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7.1.2: Summary of the three most common geometries

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    • A brief summary of the factors for predicting geometry

    The three most important factors for determining metal complex geometry in biological metal binding sites:

    1. Stabilization Energy (including LFSE)
    2. Steric interactions between ligands
    3. Protein folding or constraints caused by limitations in bond angle (geometric constraints)

    Splitting of d-orbitals in the three most-common geometries:

    Diagram of d-orbital splitting for octahedron (left), tetrahedron (middle), and square planar (right) geometries. The vertical axis on the left marks the different energy values. The barycenter, where energy equal zero, is in the middle. Energy increases up the axis with positive values and decreases down the axis with negative values. Octahedral geometry has three orbitals at -0.4 times delta-o and has two orbitals at +0.6 times delta-o. The three lower orbitals are xy, xz, and yz. The higher orbitals are z-squared and x-squared-minus-y-squared.Tetrahedral geometry has three orbitals at +0.18 times delta-o and has two orbitals at -0.27 times delta-o. The higher orbitals are xy, xz, and yz and the lower orbitals are z-squared and x-squared-minus-y-squared. Square planar geometry has one orbital at +1.23 times delta-o, one at +0.23 times delta-o, one at -0.43 times delta-o, and two at -0.51 times delta-o. The highest energy orbital is x-squared-minus-y-squared, followed by z-squared, xy and yz, then zy.

    OCTAHEDRAL (most common)

    • Is the preferred geometry for most metals because 6 ligands contribute to stabilizing electrophilic metal center.
    • Will always have more negative (stable) LFSE than analogous tetrahedral case.
    • Is more sterically crowded

    Tetrahedral (2nd most common)

    • Small \(\Delta\) means less negative LFSE (less stable in terms of LFSE)
    • Always high spin
    • Best case in terms of steric crowding around the metal center

    Square Plane (\(d^8\) and \(d^9\))

    • The bigger the \(\Delta\), the more likely it will be square planar due to huge LFSE benefit.
      • Pt and Pd are almost always square planar while Ni is often tetrahedral.
      • In the case of Ni, strong filed ligands favor square plane.
    • \(d^9\) metals prefer square plane (or something similar) as a result of Jahn-Teller distortion of octahedral geometry.
    • Highest-energy orbital is usually empty in \(d^8\).

    Attribution

    Modified or created by Kathryn Haas (khaaslab.com)

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