Spectroscopic parameters of SiC4

Chemical Physics Letters 501 (2010) 25–29

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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett

Spectroscopic parameters of SiC4 M.L. Senent a,⇑, R. Domínguez-Gómez b a b

Departamento de Química y Física Teóricas, Instituto de Estructura de la Materia, C.S.I.C., Serrano 121, Madrid 28006, Spain Departamento de Ingeniería Civil, Cátedra de Química, E.U.I.T. Obras Públicas, Universidad Politécnica de Madrid, Spain

a r t i c l e

i n f o

Article history: Received 28 August 2010 In final form 28 October 2010 Available online 30 October 2010

a b s t r a c t Structural and anharmonic spectroscopic properties of SiC4 are investigated using the RCCSD(T)-F12 method and second order perturbation theory. Observable parameters are determined for various isotopomers, 28Si12C4, 28Si13CCCC, 28SiC13CCC, 28SiCC 13CC, 28SiCCC 13C and 29SiC4. Fermi interactions are considered in the model. Results are compared with the parameters of C5. For 28Si12C4, the m1 fundamental has been found at 2094 cm1 with RCCSD(T)-F12, close to the observed value 2095.46 cm1. In addition, B0 has been determined to be 1536.29 MHz with RCCSD(T)/CBS, whereas the experimental value is 1533.8 MHz. The CASSCF/aug-cc-pVTZ equilibrium dipole moment was estimated to be 6.2112 Debyes. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction During the following years, the new astrophysical laboratories Herschel and ALMA will produce many unidentified lines, coming out from discovered and still undiscovered species. Their interpretation will require the knowledge of many spectroscopic properties of uncharacterized molecules. This fact has led to many theoretical and experimental studies of a large series of new species giving much attention to the chemistry of silicon [1–3]. Recently, the job of Si in dense molecular cloud reactions has been analyzed by Herbst et al. [1]. McKay and Charnley [2] have performed a detailed study of IRC + 10 216, which they consider the best astronomical source to test theories of the silicon astrochemistry. In the extraterrestrial chemistry, Si plays an important role because it has a significant cosmic abundance and takes part of near a 10% of the detected molecules in astrophysical objects [4]. Many sources, as circumstellar envelops and carbon-rich stars, show rich silicon chemistry in gas phase, although Si is a dustforming element by depletion. Actually, many molecular species as SiO [5], SiS [6], SiN and SiH2 [7], and several silicon bearing molecules as SiC [8], SiC2 [9], SiC4 [10], c-SiC3 [11], SiCN and SiNC [12], are listed as discovered species and many are expected to be discovered. McCarthy et al. [13,14] have outlined a long list of exotic silicon molecules of astronomical and chemical interest suitable to laboratory detection. They have taken into consideration pure silicon–carbon chains or silicon–carbon chains containing H, S and N. At the laboratory level, they have detected l-SiC3, SiC5, SiC6, SiC7, and SiC8 using Fourier transform microwave spectroscopy in a ⇑ Corresponding author. E-mail addresses: [email protected], [email protected] (M.L. Senent). 0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2010.10.061

supersonic molecular beam among the products of a gas discharge through silane and diacetylene. Many silicon–carbide molecules yield to strong electronic transitions of astronomical interest. Their study began in the ‘80s with the identification of the SiC2 radical towards IRC + 10216 [9] who had already been observed in 1926 by Merrill [15] and Sanford [16] in carbon-rich stars. Silicon carbide was found in IRC + 10 216 at fairly low temperatures [8]. The linear-SiC4 was also found in IRC + 10 216 in spite of its abundance, which is 30 times less than the SiC2 one. In their study, McKay and Charnley [2] show that SiC2 must be a parent species and neutral–neutral reactions are necessary to form SiC4. In the present letter, we use state-of-the-art ab initio calculations to determine many spectroscopic properties of linear-SiC4. For this purpose, we use the explicitly correlated method RCCSD(T)-F12A, extremely efficient from the computational point of-view [17,18]. Our work represents a new step of a series of theoretical papers that we have performed on carbon-chains [19–21]; silicon–carbon chains [22–24]; and more recently, on a large series of silicon carbides and hydrogen silicon carbides and their respective anions [24]. In our previous work [24], the equilibrium rotational constant of SiC4 was evaluated to be 1520.6 MHz and the equilibrium dipole moment 6.21 Debyes [24]. We compared these two parameters with the corresponding ones for other SiCn species, and with the B0 experimental rotational constant of 1533.8 MHz [10]. Several other theoretical and experimental studies are available and provide spectroscopic data. For example, the m1 mode fundamental frequency has been determined to be 2080.1 cm1 with FTIR spectroscopy in an Ar matrix [25] and to be 2095.46 cm1 by diode laser spectroscopy in gas phase [26]. Several previous ab initio studies are published [27–30]. Gordon et al. [28] have determined the equilibrium rotational constant Be to be 1522.6 MHz with

