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Sharelatex Example THÈSE Présentée pour obtenir le grade de DOCTEUR DE l'UNIVERSITÉ DU HAVRE par Mario HERNANDEZ-VERA Sujet de la thèse : Toward the understanding of cyanide/isocyanide abundances: Inelastic collisions and radiative transfer calculations. École doctorale Sciences Physiques, Mathématiques et de l'Information pour l'Ingénieur Soutenue le 16 décembre 2014 au Laboratoire Ondes et Milieux Complexes devant le jury composé de : M. Majdi Hochlaf Rapporteur M. Maurice Monnerville Rapporteur M. Jacek Kªos Examinateur M. Laurent Pagani Examinateur M. Alexandre Faure Examinateur M. Fabien Dumouchel Examinateur M. François Lique Directeur de thèse M. Jesús Rubayo Co-Directeur de thèse Acknowledgments These three years in Le Havre have been a great experience because of the excellent people that I have met. Without these persons, it would have been very difficult to achieve all the results and goals of my PhD work. My special thanks to Dr. Fran¸coisLique for his constant support, for all the interesting projects and for giving me the opportunity to work in his group. I would also want to express my gratitude to his family, for its solidarity and for helping me all these years. I want to thanks my old colleagues from Havana, specially Prof Dr. Jesus Rubayo Soneira, whose guide and support was decisive at the start of my career. I would like to thanks Yulia Kalugina, Fabien Dumouchel and Mathieu Lanza for all the scientific discussions. I would also like to thanks our secretary, Carole, for her skills and her patience to deal with the bureaucracy. Finally, I want to express my profound thanks to Borja, Raounak, Simon, Nezha, C´eline,Guillaume, Xue Zhou, Sylvain and all the others friends and colleagues of LOMC for their friendship and support. i ii Abstract Cyanide and isocyanide species are ubiquitous in the interstellar medium (ISM). We have studied the collisional excitation of three kind of species: the metal cyanides/isocyanides which are the most common metal-bearing molecules in the ISM; the silicon cyanide/isocyanide, and the simplest hydrogen cyanide molecule which is one of the best tracers of the dense interstellar gas. Modelling of molecular emission spectra of these species from interstellar clouds requires the calculation of rate coefficients for excitation by collisions with H2, the most abundant molecule in the cold ISM. Thus, we have used the coupled states approximation to study the rotational (de-)excitation of AlCN(1Σ), AlNC(1Σ), MgCN(2Σ), MgNC(2Σ), 2 2 SiCN( Π) and SiNC( Π) molecules by collisions with He, as a model of H2. We have also considered the rotational (de-)excitation of HCN(1Σ) molecules by ortho- H2 and para-H2 molecules using the close coupling approach. In all cases, new highly correlated potential energy surfaces have been employed. Significant differ- ences between the rate coefficients of the isomers were observed. These differences confirm that specific calculations have to be performed for each isomer in order to obtain the necessary level of details in astrophysical applications. We have also assessed the impact of our collisional rates coefficients in the molecular emission simulations using radiative transfer calculations. iii iv Contents 1 General Introduction1 1.1 Molecular astrophysics.........................1 1.2 Inelastic molecular collisions......................4 1.3 The interstellar cyanide/isocyanide compounds............6 1.4 Objective and structure of the thesis................. 11 2 Theoretical Framework 13 2.1 Born-Oppenheimer Approximation.................. 14 2.2 Ab initio quantum chemistry approaches............... 17 2.2.1 Hartree Fock Approximation.................. 18 2.2.2 Electronic correlation...................... 20 2.2.3 Basis functions......................... 23 2.3 Scattering theory............................ 24 2.3.1 Space-fixed frame........................ 24 2.3.2 Close-Coupling Approach................... 27 2.3.3 Inelastic cross section...................... 28 2.3.4 The body-fixed representation................. 30 2.3.5 Coupled-States Approach................... 32 v 2.3.6 Infinite Order Sudden Approximation............. 34 3 Rotational (de-)excitation of XCN/XNC (X=Al, Mg) by He 37 3.1 Rotational spectroscopy of XCN/XNC................ 38 3.2 Collisions of 2Σ molecules with 1S atoms............... 43 3.3 Results.................................. 46 4 Rotational (de-)excitation of SiCN/SiNC in collisions with He 57 4.1 Rotational spectroscopy of SiCN and SiNC.............. 58 4.2 Collisional excitation of 2Π molecules................ 60 4.3 Results.................................. 66 5 Rotational (de-)excitation of HCN with H2 77 5.1 Spectroscopy of HCN and H2 ..................... 78 5.2 Rotor (1Σ) - rotor(1Σ) collision.................... 