New Astronomy 16 (2011) 152–156

Contents lists available at ScienceDirect

New Astronomy

journal homepage: www.elsevier .com/locate /newast

Suggestion for the search of H2CC in cool cosmic objects

Suresh Chandra ⇑, Amit Kumar, B.K. Kumthekar, M.K. SharmaSchool of Physics, Shri Mata Vaishno Devi University, Katra 182 320 (J&K), India

a r t i c l e i n f o

Article history:Received 9 April 2010Received in revised form 18 July 2010Accepted 19 July 2010Available online 7 September 2010

Communicated by G. Brunetti

Keyword:ISM: molecules

1384-1076/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.newast.2010.07.004

⇑ Corresponding author. Present Address: Departmof Sciences, Lovely Professional University, Phagwa9915519345; fax: +91 1824 506111.

E-mail address: suresh492000@yahoo.co.in (S. Cha

a b s t r a c t

The transition 111 � 110 at 4.829 GHz of formaldehyde (H2CO) was the first one showing the anomalousabsorption, i.e., the absorption against the cosmic microwave background. Anomalous absorption is anunusual phenomena. Structure of H2CC is very similar to that of H2CO and H2CS. Both H2CO and H2CShave already been identified in a number of cosmic objects. Though H2CC is not yet identified in the cos-mic objects, we propose that H2CC may be identified in cool cosmic objects through its transition111 � 110 at 4.85 GHz in anomalous absorption.

� 2010 Elsevier B.V. All rights reserved.

1. Introduction with the help of the theoretical laboratories, such as GAUSSIAN,

Out of more than 170 molecules identified in cosmic objects, theconstituent atoms in a large number of them are H, C and O. The rea-son for this finding is the large cosmic abundances of these atoms incomparison to others. H2O and H2CO molecules have already beenidentified in a large number of cosmic objects. Though the moleculeH2CC is not yet identified in any cosmic object, H2CS has been iden-tified in some cosmic objects. The formation of H2CC is quiteprobable as the abundance of C is larger than that of S. Snyderet al. (1969) detected H2CO through its transition 110 � 111 at4.829 GHz in absorption in a number of galactic and extragalacticsources. This transition of H2CO was found in anomalous absorptionby Palmer et al. (1969) in the direction of four dark nebulae. In someobjects, this transition has however been detected in emission andeven as a maser line (Forster et al., 1980; Whiteoak and Gardner,1983). Observation of absorption against the cosmic microwavebackground (CMB) is an unusual phenomenon. Since the structureof H2CC is very similar to that of the H2CO and H2CS, in the presentinvestigation, we attempted to look into the physical conditions un-der which the transition 111 � 110 at 4.85 GHz of H2CC may be iden-tified through anomalous absorption. This transition may help inidentification of H2CC in cool cosmic objects.

2. H2CC

For the study of H2CC, we could not find any laboratory infor-mation about it. In absence of that, the study is nowadays possible

ll rights reserved.

ent of Physics, Lovely Schoolra 144 402, India. Tel.: +91

ndra).

NWCHEM. Here, we used the software GAUSSIAN 09 to optimizethe geometry of H2CC and to calculate the rotational and distor-tional constants by employing the functional B3LYP, i.e., Becke’sthree parameter exchange function B3 (Becke, 1993) with Lee, Yangand Parr’s gradient corrected exchange–correlation functional (Leeet al., 1988). This B3LYP method is used in conjunction with a cc-pVTZ basis set (Dunning, 1989; Kendall et al., 1992). The H2CC isa-type asymmetric top molecule having an electric dipole moment2.4348 Debye along the axis of the lowest moment of inertia. Thecalculated coordinates of the atoms in H2CC are given in Table 1whereas the rotational and distortional constants are given inTable 2 (column 4). In order to have knowledge about the reliabil-ity of rotational and distortional constants, in Table 2, we have gi-ven the value of rotational and distortional constants for H2CS: (i)which are derived from the laboratory spectrum (column 2) and(ii) which are obtained by using GAUSSIAN 09 where the B3LYPmethod and cc-pVTZ basis set are used (column 3). The results ob-tained for H2CS (column 3) are within accuracy of 1.4% for rota-tional constants and within few percent for the distortionalconstants as compared to those in column 2. The idea of results gi-ven in column 2 and 3 is to support that the results obtained fromthe GAUSSIAN software can be used (within some uncertainty) aslong as laboratory results are not available.

