Infrared Spectroscopy of Triatomics for Space Observation

Standards Information Network (Verlag)
  • 1. Auflage
  • |
  • erschienen am 31. Dezember 2018
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  • 236 Seiten
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978-1-119-57930-4 (ISBN)
This book is dedicated to the application of the different theoretical models described in Volume 1 to identify the near-, mid- and far-infrared spectra of linear and nonlinear triatomic molecules in gaseous phase or subjected to environmental constraints, useful for the study of environmental sciences, planetology and astrophysics. The Van Vleck contact transformation method, described in Volume 1, is applied in the calculation and analysis of IR transitions between vibration-rotation energy levels. The extended Lakhlifi-Dahoo substitution model is used in the framework of Liouville's formalism and the line profiles of triatomic molecules and their isotopologues subjected to environmental constraints are calculated by applying the cumulant expansion. The applications presented in this book show how interactions at the molecular level modify the infrared spectra of triatomics trapped in a nano-cage (substitution site of a rare gas matrix, clathrate, fullerene, zeolite) or adsorbed on a surface, and how these interactions may be used to identify the characteristics of the perturbing environment.
1. Auflage
  • Englisch
  • USA
John Wiley & Sons Inc
  • Für Beruf und Forschung
  • 6,13 MB
978-1-119-57930-4 (9781119579304)
weitere Ausgaben werden ermittelt
Pierre-Richard Dahoo is Professor at the University of Versailles St Quentin (UVSQ), researcher at LATMOS, UMR 8190 CNRS, Manager of the University Institute of Technology of Mantes-en-Yvelines and Program Manager of the Chair "Materials Simulation and Engineering" of the UVSQ in Versailles, France.

Azzedine Lakhlifi is Lecturer at the University of Franche-Comte, and researcher at UTINAM Institute, UMR 6213 CNRS, OSU THETA Franche-Comte Bourgogne, University Bourgogne Franche-Comte, Besancon, France.
Foreword ix

