08s_elecconfigs

08s_elecconfigs - MIT OpenCourseWare http:/ocw.mit.edu 5.80...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
MIT OpenCourseWare http://ocw.mit.edu 5.80 Small-Molecule Spectroscopy and Dynamics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Lecture # 8 Supplement Contents 1. Excerpts from The Spectra and Dynamics of Diatomic Molecules . . . . . . . . . . . 1 2. Electronic Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1. Excerpts from The Spectra and Dynamics of Diatomic Molecules by Professor Robert W. Field and Hel ´ `ene Lefebvre-Brion Elsevier Academic Press 2004 1
Background image of page 2
Chapter 3 Terms Neglected in the Born-Oppenheimer Approximation Contents 3.1 The Born-Oppenheimer Approximation ...... 89 3.1.1 Potential Energy Curves . . . . . . . . . . . . . . . . 90 3.1.2 Terms Neglected in the Born-Oppenheimer Approximation . . . . . . . . . . . . . . . . . . . . . 92 3.1.2.1 Electrostatic and Nonadiabatic Part of H .9 2 3.1.2.1.1 Crossing or Diabatic Curves . . . 93 3.1.2.1.2 Noncrossing or Adiabatic Curves . 94 3.1.2.2 The Spin Part of H ............. 94 3.1.2.3 Rotational Part of H ............ 96 3.2 Basis Functions . . . .................. 99 3.2.1 Hund’s Cases . . . . . . . . . . . . . . . . . . . . . . 101 3.2.1.1 DeFnition of Basis Sets . . . . . . . . . . . 103 3.2.1.2 Quantum Numbers, Level Patterns, and the E±ects of Terms Excluded from H (0) . . 113 3.2.1.3 Intermediate Case Situations . . . . . . . . 126 3.2.1.3.1 Introduction . . . . . . . . . . . . 126 3.2.1.3.2 Examples . . . . . . . . . . . . . . 127 3.2.1.4 Transformations Between Hund’s Case Ba- sis Sets . . . . . . . . . . . . . . . . . . . . 130 3.2.1.5 Spectroscopic vs. Dynamical Hund’s Cases 136 3.2.1.6 Relationship between Noncommuting Terms in H and the Most Appropriate Hund’s Case137 3.2.2 Symmetry Properties . . . . . . . . . . . . . . . . . . 138
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
± 88 Terms Neglected in the Born-Oppenheimer Approximation 3.2.2.1 Symmetry Properties of Hund’s Case (a) Basis Functions . . . . . . . . . . . . . . . 138 3.2.2.2 Symmetry Properties of non-Hund’s Case (a) Basis Functions . . . . . . . . . . . . . 146 3.2.3 Molecular Electronic Wavefunctions . . . . . . . . . 148 3.2.4 Matrix Elements between Electronic Wavefunctions 156 3.3 Electrostatic Perturbations . ............ 161 3.3.1 Diabatic Curves . . . . . . . . . . . . . . . . . . . . 163 3.3.2 Approximate Representation of the Diabatic Elec- tronic Wavefunction . . . . . . . . . . . . . . . . . . 165 3.3.3 Adiabatic Curves . . . . . . . . . . . . . . . . . . . . 168 3.3.4 Choice between the Diabatic and Adiabatic Models . 172 3.3.5 Electromagnetic Field-Dressed Diabatic and Adia- batic Potential Energy Curves . . . . . . . . . . . . 177 3.4 Spin Part of the Hamiltonian . . . . . ....... 180 3.4.1 The Spin-Orbit Operator . . . . . . . . . . . . . . . 181 3.4.2 Expression of Spin-Orbit Matrix Elements in Terms of One-Electron Molecular Spin-Orbit Parameters . 183 3.4.2.1 Matrix Elements of the l zi s zi Term . . . 183 · 3.4.2.1.1 Diagonal Matrix Elements . . . . 183 3.4.2.1.2 O±-Diagonal Matrix Elements . . 187 l + i s + l + 3.4.2.2 Matrix Elements of the i i s i Part of H SO .................... 190 3.4.3 The Spin-Rotation Operator . . . . . . . . . . . . . 191 3.4.4 The Spin-Spin Operator . . . . . . . . . . . . . . . . 196 3.4.4.1 Diagonal Matrix Elements of H SS : Calcu- lation of the Direct Spin-Spin Parameter . 196 3.4.4.2 Calculation of Second-Order Spin-Orbit Ef- fects . . . . . . . . . . . . . . . . . . . . . . 198 3.4.4.2.1 π 2 Con²guration . . . . . . . . . . 201 3.4.4.2.2 π 3 π ± (or π 3 π ± 3 and ππ ± ) Con²gu- rations . . . . . . . . . . . . . . . 201 3.4.4.3 O±-Diagonal Matrix Elements . . . . . . . 202 3.4.5 Tensorial Operators . . . . . . . . . . . . . . . . . . 203 3.5 Rotational Perturbations . .............. 210 3.5.1 Spin-Electronic Homogeneous Perturbations . . . . . 210 3.5.2 The S -Uncoupling Operator . . . . . . . . . . . . . . 212 3.5.3 The L -Uncoupling Operator . . . . . . . . . . . . . . 213 3.5.4 2 Π 2 Σ + Interaction . . . . . . . . . . . . . . . . . 217 3.6 References.
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/28/2011 for the course CHEM 5.74 taught by Professor Robertfield during the Spring '04 term at MIT.

Page1 / 33

08s_elecconfigs - MIT OpenCourseWare http:/ocw.mit.edu 5.80...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online