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M.L. Senent, R. Domínguez-Gómez / Chemical Physics Letters 501 (2010) 25–29

CCSD(T)/cc-pVTZ. In the most recent study, Sun et al. [30], have performed a detailed search of SiC4 isomers. They found 11 stable structures with MP2/6-311G(d,p) calculations, three linear geometries and 8 cyclic ones. The linear Si–C–C–C–C isomer was found to be extremely stable. With the exception of the cyclic E-isomer, which relative energy was 17.84 kcal/mol, the remaining geometries energies lie above 50 kcal/mol. 2. Computational details The energy and geometry of SiC4 have been calculated with the program suite [31]. Previous CASSCF calculations of SiC4 [24] show the mono-configurationally character of the equilibrium structure wave-function where the Hartree–Fock determinant weight is 0.93. For this reason, extensive treatments of correlation effects were included using RCCSD(T) (restricted coupled cluster theory with a perturbative treatment of triple excitations) [32,33] and the explicitly correlated method RCCSD(T)-F12A [17,18]. Although SiC4 represents a close-shell system suitable for a CCSD treatment, the RCCSD open shell algorithm implemented in MOLPRO has been tested for other carbon chains and is appropriate for further studies of anions and isomerization processes [24]. For the RCCSD(T) method, Dunning’s correlation-consistent basis sets augmented by diffuse functions cc-pVXZ (X = T,Q,5) [34,35] were used. For the explicitly correlated calculations we employed the specially optimized correlation consistent cc-pVTZ-F12 basis sets as atomic orbital set; AVNZ/MP2FIT and VNZ/JKFIT basis sets are used for the DF (density fitting integral evaluation of the F12 integrals) and RI (resolutions of the identity expansions), respectively [36,37]. To acquire reliable rotational constant a core-correlation-consistent basis set, cc-pCVTZ, was also used [38]. Anharmonic spectroscopic parameters for the ground electronic state are determined from a RCCSD(T)-F12 anharmonic force field using second order perturbation theory and our original code FIT-ESPEC [39]. More details about this code can be found in our web site (http://tct1.iem.csic.es). For the determination of the force field, 2517 geometries are used. The Hartree–Fock determinant weight varies slightly for the non-equilibrium geometries employed for the force field determination because structures have been selected close to the minimum. CASSCF theory (complete active space self consistent field) [40,41] is also employed for dipole moment calculations since RCCSD(T) wave method does not satisfy the Hellmann–Feynman theorem in the usual sense. For the CASSCF all the p-valence electrons were correlated. The core-orbitals and the r-valence-orbitals were considered doubly occupied in all the configurations, and they were optimized. MOLPRO

3. Results and discussion 3.1. The rotational constant of l-SiC4 To aid future ALMA astronomical observations or laboratory experiments, very accurate parameters are necessary. Special precision is required for the B0 rotational constant and the equilibrium dipole moment. As we first showed [24], equilibrium dipole moments of CnSi type chains increase with the number of carbon atoms. For SiC4, l has been determined to be 6.211 Debyes with CASSCF/aug-cc-pVTZ, value significantly larger than for l-C3Si (4.4016 Debyes) and for the detected c-C3Si (3.8671 Debyes), but slightly lower than for C5Si (6.4927 Debyes). In Table 1, the geometrical parameters, energies and rotational equilibrium constant calculated with RCCSD(T) and different basis sets, are shown. To increase accuracy, the Be parameter has been refined following the procedure described in Ref. [24]. Thus, the

equilibrium rotational constants obtained with RCCSD(T) and different basis sets cc-pXZ (X = T,Q,5) type, are used to determine the BCBS extrapolated parameter. For the extrapolation, we used e the following equation:

