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The reaction of polycyclic aromatic hydrocarbon anions with hydrogen
Chemical Physics 274 (2001) 11±14 www.elsevier.com/locate/chemphys
The reaction of polycyclic aromatic hydrocarbon anions with hydrogen C.W. Bauschlicher Jr. a,*, E.L.O. Bakes b a
Space Technology Division, NASA Ames Research Center, Mail Stop 230-3, Moett Field, CA 94035-1000, USA b SETI, NASA Ames Research Center, Mail Stop 245-3, Moett Field, CA 94035-1000, USA Received 6 August 2001
Abstract The reaction of naphthalene anion with an H atom to produce 1-hydronaphthalene anion is exothermic by about 50 kcal/mol. The exothermicity for the formation of 2-hydronaphthalene anion is 4.7 kcal/mol smaller. The 1-hydronaphthalene anion reacts with a second hydrogen atom to restore the naphthalene anion and produce H2 . This reaction has no barrier and is exothermic by 53.3 kcal/mol. Similar energetics are found for the analogous coronene and circumcoronene reactions. Thus the polycyclic aromatic hydrocarbon (PAH) anions can catalyse the formation of H2 , using a mechanism analogous to the PAH cations. This could have important consequences in several problems of astrophysical interest. Published by Elsevier Science B.V.
1. Introduction There is strong evidence that the unidenti®ed infrared (UIR) bands arise from polycyclic aromatic hydrocarbon (PAH) cations or closely related species [1±3]. This is based, in part, on a comparison of the observed bands with matrix isolation experiments. In these matrix experiments, stable, closed shell, neutral PAH molecules are ionized and then their IR spectra is measured. Recently Snow et al. [4] showed that such openshell cations are quite reactive. Since hydrogen atoms are abundant in many of the regions where * Corresponding author. Tel.: +1-650-604-6231; fax: +1-650604-0350. E-mail address: [email protected] (C.W. Bauschlicher Jr.).
0301-0104/01/$ - see front matter. Published by Elsevier Science B.V. PII: S 0 3 0 1 - 0 1 0 4 ( 0 1 ) 0 0 5 0 0 - 6
the UIR bands originate, it seems likely that these open-shell cations will react with the hydrogen to form more stable closed-shell cations. This radical±radical reaction has no barrier, as expected, and the ``extra'' hydrogen is bound by about 50 kcal/mol [5]. We have recently shown that the IR spectra of several of these closed-shell hydro-PAH cations are similar to the parent open-shell cations and consistent with the astrophysical observations [6]. We have also shown that these hydro-PAH cations have no barrier for the reaction with a second hydrogen atom; this reaction yields H2 and restores the original open-shell cation [5]. That is, these cations can catalytically form H2 . Modelling studies [7,8] of the interstellar medium (ISM) suggested that PAH anions are present, and that depending on conditions, the population of anions could exceed that of the cations [7]. While
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C.W. Bauschlicher Jr., E.L.O. Bakes / Chemical Physics 274 (2001) 11±14
PAH anions might be present in the cold diuse ISM [8], the low hydrogen atom density means that reactions of the anions with hydrogen atoms might not be critical to understand the chemistry and spectroscopy of these regions. However, there are regions where both anions and H atoms are believed to coexist. For example, newly formed stars in dense molecular clouds create dense, ultracompact HII regions, where the ratio of the UV ®eld (measured in Habing units of G0 ) to the electron density (in cm 3 ) lies between 1 and 10. While smaller PAHs in these regions may be radiatively destroyed, the larger PAHs may remain intact and those on the outskirts of the HII region could participate in H /H/H2 chemistry and hence in¯uence the chemical equilibrium between the HII region and its nascent molecular cloud. In addition to the ISM, other studies have shown that PAH anions are likely to form in the atmosphere of Titan [9], where one of the unanswered questions is how do H atoms recombine to form H2 , which is then transported out of the atmosphere [10,11]. Since the PAH anions are openshell species and are therefore expected to be reactive, it is possible that they can catalytically form H2 , as previously found for the cations, and therefore they could have a signi®cant in¯uence on the chemistry at the ultracompact HII region/cloud boundary and in the atmosphere of Titan. We have therefore considered the reaction of the PAH anions with hydrogen to form a closed-shell anion as well as the reaction of the hydro-PAH anions with a second hydrogen to form H2 . We have also computed synthetic IR spectra of these species to test if they are consistent with the astrophysical observations. 2. Computational methods The geometries were optimized and the harmonic frequencies and infrared intensities were computed using the B3LYP [12] hybrid [13] functional in conjunction with the 4-31G or 6-31++G** basis sets [14]. The B3LYP calculations were performed using the G A U S S I A N 9 8 computer code [15]. To compute the synthetic spectra, we scale the computed 4-31G frequencies by 0.958 and use a full width at half maximum of 30 cm 1 , which is the natural line width of large molecules emitting un-
der the conditions of the ISM [1]. This is the same approach as used in previous work and its accuracy has been discussed in previous publications [6,16]. 3. Results and discussion We ®rst consider the reaction of naphthalene anion with H to form the 1- and 2-hydrospecies. Since these are radical±radical reactions, they are expected to have no barrier, and we are unable to ®nd one. The two reactions are exothermic by 50.3 and 45.7 kcal/mol, respectively (Table 1). For the 1-hydrospecies, the result obtained using the larger 6-31++G** basis set is only 1.2 kcal/mol larger. We wish to stress that the C±H bonding is covalent and not electrostatic; this is clear from the geometry, where, in addition to the seven aromatic C±H bonds, there are two aliphatic C±H bonds with (computed using bond lengths of 1.10 and 1.12 A the 6-31++G** basis set). For the 1-hydronaphthalene anion, the two bond lengths are not equal, since the carbon ring puckers when the hydrogen is added. The puckered structure is 1.2 kcal/mol more stable than the planar carbon species. For the other PAHs considered in this work, the planar carbon skeletons are a minimum. The reaction of the 1-hydronaphthalene anion with H to restore the naphthalene anion and produce H2 is exothermic by 53.1 kcal/mol. Using the larger basis set does not signi®cantly aect this result. Using standard optimization procedures, we were unable to ®nd any barrier for this reaction. Therefore we computed the energy as a function of the C±H and H±H distances, with all other parameters optimized. This potential energy surface is shown in Fig. 1 and it is clear that there is no barrier connecting reactants with products. Thus napthalene anion can catalytically produce H2 in two barrierless reactions. Unfortunately, our calculations do not yield the rate of these reactions and we are currently trying to extend this work to include the calculation of the rate constants for these potentially very important mechanisms for the production of H2 . Naphthalene anion is too small to be representative of species in the ISM, and therefore we also computed the energies for the reaction of
C.W. Bauschlicher Jr., E.L.O. Bakes / Chemical Physics 274 (2001) 11±14
13
Table 1 Summary of the computed energetics (in kcal/mol) at the B3LYP level of theory Reaction naphthalene H ! 1-hydronaphthalene naphthalene H ! 2-hydronaphthalene 1-hydronaphthalene H ! naphthalene H2 coronene H ! 1-hydrocoronene 1-hydrocoronene H ! coronene H2 circumcoronene H ! 1-hydrocircumcoronene 1-hydrocircumcoronene H ! circumcoronene H2 circumcoronene H ! 3-hydrocircumcoronene 3-hydrocircumcoronene H ! circumcoronene H2
4-31G 50.3
6-31++G** 51.5
45.7 53.1
52.4
46.2 57.2 38.0 65.4 50.2 53.2
Fig. 1. The potential energy surface for the reaction of H with 1-hydronaphthalene anion to yield naphthalene anion plus H2 .