2.1. Energy levels and Einstein A-coefficients

In the present investigation, we want to address the cool cosmicobjects having kinetic temperature of few tens of Kelvin. Therefore,we are concerned with the rotational transitions in the groundvibrational and ground electronic states. Owing to the paralleland anti-parallel orientations of nuclear spins of two hydrogen

Table 1Coordinates of atoms in H2CC.

Atom x y z

C 0.0 0.0 0.816338C 0.0 0.0 �0.474652H 0.0 0.936624 �1.025058H 0.0 �0.936624 �1.025058

Table 2Rotational and distortional constants in MHz.

Const. H2CSa H2CSb H2CCb

A 2.916133419858d + 5 2.9559683148d + 5 2.8580634976d + 5B 1.76989948807d + 4 1.771445849d + 4 3.990061727d + 4C 1.66524986641d + 4 1.671384778d + 4 3.504935174d + 4DJ 0.190210847d � 1 0.1832099422d � 1 0.4303470129d � 1DJK 0.522283353d0 0.5161191998d0 0.2086942052d + 2DK 0.23344325d + 2 0.2273818986d + 2 0.5404296022d + 1d1 �0.12084913d � 2 �0.1105639313d � 2 �0.1442206965d � 1d2 �0.17734329d � 3 �0.1468658177d � 3 �0.2660566387d � 1HJ �3.3329d � 9HJK 1.487734d � 6HkJ �2.8222103d � 5HK 5.95849d � 3h1 3.085179d � 9h2 1.65623d � 9h3 0.32731d � 9LJK 0.19622d � 9LKKJ �2.07881d � 8LK �2.1726d � 6l1 �0.37662d � 12

a Maeda et al. (2008)b Gaussian 09.

S. Chandra et al. / New Astronomy 16 (2011) 152–156 153

atoms in the molecule, the H2CC can have two species, known asthe ortho (I = 1) and para (I = 0). These two species behave as ifthey are two distinct molecules and there are no transitions be-tween them. The energy levels and Einstein A-coefficient are calcu-lated following the method discussed by Chandra et al. (2010).Using the rotational and distortional constants (Table 2), we ob-tained rotational energy levels and the lowest 25 of them, ac-counted for in the present investigation, are given in Table 3.These levels are connected by 33 radiative transitions for whichthe Einstein A-coefficients and l2S(2I + 1) are given in Table 4.Here, I = 1 for the nuclear spin of ortho specie.

In order to check about the reliability of rotational and distor-tional constants, we have given in Table 2 the value of rotationaland distortional constants for H2CS: (i) which are derived fromthe laboratory spectrum (column 1) and (ii) which are obtainedby using GAUSSIAN 09 where the B3LYP method and cc-pVTZ basisset are used (column 2). These parameters also are used separately

Table 3Energy of rotational levels in ortho-H2CC.a

Level E (MHz) Level E (MHz) Level E (MHz)

11,1 320808.444 51,4 1407775.096 43,2 2980455.25511,0 325659.594 61,6 1769366.248 43,1 2980459.49721,2 465772.723 61,5 1871140.921 53,3 3353543.90321,1 480325.481 71,7 2275805.927 53,2 3353560.88931,3 683173.261 71,6 2411423.190 91,9 3504584.30031,2 712276.095 33,1 2682028.424 91,8 3722094.34341,4 972955.755 33,0 2682029.029 63,4 3801327.98141,3 1021452.631 81,8 2854253.778 63,3 3801379.00251,5 1335049.059

a Molecular constants used are obtained from Gaussian 09.

for calculating the values of rotational energy levels and radiativetransition probabilities between the levels.

