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R-Matrix Calculations on Molecules of Astrophysical Interest Using Quantemol-N

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R-Matrix Calculations on Molecules of Astrophysical Interest Using Quantemol-N R-matrix Calculations on Molecules of Astrophysical Interest using Quantemol-N Hemal Naren Varambhia A thesis submitted to University College London for the degree of Doctor of Philosophy Department of Physics and Astronomy University College London January 2010 I, Hemal Naren Varambhia, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. 1 Acknowledgements In accordance with tradition, I must first thank my parents for their constant, loving and encouraging support throughout the period of the Ph.D. The thesis is entirely dedicated to them. I also thank Prof. Tennyson and Dr. Dan Brown for accepting me as a Ph.D student and as CASE student with Quantemol Ltd. It was an immense pleasure to work with the Company and on Quantemol-N, which, I am certain, will go from strength to strength. I thank Prof. Tennyson for his support, his patience and time in answering my many questions on the R-matrix method and scattering theory and his allowing me to work independently and collaborate with external research groups. Formally, I wish to thank Dr. Sumona Gangopadhyay, Harshit Kothari and Prof. Joshipura for providing me with their SiO and CO ionisation cross section data which are presented in this thesis, all his students: Harshad Bhutadia, Dr. Kirtibhai Korot, Foram Shelat, Dr. Bhushit Vaishnav and his colleagues Drs. Chetan Limbachiya and Minaxi Vinodkumar for their friendship, hospitality and care during my time in Ahmedabad and Sardar Patel University, Anand. A number of the R-matrix studies presented here were part of a collaboration with scientists outside of UCL: the electron scattering study on CS (chapter 8) was carried out with Drs. Tom Field and Karola Graupner of Queen’s University Belfast (QUB) and some of the conclusions and observations presented here were theirs. I thank them for allowing me to collaborate with them and to present the work in my thesis; the SiO study (chapter 7) was one carried out with Prof. K. L. Baluja and Dr. Monika Gupta of the University of Delhi (DU); and chapter 10, on the electron-impact rotational excitation of HCN, HNC, DCN and DNC, was carried out with Dr. Alex Faure of the Observatoire de Grenoble, France. Some of the astrophysical conclusions drawn in that chapter are entirely due to his insights. 2 During the course of the Ph.D, I travelled overseas to Belgrade, Serbia to assist the Institute of Physics at Belgrade in installing Quantemol-N. Accordingly I thank Prof. Zoran Lj. Petrovi´c,Dr. Marija Radmilovi´c-Radjenovi´cand Marija Vrani´cfor their most kind hospitality during the visit, and for the opportunity to discuss my work in the form of a presentation to the various research groups stationed there. I sincerely hope that Quantemol-N continues to be of use to them in their research. Very special thanks must go to James Munro for helping me develop my JAVA programming skills and my programming skills generally, ones that I value greatly. In- deed I attribute my enthusiasm for computer programming enitirely to James’ guidance. Thanks also to Amar Dora, Alex Faure, Jan Franz, Jimena Gorfinkiel, Alex Harvey, Chris Hadley, Chiarra Piccarreta, Bruno Silva and Michal Tarana for very useful discus- sions and friendship. I must also thank Prof. and Mrs. Baluja and Jasmeet Rajvanshi for their warm friendship and very kind hospitality during my visit to DU and to their homes. Specif- ically to Prof. Baluja, I thank him for his kind invitation for me to come to Delhi and many useful discussions on the R-matrix formalism, and thanks also to Dr. Savinder Kaur for her friendship and care during my time in Delhi. Finally, I also thank Dr. Chirag V. Pandya for kindly inviting me to visit the M. G. Science Institute in Ahmedabad and his family for their hospitality as well. 3 Abstract We have carried out a series of ab initio R-matrix calculations at the static exchange and close-coupling levels of approximation on molecules of astrophysical interest. These in- clude the polar triatomics HCN and HNC (hydrogen isocyanide) and their isotopologues DCN and DNC, the diatomics CS (carbon monosulphide) and SiO (silicon monoxide), the weakly polar CO molecule and the non-polar CH4 molecule. With the exception of CO, all the calculations presented here were carried out using the software ‘Quantemol-N’ which provides an intuitive user-friendly interface to the UK polyatomic R-matrix codes. A chapter is devoted to the discussion on the software: how to prepare an R-matrix calculation using it, its present capabilities and future development. The ultimate aim of this thesis is to demonstrate the need to account for electron- induced chemistry in any astrophysical model. We seek to show that in the case of polar molecules, namely, those molecules with large dipole moments, electron collisions are the dominant mechanism of rotational excitation in comets and other astrophysical bodies. Specifically, we will show that electron-impact excitation rate coefficients are several orders of magnitude higher than the corresponding atom-molecule ones. The thesis concludes with a summary of the key findings and opportunities (and where necessary improvements) that may arise from them. All the scattering equations presented here used atomic units. 