Skip to main content
Chemistry LibreTexts

7: Further Characterization of Molecular Orbitals

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    The most elementary molecular orbital models contain symmetry, nodal pattern, and approximate energy information

    • 7.1: The LCAO-MO Expansion and the Orbital-Level Schrödinger Equation
      In the simplest picture of chemical bonding, the valence molecular orbitals are constructed as linear combinations of valence atomic orbitals according to the LCAO-MO formula.
    • 7.2: Determining the Effective Potential
      In the most elementary models of orbital structure, the quantities that explicitly define the potential V are not computed from first principles as they are in so-called ab initio methods. Rather, either experimental data or results of ab initio calculations are used to determine the parameters in terms of which V is expressed. The resulting empirical or semi-empirical methods discussed below differ in the sophistication.
    • 7.3: The Hückel Parameterization
      The Hückel mode is the most simplified orbital-level model. Its implementation requires knowledge of the atomic resonance and exchange values, which are eventually expressed in terms of experimental data, as well as a means of calculating the geometry dependence of the βμ,νβμ,ν 's (e.g., some method for computing overlap matrices Sμ,νSμ,ν ).
    • 7.4: The Extended Hückel Method
      It is well known that bonding and antibonding orbitals are formed when a pair of atomic orbitals from neighboring atoms interact. The energy splitting between the bonding and antibonding orbitals depends on the overlap between the pair of atomic orbitals.

    This page titled 7: Further Characterization of Molecular Orbitals is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Jack Simons via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.