Be ¼ BCBS þ B1e ðY þ 1Þ3 þ B2e ðY þ 1Þ5 þ    e

ð1Þ

where Y = 3,4 and 5 for X = T, and 5. Thus, DBCBS is found to be e 1522.41 MHz. Afterwards, BCBS has been corrected adding up the DBCore coree e core correlation (DBe = Be(cc-pVCTZ, n = 1)  Be(cc-pVTZ, n = 8)). On the other hand, the observable parameter B0 is connected to Be by the equation:

B0 ¼ Be þ DBvib þ DBel

ð2Þ

where DBvib is the vibrational correction calculated (as described below) using an anharmonic force field and second order perturbation theory. DBel, the electronic contribution, is usually negligible (see Ref. [24] and Ref. in.).

Thus; B0 ¼ BCBS þ DBcore þ DBvib e e For SiC4, Bcore = 9.61 MHz, DBvib = 4.27 MHz, and B0 is detere mined to be 1536.29 MHz, close to the experimental value of 1533.8 MHz [10,25]. In Table 1, bond distances and energies are also shown. The RCCSD(T)-F12A/cc-pVTZ-F12 and the RCCSD(T) results obtained with different basis sets, are compared. It is generally accepted that the F12A explicitly correlated correction, recently implemented in MOLPRO, slightly overestimates the correlation effects [29]. For SiC4, the RCCSD(T)-F12 electronic energy is slightly lower than the RCCSD(T)/CBS one. It has to be taken into consideration that this last energy has been calculated using Eq. (1). The capability of both methods RCCSD(T) and RCCSD(T)-F12A for the determination of structural parameters and significant spectroscopic properties (rotational constants), is compared. The very efficient RCCSD(T)-F12 procedure [17,18], recently implemented in MOLPRO [31], provides results as accurate as those of RCCSD(T)/cc-pV5Z, while the computational expenses decreases significantly. 3.2. The infrared spectra of l-SiC4 (X1R+) isotopomers Rovibrational spectroscopic parameters for six isotopic varieties of SiC4, determined with second order perturbation theory and an RCCSD(T)-F12 anharmonic force field, are shown in Tables 2 and 3. In Table 2, the values of the most abundant isotopomer are compared with experimental data and with the corresponding values for the parent C5 pure carbon chain. Thus, the effect of the substitution of a carbon atom by an isovalent silicon atom can be estimated. Calculated spectroscopic properties of C5 are compared with our previous CASPT2 calculations [20] and previous experimental data [42–49]. In Table 3, the parameters of the different isotopomers, 28Si12C4, 28Si13CCCC, 28SiC13CCC, 28SiCC 13CC, 28SiCCC 13C and 29SiC4, are compared. Band center displaced by Fermi interactions are stand up in black. Relative intensities have been calculated with RHF and the standard methods implemented in MOLPRO [31]. The parameters of SiC4 and C5 have been derived from the fulldimensional RCCSD(T)-F12/cc-pVTZ-F12 quadratic, cubic and quartic force fields, containing four-coupling terms. For both species, the force field was determined by fitting 2517 relative energies up to 5000 cm1 to a Taylor series containing 316 basis functions. The analytical form of the potential energy surfaces may be written as:

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M.L. Senent, R. Domínguez-Gómez / Chemical Physics Letters 501 (2010) 25–29

Table 1 Structural parameters (in Å) and equilibrium rotational constants (in MHz) of linear-SiC4 calculated with RCCSD(T) and RCCSD(T)-F12A theory and different basis sets and set of frozen core orbitals.