Preface xi

Chapter 1 Symmetry of Triatomic Molecules 1

1.1. Introduction 1

1.2. The symmetry group of the Hamiltonian of a triatomic molecule 3

1.3. Symmetry of the nonlinear triatomic molecule (O3) 6

1.3.1. The nonlinear asymmetric molecule O3 ( 16O16O18O (668)) 8

1.3.2. The nonlinear symmetric molecule O3 (16O16O16O (666)) 9

1.3.3. Symmetry of eigenstates of a nonlinear molecule 11

1.4. Symmetry of the linear triatomic molecule (CO2) 15

1.4.1. The linear asymmetric molecule CO2 (16O12C18O (628)) 17

1.4.2. The linear symmetric molecule CO2 (16O12C16O (626)) 19

1.5. Selection rules 20

1.5.1. Symmetry of the eigenstates of a triatomic molecule taking into account the nuclei spins 21

Chapter 2 Energy Levels of Triatomic Molecules in Gaseous Phase 25

2.1. Introduction 26

2.2. Vibrational-rotational movements of an isolated molecule 27

2.3. Vibrational movements of an isolated triatomic molecule 34

2.3.1. Nonlinear triatomic molecules 35

2.3.2. Linear triatomic molecules 36

2.3.3. Introduction of the perturbative Hamiltonians H1, H2, H3 37

2.3.4. Transitions between two vibrational levels: selection rules 38

2.4. Rotational movement of an isolated rigid molecule 40

2.4.1. Linear triatomic molecules 42

2.4.2. Symmetric top molecules 42

2.4.3. Nonlinear triatomic molecules 43

2.4.4. Transitions between rotational levels 46

2.5. Vibrational-rotational energy levels of an isolated triatomic molecule 47

2.6. Rovibrational transitions: selection rules 48

2.6.1. Dipole moment in terms of normal coordinates 50

2.7. Appendices 56

2.7.1. Rotational matrix 56

2.7.2. Perturbative Hamiltonians of vibration and vibration-rotation coupling 59

2.7.3. Components of the angular momentum 60

2.7.4. Rotational Hamiltonian of a symmetric top 60

2.7.5. Elements of the rotational matrix 61

2.7.6. Vibrational anharmonic constants 62

Chapter 3 Clathrate Nano-Cages 65

3.1. Introduction 66

3.2. Clathrate structures 67

3.3. Inclusion model of a triatomic molecule in a clathrate nano-cage 69

3.3.1. Inclusion model 69

3.3.2. Interaction potential energy 71

3.4. Thermodynamic model of clathrates 73

3.4.1. Occupation fractions and Langmuir constants 74

3.4.2. Determination of the Langmuir constants 74

3.4.3. Application to triatomic molecules 75

3.5. Infrared spectrum of a triatomic in clathrate matrix 79

3.5.1. Infrared absorption coefficient 79

3.5.2. Hamiltonian of the system and separation of movements 79

3.5.3. Vibrational motions 83

3.5.4. Orientational motion 83

3.5.5. Translational motion 84

3.5.6. Bar spectra 84

3.6. Application to the CO2 molecule 86

3.6.1. Vibrational motions 86

3.6.2. Orientational motion 88

3.6.3. Translational motion 94

3.6.4. Bar spectra 95

3.7. Appendices 98

3.7.1. Non-zero orientation matrix elements used to calculate the corrections to first-order perturbation energies 98

3.7.2. Correction to eigenenergies of the orientation Hamiltonian 99

3.7.3. Expressions of the vector components derivatives of the dipole moment with respect to the normal vibrational coordinates 102

3.7.4. Expressions of the orientational transition elements in the approximation of harmonic librators 102

Chapter 4 Nano-Cages of Noble Gas Matrices 107

4.1. Introduction 108

4.2. The theoretical molecule-matrix model 110

4.2.1. Site inclusion model 110

4.2.2. 12-6 L-J potential 112

4.2.3. Site distortion 116

4.2.4. Coupling of the molecule-matrix system 118

4.2.5. Vibrational frequency displacements 119

4.2.6. The calculation of the orientational modes 123

4.2.7. Bar spectra and spectral profiles 124

4.3. Application to triatomic molecules 126

4.3.1. The triatomic molecule C3 126

4.3.2. The nonlinear triatomic molecule O3 135

4.4. Appendix: Program for determining the equilibrium configuration of an O3 molecule in a noble gas matrix nano-cage 140

Chapter 5 Effect of Nano-Cages on Vibration 145

5.1. Introduction 145

5.2. The theoretical molecule-matrix model 146

5.3. Calculation of the shift of vibrational frequencies 147

5.3.1. Calculation principle 147

5.3.2. Application of the MAPLE program 151

5.4. Application to linear triatomic molecules 155

5.4.1. Experimental study of linear triatomic molecules (CO2, N2O) 155

5.4.2. Frequency shift calculation for degenerate mode 2 156

5.4.3. Calculation results for linear triatomic molecules (CO2, N2O) 158

5.5. Appendices 163

5.5.1. Transition from Cartesian coordinates to normal coordinates 163

5.5.2. MAPLE program for displacement/shifts of vibrational frequency modes of a CO2 molecule in a noble gas nano-cage matrix 166

Chapter 6 Adsorption on a Graphite Substrate 173

6.1. Molecule adsorbed on a graphite substrate (1000) at low temperature 173

6.1.1. Astrophysical context 173

6.1.2. Molecule adsorbed onto a graphite substrate 175

6.1.3. Graphite substrate-molecule interaction energy 176

6.2. Adsorption observables at low temperature 178

6.2.1. Equilibrium configuration and potential energy surface 178

6.2.2. Adsorption energy 181

6.2.3. Diffusion constant 181

6.3. Interaction energy between two molecules 183

6.3.1. Electrostatic contribution 184

6.3.2. Induction contribution 187

6.3.3. Dispersion-repulsion contribution 188

6.4. Appendices 188

6.4.1. Expressions of action tensors 188

6.4.2. Multipolar moments and dipolar polarizability of a molecule relative to the fixed (absolute) reference frame 191

6.4.3. Code in the FORTRAN language for the calculation of the interaction potential energy between two molecules 191

Bibliography 203

Index 211


In the preface to Volume 1 [DAH 17], the importance of spectroscopy was emphasized, both from a theoretical and an instrumental point of view, for the analysis of observations of chemical species, molecules, radicals and ions. In the infrared (IR), using various types of spatial observation instruments, it is possible to detect molecules or chemical species (ions, radicals, macromolecules, nano-cages, etc.) present in the atmospheres of planets, Earth included, and their satellites, in interstellar media, comets or exoplanets, for example.

