Hi @raghavv, and welcome to the forum!

Usually with VQE, single point calculations are the normal route, however, it is possible to use VQE for geometry optimzation.

When calculating a single VQE instance energy, one usually chooses a fixed geometry starting point for the molecule to generate a given Hamiltonian.

An optimization step is then performed over a set of parameters used to prepare a quantum state which is then used to calculate the energy for the Hamiltonian.

As an example, we can calculate the energy using:

E = \langle\Psi(\theta)|H|\Psi(\theta)\rangle = \langle 0 | U^{\dagger}_{\theta} H U_{\theta} | 0 \rangle

By optimizing over the parameters \theta we can find the quantum state |\Psi(\theta)\rangle that minimizes the energy of the Hamiltonian for our fixed geometry, and from the above expectation value calculation, the resulting numerical value.

If you wanted to find the optimal geometry configuration, we can calculate more energies with different geometries, giving us a new Hamiltonian for each.

It is then possible to use the differences in these energies in an outer optimization stage to find the optimal positions for a molecule.

It can also be noted that you are free to optimize over any parameter you’d like.

I hope this helped!