Mueller Fundamentals of Quantum Chemistry

Molecular Spectroscopy and Modern Electronic Structure Computations
1. Auflage 2007
ISBN: 978-0-306-47566-5
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 278 Seiten

This text is designed as a practical introduction to quantum chemistry. Quantum chemistry is applied to explain and predict molecular spectroscopy and the electronic structure of atoms and molecules. In addition, the text provides a practical guide to using molecular mechanics and electronic structure computations including ab initio, semi-empirical, and density functional methods. The use of electronic structure computations is a relevent subject as its applications in both theoretical and experimental chemical research are increasingly prevalent.

The chemistry student's interest should be established early on in the text where quantum mechanics is developed by applying it to molecular spectroscopy. Questions throughout the text labelled as "chemical connection" and "points of further understanding" focus on conceptual understanding and consequences of quantum mechanics. These questions can be used as a basis for classroom discussion, which may encourage co-operative learning techniques.  

Autoren/Hrsg.

Mueller, Michael P.

Inhaltsverzeichnis

1;Foreword;5
2;Preface;7
3;Acknowledgments;9
4;Contents;11
5;Chapter 1 Classical Mechanics;14
5.1;1.1 NEWTONIAN MECHANICS;14
5.2;1.2 HAMILTONIAN MECHANICS;16
5.3;1.3 THE HARMONIC OSCILLATOR;18
6;Chapter 2 Fundamentals of Quantum Mechanics;27
6.1;2.1 THE DE BROGLIE RELATION;27
6.2;2.2 ACCOUNTING FOR WAVE CHARACTER IN MECHANICAL SYSTEMS;29
6.3;2.3 THE BORN INTERPRETATION;31
6.4;2.4 PARTICLE-IN-A-BOX;33
6.5;2.5 HERMITIAN OPERATORS;40
6.6;2.6. OPERATORS AND EXPECTATION VALUES;40
6.7;2.7 THE HEISENBERG UNCERTAINTY PRINCIPLE;42
6.8;2.8 PARTICLE IN A THREE-DIMENSIONAL BOX AND DEGENERACY;46
7;Chapter 3 Rotational Motion;50
7.1;3.1 PARTICLE-ON-A-RING;50
7.2;3.2 PARTICLE-ON-A-SPHERE;55
8;Chapter 4 Techniques of Approximation;67
8.1;4.1 VARIATION THEORY;67
8.2;4.2 TIME INDEPENDENT NON-DEGENERATE PERTURBATION THEORY;73
8.3;4.3 TIME-INDEPENDENT DEGENERATE PERTURBATION THEORY;89
9;Chapter 5 Particles Encountering a Finite Potential Energy;98
9.1;5.1 HARMONIC OSCILLATOR;98
9.2;5.2 TUNNELING, TRANSMISSION, AND REFLECTION;109
10;Chapter 6 Vibrational/Rotational Spectroscopy of Diatomic Molecules;126
10.1;6.1 FUNDAMENTALS OF SPECTROSCOPY;126
10.2;6.2 RIGID ROTOR HARMONIC OSCILLATOR APPROXIMATION (RRHO);128
10.3;6.3 VIBRATIONAL ANHARMONICITY;141
10.4;6.4 CENTRIFUGAL DISTORTION;145
10.5;6.5 VIBRATION-ROTATION COUPLING;148
10.6;6.6 SPECTROSOPIC CONSTANTS FROM VIBRATIONAL SPECTRA;149
10.7;6.7 TIME DEPENDENCE AND SELECTION RULES;153
11;Chapter 7 Vibrational and Rotational Spectroscopy of Polyatomic Molecules;163
11.1;7.1 ROTATIONAL SPECTROSCOPY OF LINEAR POLYATOMIC MOLECULES;163
11.2;7.2 ROTATIONAL SPECTROSCOPY OF NON-LINEAR POLYATOMIC MOLECULES;169
11.3;7.3 INFRARED SPECTROSCOPY OF POLYATOMIC MOLECULES;181
12;Chapter 8 Atomic Structure and Spectra;190
12.1;8.1 One-Electron Systems;190
12.2;8.2 THE HELIUM ATOM;204
12.3;8.3 ELECTRON SPIN;212
12.4;8.4 COMPLEX ATOMS;213
12.5;8.5 SPIN-ORBIT INTERACTION;220
12.6;8.6 SELECTION RULES AND ATOMIC SPECTRA;230
13;Chapter 9 Methods of Molecular Electronic Structure Computations;235
13.1;9.1 THE BORN-OPPENHEIMER APPROXIMATION;235
13.2;9.2 THE MOLECULE;237
13.3;9.3 MOLECULAR MECHANICS METHODS;245
13.4;9.4 AB INITIO METHODS;248
13.5;9.5 SEMI-EMPIRICAL METHODS;262
13.6;9.6 DENSITY FUNCTIONAL METHODS;264
13.7;9.7 COMPUTATIONAL STRATEGIES;268
14;Appendix I Table of Physical Constants;272
15;Appendix II Table of Energy Conversion Factors;273
16;Appendix III Table of Common Operators;274
17;Index;275
18;More eBooks at www.ciando.com;0

Leseproben

Chapter 6
Vibrational/Rotational Spectroscopy of Diatomic Molecules (p. 113-114)

This chapter focuses on applying the fundamentals of quantum mechanics developed in the previous chapters to interpreting the vibrational and rotational transitions that occur within diatomic molecules in infrared spectroscopy. Analysis of an infrared spectrum of a diatomic molecule results in structural information about the molecule and the energy differences between the molecule’s vibrational and rotational eigenstates.


6.1 FUNDAMENTALS OF SPECTROSCOPY

Molecular spectroscopy is a means of probing molecules and most often involves the absorption of electromagnetic radiation. The absorbed electromagnetic radiation results in transitions between eigenstates of a molecule. The type of eigenstates involved in a transition depends on the energy of the radiation absorbed. Figure 6-1 shows an electromagnetic spectrum along with the relative energies, wavelengths, and frequencies associated with each type of radiation. Absorbed ultraviolet and visible radiation generally results in transitions amongst electronic eigenstates. Absorbed infrared radiation results in changes in vibrational and rotational eigenstates. Absorbed microwave radiation results in changes in rotational eigenstates.

The specific wavelengths of radiation that are absorbed in each region of the electromagnetic spectrum depend on the energy difference between the eigenstates of a molecule. As an example, a diatomic molecule with a "stiff" bond will absorb at a higher energy photon (shorter wavelength) than another diatomic molecule with a less "stiff" bond.

The absorbed radiation in a spectrum provides information on the energy differences amongst various eigenstates of a molecule; however, it does not provide any information on the actual eigenstates involved in the transitions. Quantum mechanics is needed in order to analyze a spectrum in terms of assigning an absorption in a spectrum to a specific transition in eigenstates of a molecule. The energy of a photon of electromagnetic radiation is inversely proportional to its wavelength