We calculated the Einstein A-coefficient for these two sets forrotational and distortional constants of H2CS and found that thevalues of Einstein A-coefficients for these two sets are within 10percent, which is not very large. This test provides a confidencethat the Einstein A-coefficient for H2CC may be considered reliablewithin an accuracy of 10 percent.

3. Basic formulation

In our investigation, we solved a set of statistical equilibriumequations coupled with equations of radiative transfer, as dis-cussed by Chandra et al. (2010) for H2CS. This set of equations issolved through iterative procedure for the free parameters molec-ular hydrogen density nH2 , and c � nmol/(dvr/dr), where nmol is den-sity of the molecule and (d vr/dr) velocity-gradient.

3.1. Collisional rates

In the present investigation, besides the radiative transitionprobabilities, the collisional rate coefficients are required as inputparameters. Though the collisional transitions are not restrictedthrough any selection rules, computation of them is a quite cum-bersome task. Collisional rate coefficients for the rotational transi-tion Js ? J0s0 at the kinetic temperature T, averaged over theMaxwellian distribution is (Chandra and Kegel, 2000)

CðJs! J0s0jTÞ ¼ 8kTpl

� �1=2 1kT

� �2 Z 1

0rðJs! J0s0jEÞ E e�E=kT dE

where the cross section r(Js ? J0s0jE) for the transition is

rðJs! J0s0jEÞ ¼ ð2J0 þ 1ÞXLMM0

SðJ; s; J0; s0jL;M;M0Þ qðL;M;M0jEÞ

Here, the sum is finite, limited by triangle inequalities on J, J0 and Land each of the M and M0 can independently assume the valuesranging from �L to +L. q(L,M,M0jE) are the parameters obtainedfrom the MOLSCAT (Hutson and Green, 1995). The spectroscopiccoefficients, S(J,s, J0,s0jL,M,M0), depend on the wave-functions ofthe molecules and on the angular momentum coupling factors:

SðJ; s; J0; s0jL;M;M0Þ

¼X

p;p0 ;q;q0gp

Js gqJs gp0

J0s0 gq0

J0s0 ð�1Þp0þq0 J L J0

�p M p0

� �� J L J0

�q M q0

� �

These spectroscopic coefficients, S(J,s, J0,s0jL,M,M0) are obviouslyindependent of collision dynamics. Thus, the collisional rate coeffi-cient is

CðJs! J0s0jTÞ ¼ ð2J0 þ 1ÞXLMM0

SðJ; s; J0; s0; jL;M;M0Þ QðL;M;M0jTÞ

where

QðL;M;M0jTÞ ¼ 8kTk

pl

� �1=2 1kTk

� �2 Z 1

0qðL;M;M0jEÞ E e�E=kT dE

Now, owing to symmetries of gKJs; SðL;M;M0Þ ¼ SðL;M0MÞ; so that

only the real part of Q(L,M,M0) is required, and the cross sectionsare real. Work in this direction is in progress.

Since, these required collisional rates are not available in the lit-erature, in absence of collisional rates, qualitative investigation canbe carried out by choosing some scaling laws, which do not favourany anomalous behaviour from their own. In the present investiga-tion, the rate coefficients for downward transitions J0k0ak0c

! Jkakcat a

kinetic temperature Tk are taken as (Chandra et al., 2007)

Table 4Einstein A-coefficients and l2S(2I + 1) for transitions.a

Transition A-coeff (s�1) 3l2S (D2) Transition A-coeff (s�1) 3l2S (D2)

