9: Molecules
- Page ID
- 419514
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Quantum mechanics can be used to predict a large number of properties, especially those related to electronic spectroscopy, for diatomic molecules. A number of the concepts discussed in this chapter can be expanded to explain a great deal of the behavior of polyatomic molecules as well.
- 9.1: Potential Energy and the Hamiltonian
- The first task of applying quantum mechanics to a problem is writing the Hamiltonian.
- 9.2: The Born-Oppenheimer Approximation
- The Born-Oppenheimer approximation is made in order to simplify the problem in the case of a molecule.
- 9.3: Molecular Orbital Theory
- There are a number of ways to describe the electronic structure in diatomic molecules and the wavefunctions that are needed for the descriptions.
- 9.4: Hund's coupling cases (a) and (b)
- There are clearly sources of angular momentum in a molecule due to orbital and spin considerations. But unlike atoms, molecules can also have angular momentum contributions from molecular rotation.
- 9.5: Diatomic Term Symbols
- A term symbol for a diatomic molecule contains a great deal of information about symmetry properties of the wavefunction which describes the electronic state.
- 9.6: Herzberg Diagrams
- One of the important reasons for describing the electronic structures and angular momentum coupling in diatomic molecules is to apply these descriptions to the prediction of the rotational branch structure in molecular spectra.
- 9.7: Vibronic Transitions
- Just as rotational motion is important in understanding vibrational spectra, vibrational (as well as rotational) motion(s) are important in understanding electronic transition is molecules.
- 9.8: Term Symbols for Polyatomic Molecules
- Term symbols are used to designate electronic states of polyatomic molecules, much the same as they are used to designate electronic states for both atomic systems and diatomic molecules.
- 9.9: Group Theoretical Approach to Molecular Orbitals
- One of the more powerfully predictive things we can do with Group Theory is predict the symmetries of molecular orbitals. Molecular orbital symmetries can have huge ramification on chemical bonding and chemical reactions.
Thumbnail: A covalent bond forming \(\ce{H2}\) where two hydrogen atoms share the two electrons. (CC BY-SA 3.0; Jacek FH via Wikipedia; modified by LibreTexts)