The electron probability density isosurface defines the shape of the molecule and follows the relative outline defined by the atoms themselves. The electron probability density isosurface is usually drawn so that there is a particular probability, often 90%, that the electrons will be within the region of space enclosed by the surface.
The underlying electron probability density contours of molecular orbitals can be visualized by coloring the electron density volume isosurface.
Contours in xy Plane
The electron probability density of the molecular orbital may be represented with a two dimensional isocontour map.The isocountour lines (lines along which electron denisty is constant) are between the colored regions in the diagram.
Plane Contour / Isosurface
This graphic compares electron density isocontours in the xy plane with the three-dimensional isosurface for the s 2px (sigma bonding) molecular orbital of the nitrogen molecule.
The isocountour lines (lines along which electron denisty is constant) are between the colored regions in the diagram.
HOMO Density & Plane
In this graphic, the two dimensional electron probability density isocontours of the nitrogen molecule HOMO (shown on the left) have been mapped onto an isosurface for the electron density of the molecule (shown on the middle right). This model shows the location of the HOMO lobes within the space occupied by the molecule. This representation is valuable because it locates on a surface that encloses a large percentage of the molecule's electron density, the areas where the most loosely bound electrons reside. In this example, the red areas at each end of the molecule indicate where on the isosurface the HOMO electron density is greatest.
In this example only outer green lobes of the HOMO (upper right) are visible on the surface. The center blue lobe has a much smaller volume and is hidden inside.