11,0 ? 11,1 4.037E-09 27.3 21,2 ? 11,1 6.463E-05 27.321,1 ? 11,0 7.849E-05 27.3 21,1 ? 21,2 3.632E-08 15.231,3 ? 21,2 2.768E-04 48.6 31,2 ? 21,1 3.362E-04 48.631,2 ? 31,3 1.453E-07 10.6 33,0 ? 33,1 1.177E-20 95.741,4 ? 31,3 7.169E-04 68.3 43,2 ? 33,1 3.654E-04 31.941,3 ? 31,2 8.707E-04 68.3 43,1 ? 33,0 3.655E-04 31.941,3 ? 41,4 4.034E-07 8.2 43,1 ? 43,2 2.428E-18 73.851,5 ? 41,4 1.465E-03 87.5 53,3 ? 43,2 1.068E-03 58.351,4 ? 41,3 1.779E-03 87.5 53,2 ? 43,1 1.068E-03 58.351,4 ? 51,5 9.076E-07 6.7 53,2 ? 53,3 1.039E-16 60.161,6 ? 51,5 2.599E-03 106.3 63,4 ? 53,3 2.198E-03 82.061,5 ? 51,4 3.156E-03 106.3 61,5 ? 61,6 1.779E-06 5.771,7 ? 61,6 4.198E-03 125.0 71,6 ? 61,5 5.097E-03 124.971,6 ? 71,7 3.162E-06 4.9 81,8 ? 71,7 6.339E-03 143.581,7 ? 71,6 7.694E-03 143.5 81,7 ? 81,8 5.229E-06 4.391,9 ? 81,8 9.096E-03 162.0 91,8 ? 81,7 1.104E-02 161.991,8 ? 91,9 8.175E-06 3.9

a Molecular constants used are obtained from Gaussian 09.

154 S. Chandra et al. / New Astronomy 16 (2011) 152–156

C J0k0ak0c! Jkakc

� �¼ 1� 10�11ð2J þ 1Þ

ffiffiffiffiffiffiTk

30

rð1Þ

This relation for collisional rate coefficients can be interpreted asthe cross-section times the thermal velocity. This empirical formulafor calculating collisional rates is quite common (Sharma and Chan-dra, 2001; Chandra and Shinde, 2004; Chandra et al., 2005; Chandraand Shinde, 2008). We, therefore, use this formulation in the pres-ent work as well. Moreover, these rates have no selectivity and donot support any anomalous behaviour from their own. For upwardcollisional rate coefficients, we accounted for the fact that thedownward and upward collisional rate coefficients are relatedthrough the detailed equilibrium (Chandra and Kegel, 2000).

3.2. Anomalous absorption

For anomalous absorption, the excitation temperature Tex,brightness temperature TB and the background temperature Tbg

satisfy the condition 0 < Tex < TB < Tbg (Chandra et al., 2007, 2010).Here, the CMB temperature is 2.73 K. We found that for anomalousabsorption for the transition 111 � 110, we should have C(111 ?211) < C(110 ? 212) (Chandra et al., 2010). This shows that the tran-sition between the levels 111 and 110 would show absorptionagainst the CMB provided C(111 ? 211) < C(110 ? 212). Since Eq.(1) gives C(111 ? 211) = C(110 ? 212), we have to modify eitherC(111 ? 211), C(110 ? 212) or both of them in order to get anoma-lous absorption.

4. Results and discussion

In the present investigation, a set of 25 linear equations cou-pled with 33 equations of radiative transfer is solved throughthe iterative procedure for the given values of nH2 and c. In orderto include a large number of cosmic objects where H2CC may befound, numerical calculations are carried out for the wide rangesof physical parameters. In the present investigation, we have ta-ken c = 10�6 cm�3 (km/s)�1 pc and 10�5 cm�3 (km/s)�1 pc. Themolecular hydrogen density nH2 is varied over the range from103 to 107 cm�3, and calculations are made for the kinetic tem-peratures 10, 20, 30 and 40 K, as the temperature in a cool cosmicobject would be around that.

