Ab Initio Study of Inelastic Collision Processes for Astronomical Applications Lei Song Preliminary version – January 29, 2016 The work described in this thesis was performed as part of the Dutch Astro- chemistry Network, a research program of the Netherlands Foundation for Scientific Research (NWO) and its subdivisions Chemistry (CW) and Exact Sciences (EW). Printed by Ipskamp Drukkers B.V., Enschede ISBN: Preliminary version – January 29, 2016 Ab Initio Study of Inelastic Collision Processes for Astronomical Applications PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Radboud Universiteit Nijmegen op gezag van de rector magnificus, volgens besluit van het college van decanen in het openbaar te verdedigen op donderdag 3 maart 2016 om 12.30 uur precies door Lei Song geboren op 5 januari 1986 te Qingdao, China Preliminary version – January 29, 2016 promotoren: Prof. dr. ir. Gerrit C. Groenenboom Prof. dr. ir. Ad van der Avoird manuscriptcommissie: Prof. dr. David H. Parker Prof. dr. Ewine F. van Dishoeck Universiteit Leiden Prof. dr. Marc C. van Hemert Universiteit Leiden Preliminary version – January 29, 2016 CONTENTS 1introduction 1 1.1 Astrochemistry background 1 1.2 Theoretical methods 4 1.2.1 Solving the electronic Schrödinger equation 6 1.2.2 Solving the nuclear Schrödinger equation 7 1.3 CO collisions with its partners H, He and H2 11 2h-co potential energy surface 15 2.1 Introduction 16 2.2 Ab initio calculations 17 2.3 Fit procedure 19 2.4 Results and discussion 22 2.4.1 Potential surface 23 2.4.2 Vibrational frequencies and rotational constants of HCO 27 2.5 Conclusions 31 3h-co rate coefficients for pure rotational transi- tions 33 3.1 Introduction 34 3.2 Computational approach 37 3.3 Results and discussion 38 3.4 Astrophysical applications 42 3.5 Conclusion 46 4h-co scattering calculation for ro-vibrational tran- sitions 47 4.1 Introduction 48 4.2 Calculations 50 4.2.1 Theoretical methods 50 4.2.2 Computational details 52 4.3 Results and discussion 54 4.3.1 Convergence test 54 4.3.2 Tests of the CS and IOS approximations 54 4.3.3 Cross sections 58 4.3.4 Vibrational quenching rate coefficients 62 4.4 Conclusions 63 5h-co rate coefficients for ro-vibrational transitions 65 5.1 Introduction 66 5.2 Theory 68 5.2.1 Equations for rate coefficients 68 5.2.2 Extrapolation method 69 5.3 Results 70 5.3.1 Rate coefficients from quantum scattering calculations 70 5.3.2 Extrapolated rate coefficients 73 5.4 Astrophysical models 76 v Preliminary version – January 29, 2016 5.4.1 ProDiMo slab and disk models 76 5.4.2 Slab model results 77 5.4.3 Disk model results 79 5.5 Conclusions 80 6ar-co scattering for pure rotational transitions 81 6.1 Introduction 82 6.2 Experimental Methods 83 6.3 Theoretical Methods 84 6.4 Results and Discussion 85 6.4.1 Overview 85 6.4.2 Mathematical foundation 89 6.4.3 Sensitivity 92 6.5 Conclusion 94 7he-co scattering for pure rotational transitions 95 7.1 Introduction 96 7.2 Experimental Method 98 7.3 Theoretical method 103 7.4 Results and discussion 104 7.4.1 Theoretical results 104 7.4.2 Vector Correlations 106 7.4.3 Experimental results 108 7.4.4 Discussion 114 7.5 Conclusion 118 8h2 -co scattering calculations 121 8.1 Introduction 122 8.2 Computational details 122 8.3 Theoretical results 123 8.4 Conclusion 126 bibliography 127 summary 145 samenvatting 149 XÅ 153 list of publications 155 curriculum vitae 157 acknowledgements 159 Preliminary version – January 29, 2016 ACRONYMS 2D two-dimensional 3D three-dimensional AGN active galactic nucleus BF body-fixed BO Born-Oppenheimer CASSCF complete active space self-consistent field CBS complete basis set CC close-coupling CCSD(T) single and double excitation coupled cluster method with pertur- bative triples CI configuration interaction CS coupled state DCS differential cross section DFT density functional theory DVR discrete variable representation FIR far-infrared icMRCI internally contracted multireference configuration interaction ICS integral cross section IOS infinite order sudden IR infrared ISM interstellar medium LAMDA Leiden Atomic and Molecular Database LTE local thermodynamic equilibrium LWS Long Wavelength Spectrometer HF Hartree Fock MP Møller-Plesset vii Preliminary version – January 29, 2016 MRCI multi-reference configuration interaction NIR near-infrared PDDCS polarization-dependent differential cross section PDR photon-dominated region PES potential energy surface PPD protoplanetary disk REMPI resonance enhanced multiphoton ionization RHF restricted Hartree-Fock RKHS reproducing kernel Hilbert space RKR Rydberg-Klein-Rees RMSE root-mean-square error SAPT symmetry-adapted perturbation theory SCF self-consistent field SF space-fixed sinc-DVR sinc-function discrete variable representation SST Spitzer Space Telescope UV ultraviolet VMI velocity map imaging VUV vacuum ultraviolet WKS Werner-Keller-Schinke ZEST zero-energy scaling technique Preliminary version – January 29, 2016 INTRODUCTION 1 This thesis mainly focuses on ab initio calculations for inelastic collision processes of carbon monoxide, CO, colliding with hydrogen and helium atoms, H and He, and with hydrogen molecules, H2. This introductory chapter presents the astrochemistry background, the theoretical methods applied, and the current status of the research on these scattering processes. 