## Variational principles for critical parameters and ionization energies of
quantum systems

Alexei Sergeev and Sabre Kais

*Purdue University, Department of Chemistry*

*West Lafayette, IN 47906*

Non-traditional applications of variational methods were proposed both for
critical parameters (when the energy crosses the ionization threshold) and
for the energy below and above ionization threshold.

If the critical parameter enters the Schrodinger equation linearly, then
the equation for critical parameters can be considered as a generalized
eigenvalue equation with a non-trivial weight operator. Consider, for example,
a two-electron atom

H = p12/2 + p22/2 - Z/r1 - Z/r2 + 1/r12

with a charge Z treated as a continuous parameter . . .

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Designed by A. Sergeev.