coronene anion and circumcoronene anion with one and two hydrogens. The computed energetics are similar to those found for naphthalene. Therefore, we believe that the catalytic formation of H2 can occur for large PAH anions, as well as, for small ones (Table 1). In Fig. 2, we give the synthetic spectra of coronene cation and anion and 1-hydrocoronene cation and anion. The synthetic spectra of several circumcoronene related species are shown in Fig. 3. For the hydrospecies, the extra hydrogen adds the aliphatic C±H stretch and broadens the bands below 1800 cm 1 . For coronene, circumcoronene, and the hydrospecies, the anion stretching C±H intensity is much stronger than for the cation. The anion intensities below 1800 cm 1 are comparable with the cations. This is dierent from the neutral species, where the intensity in 600±1800 cm 1 region is much weaker than found for the cations and anions. The anion spectra are consistent with the observed emission in regions of the ISM where the ratio of the UV ®eld to the electron density is small [7]. The hydrospecies add a small feature at 3.4 lm, and this is consistent with a weak 3.4 feature in the
Fig. 2. The synthetic spectra of coronene cation and anion and 1-hydrocoronene cation and ion.
14
C.W. Bauschlicher Jr., E.L.O. Bakes / Chemical Physics 274 (2001) 11±14
portance of the PAH mechanism, and we are currently exploring this question for both the PAH anions and cations.
References
Fig. 3. The synthetic spectra of circumcoronene neutral, cation, anion and 1-hydrocircumcoronene and 3-hydrocircumcoronene anions.
ISM emission spectra. While a 3.4 lm band is observed in absorption in the cold diuse ISM across the entire galaxy, no 3.3 lm feature is observed [17] in absorption. Since our calculations show that for the hydroanions the 3.3 lm band is stronger than the 3.4 lm band, we conclude that their concentration, and those of other PAHs (which have a 3.3 lm band), is low in the cold diuse ISM. 4. Conclusions We have shown that PAH anions can catalytically form H2 from H atoms. The IR spectra of hydrointermediate are not inconsistent with the astrophysical observations. Since the catalytic formation of H2 could explain some unresolved astronomical questions, the next step is the evaluation of the rate constants to determine the im-
[1] L.J. Allamandola, A.G.G.M. Tielens, J.R. Barker, Astrophys. J. Supp. 71 (1989) 733. [2] J.L. Puget, A. Leger, Ann. Rev. Astron. Astophys. 27 (1989) 161. [3] J. Szczepanski, M. Vala, Nature 363 (1993) 699. [4] T.P. Snow, V. Le Page, Y. Keheyan, V.M. Bierbaum, Nature 391 (1998) 259. [5] C.W. Bauschlicher, Astrophys. J. 509 (1998) L125, and erratum 517 (1999) L67. [6] D.M. Hudgins, C.W. Bauschlicher, L.J. Allamandola, Spectrochim. Acta A 57 (2001) 907. [7] E.L.O. Bakes, A.G.G.M. Tielens, C.W. Bauschlicher, Astrophys. J. 556 (2001) 501. [8] F. Salama, E.L.O. Bakes, L.J. Allamandola, A.G.G.M. Tielens, Astrophys. J. 459 (1996) 621. [9] E.L.O. Bakes, C.W. Bauschlicher, C.P. McKay, Icarus, in press. [10] Y.L. Yung, M. Allen, J.F. Pinto, Astrophys. J. Supp. 55 (1984) 465. [11] D. Toublanc, J.P. Parisot, J. Brillet, D. Gautier, F. Raulin, C.P. McKay, Icarus 113 (1995) 2. [12] P.J. Stephens, F.J. Devlin, C.F. Chabalowski, M.J. Frisch, J. Phys. Chem. 98 (1994) 11623. [13] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [14] M.J. Frisch, J.A. Pople, J.S. Binkley, J. Chem. Phys. 80 (1984) 3265, and references therein. [15] G A U S S I A N 9 8 , Revision A.7, M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery Jr., R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Cliord, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, A.G. Baboul, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople, Gaussian, Inc., Pittsburgh PA, 1998. [16] C.W. Bauschlicher, S.R. Langho, Spectrochim. Acta A 53 (1997) 1225. [17] J.E. Chiar, A.G.G.M. Tielens, D.C.B. Whittet, W.A. Schutte, A.C.A. Boogert, D. Lutz, E.F. van Dishoeck, M.P. Bernstein, Astrophys. J. 537 (2000) 749.
