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## Über dieses Buch

This book explains the usage and application of Molecular Quantum Dynamics, the methodology where both the electrons and the nuclei in a molecule are treated with quantum mechanical calculations. This volume of Lecture Notes in Chemistry addresses graduate students and postdocs in the field of theoretical chemistry, as well as postgraduate students, researchers and teachers from neighboring fields, such as quantum physics, biochemistry, biophysics, or anyone else who is interested in this rising method in theoretical chemistry, and who wants to gain experience in the opportunities it can offer. It can also be useful for teachers interested in illustrative examples of time-dependent quantum mechanics as animations of realistic wave packets have been designed to assist in visualization.

Assuming a basic knowledge about quantum mechanics, the authors link their explanations to recent experimental investigations where Molecular Quantum Dynamics proved successful and necessary for the understanding of the experimental results. Examples including reactive scattering, photochemistry, tunneling, femto- and attosecond chemistry and spectroscopy, cold chemistry or crossed-beam experiments illustrate the power of the method. The book restricts complicated formalism to the necessary and in a self-contained and clearly explained way, offering the reader an introduction to, and instructions for, practical exercises. Continuative explanation and math are optionally supplemented for the interested reader.

The reader learns how to apply example simulations with the MCTDH program package (Multi Configuration Time Dependent Hartree calculations). Readers can thus obtain the tools to run their own simulations and apply them to their problems. Selected scripts and program code from the examples are made available as supplementary material.

This book bridges the gap between the existing textbooks on fundamental theoretical chemistry and research monographs focusing on sophisticated applications. It is a must-read for everyone who wants to gain a sound understanding of Molecular Quantum Dynamics simulations and to obtain basic experience in running their own simulations.

## Inhaltsverzeichnis

### Chapter 1. Introduction

Abstract
The main goal of this book is to illustrate how the concept of a wavepacket becomes central in quantum mechanics when turning to concrete applications, for instance in molecular physics and chemistry. In other words, the Schrödinger equation in its time-dependent form provides the central framework here.
Fabien Gatti, Benjamin Lasorne, Hans-Dieter Meyer, André Nauts

### Erratum to: Applications of Quantum Dynamics in Chemistry

Without Abstract
Fabien Gatti, Benjamin Lasorne, Hans-Dieter Meyer, André Nauts

### Chapter 2. Quantum Mechanical Background

Abstract
Quantum mechanics is certainly one of the most successful theories in science. It has deeply influenced many areas of pure and applied physics and pervades many branches of science, from physics, matter sciences, computer science to chemistry and even to molecular biology. However, quantum mechanics has to face several conceptual difficulties of which most relate to the process of quantum measurement and its randomness so that, almost one century after its birth, a complete consensus has still not been reached concerning the interpretation of the theory and its foundations. However, in the present book, we will adopt what can be viewed as a pragmatic approach in which quantum mechanics is regarded as an operational theory designed to predict the outcomes of measurements on physical systems under well-defined conditions.
Fabien Gatti, Benjamin Lasorne, Hans-Dieter Meyer, André Nauts

### Chapter 3. Molecular Hamiltonian Operators

Abstract
In the present book, we will consider molecular systems either isolated or in interaction with external electromagnetic fields. In a bottom-up approach, which we will try to follow here, a molecule, or more generally a molecular system, is regarded as a collection of electrons and nuclei in interaction with each other and possibly with external fields.
Fabien Gatti, Benjamin Lasorne, Hans-Dieter Meyer, André Nauts

### Chapter 4. Vibronic Couplings

Abstract
Photoinduced processes (photochemical and photophysical) often involve vibronic couplings that are responsible of ultrafast radiationless decay processes from an excited electronic state to a lower-energy one (typically , internal conversion , between same-spin electronic states, or intersystem crossing for different spins ; note that corresponding light-emitting processes are called fluorescence and phosphorescence, respectively). In such a situation, the excess energy first given to the molecule through light absorption is converted into electronic excitation and then transformed into vibrational excitation.
Fabien Gatti, Benjamin Lasorne, Hans-Dieter Meyer, André Nauts

### Chapter 5. Choosing the Set of Coordinates for the Nuclei

Abstract
Once the potential energy surfaces have been calculated, the Schrödinger equation for the nuclei has to be solved. Before solving the nuclear Schrödinger equations, one key issue in molecular quantum dynamics is the choice of the 3N-6 internal nuclear coordinates, $${{\varvec{q}}}$$, and the three Euler angles, $${\varvec{\Theta }}$$, introduced in Chap. 3. $${{\varvec{q}}}$$ describe the shape of the molecule (the molecular geometry) and $${\varvec{\Theta }}$$ parametrize the BF frame and thus the overall rotation of the molecule.
Fabien Gatti, Benjamin Lasorne, Hans-Dieter Meyer, André Nauts

