Polyelectronic systems ground states

Stabilizing resonances also occur in other systems. Some well-known ones are the allyl radical and square cyclobutadiene. It has been shown that in these cases, the ground-state wave function is constructed from the out-of-phase combination of the two components [24,30]. In Section HI, it is shown that this is also a necessary result of Pauli s principle and the permutational symmetry of the polyelectronic wave function When the number of electron pairs exchanged in a two-state system is even, the ground state is the out-of-phase combination [28]. Three electrons may be considered as two electron pairs, one of which is half-populated. When both electron pahs are fully populated, an antiaromatic system arises ("Section HI). 

Indeed, the techniques of repeated diagonalization of the Hamiltonian on a large basis set and the search for resonance states from the numerical features of the roots upon variation of the function space may lead to reliable conclusions for models or for certain cases of ground shape resonances or of low-lying states of simple systems for which the chosen function space happens to describe the inner part of the resonance accurately. However, it was evident in the late 1960s that such methods had (have) certain limitations when it comes to the MEP in complex, polyelectronic systems. For example, for complex spectra of polyelectronic systems the root-identification criteria may not always lead to physically correct results, even qualitatively. Thus, in spite of careful (and computationally costly) examination, resonance states may be missed or roots may be wrongly attributed to resonances that do not exist. 

In a series of papers since 1993-1994, we have demonstrated that it is possible to solve quantitatively a variety of TDMEPs in atoms and small molecules, by expanding the nonstationary in terms of the state-specific wavefunc-tions for the discrete and the continuous energy spectrum of the unperturbed system. This SSEA to the solution of the TDSE bypasses the serious, and at present insurmountable, difficulties that the extensively used "grid" methods have, when it comes to solving problems with arbitrary polyelectronic, ground or excited states. Furthermore, it allows, in a transparent and systematic way, the monitoring and control of the dependence of the final resulfs on the type and number of fhe sfafionary states that enter into the expansion that defines fhe wavepackef 4>(f). 

---