The reaction of polycyclic aromatic hydrocarbon anions with hydrogen C.W. Bauschlicher Jr. a,*, E.L.O. Bakes b a
Space Technology Division, NASA Ames Research Center, Mail Stop 230-3, Moett Field, CA 94035-1000, USA b SETI, NASA Ames Research Center, Mail Stop 245-3, Moett Field, CA 94035-1000, USA Received 6 August 2001
Abstract The reaction of naphthalene anion with an H atom to produce 1-hydronaphthalene anion is exothermic by about 50 kcal/mol. The exothermicity for the formation of 2-hydronaphthalene anion is 4.7 kcal/mol smaller. The 1-hydronaphthalene anion reacts with a second hydrogen atom to restore the naphthalene anion and produce H2 . This reaction has no barrier and is exothermic by 53.3 kcal/mol. Similar energetics are found for the analogous coronene and circumcoronene reactions. Thus the polycyclic aromatic hydrocarbon (PAH) anions can catalyse the formation of H2 , using a mechanism analogous to the PAH cations. This could have important consequences in several problems of astrophysical interest. Published by Elsevier Science B.V.
1. Introduction There is strong evidence that the unidenti®ed infrared (UIR) bands arise from polycyclic aromatic hydrocarbon (PAH) cations or closely related species [1±3]. This is based, in part, on a comparison of the observed bands with matrix isolation experiments. In these matrix experiments, stable, closed shell, neutral PAH molecules are ionized and then their IR spectra is measured. Recently Snow et al. [4] showed that such openshell cations are quite reactive. Since hydrogen atoms are abundant in many of the regions where * Corresponding author. Tel.: +1-650-604-6231; fax: +1-650604-0350. E-mail address: [email protected] (C.W. Bauschlicher Jr.).
0301-0104/01/$ - see front matter. Published by Elsevier Science B.V. PII: S 0 3 0 1 - 0 1 0 4 ( 0 1 ) 0 0 5 0 0 - 6
the UIR bands originate, it seems likely that these open-shell cations will react with the hydrogen to form more stable closed-shell cations. This radical±radical reaction has no barrier, as expected, and the ``extra'' hydrogen is bound by about 50 kcal/mol [5]. We have recently shown that the IR spectra of several of these closed-shell hydro-PAH cations are similar to the parent open-shell cations and consistent with the astrophysical observations [6]. We have also shown that these hydro-PAH cations have no barrier for the reaction with a second hydrogen atom; this reaction yields H2 and restores the original open-shell cation [5]. That is, these cations can catalytically form H2 . Modelling studies [7,8] of the interstellar medium (ISM) suggested that PAH anions are present, and that depending on conditions, the population of anions could exceed that of the cations [7]. While
12
C.W. Bauschlicher Jr., E.L.O. Bakes / Chemical Physics 274 (2001) 11±14
PAH anions might be present in the cold diuse ISM [8], the low hydrogen atom density means that reactions of the anions with hydrogen atoms might not be critical to understand the chemistry and spectroscopy of these regions. However, there are regions where both anions and H atoms are believed to coexist. For example, newly formed stars in dense molecular clouds create dense, ultracompact HII regions, where the ratio of the UV ®eld (measured in Habing units of G0 ) to the electron density (in cm 3 ) lies between 1 and 10. While smaller PAHs in these regions may be radiatively destroyed, the larger PAHs may remain intact and those on the outskirts of the HII region could participate in H /H/H2 chemistry and hence in¯uence the chemical equilibrium between the HII region and its nascent molecular cloud. In addition to the ISM, other studies have shown that PAH anions are likely to form in the atmosphere of Titan [9], where one of the unanswered questions is how do H atoms recombine to form H2 , which is then transported out of the atmosphere [10,11]. Since the PAH anions are openshell species and are therefore expected to be reactive, it is possible that they can catalytically form H2 , as previously found for the cations, and therefore they could have a signi®cant in¯uence on the chemistry at the ultracompact HII region/cloud boundary and in the atmosphere of Titan. We have therefore considered the reaction of the PAH anions with hydrogen to form a closed-shell anion as well as the reaction of the hydro-PAH anions with a second hydrogen to form H2 . We have also computed synthetic IR spectra of these species to test if they are consistent with the astrophysical observations. 