In Figure 6 we display contour plots that show the evolution of the charge distribution in QR with off-center donor in the ground state
under growing magnetic field.
To obtain the mass and residues of the radial excitations from the sum rules, we take the mass of the ground state
as an input parameter.
The last pathway involves the lengthening [C.sub.spiro]-N bond and the internal conversion from the electronically excited states to the SP ground state
through [CI.sub.S1/S0] (CN) [38-40].
All the ground state
structures of the [Ni.sub.2][Al.sub.6], [Ni.sub.2][Al.sub.7], and [Ni.sub.2][Al.sub.9] clusters have the same [C.sub.2v] symmetry.
In this work, a special emphasis is given to the following issue: Contrary to a naive expectation, even the ground state
of a simple atom is written as a sum of more than one configuration.
The observed lineshapes for the purely long-range [0.sup.-.sub.g], molecular state enable as to establish key features of the ground state
In other words, all the ground states
with different aligned directions have the same energy, and so infinitely many ground states
can exist realizing the infinitely degenerate ground states
Exposing such a confined particle to a pulse of laser light of precisely the right wavelength and duration can readily kick it into an excited energy state; a second laser pulse can restore it to its ground state
Recently some of us have shown that coherently with Lieb's theorem triangular structures have high-spin ground states
and are ferromagnetic, while hexagonal and rhomboidal ones are open-shell low-spin structures of very high multireference character.
The results are interpreted in terms of the geometry of conical intersection (CI) between the first singlet ([S.sub.1]) excited state and ground state
([S.sub.0]), which was optimized by using CASSCF method.
The current paper is mainly motivated by  and applies the least energy solution obtained in [17,18] to show the existence of the ground state
solution to the critical system (2) under proper conditions.