Ethene

For two plain carbon atoms, two p orbitals combine as such:

To enable free rotation around a double bond, we just need to excite an electron from pi to pi* using uv - which results in no overall pi bonding:

A example of this being useful is the conversion of maleic acid to fumaric acid:

Maleic acid has very few uses, but fumaric acid is found in the body as part of the citric acid cycle, and is a common food additive (E297) used as an acidity regulator. It is easy to separate since fumaric acid has a boiling point over 100 degrees higher. Can you tell why?

It is because maleic acid forms intramolecular hydrogen bonds, hence forms less intermolecular ones.