RCCSD(T)

RCCSD(T)-F12A a b

Basis set

na

Si–C1

C1–C2

C2–C3

C3–C4

E

Be

cc-pVTZ cc-pVQZ cc-pV5Z CBSb aug-cc-pVTZ cc-pCVTZ cc-pVTZ-F12

8 8 8 8 8 1 8

1.7058 1.6991 1.6964

1.2797 1.2767 1.2762

1.3040 1.3021 1.3017

1.2881 1.2843 1.2834

1.7067 1.6972 1.6974

1.2799 1.2766 1.2762

1.3051 1.3016 1.3010

1.2880 1.2845 1.2836

440.944249 440.991643 441.006269 441.017768 440.954715 441.439018 441.023077

1511.90 1520.15 1522.55 1522.41 1510.58 1521.51 1522.31

n = number of frozen core orbitals. CBS = complete basis set (cc-pV1Z).

Table 2 Spectroscopic parametersa of C5 and SiC4 calculated from an anharmonic RCCSD(T)-F12A/cc-pVTZ-F12 force field and second order perturbation theory. C5 Present work

x3 (ru) x1 (rg) x4 (ru) x2 (rg) x6 (pu) x5 (pg) x7 (pu) m3 (ru)

2219 1988 1453 778 540 201 106 2162

m1 (rg) m4 (ru)

1948 1439

m2 (rg)

777

m6 (pu) m5 (pg) m7 (pu)

530 197 106 2537.63 2547.02 0.11 971 2534.00 2537.65 2540.74 2544.28 2556.93 2551.75 2557.50 1.0133 2.2319 4.1193

Be B0 D0 B (m3) B (m1) B (m4) B (m2) B (m6) B (m5) B (m7) |q6| |q5| |q7|

Experimental

2169.44b, 2157.0c 2169.4404d 2169.4410e 1446.6f, 1443.2c 775.8c, 798 ± 45g 535h 216h, 218 ± 13e 102i, 118 ± 13e 2557.63e 0.161e 2545.040e

2.36e 3.99e

SiC4 Present work

Experimental

2210 1962 1433 750 452 221 106 2189

CASPT2 Ref. [20]

x1 (r) x2 (r) x3 (r) x4 (r) x5 (p) x6 (p) x7 (p) m1 (r)

2140 1850 1167 572 532 197 84 m (Ir%) 2094 (100)

2095.46j 2080.1k

1910 1422

m2 (r) m3 (r)

1824 (7) 1167 (2)

817

m4 (r)

574 (1)

447 218 102 2472.3 2485.8 0.118

m5 (p) m6 (p) m7 (p)

526 (0.4) 194 (0.1) 84 (0.0) 1522.31 1526.58 0.0469 1519.68 1521.34 1522.69 1524.94 1528.66 1531.72 1532.44 0.3735 0.8199 0.8720

1.05 3.93

Be B0 D0 B (m1) B (m2) B (m3) B (m4) B (m5) B (m6) B (m7) q5 q6 q7

1533.77j,l] 0.05827l 1526.41j

a

x, m, and a (104) in cm1; Be, B0 and qt in MHz; and D0 in kHz; in frequencies displaced by Fermi interactions, in black; Ir% = Relative infrared intensities.

b

Astrophysical observations [42]. IR (Kr matrix) [43]. Diode laser absorption spectroscopy [44]. Diode laser absorption spectroscopy gas phase [45]. IR (Ar matrix) [46]. Anion photoelectron spectroscopy [47]. Anion photodetachment spectroscopy [48]. FIR astrophysical observation [49]. Infrared diode laser spectroscopy (gas phase) [26]. FTIR (Ar matrix) [25]. Astrophysical observations and microwave spectroscopy [10].

c d e f g h i j k l

Vðq1 ; q2 ; . . . ; qn Þ ¼

n X n n X n X n X X 1 1 fij qi qj þ fijk qi qj qk 2 6 i1 j1 i1 j1 k1

þ

n X n X n X n X 1 fijkl qi qj qk ql ; 24 i1 j1 k1 l1

We used the angle definition for linear molecules of Hoy et al. [50]. The geometries have been selected around the local minima (see Table 1) by taking increments of 0.03A, 3.0° and 5.0° for the

stretching, bending angles and torsional angles. We obtained R2 = 1.0 and r = 0.73 cm1 for SiC4 and R2 = 1.0 and r = 0.88 cm1 for C5. Present parameters may be employed to evaluate the capability of the RCCSD(T)-F12A method for obtaining spectroscopic parameters, since previous experimental and calculated data are available for C5. In general, with few exceptions, anharmonic frequencies, l-doubling constants and rotational constants agree more with the available observed data than previous theoretical