One of the most striking observations using ground-based instruments or embedded in space probes or telescopes was listed to show the diversity of discoveries that can lead to advances in the field of astrophysics or cosmology. Note, in particular, the observations mentioned in the preface to Volume 1 [DAH 17], that is:

And very recently, on September 14, 2015, the LIGO (Laser Interferometer Gravitational-Wave Observatory) detects for the first time, the distortions caused by gravitational waves in space-time, predicted by Einstein's theory of general relativity and generated by two black holes that collide nearly 1.3 billion light-years away.

This earned its authors, Barry C. Barish, Kip S. Thorne and Rainer Weiss, the Nobel Prize in Physics in 2017.

Advances in modern detection systems (Planck and Hubble telescopes) and large telescopes that are continually improved and programmed to be sent into space (NASA James Webb Space Telescope (2020), European Extremely Large Telescope (E-ELT) (2024)) can probe the universe to better understand its origin and what it comprises (less than 5% of visible matter, about 25% of dark matter and the rest of dark energy (70%) responsible for a force that repels gravity), to observe exoplanets or black holes, or to measure its expansion. All of these space observations lead astronomers and physicists to rework the cosmological model and revisit Einstein's equation as part of his theory of general relativity published in 1915. Similarly, planet exploration programs using robotic and communicating instruments, such as that of Mars Rover 2020, open the way to observations and analysis data that will have to be interpreted through theoretical models adapted to different areas of the electromagnetic spectrum such as that of IR spectroscopy, which is the focus of this volume.

Referring to the preface to Volume 1 [DAH 17], it should be recalled that spectroscopy not only makes it possible to determine the structure of chemical species (in the gas phase, liquid phase or solid phase) by applying the methods and tools of theoretical spectroscopy, but also helps to identify species (atoms, molecules, molecular fragments, radicals, etc.) in different environments (nano-cavities, media containing different species, ice surface, dust surface, etc.). The species themselves can be used as probes to characterize the environment (temperature, pressure, composition) and determine its nature by relying on the theoretical models developed to analyze the corresponding data.

This book describes the theoretical methods that are used in fundamental research to interpret the spectra of triatomic molecules observed in the infrared domain when these molecules are subjected to an environment where the temperature and the pressure modify their infrared spectra in the gas phase or in nano-cages. In this book, we describe the theoretical models that have been developed to study triatomic molecules in the gas phase as well as the modification of the infrared spectra of these molecules such as the displacement of the centers of bands or the modification of the rovibrational spectrum in nano-cages or on surfaces.

IR spectroscopic analysis is of fundamental interest to atmospheric physics. Ozone (O3) or water vapor (H2O) molecules, which are nonlinear triatomic molecules, given their role in energy exchanges with solar radiation and their implications for chemical equilibrium reactions with other minority constituents present in the atmosphere and in the clouds, are among the most studied gas phase molecules both experimentally and theoretically. Similarly, CO2 or N2O molecules, which are linear triatomic molecules and minor constituents of Earth's atmosphere, play a non-negligible role in the radiative budget. The CO2 molecule is a molecule that participates in global warming as a GHG (greenhouse gas).

This book is intended for Master's and PhD students, teachers and researchers, astronomers and astrophysicists who analyze the data corresponding to the interaction of electromagnetic radiation with matter in the infrared domain, in order to identify the chemical species and their environments.