### Chapter 6. The Kinetic Energy Operator in Curvilinear Coordinates

Abstract
The present chapter is intended as a rather in-depth introduction to the classical kinetic energy and the quantum kinetic energy operator for the nuclei, denoted T and $$\hat{T}$$, respectively, in the following. The positions of the particles will be described by means of generalized curvilinear coordinates .
Fabien Gatti, Benjamin Lasorne, Hans-Dieter Meyer, André Nauts

### Chapter 7. Group Theory and Molecular Symmetry

Abstract
In various chapters of this book, we have mentioned how a group-theoretical approach could be applied to molecular symmetry and help in the context of vibrational and vibronic problems.
Fabien Gatti, Benjamin Lasorne, Hans-Dieter Meyer, André Nauts

### Chapter 8. Introduction to Numerical Methods

Abstract
The present chapter is dedicated to the numerical methods for solving the time-dependent Schrödinger equation for the nuclei.
Fabien Gatti, Benjamin Lasorne, Hans-Dieter Meyer, André Nauts

### Chapter 9. Infrared Spectroscopy

Abstract
Molecular quantum dynamics has given rise to many applications of relevance for astrophysics, astrochemistry and atmospheric chemistry.
Fabien Gatti, Benjamin Lasorne, Hans-Dieter Meyer, André Nauts

### Chapter 10. Photodissociation Spectroscopy

Abstract
In the previous chapter, we have considered transitions induced by absorption of light between vibrational states in the electronic ground state only. In the present chapter, we stay within the framework of the Born-Oppenheimer approximation but we consider transitions from the electronic ground state to another electronic state that is dissociative. In other words, the absorption of the electromagnetic energy of light, typically in the ultraviolet (UV) domain, induces a fragmentation of a bound molecule. Photodissociations of small polyatomic molecules are the motors for many important chain reactions determining the complex chemistry of the atmosphere and the starting points for many chemical lasers [1]. We consider here two examples: the photodissociations of NOCl and ozone.
Fabien Gatti, Benjamin Lasorne, Hans-Dieter Meyer, André Nauts

### Chapter 11. Bimolecular Reactions

Abstract
Another class of important elementary processes in chemistry are bimolecular processes, i.e. processes where two molecules collide and exchange energy, atoms or groups of atoms. Understanding these elementary processes at their most fundamental level is a challenging task of tremendous practical importance for industrial reasons, if the elementary process is the rate determining step of an important industrial chemical reaction.
Fabien Gatti, Benjamin Lasorne, Hans-Dieter Meyer, André Nauts

### Chapter 12. Vibronic Coupling

Abstract
In polyatomic molecules, non-Born-Oppenheimer processes occur mainly around topographical features joining different PESs, known as conical intersections [13] and introduced in Chap. 4. A conical intersection induces strong couplings between electrons and nuclei. It acts as a funnel through which a new chemical reaction can occur and enables rapid conversion of the excess electronic energy into nuclear motion [4]. Thus, conical intersections are a central paradigm for understanding reaction mechanisms in photochemistry and photobiology, as important as transitions states in thermal chemistry [5].
Fabien Gatti, Benjamin Lasorne, Hans-Dieter Meyer, André Nauts

### Chapter 13. Control of Molecular Processes

Abstract
In the previous applications, we have considered only “artificial” wavepackets, i.e. wavepackets that generally do not correspond to any realistic experimental situation. The mathematical properties of the wavepackets allowed us to obtain absorption spectra and cross sections including all the quantum effect that can impact a molecular process. All the systems were assumed to be isolated and no quantum decoherence occurred during the propagations of the wavepackets. However, wavepackets are not only mathematical tools to obtain some measured physical quantities, they can be created experimentally. Since the advent of lasers, coherent sources of light can be produced that can in turn create coherent superpositions of molecular states and thus molecular wavepackets. Quantum coherence will finally be dissipated by interaction with the environment but, before this, quantum coherence may be preserved during a time that is sufficient to trigger a new type of chemical process.
Fabien Gatti, Benjamin Lasorne, Hans-Dieter Meyer, André Nauts

### Backmatter

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