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M.L. Senent, R. Domínguez-Gómez / Chemical Physics Letters 501 (2010) 25–29

Table 3 Spectroscopic parametersa of SiC4 isotopomers calculated from an anharmonic RCCSD(T)-F12A/cc-pVTZ-F12 force field and second order perturbation theory.

x1 (r) x2 (r) x3 (r) x4 (r) x5 (p) x6 (p) x7 (p) m1 (r) m2 (r) m3 (r) m4 (r) m5 (p) m6 (p) m7 (p) Be B0 D0

a1 a2 a3 a4 a5 a6 a7 B (m1) B (m2) B (m3) B (m4) B (m5) B (m6) B (m7) |q6| |q5| |q7|

SiC4

Si13CCCC

SiC13CCC

SiCC13CC

SiCCC13C

29

2140 1850 1167 572 532 197 84 2094 1824 1167 574 526 194 84 1522.31 1526.58 0.0469 2.3005 1.7465 1.2961 0.5463 0.6954 1.7152 1.9568 1519.68 1521.34 1522.69 1524.94 1528.66 1531.72 1532.44 0.3735 0.8199 0.8720

2134 1836 1153 566 532 196 84 2089 1809 1157 569 526 193 83 1475.33 1479.49 0.0437 2.2586 1.6887 1.2400 0.5146 0.6746 1.6812 1.8830 1472.72 1474.42 1475.77 1477.94 1481.51 1484.53 1485.13 0.3510 0.7755 1.1776

2110 1827 1167 568 527 194 84 2066 1802 1164 570 522 191 84 1504.65 1508.78 0.0459 2.3115 1.6330 1.2857 0.5363 0.6869 1.6531 1.9207 1501.85 1503.88 1504.92 1507.17 1510.84 1513.73 1514.53 0.3679 0.8163 1.8305

2105 1840 1156 571 519 197 84 2062 1813 1157 570 514 194 83 1520.20 1524.46 0.0468 2.1965 1.7998 1.2662 0.5467 0.6798 0.7129 1.9324 1517.46 1519.06 1520.66 1522.82 1526.49 1529.59 1530.25 0.3817 0.8183 1.8815

2130 1824 1150 572 528 195 83 2086 1798 1141 573 523 192 83 1520.71 1524.85 0.0467 2.2536 1.7256 1.2865 0.5442 0.6870 1.6767 1.9216 1518.10 1519.68 1521.00 1523.22 1526.91 1529.88 1530.61 0.3751 0.8288 1.8940

2140 1850 1165 566 532 197 84 2094 1823 1164 569 526 194 84 1498.93 1503.14 0.0456 2.2594 1.7176 1.2742 0.5369 0.6833 1.6856 1.9278 1496.37 1497.99 1499.32 1501.53 1505.19 1508.19 1508.92 0.3622 0.7952 1.8205

Si CCCC

a x, m, and a (104) in cm1; Be, B0 and qt in MHz; and D0 in kHz; in frequencies displaced by Fermi interactions, in black.

works see Ref. [20] and references in it. For example, the m4 IR active fundamental transition, determined at 1422 cm1 with CASPT2 and observed between 1443.2 and 1446 cm1 [44,41], is now determined to lie at 1439 cm1. This very intense band [20] represents an important tool for the astronomical detection of the molecule [20]. The band centre was also calculated using a CEPA scaling force field at 1478 cm1 [20 and ref. in.]. Another IR active stretching m1, now at 2162 cm1, was calculated at 2189 cm1 with CASPT2 whereas it has been observed 2169 cm1 [40,42,43]. However, with respect to the three bending modes (m5 = 197; m6 = 530; m7 = 106 cm1 with RCCSD(T)-F12A), it is difficult to assert what of the theoretical methods is the most accurate because the experimental data derived from different experimental techniques, are divergent. In addition, the effect of the force field four-coupling terms is important and very sensitive to the linear fit of the surface. The m7 mode, that plays an important role for the astrophysical detection by FIR techniques, has been determined to be x7 = 106 cm1 and m7 = 106 cm1 with RCCSD(T)-F12, and to be x7 = 106 cm1 and m7 = 102 cm1 with CASPT2 [20]. The very small CASPT2 anharmonic corrections, which shift the band 4 cm1, are now much smaller. Few experiments are available for SiC4. Only the most abundant isotopomer has been object of many of the previous studies. For other isotopes, Gordon et al. [29] have performed ab initio calculations using a cubic force field. Laboratory microwave experiments and astronomical observations supply rotational constants (B0 = 1533.77 MHz and D0 = 0.05827 kHz [10]), although, to our knowledge, only the most intense IR active mode m1 has been measured. In Argon matrix, the fundamental m1, has been observed at

