Molecular structures quantum system resonances

The discussions that may be given of resonance in various molecules may seem to the reader to be so far from quantitative in nature as to be without value. It is true that the picture presented of the structure of a resonating molecule is often rather indefinite but in the years that have gone by since the quantum-mechanical resonance phenomenon was first applied to problems of molecular structure encouraging progress has been made in the formulation of a semiquantitative system, with the aid of both experimental and theoretical methods, and we can hope for further progress in the future. 

The sum includes all intermediate complexes, the SPi-x (or transition structures acting as resonances, as it were) and those states belonging to different continua the number of particles being conserved. Eoko represents the ro-vibrational eigenvalues of the asymptotic systems. For quantum transition states or molecular complexes, the system is represented by a supermolecule. It is interesting to note that the asymptotic quantum states of the total hamiltonian H do converge to those of Hom-... 

Quantum computational methods are mainly used in systems for which electronic properties are of interest, such as molecular orbitals. Nuclear Magnetic Resonance (NMR) spectra, and polarizability. Usually an optimization process is carried out [3]. It consists in finding the structure which exhibits the lowest energy. The prerequisite in manipulating approximations to solve the Schrodinger equation gives rise to different approaches. They can be roughly classified into three major types ab initio (Hartree-Fock method and derivatives), density functional theory (DFT), and semiempirical methods, ab initio is a Latin locution which means from the... 

At the end of this section, one should note, that the quantum mechanical system in a potential cavity of large size may also be described as a system of discrete spectrum states with energies being almost constant and a system of decreasing stationary states for an enlarged "potential box". It is well known that the system of typical "ladder" structures in the spectrum gives rise to resonant states of molecular systems (see e.g. [92,93] and references therein), but the resonant states (the poles of continuation in a complex plane for the resolvent matrix elements) are a special field of Quantum Science and we shall not consider them here (see [5], Sect. XII.6 for discussions, or [55], Sect. 3). 

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