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Conditions to use different Schrodinger Equation forms

Every molecular system has an energy associated with it. This energy might show a shift depending on the surrounding environment or internal variations. Magnetic dipoles present in a molecular system in the form of electrons and the nuclei is one such reason for the energy shift. But the effect of these magnetic dipoles on the energy shifts will be much less which can be accounted by considering perturbation theory. Chemical binding energies on the other hand are responsible for the major shifts in energy of a molecular system. Thus the focus is shifted towards the valence electrons responsible for most of the chemical activity of a molecule. The valence electrons are separated from the core electrons. The core electrons are treated approximately. This reduces the efforts of considering the relativistic effects affecting the core electrons, and thus can now be ignored. What are relativistic effect? It has been nicely explained by Ermler and Pitzer in the introduction of th