4 Contents 1 Electron-Molecule Scattering and its Applications 20 1.1 Overview . 20 1.2 Low-Energy Processes . 21 1.3 Electron-Molecule Collisions in Astrophysics and Previous Studies . 22 1.4 Objectives . 24 1.5 Layout of the Thesis . 25 2 Theoretical Pre-requisites 28 2.1 The Electron-Molecule Scattering Problem . 28 2.2 Born-Oppenheimer Approximation . 31 2.3 Hartree-Fock Approximation . 33 2.3.1 Introduction of a Basis: The Roothan Equations . 35 2.3.2 The Self-Consistent Field Optimisation . 36 2.3.3 Basis Sets . 38 2.4 Configuration Interaction Method . 38 2.4.1 Natural Orbitals . 40 2.5 The Fixed-Nuclei Formulation . 41 2.6 Adiabatic Nuclei Approximation . 43 2.7 Other Methods . 43 2.7.1 Complex Kohn Variational Method . 43 2.7.2 Schwinger Multichannel Method . 44 3 The ab initio R-matrix method 46 3.1 Introduction . 46 5 CONTENTS 3.2 Scattering By a Potential Well . 48 3.2.1 The Inner Region . 48 3.2.2 The External Region . 49 3.3 The Internal Region for Multichannel Electron-Molecule Scattering . 51 3.3.1 Derivation of the R-matrix . 52 3.3.2 The Trial Inner Region Scattering Wavefunction . 54 3.4 The Outer Region for Multichannel Electron-Molecule Scattering . 56 3.4.1 Equations of motion . 56 3.4.2 Electron Scattering by Polar Molecules . 58 3.4.3 Multichannel Resonances . 60 3.4.4 T-matrix transformations . 62 3.5 Additional Scattering Quantities Required in Astrophysics . 63 3.5.1 Rotational Cross sections . 63 3.5.2 Hyperfine Rate Coefficients . 64 3.6 UK R-matrix Package Structure and the Computational Implementation of the Theory . 66 3.6.1 Inner Region . 66 3.6.2 Outer region . 70 3.7 Contributions to the R-matrix package . 71 3.7.1 SWMOL3 . 71 3.7.2 DENPROP . 72 3.8 PythonHyperfines . 74 3.9 New Developments . 76 4 Quantemol-N: An Expert System for the Calculation of Electron-Molecule Scattering using the R-matrix Method 77 4.1 Introduction . 77 4.2 The Quantemol-N Approach . 78 4.2.1 Ordinary Calculation Setup . 78 4.2.2 Batch Calculations . 80 4.2.3 Results . 87 4.3 The Author’s Contribution . 90 4.3.1 Tutorial facility . 90 4.3.2 R-matrix calculation queuing system . 90 6 CONTENTS 4.3.3 Automation of the SCF optimisation . 92 4.3.4 Automated Generation of the Target Complete Active Space . 93 4.3.5 BEB Electron-Impact Ionisation Cross Section . 94 4.3.6 Theoretical Model Documentation . 94 4.3.7 Current and Future Projects . 95 4.4 Conclusion . 95 5 Electron Collision with the HCN and HNC Molecules using the ab initio R-Matrix Theory 96 5.1 Introduction . 96 5.2 Previous Quantum Chemistry and Electron Scattering Studies on HCN . 97 5.3 Previous Quantum Chemistry and Electron Scattering Studies of HNC . 100 5.4 HCN and HNC Quantum Chemistry Model . 100 5.5 HCN and HNC Scattering Calculation . 102 5.5.1 Eigenphase Sums and Resonance Parameters . 104 5.5.2 Electronic Excitation . 109 5.6 Conclusion . 110 6 Electron Collision with the CO Molecule 114 6.1 Introduction . 114 6.2 Previous Quantum Chemistry and Electron Scattering Studies . 115 6.3 Quantum Chemistry Model of CO . 120 6.4 Scattering Model for CO . 121 6.5 Scattering Observables . 123 6.5.1 Eigenphase Sums and Resonances . 123 6.5.2 Electron-Impact Excitation and Ionisation . 125 6.5.3 Differential Cross Sections . 127 6.6 Conclusion . 131 7 Electron Collision with the Silicon Monoxide (SiO) Molecule 133 7.1 Introduction . 133 7.2 Quantum Chemistry Model . 135 7.3 Scattering Model . 138 7.4 Results . 140 7.4.1 Eigenphase Sums, Resonances and Bound States . 140 7 CONTENTS 7.4.2 Inelastic and Ionisation Cross Sections . 143 7.4.3 Rotational Differential Cross Section and Integral Cross Sections . 145 7.5 Rotational Rate Coefficients . 148 7.6 Conclusion . 151 8 Electron Scattering by the Carbon Monosulphide (CS) Molecule 155 8.1 Introduction . 155 8.2 Previous Quantum Chemistry and Electron Scattering Studies . 157 8.3 Quantum Chemistry Model . 159 8.4 Scattering Model . 164 8.5 Results . 165 8.5.1 Eigenphase Sums, Resonances and Bound States . 165 8.5.2 Electronic Excitation Cross Sections .
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