81 5.3 Results.................................. 84 6 Radiative transfer calculations 93 6.1 Radiative transfer calculations..................... 94 6.2 Results.................................. 96 7 Conclusions 107 A Numerical calculations 115 B J. Chem. Phys., 139, 224301 (2013) 127 Bibliography 137 vi List of Figures 2.1 Space-fixed (XYZ) reference frame................... 25 2.2 (Oxyz) is the BF reference frame. (OXY Z) is the SF reference frame. A rotation of Euler angles (Φ; Θ; 0) brings the (OXY Z) frame into the (Oxyz) frame...................... 30 3.1 Intermolecular bond distances, rotational constant (B), dipole mo- ment (µ) and relative energy (Er) of AlCN{AlNC isomers...... 39 3.2 Intermolecular bond distances, rotational constant (B), dipole mo- ment (µ) and relative energy (Er) of MgCN{MgNC isomers..... 40 1 3.3 Rotational energy (cm− ) levels of the AlCN/AlNC (red lines) and MgCN/MgNC (blue lines)....................... 42 3.4 Comparison between the recoupling formulation RC-IOS (this work) and the recoupling formulation RC-CC. Figures a) and b) represent the results for MgNC molecule. Figures c) and d) represent the results for MgCN molecule....................... 45 4.1 Intermolecular bond distances, rotational constant (B), dipole mo- ment (µ) and relative energy (Er) of SiCN{SiNC isomers....... 59 vii 5.1 Intermolecular bond distances, rotational constant (B) and dipole moment (µ) of HCN and H2 molecules................. 79 1 5.2 First rotational energy (cm− ) levels of the HCN molecules and the p-H2 and o-H2 nuclear spin isomers.................. 80 7.1 HCN{p-H2 and HNC{p-H2 de-excitation rate coefficients from the initial level j = 5 at 10 K ........................ 109 7.2 Solid lines: brightness temperature obtained with p-H2 in colli- sions with HCN (blue lines) and in collisions with HNC (red lines). Dashed lines: brightness temperature obtained with He scaled rate coefficients. All calculations were performed with RADEX code.... 111 viii List of Tables A.1 The MOLSCAT parameters for the CS calculations of the AlCN-He collisional system............................ 120 A.2 The MOLSCAT parameters for the CS calculations of the AlNC-He collisional system............................ 120 A.3 The MOLSCAT parameters for the CS calculations of the MgCN-He collisional system............................ 121 A.4 The MOLSCAT parameters for the CS calculations of the MgNC-He collisional system............................ 121 A.5 The MOLSCAT parameters for the CC calculations of the HCN{ para-H2 collisional system....................... 122 A.6 The MOLSCAT parameters for the CC calculations of the HCN{ ortho-H2 collisional system....................... 122 A.7 The Hibridon parameters for the CS calculations of the SiCN{He collisional system............................ 124 A.8 The Hibridon parameters for the CS calculations of the SiNC{He collisional system............................. 125 ix x Chapter 1 General Introduction 1.1 Molecular astrophysics Observers of the night-time sky of XIX century ignored the significant amount of cold matter hidden in the large spaces amongst the stars. Presently, we know that this tenuous medium, the so-called \interstellar-medium" (ISM), is formed of gas (atoms, molecules, ions, and electrons) and dust (tiny solid particles). Despite its large spatial dimensions, it accounts for only 10{15 % of the total mass of our galaxy [1]. Most of the interstellar matter comes from the ejections of the stars, continuously via stellar winds, or instantaneously via supernova explosions. Stars also affect the interstellar matter through their radiation and gravitational field. At the same time, the chemical and physical conditions of the interstellar matter define the birthplace of stars and impact their future characteristics. Therefore, the dynamics and the chemistry of ISM are of fundamental interest in modern astrophysics. 1 The interstellar matter manifests itself by different optical phenomena. Through their absorption and scattering, small dust grains give rise to extinction of light from distant stars. Besides, observed starlight polarization is believed to be caused by selective absorption of magnetically aligned interstellar dust grains [2]. On the other hand, molecular and atomic gases manifest themselves through the formation of absorption lines in stellar spectra and through emissions of light. The first interstellar molecules (CH, CH+ , and CN) were discovered in the late 1930s [3{5], through optical absorption lines they produce in stellar spectra. The important atomic hydrogen was observed by the detection of its hyperfine 21 cm line [6] in 1951. Twenty years later, the observations of the Aerobee-150 rocket, above the Earths atmosphere, allow detecting the most abundant interstel- lar molecule, H2,
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