1.1 astrochemistry background The Universe is a combination of time, space, matter, and energy. [1] Dark matter is estimated to compose 85% of the total matter in the observable Universe, while only a small fraction of the Universe is made of molecules. [2] Still, some scientists refer in particular to the “Molecular Universe” [3, 4, 5] to emphasize the importance of molecules in the formation and evolution of planets, stars and galaxies. By now, nearly 180 different molecular species (not counting isotopologues) have been detected, from simple diatomic molecules such as H2, CO, O2, and CS to complex polyatomic molecules like hydrocarbon chains, and the C60 and C70 fullerenes. Figure 1.1 shows that a diversity of molecules is present in the life-cycle of the interstellar medium. The cycle of molecular material in the interstellar medium starts from the diffuse interstellar medium, to dense molecular clouds where stars and planets form, and finally back to the interstellar medium with the ex- plosion of stars. After that, a new cycle starts. In this process, heavier Figure 1.1: The life cycle of the interstellar medium. Adapted from Ref. [4] Preliminary version – January 29, 2016 2introduction Figure 1.2: An overview of the molecular lines and the range of physical conditions where they can probe effectively. Figure from Ref. [4] elements are created and become more and more abundant. At the same time, more complex molecular material will be present in the next cycle. To understand the origin and evolution of molecules in space and their role in the Universe, astronomical and chemical knowledge should be combined. Astrochemistry is at the interface of astronomy, chemistry, and molecular physics. [6] This discipline was born in the early 1970s, and its essential sub- ject matter was defined by Dalgarno [7] as “the formation, destruction, and excitation of molecules in astronomical environments and their influence on the structure, dynamics, and evolution of astronomical objects”. The formation, destruction and excitation of molecules are strongly related to the collisional, radiative and chemical processes occurring in astronomical environments. A tremendous amount of microscopic molecular processes results in the macroscopic evolution of stars, planets and galaxies. Not only molecular processes are important, but also the molecules themselves play a signifi- cant role in astrochemistry research. This stems from the fact that molecules are outstanding tracers of the physical conditions in their resident regions. The molecular electronic, vibrational and rotational spectra can reveal the abundance and excitation of molecules, which are determined by the ra- diation from surrounding stars [8] and by collisions. Molecular collisions are sensitive to the physical conditions such as the gas kinetic temperature and the density. Therefore, molecules can be used as “thermometers” and “barometers” of emitting gas by means of spectral surveys. [4] Figure. 1.2 presents an overview of often-used molecular lines and the range where these lines can be used as effective “thermometers” and “barometers”. As shown in Fig. 1.2, CO is an excellent molecular tracer, which is effective for a large range of kinetic temperatures and molecular hydrogen density. Ro- tational lines of CO probe the lower density and lower temperature range, Preliminary version – January 29, 2016 1.1astrochemistrybackground 3 Figure 1.3: A typical CO astronomical spectrum of the vibration-rotation lines at 4.7µm obtained with VLT-CRIRES. Infrared image with the Spitzer Space Telescope of the central part of Ophiuchus. The SR 21 is one of the young stars. (Image credit: NASA/JPL-Caltech/ESO VLT-CRIRES; K.M. Pontoppidan) while CO ro-vibrational lines are used in the dense, hot gas near a star or in a planet-forming disk. [4, 9]. Molecular hydrogen, as the most abundant molecule in the Universe, is another important tracer for studying the phys- ical properties of molecular clouds. It works in the low density and high temperature range, because of facile low-J rotational transitions in the low- density region and its large energy spacing of rotational and vibrational energy levels. In addition, other tracer species such as OH, CS, H2O, and NH3 are present in the regions indicated in Fig 1.2. The electromagnetic spectra of these molecular tracers provide clues in the investigation of our Universe. Astrochemists utilize astronomical ob- servations, laboratory experiments, theoretical computations, and models. Spectroscopy is a key method of investigation for observational astronomy. Progress in telescopes equipped with highly sensitive detectors advances the observations. The observed spectral range becomes larger and the reso- lution of astronomical spectra becomes higher.