The collisional rates obtained from Eq. (1) give C(111 ? 211) =C(110 ? 212). Hence, the required condition C(111 ? 211) <C(110 ? 212) is not produced. This condition can be produced eitherby increasing the collision rates between the levels 110 and 212 by

some positive factor greater than 1 or by reducing the collisionrates between the levels 111 and 211 by a positive factor greaterthan 1 or by doing both.

(i) We increased the collisional rates for the transitionsbetween the levels 110 and 212 by a factor of 2 and the resultgiven in Fig. 1 are the brightness temperature TB (K) (column1), as a function of hydrogen density nH2 for kinetic temper-atures of 10, 20, 30 and 40 K for the transition 110 � 111 ofH2CC. Solid line is for c = 10�5 cm�3 (km/s)�1 pc and the dot-ted line for c = 10�6 cm�3 (km/s)�1 pc. Keeping in view theaccuracy of collisional rates available for some molecules,the factor of 2 is not very large. In order to investigate sen-sitivity of our results to the collisional rates, we enhancedthe collisional rates for the transitions with Dka = 0 by a fac-tor of 10, which may be taken as an extreme case (Chandraand Shinde, 2004). The absorption feature of the line isfound to remain unaffected. However, the position of theminimum value of TB is found to shift towards the low den-sity region. With enhanced collisional rates the results forthe brightness temperature TB (K) are shown in column 2of Fig. 1.

(ii) When, we reduced the collisional rates for the transitionsbetween the levels 111 and 211 by a factor of 2, the resultsgiven in Fig. 2 are the brightness temperature TB (K) (column1), as a function of hydrogen density nH2 for kinetic temper-atures of 10, 20, 30 and 40 K for the transition 110 � 111 ofH2CC. Solid line is for c = 10�5 cm�3 (km/s)�1 pc and the dot-ted line for c = 10�6 cm�3 (km/s)�1 pc. In order to investigatesensitivity of our results to the collisional rates, here also weenhanced the collisional rates for the transitions withDka = 0 by a factor of 10. The absorption feature of the lineis found to remain unaffected. However, the position of theminimum value of TB is found to shift towards the low den-sity region. The results for the brightness temperature TB (K)are shown in column 2 of Fig. 2.

Figs. 1 and 2 shows qualitatively that the transition 111 � 110

may show anomalous absorption. However, for the quantitative re-sults, we have to go for the calculations for collisional rates.

4.1. Density dependence

Variation of brightness temperature TB (K) with the molecularhydrogen density nH2 shows that the maximum anomalous absorp-

1.5

2.0

2.5

3.0

3.5

T=

10K

3 4 5 6 7

log(nH2/cm

-3)

1.5

2.0

2.5

3.0

3.5

3 4 5 6 7

log(nH2/cm

-3)

1.5

2.0

2.5

3.0

3.5

3 4 5 6 7

log(nH2/cm

-3)

1.5

2.0

2.5

3.0

3.5

3 4 5 6 7

log(nH2/cm

-3)

1.5

2.0

2.5

3.0

3.5

T=

20K

3 4 5 6 71.5

2.0

2.5

3.0

3.5

3 4 5 6 71.5

2.0

2.5

3.0

3.5

3 4 5 6 71.5

2.0

2.5

3.0

3.5

3 4 5 6 7

1.5

2.0

2.5

3.0

3.5

T=

30K

3 4 5 6 71.5

2.0

2.5

3.0

3.5

3 4 5 6 71.5

2.0

2.5

3.0

3.5

3 4 5 6 71.5

2.0

2.5

3.0

3.5

3 4 5 6 7

1.5

2.0

2.5

3.0

3.5

T=

40K

3 4 5 6 71.5

2.0

2.5

3.0

3.5

3 4 5 6 71.5

2.0

2.5

3.0

3.5

3 4 5 6 71.5

2.0

2.5

3.0

3.5

3 4 5 6 7

TB TB TB TB

Fig. 1. Variation of brightness temperature TB (K) (column 1), versus hydrogen density nH2 for kinetic temperatures of 10, 20, 30 and 40 K for the transition 110 � 111 of H2CC.Solid line is for c = 10�5 cm�3 (km/s)�1 pc, and the dotted line for c = 10�6 cm�3 (km/s)�1 pc. For these results, given here, the collisional rates between the levels 110 and 212

