I have a question about the ActiveSpaceTransformer which is used in vqe calculations for a molecule of LiH in Qiskit. In the documentation the inactive Fock operator is defined.I don't understand why is the inactive Fock operator defined in that way, what is his physical meaning? Then, Why are we substituting the one body integral with the inactive Fock operator in the original hamiltonian?
The inactive Fock operator is the outcome of downfolding the inactive orbitals into the active space. This is explained in quite some detail in various quantum chemistry textbooks. A short summary of it can be found in the paper this is linked by the ActiveSpaceTransformer documentation page, namely this preprint. You will want to look at section II.A in particular. It also contains further references with lengthier explanations.