Potential energy distribution ground state

The determination of the ground state energy and the ground state electron density distribution of a many-electron system in a fixed external potential is a problem of major importance in chemistry and physics. For a given Hamiltonian and for specified boundary conditions, it is possible in principle to obtain directly numerical solutions of the Schrodinger equation. Even with current generations of computers, this is not feasible in practice for systems of large total number of electrons. Of course, a variety of alternative methods, such as self-consistent mean field theories, also exist. However, these are approximate. 

TABLE 3. Fundamental vibrational frequencies (cm-1) and associated potential energy distributions of aniline in its ground electronic (singlet) state. Calculated values were obtained from scaled B3LYP/6-311++G(3df,2p) harmonic frequencies... 

The rare gas excimer lasers are based on bound-continuum transitions from an excited diatomic species to its dissociative ground state. The observed continuum emission is a superposition of the Franck-Condon factors from the vibrational levels of the upper state. Thus these molecular dissociation lasers display relatively broad fluorescence as a consequence of the steeply repulsive ground-state potential, and there is always a population inversion on such transitions. However, the net gain is significantly lower than that for a bound-bound transition because of the distribution of oscillator strength over the broad fluorescence band. Figure 1 illustrates schematic potential energy curves for such transitions in the excimer and exciplex lasers. 

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