Bound states and notion of potential energy surface

1 Bound states and notion of potential energy surface 

It is generally accepted that one of the most successful fields in theoretical chemistry is the so-called quantum chemistry. This is an electronic stationary-state structure theory based on the fixed nuclei (Born-Oppenheimer) approximation, which is the eigenvalue problem with respect to the electronic Hamiltonian H (r R) at each nuclear configuration, that is 

Quantum chemistry serves as quite a reliable tool for the interpretation and prediction of complex chemical phenomena and can aid in designing novel molecules prior to experimental synthesis. The result is a great contribution to chemistry and thereby human society. Techniques have been developed there that are highly sophisticated and are aimed at the study of larger molecular systems with faster and more accurate computation so as to make it possible treat the more realistic molecules found in nature. 

There are many excellent monographs for quantum chemistry such as Ref. [176] and one of the latest and extensive review articles is Ref. [517]. 

The first approach to the exact electronic ground state o(r R) is usually the Hartree-Fock method using a single Slater determinant that is composed of molecular orbitals, that is 

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