Re: what applies force from the mean position of a vibrating molecule?

Sanket,

It appears that you reading a specific passage when you refer to the equation, "e=e1+e2+e3+e4 where e3 and e4 are kinetic and potential energies of vibration". Without a reference to that source, I can only guess about the situation which it is describing.

The paragraph might be describing a molecule in a crystal lattice that undergoes simple harmonic motion (SHM) about its equilibrium position. The restoring force in this case is the electromagnetic interaction of the molecule with its neighbors.

Alternatively, the paragraph might be describing the vibrational excitation of a single molecule. In this case, the restoring force is provided by the electromagnetic bonds between the atoms that comprise the molecule.
http://en.wikipedia.org/wiki/Molecular_vibration

In general, though, it is not true that "any substance" executes SHM. Molecules of a gas, for example, certainly do not undergo SHM when heated for exactly the reason you stated: there is nothing to provide a restoring force; there is no mechanism for returning the molecule to its original position. The gas molecules are in motion, but just not simple harmonic motion.

--Dr. Randall J. Scalise
http://www.physics.smu.edu/scalise