2080.1 cm1 [25], whereas, in gas phase, the band lies at 2095.46 cm1 [26]. Our calculations provide a very accurate bend center at 2094 cm1, that allows us to be confident with our results. Low frequencies are obtained to lie at 526 cm1 (CCC bending), 194 cm1 (CCC bending) and 84 cm1 (CCSi bending). These modes, all of them IR active, can be considered for detection by FIR techniques although their relative intensities with respect to the stretching modes are not significant. As was observed for C5, anharmonic effects on them are very small. As was expected, large differences between the SiC4 and C5 correspond to the vibrational modes whose silicon atom coordinate weights are more important (m4 (C–Si stretching), m4 (C–Si stretching), and m7 (CCSi bending). Table 2 show the Be equilibrium rotational constant (1522.31 MHz) and the B0 rotational constant (1526.58 MHz) of SiC4. DBvib (see Eq. (2)) is the difference between both parameters. Finally, Table 3 displays the anharmonic spectroscopic parameters for various isotopomers (28Si13CCCC, 28SiC13CCC, 28SiCC 13CC, 28 SiCCC 13C and 29SiC4). They are compared with the corresponding properties of the most abundant one, 28Si12C4. Our harmonic frequency shifts compare well with the previous results of Ref. [29] performed using a CCSD(T) cubic force field. All these species contain 13C or 29Si, which are isotopes relatively abundant in astrophysical sources. As can be expected, large isotopic shifts are connected to the stretching modes, whereas the very large amplitude bending modes keep up invariable. For rotational constants and l-doubling constants, large changes take place if the atoms connected by the Si–C bond are isotopically substituted. Otherwise, isotopic substitution effects are lower than vibrational effects for rotational constants. 4. Conclusions In this Letter, spectroscopic parameters of linear-SiC4 and five isotopomers containing 13C and 29Si are derived from highly correlated ab initio methods. With RCCSD(T) theory and a complete basis set, B0 is determined to be 1536.29 MHz, close to the experimental value of 1533.8 MHz. Anharmonic spectroscopic parameters (frequencies, rotational and centrifugal distortion constants, l-doubling constants) are obtained from a RCCSD(T)-F12/cc-pVTZ-F12 force field containing four-coupling terms. The very efficient RCCSD(T)-F12 provides results as accurate as those of RCCSD(T)/cc-pV5Z, while the computational expenses decrease significantly. Results for the different isotopomers are compared. They are also compared with the parameters for the C5 isovalent species obtained at the same level of theory. Although, there is not many available experimental data for SiC4, we are confident in our frequencies since the m1 stretching has been determined to lie at 2094 cm1, whereas it has been observed at 2095.46 cm1 with IR diode laser spectroscopy. Low frequencies are obtained to lie at 526, 194 and 84 cm1. Acknowledgments The authors acknowledge the Ministerio de Ciencia e Innovación of SPAIN for the grants AYA2008-00446 and AYA2009-05801-E/ AYA and to CESGA for computing facilities. References [1] E. Herbst, T.J. Millar, S. Wlodeck, D-K-. Bohme, Astron. Astrophys. 222 (1989) 205. [2] D.D.S. McKay, S.B. Charnley, Mon. Not. R. Astron. Soc. 793 (1999) 302. [3] C.M. Walmley, G. Pineau des Forêts, D.R. Flower, Astron. Astrophys. 342 (1999) 542. [4] L. Colangeli et al., Astron. Astrophys. Rev 11 (2003) 97.

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