PD Dr. Stefan Immel - Organic Chemisty

The molecular orbitals (MOs) of molecules can be constructed by linear combination of atomic orbitals (LCAO). Though the exact Schrödinger equation is unsolvable for many electron systems such as molecules, the solution can be numerically approximated by ab initio or density functional (DFT) theory. This page gives an overview on the molecular orbitals of various compunds calculated by DFT methods using a B3LYP/6-311+G(d,p) basis set.

Click the folders in the list below to access 3D-models of the corresponding molecular orbitals:

All MO representations are 90% isocontour probability surfaces of the electron density (ψ²), i.e. they resemble the spatial volume around the nuclei of the molecule in which the electrons are found with the corresponding certainty. The different colors (yellow and blue) represent regions with opposite sign of the wave function ψ; nodal planes (not necessarily real "planar" planes) were ψ passes through zero and changes sign are indicated in orange.

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a) Name and chemcal formula; b) Total SCF-derived electron density (sum over all MOs) shown at the 99% level (blue contours) by default, additional contours indicate 95, 90, 80, 70, 60, and 50% probability levels colored from blue to red; c) Occupied and unoccupied (virtual) molecular orbitals (MOs) in the order of increasing energy, only the "most interesting" valence π-orbitals are shown, core orbitals have been omitted. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are separated by the vertical line, in some cases degenerate occupied or unoccupied MOs are not specifically marked as such (orbital energies are displayed as mouse tooltips for the corresponding thumbnails). Nodal planes (Ψ = 0.0) of the MOs are indicated by orange 3D-isocontours, blue and yellow volumes display regions of the wave function of opposite sign. All MOs are plotted at the 90% probability level of the corresponding MO electron density (Ψ²).

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Notes: All molecular orbitals were calculated by DFT methods using a B3LYP/6-311+G(d,p) basis set. All MO representations are 90% isocontour probability surfaces of the electron density (Ψ²), i.e. they resemble the spatial volume around the nuclei of the molecule in which the electrons are found with a 90% certainty. The different colors (yellow and blue) represent spatial regions with opposite sign of the wave function Ψ; nodal planes (indicated in orange, not necessarily real "planar" planes) indicate areas were Ψ passes through zero and changes sign (→ Ψ² = 0.0, planes of zero electron density for a given orbital). The total electron density contour (99% level over all MOs) renders the molecule with its characteristic shape.
3D-Models are displayed using the Jmol Applet without the need to install any other plugins with your browser. Isocontour surfaces, nodal planes, and electron density contours may represent large files (100-1000 KBytes) which may take a moment to download. All graphics and isocontour surfaces shown on this page were created using the MolArch⁺ program in combination with the POVRAY Persistence of Vision Raytracer. Electron densities were calculated on three dimensional grids for the corresponding molecules using the Gaussian 03 Cubegen program.
Additional information on hydrogenic atomic orbitals and molecular can be obtained from the "Tutorials" section of this web site.