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 styrene, nitrobenzene, and anisole 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.

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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, plots for the molecular orbitals (only π-framework, σ-orbitals are not shown) of styrene (left), nitrobenzene (center), and anisole (right) are given.

For styrene, the three lowest energy occupied π-orbitals display similar shapes to those found for the orbitals of benzene. The fourth and highest occupied molecular π-orbital (HOMO) of styrene displays larger electron densities (i.e. large atomic orbital coefficients) in the β-position (at the terminal =CH₂ group) than at the α-carbon atom (i.e. -CH=). Additionally, the atomic orbital coefficients are larger in the para- and ortho-locations compared to the meta-carbon atom. These β-, para-, and ortho-positions are exactly those preferably attacked by electrophiles (electrophiles are potentially positively charged reagents with a low-energy unoccupied molecular orbital LUMO, which interacts with the HOMO of the corresponding substrates).

Similar arguments apply to the HOMO of anisole (depicted on the right), showing the preferred electrophilic substitution at the para- and ortho-positions. The shapes of the low-energy orbitals differ from those found for styrene, partly due to the presence of the electronegative oxygen atom.

For nitrobenzene, the order of the two highest-energy occupied orbitals are reversed compared to styrene and anisole. The HOMO displays larger orbital coefficients in the meta-location compared to the ortho-carbon atom (and a nodal plane passing through the para-carbon, i.e. an atom orbital coefficient of zero at this site). Consequently, nitrobenzene is attacked by electrophiles in the meta-position.

The thumbnail images below provide links to access to enlarged graphics as well as 3D-models (VRML) of the orbitals, respectively. Further informations on atomic orbitals (AOs) are available from the gallery of hydrogenic orbitals and hybrid orbitals.

Styrene (C6H5-CH=CH2)

Nitrobenzene (C6H5-NO2)

Anisole (C6H5-OCH3)

Nodesa)

90%b)

90-25%c)

3Dd)

Nodesa)

90%b)

90-25%c)

3Dd)

Nodesa)

90%b)

90-25%c)

3Dd)

- e)

- e)

- e)

- e)

- e)

- e)

- e)

- e)

Notes: a) Nodal planes (ψ = 0.0); b) 90% Probability contours of MO electron density (ψ^2); c) 90, 80, 70, 60, 50, 40, and 25% Probability contours; d) 3D-Models require a VRML plugin to be installed (large files with sizes between 1000-5400 KBytes); files have been reduced in resolution to save band-width; e) Orbital not shown.

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.