2. Computational methods The geometries were optimized and the harmonic frequencies and infrared intensities were computed using the B3LYP [12] hybrid [13] functional in conjunction with the 4-31G or 6-31++G** basis sets [14]. The B3LYP calculations were performed using the G A U S S I A N 9 8 computer code [15]. To compute the synthetic spectra, we scale the computed 4-31G frequencies by 0.958 and use a full width at half maximum of 30 cm 1 , which is the natural line width of large molecules emitting un-
der the conditions of the ISM [1]. This is the same approach as used in previous work and its accuracy has been discussed in previous publications [6,16]. 3. Results and discussion We ®rst consider the reaction of naphthalene anion with H to form the 1- and 2-hydrospecies. Since these are radical±radical reactions, they are expected to have no barrier, and we are unable to ®nd one. The two reactions are exothermic by 50.3 and 45.7 kcal/mol, respectively (Table 1). For the 1-hydrospecies, the result obtained using the larger 6-31++G** basis set is only 1.2 kcal/mol larger. We wish to stress that the C±H bonding is covalent and not electrostatic; this is clear from the geometry, where, in addition to the seven aromatic C±H bonds, there are two aliphatic C±H bonds with (computed using bond lengths of 1.10 and 1.12 A the 6-31++G** basis set). For the 1-hydronaphthalene anion, the two bond lengths are not equal, since the carbon ring puckers when the hydrogen is added. The puckered structure is 1.2 kcal/mol more stable than the planar carbon species. For the other PAHs considered in this work, the planar carbon skeletons are a minimum. The reaction of the 1-hydronaphthalene anion with H to restore the naphthalene anion and produce H2 is exothermic by 53.1 kcal/mol. Using the larger basis set does not signi®cantly aect this result. Using standard optimization procedures, we were unable to ®nd any barrier for this reaction. Therefore we computed the energy as a function of the C±H and H±H distances, with all other parameters optimized. This potential energy surface is shown in Fig. 1 and it is clear that there is no barrier connecting reactants with products. Thus napthalene anion can catalytically produce H2 in two barrierless reactions. Unfortunately, our calculations do not yield the rate of these reactions and we are currently trying to extend this work to include the calculation of the rate constants for these potentially very important mechanisms for the production of H2 . Naphthalene anion is too small to be representative of species in the ISM, and therefore we also computed the energies for the reaction of
C.W. Bauschlicher Jr., E.L.O. Bakes / Chemical Physics 274 (2001) 11±14
13
Table 1 Summary of the computed energetics (in kcal/mol) at the B3LYP level of theory Reaction naphthalene H ! 1-hydronaphthalene naphthalene H ! 2-hydronaphthalene 1-hydronaphthalene H ! naphthalene H2 coronene H ! 1-hydrocoronene 1-hydrocoronene H ! coronene H2 circumcoronene H ! 1-hydrocircumcoronene 1-hydrocircumcoronene H ! circumcoronene H2 circumcoronene H ! 3-hydrocircumcoronene 3-hydrocircumcoronene H ! circumcoronene H2
4-31G 50.3
6-31++G** 51.5
45.7 53.1
52.4
46.2 57.2 38.0 65.4 50.2 53.2
Fig. 1. The potential energy surface for the reaction of H with 1-hydronaphthalene anion to yield naphthalene anion plus H2 .
