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.

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This page gives an overview on the molecular orbitals of benzene calculated by DFT methods using a B3LYP/6-311++G** basis set. All MO representations are 90% or 90-25% iso-contour 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.

• Total Electron Density of Benzene
• Molecular Orbitals of Benzene

Click on the small images below with blue background below to obtain an enlarged view - the images with black background provide links to the corresponding 3D-models (VRML-type models); these links will open in a new window.

Below on the right, the schematic drawing indicates the major contributions of atomic orbitals (AOs) to the molecular orbitals (MOs) of benzene. With increasing energy of the orbitals (from bottom to top), the number of nodal planes (not necessarily real "planar" planes) increases and the symmetry decreases. For benzene, there are six π-electrons (C₆H₆) and three occupied π-orbitals (σ-orbitals are not shown here). The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are both doubly degenerate. The π-MOs are constructed from the carbon 2p_z-orbitals; note the increasing number of nodal planes. Further informations on AOs are available from the gallery of hydrogenic orbitals and hybrid orbitals.

The thumbnail images on the left provide access to enlarged graphics as well as 3D-models (VRML) of the orbitals, respectively. All images and models are scaled relative to each other, except the ones for the highest unoccupied orbital (reduced to approx. 60%).

No.a)	Labelb)		Nodesc)	90%d)	90-25%e)	3Df)
4	(B2g)
3b	(E2u/A'')
3a	(E2u/A')
2b	(E1g/A'')
2a	(E1g/A')
1	(A2u)

Notes: a) Orbital number (see scheme on the right, degenerate orbitals with equal energy are denoted by same numbers); b) Label (symmetry descriptor in parenthesis); c) Nodal planes (ψ = 0.0); d) 90% Probability contours of MO electron density (ψ^2); e) 90, 80, 70, 60, 50, 40, and 25% Probability contours; f) 3D-Models require a VRML plugin to be installed (large files with sizes between 500-4700 KBytes); files have been reduced in resolution to save band-width.

For a more detailed description of atomic orbitals see the corresponding gallery of orbitals. All graphics and iso-contour surfaces shown on this page were created using the MolArch⁺ program and POVRAY Persistence of Vision Raytracer. Electron densities were calculated on three dimensional grids for the corresponding molecules using the JAGUAR program.