are increased by a factor of 2. The brightness temperature TB (K) (column 2) is when the rates for the transitions with Dka = 0 are enhanced by a factor of 10. Column 3 givesthe brightness temperature of the transition 110 � 111 of H2CO where rotational and distortional constants of Brünken et al. (2003) are used. The brightness temperature incolumn 4 is for the transition 110 � 111 of H2CS where the rotational and distortional constants of Maeda et al. (2008) are used.

S. Chandra et al. / New Astronomy 16 (2011) 152–156 155

tion occurs around a density of 104.5 cm�3. For the higher densitiesthe brightness temperature TB (K) increases and goes to a valuehigher than the background temperature (2.73 K) and then satu-rates to the value of the background temperature. In the lowdensity region also the brightness temperature TB (K) tends tothe background temperature.

4.2. Temperature dependence

Figs. 1 and 2 show that the maximum anomalous absorption isat the kinetic temperature of 10 K. The anomalous absorption de-creases as the kinetic temperature in the cosmic object increases.

4.3. Comparison with H2CO and H2CS

In order to support our investigation, we performed the calcula-tions for H2CO and H2CS molecules where the molecular and dis-tortional constants are taken from Brünken et al. (2003) andMaeda et al. (2008), respectively. Though the collisional rates for

H2CO are given by Green et al. (1978), but for H2CO also we usedthe scaled values given by Eq. (1) and considered the similar mod-ifications for collisional rates. Collisional rates for H2CS are notavailable and for that also the rates are calculated with the helpof Eq. (1) along with the modifications. The brightness temperatureTB for the transition 111 � 110 of H2CO and H2CS are given in col-umn 3 and column 4, respectively, in Figs. 1 and 2. Figs. 1 and 2show that the results in columns 1, 3 and 4 are almost similar innature. It gives an impression that H2CC may be identifiedin cool cosmic objects through its transition 111 � 110 in anomalousabsorption. Moreover, the anomalous absorption for H2CC isfound to be larger than that for H2CO. It is much larger than thatof H2CS.

Since we have used the scaled values of collisional rates forH2CC, and therefore, our results are qualitative in nature. We foundthat the 111 � 110 may show anomalous absorption around thedensity of 104.5 cm�3. This transition may help in identificationof the molecule in cool cosmic objects, because the kinetic temper-ature may not be sufficient for generating the emission spectrum.

1.5

2.0

2.5

3.0

3.5

T=

10K

3 4 5 6 7

log(nH2/cm

-3)

1.5

2.0

2.5

3.0

3.5

3 4 5 6 7

log(nH2/cm

-3)

1.5

2.0

2.5

3.0

3.5

3 4 5 6 7

log(nH2/cm

-3)

1.5

2.0

2.5

3.0

3.5

3 4 5 6 7

log(nH2/cm

-3)