coronene anion and circumcoronene anion with one and two hydrogens. The computed energetics are similar to those found for naphthalene. Therefore, we believe that the catalytic formation of H2 can occur for large PAH anions, as well as, for small ones (Table 1). In Fig. 2, we give the synthetic spectra of coronene cation and anion and 1-hydrocoronene cation and anion. The synthetic spectra of several circumcoronene related species are shown in Fig. 3. For the hydrospecies, the extra hydrogen adds the aliphatic C±H stretch and broadens the bands below 1800 cm 1 . For coronene, circumcoronene, and the hydrospecies, the anion stretching C±H intensity is much stronger than for the cation. The anion intensities below 1800 cm 1 are comparable with the cations. This is dierent from the neutral species, where the intensity in 600±1800 cm 1 region is much weaker than found for the cations and anions. The anion spectra are consistent with the observed emission in regions of the ISM where the ratio of the UV ®eld to the electron density is small [7]. The hydrospecies add a small feature at 3.4 lm, and this is consistent with a weak 3.4 feature in the
Fig. 2. The synthetic spectra of coronene cation and anion and 1-hydrocoronene cation and ion.
14
C.W. Bauschlicher Jr., E.L.O. Bakes / Chemical Physics 274 (2001) 11±14
portance of the PAH mechanism, and we are currently exploring this question for both the PAH anions and cations.
References
Fig. 3. The synthetic spectra of circumcoronene neutral, cation, anion and 1-hydrocircumcoronene and 3-hydrocircumcoronene anions.
ISM emission spectra. While a 3.4 lm band is observed in absorption in the cold diuse ISM across the entire galaxy, no 3.3 lm feature is observed [17] in absorption. Since our calculations show that for the hydroanions the 3.3 lm band is stronger than the 3.4 lm band, we conclude that their concentration, and those of other PAHs (which have a 3.3 lm band), is low in the cold diuse ISM. 4. Conclusions We have shown that PAH anions can catalytically form H2 from H atoms. The IR spectra of hydrointermediate are not inconsistent with the astrophysical observations. Since the catalytic formation of H2 could explain some unresolved astronomical questions, the next step is the evaluation of the rate constants to determine the im-
[1] L.J. Allamandola, A.G.G.M. Tielens, J.R. Barker, Astrophys. J. Supp. 71 (1989) 733. [2] J.L. Puget, A. Leger, Ann. Rev. Astron. Astophys. 27 (1989) 161. [3] J. Szczepanski, M. Vala, Nature 363 (1993) 699. [4] T.P. Snow, V. Le Page, Y. Keheyan, V.M. Bierbaum, Nature 391 (1998) 259. [5] C.W. Bauschlicher, Astrophys. J. 509 (1998) L125, and erratum 517 (1999) L67. [6] D.M. Hudgins, C.W. Bauschlicher, L.J. Allamandola, Spectrochim. Acta A 57 (2001) 907. [7] E.L.O. Bakes, A.G.G.M. Tielens, C.W. Bauschlicher, Astrophys. J. 556 (2001) 501. [8] F. Salama, E.L.O. Bakes, L.J. Allamandola, A.G.G.M. Tielens, Astrophys. J. 459 (1996) 621. [9] E.L.O. Bakes, C.W. Bauschlicher, C.P. McKay, Icarus, in press. [10] Y.L. Yung, M. Allen, J.F. Pinto, Astrophys. J. Supp. 55 (1984) 465. [11] D. Toublanc, J.P. Parisot, J. Brillet, D. Gautier, F. Raulin, C.P. McKay, Icarus 113 (1995) 2. [12] P.J. Stephens, F.J. Devlin, C.F. Chabalowski, M.J. Frisch, J. Phys. Chem. 98 (1994) 11623. [13] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [14] M.J. Frisch, J.A. Pople, J.S. Binkley, J. Chem. Phys. 80 (1984) 3265, and references therein. [15] G A U S S I A N 9 8 , Revision A.7, M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery Jr., R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Cliord, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, A.G. Baboul, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople, Gaussian, Inc., Pittsburgh PA, 1998. [16] C.W. Bauschlicher, S.R. Langho, Spectrochim. Acta A 53 (1997) 1225. [17] J.E. Chiar, A.G.G.M. Tielens, D.C.B. Whittet, W.A. Schutte, A.C.A. Boogert, D. Lutz, E.F. van Dishoeck, M.P. Bernstein, Astrophys. J. 537 (2000) 749.