Fabien Gatti

Applications of Quantum Dynamics in Chemistry

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. n nAssuming 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. n nThe 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. n nThis 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.

Computing energy levels of CH4, CHD3, CH3D, and CH3F with a direct product basis and coordinates based on the methyl subsystem

Quantum mechanical calculations of ro-vibrational energies of CH4, CHD3, CH3D, and CH3F were made with two different numerical approaches. Both use polyspherical coordinates. The computed energy levels agree, confirming the accuracy of the methods. In the first approach, for all the molecules, the coordinates are defined using three Radau vectors for the CH3 subsystem and a Jacobi vector between the remaining atom and the centre of mass of CH3. Euler angles specifying the orientation of a frame attached to CH3 with respect to a frame attached to the Jacobi vector are used as vibrational coordinates. A direct product potential-optimized discrete variable vibrational basis is used to build a Hamiltonian matrix. Ro-vibrational energies are computed using a re-started Arnoldi eigensolver. In the second approach, the coordinates are the spherical coordinates associated with four Radau vectors or three Radau vectors and a Jacobi vector, and the frame is an Eckart frame. Vibrational basis functions are products of contracted stretch and bend functions, and eigenvalues are computed with the Lanczos algorithm. For CH4, CHD3, and CH3D, we report the first J > 0 energy levels computed on the Wang-Carrington potential energy surface [X.-G. Wang and T. Carrington, J. Chem. Phys. 141(15), 154106 (2014)]. For CH3F, the potential energy surface of Zhao et al. [J. Chem. Phys. 144, 204302 (2016)] was used. All the results are in good agreement with experimental data.

Control of Molecular Processes

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.

The Influence of Renner-Teller Coupling between Electronic States on H+CO Inelastic Scattering

We examine the excitation of carbon monoxide from its rovibrational ground state via collisions with a hydrogen atom. Calculations employ the Multi-Configuration Time-Dependent Hartree method and treat the nonadiabatic dynamics with the inclusion of both the ground and the Renner-Teller coupled first excited electronic states. For this purpose, a new set of recently presented global HCO Potential Energy Surfaces (PESs) that cover the 0-3 eV range of energy is used. The results obtained here considering only the ground state (without the Renner-Teller coupling) are in qualitative agreement with those available in the literature. The Renner-Teller effect is known to have an important effect on the spectroscopy of the system, and its inclusion and effects on the dynamics for the processes described in this paper are fairly significant also. The results of this study indicate that for certain very particular initial conditions rather dramatic effects can be observed.

The Kinetic Energy Operator in Curvilinear Coordinates

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 .

Introduction to Numerical Methods

The present chapter is dedicated to the numerical methods for solving the time-dependent Schrodinger equation for the nuclei.

Quantum Mechanical Background

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.

Choosing the Set of Coordinates for the Nuclei

Once the potential energy surfaces have been calculated, the Schrodinger equation for the nuclei has to be solved. Before solving the nuclear Schrodinger 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.

Group Theory and Molecular Symmetry

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.

Molecular Hamiltonian Operators

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.