EHMO (Extended Hückel Molecular Orbital Theory)
Definition and meaning of EHMO (Extended Hückel Molecular Orbital Theory) in chemistry.
EHMO (Extended Hückel Molecular Orbital theory) is a semi-empirical quantum chemical method that calculates approximate molecular orbitals using all valence atomic orbitals of a molecule, not just its pi system. It extends simple Hückel theory to three-dimensional, non-planar, and inorganic molecules by including sigma bonding and explicit orbital overlap.
In more detail
Developed by Roald Hoffmann in 1963, EHMO builds a secular matrix from valence-orbital ionization energies (diagonal terms) and off-diagonal terms estimated from orbital overlap via the Wolfsberg-Helmholz approximation, then solves for orbital energies and coefficients. Because electron-electron repulsion is not treated explicitly and no self-consistent field iteration is performed, the method gives only qualitative or semi-quantitative results, but it is fast and reveals orbital symmetry and shape clearly. It became a key tool for rationalizing the geometries and reactivity of organometallic and main-group compounds and underpinned analysis of orbital symmetry in pericyclic reactions.
Key facts
| Field | Physical Chemistry |
|---|---|
| Developed by | Roald Hoffmann, 1963 |
| Type | Semi-empirical, non-self-consistent MO method |
| Key approximation | Wolfsberg-Helmholz off-diagonal terms |
EHMO calculations were used by Hoffmann to explain the preferred bent versus linear geometries of transition-metal complexes and to construct the frontier-orbital pictures behind the Woodward-Hoffmann rules for electrocyclic ring closures.
Frequently asked questions
How does EHMO differ from simple Hückel theory?
Simple Hückel theory treats only pi electrons in planar conjugated systems and ignores orbital overlap, while EHMO includes all valence electrons (sigma and pi), uses explicit overlap integrals, and applies to three-dimensional molecules, including inorganic and organometallic complexes.
Is EHMO still used today?
It is rarely used for quantitative energetics now that ab initio and density functional theory methods are widely available, but it remains a useful qualitative tool for visualizing orbital symmetry and shape.