Question

What are the shapes, including the locations of the nuclei, of σ and σ* orbitals?

Answer 1

All σ and σ* orbitals have cylindrical symmetry. They look the same after you rotate them by any amount about the internuclear axis.

The σ* orbital has a nodal plane half-way between the two nuclei and perpendicular to the internuclear axis.

Most of the diagrams in textbooks, like the one above, are schematic diagrams, but they all show the node and the cylindrical symmetry.

You can see the computer-generated shapes and the positions of the nuclei in the following links.

http://winter.group.shef.ac.uk/orbitron/MOs/H2/1s1s-sigma/index.html

http://winter.group.shef.ac.uk/orbitron/MOs/H2/1s1s-sigma-star/index.html