The first part of the book, which consists of the first two chapters, describes the theoretical models developed for the study of triatomic vibrational-rotational spectra. It was partly inspired by the second year Master's courses (Master 2) in Molecular Physics by G. Amat at UPMC and those by J.M. Flaud and C. Camy-Peyret at DEA (Master 2), "Laser and Matter" at UPSUD, and laboratory research at CNRS, a research organization in France, involved in spectroscopic studies of triatomic molecules in the IR domain, either at UPMC (Group of G. Amat, L. Henry, J.M. Flaud and C. Camy-Peyret, A. Perrin, etc.) or UPSUD (Group of M. Barchewitz, G. Graner, C. Boulet, etc.). The second part, which includes the next three chapters, describes the theoretical models also developed in research to analyze the observations made on triatomic molecules when they are isolated in condensed phase media. This work was initiated in particular in the group Molecular Physics group of Besançon (L. Galatry, D. Robert, J. Bonamy, L. Bonamy, C. Girardet, A. Lahklifi, etc.) and continued, thereafter, in collaboration with researchers from laboratories in the Paris region (L. Abouaf, B. Gauthier, H. Dubost, P.R. Dahoo, etc.) to study molecules in different media and subjected to interactions, whose effects are particularly apparent at the nanometer scale, which modify the profile of the IR spectra of these molecules. The theoretical inclusion model or Lakhlifi-Dahoo extended model is explained with the programs which make it possible to calculate the IR spectra of the triatomics in nano-cages. Finally, in the third part, we present some applications of models, for the study of triatomic molecules, described in the second part.

In Chapter 1, we show how to use the symmetry properties of linear and nonlinear triatomic molecules to predict the structure of the vibrational-rotational IR spectrum, taking into account the symmetry of the states between which the possible transitions occur and that of the operator inducing these transitions (dipole moment or polarization tensor). The symmetry properties are also used to apply the contact transformation method to the vibrational-rotational Hamiltonian of nonlinear triatomic molecules in order to solve the eigenvalue equation to determine the energy levels of these molecules, in particular for the rotational degrees of freedom passing from the basis set constructed on the quantum numbers of the symmetric prolate and oblate rotors to the Wang basis set, eigenfunctions of the symmetry group D2 (or V).

In Chapter 2, as in Volume 1 [DAH 17], special emphasis is placed on the use of group theory to construct the vibrational-rotational Hamiltonian and to infer selection rules as a result of the interaction between light and molecules for electrical dipolar transitions in infrared spectroscopy. The theoretical models used in the context of the contact transformation are recalled to study the vibrational and rotational movements of linear and nonlinear triatomic molecules.

In Chapter 3, it is shown that a molecule trapped in a nano-cage of a clathrate crystal is subjected to an anisotropic force field due to the interaction with crystal water molecules. The theoretical inclusion model or Lakhlifi-Dahoo extended model described in this chapter makes it possible to determine the favorable trapping sites (cage structure) of the molecular species according to their structure and size. The Langmuir constants used for calculating the abundances of trapped species, in the Van der Waals-Platteeuw thermodynamic model, are determined and presented in the simple van't Hoff form. The results of the calculations concerning some triatomic molecules are presented. On the contrary, the vibrational and rotational energy levels of the trapped molecule are perturbed. The frequencies of the vibrational transitions are shifted, generally, by a few percent, while the rotational spectrum as well as the translation movement of the molecule's center of mass undergo important modifications. The inclusion model also makes it possible to calculate the modified spectrum, using an approach similar to that described in Chapter 3 of Volume 1 [DAH 17] concerning the calculation of the shifts and the widths of the spectral lines. To illustrate these calculations, we focused on CO2, a highly studied species because of its importance in planetary atmospheres.

In Chapter 4, the comparison of simulation results with high-resolution IR spectroscopy observations of samples diluted in solid media such as rare gas matrices revealed two trapping sites for C3 and O3, in rare gas matrices, a single site and a double site, in a face-centered cubic lattice. As for the molecule-matrix coupling, it is different at the two sites, the energy relaxation being affected by multiphonon direct transfer at one site and by another mechanism at the other. The presence of the molecule in the crystal lattice...

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