What is Deperturbation Anyway

An effective Hamiltonian is profoundly different from an exact Hamiltonian. This is a reason for imperfect communication between experimentalists and ab initio theorists. The two communities use the same symbols and language to refer to often quite different molecular properties. The main difference between effective and exact Hamiltonians is that the molecule gives experimentalists an empirical basis set that has been prediagonalized implicitly to account for the infinite number of remote perturbers . This is the Van Vleck or contact transformation, but it is performed by the molecule, not by a graduate student. The basis set is truncated and the dynamics occurs in a reduced-dimension state space. 

The molecule also chooses the physically appropriate basis set. Sometimes the molecule suggests to the experimentalist one basis set to describe an exper-imentally-realizable pluck and a different basis set to describe the post-pluck dynamics. No matter what basis set the molecule chooses, there always will be some pairs of basis states connected by an off-diagonal matrix element of H(b larger than their difference in zero-order energies. Under such circumstances, nondegenerate perturbation theory fails and a quasi-degenerate block of the Heff 

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