1.5

2.0

2.5

3.0

3.5

T=

20K

3 4 5 6 71.5

2.0

2.5

3.0

3.5

3 4 5 6 71.5

2.0

2.5

3.0

3.5

3 4 5 6 71.5

2.0

2.5

3.0

3.5

3 4 5 6 7

1.5

2.0

2.5

3.0

3.5

T=

30K

3 4 5 6 71.5

2.0

2.5

3.0

3.5

3 4 5 6 71.5

2.0

2.5

3.0

3.5

3 4 5 6 71.5

2.0

2.5

3.0

3.5

3 4 5 6 7

1.5

2.0

2.5

3.0

3.5

T=

40K

3 4 5 6 71.5

2.0

2.5

3.0

3.5

3 4 5 6 71.5

2.0

2.5

3.0

3.5

3 4 5 6 71.5

2.0

2.5

3.0

3.5

3 4 5 6 7

TB TB TB TB

Fig. 2. Variation of brightness temperature TB (K) (column 1), versus hydrogen density nH2 for kinetic temperatures of 10, 20, 30 and 40 K for the transition 110 � 111 of H2CC.Solid line is for c = 10�5 cm�3 (km/s)�1 pc, and the dotted line for c = 10�6 cm�3 (km/s)�1 pc. For these results, given here, the collisional rates between the levels 111 and 211

are reduced by a factor of 2. The brightness temperature TB (K) (column 2) is when the rates, for the transitions with Dka = 0 are enhanced by a factor of 10. Column 3 gives thebrightness temperature of the transition 110 � 111 of H2CO where rotational distortional constants of Brünken et al. (2003) are used. The brightness temperature in column 4is for the transition 110 � 111 of H2CS where the rotational and distortional constants of Maeda et al. (2008) are used.

156 S. Chandra et al. / New Astronomy 16 (2011) 152–156

But the anomalous absorption may be observed as the ground stateis always populated.

Our next attempt is to calculate collisional rates so that the re-sults could be improved.

Acknowledgments

Part of this work was done during the visit to IUCAA, Pune.Financial supports from IUCAA, Pune and from the SMVD Univer-sity, Katra (J&K) are thankfully acknowledged. Thanks are due toDr. A.S. Chaudhari, Nanded for providing GAUSSIAN 09 results gi-ven in Table 2.

References

Brünken, S., Müller, H.S.P., Lewen, F., Winnewisser, G., 2003. Phys. Chem. Chem.Phys. 5, 1515.

Becke, A.D., 1993. J. Chem. Phys. 98, 5648.Chandra, S., Kumar, Amit, Sharma, M.K., 2010. New Astron. 15, 318.Chandra, S., Kegel, W.H., 2000. A& AS 142, 113.Chandra, S., Musrif, P.G., Shinde, S.V., Shinde, S.A., 2005. New Astron. 11, 166C.Chandra, S., Shinde, S.A., 2004. A& A 423, 325.Chandra, S., Shinde, S.V., 2008. BASI 36, 55C.Chandra, S., Shinde, S.V., Kegel, W.H., Sedlmayr, E., 2007. A& A 467, 371.Dunning, T.H., 1989. J. Chem. Phys. 90, 1007.Forster, J.R., Goss, W.M., Wilson, T.L., Downes, D., Dickel, H.R., 1980. A& A 84, L1.Green, S., Garrison, B.J., Lester Jr., W.A., Miller, W.H., 1978. ApJS 37, 321.Hutson, J.M., Green, S., 1995. MOLSCAT Version 14 distributed by Collaborative

Computational Project 6, Daresbury Laboratory: U.K. Engineering and PhysicalSciences Research Council.

Kendall, R.A., Dunning, T.H., Harrison, R.J., 1992. J. Chem. Phys. 96, 6796.Lee, C., Yang, W., Parr, R.G., 1988. Phys. Rev. B37, 785.Maeda, A., Medvedev, I.R., Winnewisser, M., De Lucia, F.C., Herbst, E., Müller, H.S.P.,

Koerber, M., Endres, C.P., Schlemmer, S., 2008. ApJS 176, 543.Palmer, P., Zuckerman, B., Bhul, D., Snyder, L.E., 1969. ApJ 156, L147.Sharma, A.K., Chandra, S., 2001. A & A 376, 333.Snyder, L.E., Bhul, D., Zuckerman, B., Palmer, P., 1969. Phys. Rev. Lett. 22, 679.Whiteoak, J.B., Gardner, F.F., 1983. MNRS 205, 27.