5: Molecular Orbitals
- Page ID
- 60547
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)
Molecular orbitals possess specific topology, symmetry, and energy-level patterns.
- 5.1: Orbital Interaction Topology
- The pattern of molecular orbital energies can often be 'guessed' by using qualitative information about the energies, overlaps, directions, and shapes of the atomic orbitals that comprise the molecular orbitals.
- 5.2: Orbital Symmetry
- Symmetry provides additional quantum numbers or labels to use in describing the molecular orbitals. Each such quantum number further sub-divides the collection of all molecular orbitals into sets that have vanishing Hamiltonian matrix elements among members belonging to different sets.
- 5.3: Linear Molecules
- Linear molecules belong to the axial rotation group. Their symmetry is intermediate in complexity between nonlinear molecules and atoms.
- 5.4: Atoms
- Atoms belong to the full rotation symmetry group; this makes their symmetry analysis the most complex to treat.