2

ð6Þ

where the cross terms of Eq. (3) have been neglected. The obtained expansion coefficients are reported in Table 7 with the root mean square (rms) residuals and the theoretical values. For the acidic deuterated species, the data allow only for the evaluation of the ais as difference between the first excited state and the ground state. The resulting values are listed in Table 7 as a0s , and have been calculated also for the parent species. The good agreement between the theoretical and the experimental values (vibrational wavenumbers and ais coefficients of the CAC mode torsion) justifies the use of the computed vibration–rotation interaction constants to calculate the zero-point vibrational corrections to the experimental rotational constants obtaining the so called semi-empirical equilibrium constants collected in Table 8.

Table 9 Experimental (rs, r es , r0) and theoretical (aug-cc-pVTZ basis set) PAS coordinates of the three carbon frame and the hydroxyl hydrogen in s-cis and s-trans acrylic acid. See Fig. 1 for labeling of the atoms. rs 1) s-cis

r es

r0

B3LYP

MP2

rs 2) s-trans

r es

r0

B3LYP

MP2

C1

a (Å) b (Å

±2.0106(8) ±0.03(5)

±2.005 ±0.015

2.011 0.019

2.014 0.019

2.008 0.018

±1.9768(8) ±0.06(2)

±1.973 ±0.055

1.972 0.125

1.981 0.058

1.975 0.047

C2

a (Å) b (Å)

±0.857(2) ±0.652(2)

±0.852 ±0.655

0.859 0.992

0.863 0.641

0.854 0.653

±0.859(2) ±0.675(2)

±0.857 ±0.676

0.893 0.645

0.865 0.664

0.854 0.680

C3

a (Å) b (Å)

±0.423(4) ±0.04(4)

±0.432 ±0.075

0.430 0.080

0.431 0.080

0.430 0.080

±0.494(3) ±0.06(2)

±0.497 ±0.097

0.496 0.112

0.499 0.096

0.499 0.093

H6

a (Å) b (Å)

±2.2764(7) ±0.218(7)

±2.272 ±0.212

2.280 0.233

2.285 0.252

2.275 0.227

±1.448(1) ±1.506(1)

±1.437 ±1.511

1.497 1.469

1.462 1.516

1.432 1.521

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4.3. Molecular structure The available rotational constants allow the determination of the Kraitchman’s substitution coordinates [32] of the three carbon atoms and of the hydroxyl hydrogen, given in Table 9. We imposed the constrain of planarity and used Costain’s uncertainties [33]. The C1 and C3 atoms almost lie on the a-principal axis, with very small (<0.1 Å) b-coordinates, which are then affected by large uncertainties. Nevertheless from the substitution coordinates of the three carbon atoms, and choosing the algebraic sign in accord with the theoretical values, we estimated the structure of the carbon’s backbone, reported in Table 10. As proposed by Craig and coworkers for butadiene [34], Kraitchman’s procedure was also applied to the semi-empirical equilibrium rotational constants obtaining the so-called ‘‘rs/re’’ structural parameters. We also give this kind of data in Tables 9 and 10, but use, for sake of simplicity, the symbol res . Adjusted structural parameters (r0) were deduced from the B3LYP ones that were used as initial geometry in a least-squares structural refinement used to reproduce the experimental ground state rotational constants, fifteen for each conformer. Kisiel’s STRFIT program has been used for the fit, and equal weights have been used for all constants [35]. 5. Conclusions The experimental investigation of AA was extended to the 6–18.5 GHz and 52–74.4 GHz ranges. The measurements were conducted in supersonic expansion conditions achieving rotational temperatures comparable with those of the ISM: about 1 and 10 K for the lower and higher frequency experiments, respectively. The global fitting of all available data allowed for the determination of the quartic centrifugal distortion constants, useful to obtain better predictions of the transition lines at higher frequencies. Considering the intensity distribution at higher temperatures, it can be seen that the maximum shifts to higher rotational quantum numbers and higher frequencies but the spreading of the population causes an overall decrease in intensity. It will thus be very important, after having achieved the best possible analysis in the lower frequency region, to move to higher frequencies, which has been already undertaken. The 13C mono-substituted isotopologues species were observed in natural abundance and the spectra were assigned for the first time, allowing for the search in the ISM. Low frequency, high resolved microwave measurements on acidic deuterated AA allowed for the determination of nuclear quadrupole coupling constants. Theoretical and experimental data were used to obtain precise information on the structure of the conformers. Our present data will be helpful for identifying AA by observation in the radiofrequency range using new telescopes such as the ALMA array, since it is quite likely that this species is present with detectable abundances in star-forming regions. This is due to the fact that substances formed on grain surfaces can be desorbed from the grains during the temperature rise encountered during star formations. In other sources like dark clouds such compounds are likely to remain frozen out on the grains. Acknowledgments We thank the Italian MIUR (PRIN Project 2010ERFKXL_001) and the University of Bologna for financial support (RFO). G. F. also thanks the China Scholarships Council (CSC) for financial support. Appendix A. Supplementary material Supplementary data for this article are available on ScienceDirect (www.sciencedirect.com) and as part of the Ohio State

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