This chapter derives the quantum mechanical tools for treating the interaction of molecules with static and dynamic fields, i.e., perturbation theory. The first part is concerned with static fields and presents time-independent perturbation and time-independent response theories. It discusses the Hellmann-Feynman theorem and the general concept of density matrices. The second part considers oscillating fields and develops time-dependent perturbation theory in the form of a time-dependent response theory. The important concept of a response function or polarization propagator is defined and discussed in detail. Expressions for the transition probabilities and rates are also derived and the Ehrenfest and hypervirial theorems are presented.
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