Infrared Spectroscopy of Triatomics for Space Observation

By Pierre-Richard Dahoo and Azzedine Lakhlifi

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.

• Language: English
• Publisher: Wiley
• Release date: Dec 31, 2018
• ISBN: 9781119579304

Book preview

Foreword

Space is an extraordinary laboratory for glimpsing the extent and complexity of physical phenomena at work in nature. It offers extreme environments that humans cannot reproduce on Earth. Temperatures reach absolute zero in dense interstellar clouds and reach trillions of degrees around super massive black holes. The density of the diffuse nebulae is lower than that produced by the best terrestrial vacuum generators; the density of the residues of dead stars is so great that the matter becomes unstructured.

Even if these laboratories are mostly inaccessible to humans and even to space probes (except for a few stars in the solar system), a colossal amount of information is contained in the light that passes through space. When light rays meet the mirrors of our telescopes, they are focused on increasingly powerful detectors and analytical instruments.

The spectral analysis of light, split into an optical prism, is particularly rich in information about the physicochemical nature of stars and their environment. Like a fingerprint, each of the chemical elements leaves a unique signature in the spectrum of light, making it possible to specify the chemical composition of stars. The shape of these spectral lines also testifies to the physical conditions that reign at the source of this light.

Nevertheless, according to the 19th-Century positivist philosopher Auguste Comte, all the chemical elements in the solar system – including those found in living beings – have a cosmic origin. The elements can thus be classified into a small number of families, which are defined by the process that created them: the Big Bang (hydrogen and helium), nuclear reactions in stars (carbon, nitrogen, etc.), explosions of supernovae (oxygen, phosphorus, sulfur, iron, etc.), fusion of neutron stars (francium, uranium, thorium, etc.) and the spallation of cosmic rays (boron, beryllium).

The surface of the Earth is the shore of the cosmic ocean […] We’re made of star stuff. We are a way for the cosmos to know itself. Expressed in a poetic way by the astrophysicist Carl Sagan, it seems that our cosmic origin and the detailed understanding of atoms and molecules take on a meaning that surpasses us.

In a famous analogy, Richard Feynman likens the physicist to an insect floating in the corner of a pool, rising and falling with the waves, and trying to reconstruct what is happening in this pool simply by measuring the height of the electromagnetic waves. The astrophysicist is also striving towards the goal of discovering and understanding what is happening in the cosmic ocean, by the mere observation of electromagnetic waves that reach the shore.

Spectroscopy in all its facets (instruments, theoretical frameworks, analyses and techniques) is today a vast field with multiple ramifications. It is without a doubt the most powerful, the finest and most universally used tool available to translate these waves into a coherent vision of the universe on all scales, from the infinitely small to the infinitely large.

An entity is more than just the sum of its parts, as Aristotle had already formulated several millennia ago.

The authors, specialists in modeling and spectroscopy, show us the theoretical models of triatomic molecules and their infrared spectra in different environments of space. This book adds a string to the bow, adding to our understanding of this part of the entity.

Céline REYLÉ

Astrophysicist at Institut UTINAM

Science Observatory at Univers Franche-Comté Bourgogne

Preface

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 Masterʼs 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 Masterʼs 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 modifies the thermal properties of the solid environment as a result of slow modes related to the constrained rotational movements of the molecule and which generate the orientational modes. In the case of ozone, the coupling between the phonons and the slow modes of the trapped molecule must be included to interpret the temperature dependence on the linewidths for the two sites.

In Chapter 5, the focus is on the effect of an electromagnetic environment, present in a nano-cage, on the electronic potential that drives the movement of nuclei in a linear triatomic molecule. In a rare gas matrix, the nano-cage consists of a nano-site built on the replacement of an atom of the matrix (single substitution site S1) or of two atoms of the matrix (double substitution site S2) by the triatomic molecule. The methods of solid-state physics and molecular physics of dilute (gas phase) media are applied to the condensed phase of the molecule–matrix system to calculate the effect of the electromagnetic environment on the molecule vibrations. Two conditions are necessary for the molecule–matrix environment dynamic coupling to be effective: the site symmetry must be compatible with that of the molecule and the vibrational energies of the condensed phase must be of the same order of magnitude as those of the molecule vibrations. Calculations show that this dynamic coupling is negligible with respect to the static coupling: the electromagnetic field mainly polarizes the peripheral electronic orbitals of the molecule and slightly modifies the electronic potential that drives the movement of the nuclei. This Stark effect is the predominant effect that is responsible for the displacement of vibrational frequencies, high frequencies, in IR.

In Chapter 6, two examples of triatomic molecules illustrate the application of the theoretical models, described in the previous chapters, on the adsorption phenomenon of a molecule onto a substrate (here, graphite). On the one hand, the equilibrium configuration and the adsorption energy of the adsorbed molecule are determined by the minimization of the molecule–surface interaction potential energy. On the other hand, the diffusion constant is calculated after determining the diffusion valley. Finally, in the context of a possible bridging among adsorbed molecules, the electrostatic and induction interaction energies between two multipolar molecules up to the octupole–octupole order are presented with a program in FORTRAN language to compute them.

Pierre Richard DAHOO

Azzedine LAKHLIFI

October 2018

1

Symmetry of Triatomic Molecules

With regard to the rotational and vibrational spectroscopy of a molecule, it is necessary to solve the Schrödinger eigenvalue equation to determine the quantum energy levels between which a transition leading to its spectral signature takes place. The study of these spectra makes it possible to determine its structure in rotational spectroscopy and the force fields responsible for the chemical bonds in vibrational spectroscopy. The symmetry of a molecule greatly influences the appearance of its absorption, emission or diffusion spectra. Based on the applications of group theory, it is possible to characterize the vibrational and rotational degrees of freedom of a triatomic molecule by the symmetry characteristics found in the structure corresponding to the molecule and to determine the transitions that are likely to be observed in an experiment, commonly called selection rules. Although the link between symmetry causes and symmetry effects are not directly obvious, as stated by Pierre Curie, it is easy to observe the consequences of the symmetry properties of molecules on the structure of the observed spectra, in absorption or emission spectroscopy or in Raman spectroscopy. Theoretical methods developed by J.M. Flaud and C. Camy-Peyret to establish the vibrational–rotational Hamiltonian of nonlinear triatomic molecules (H2O, O3, etc.) within the application of contact transformations of J.H. Van Vleck, based on J.K.G. Watson’s work, show the need to consider the symmetries of the molecular structure to establish the correlation between the results of computations and observations.

1.1. Introduction

The vibrational and rotational spectroscopic study of triatomic molecules corresponds to the analysis of spectra resulting from absorption, emission or scattering processes of photons in the low-energy domain, ranging from microwaves to ultraviolet waves. In molecular physics, to determine the rovibrational energy levels of a molecule, the molecular Hamiltonian, established by E.B. Wilson and J.B. Howard [WIL 36], reformulated by B.T. Darling and B.M. Dennison [DAR 40] and further simplified by J.K.G. Watson [WAT 68], is used in the context of J.H. Van Vleck’s contact transformation [VAN 29, ALI 85] to determine the vibrational–rotational energy levels at different orders of approximation. The formalization of this method can be found in Chapter 2 of Volume 1 [DAH 17], with its application to diatomic molecules illustrated. This method uses unitary transformations that make it possible to group the Hamiltonian into interacting polyads and to obtain a block-like matrix form that is easier to diagonalize. From the method proposed by J.K.G. Watson [WAT 67a, WAT 67b, WAT 67c] to study isolated states