Ordered ground states

The off-diagonal elements in this representation of h and v are the zero vector of lengtii (for h) and matrix elements which couple the zeroth-order ground-state eigenfunction members of the set q (for v) ... 

However, if the zeroth-order ground-state energy is well separated from low lying excited states, the diagonal... 

The ability to stabilize different conformers of the higher order, ground-state Rg " XY complex opens a new avenue for dynamics and energy-transfer studies. Since all of the observed He ICl and He Br2 features follow the band-shift rule the He atoms must not be strongly interacting in either the ground or excited electronic states. It therefore seems likely that transitions of the... 

The zero-order ground state spin-orbit wave functions for these systems, obtained as previously described (41), have therefore been used to calculate the magnetic susceptibilities via the Van Vleck equation... 

We will discuss aromatic heterocycles in the following order ground-state properties (Sect. 3), reactivity (Sect. 4), spectroscopy (Sect. 5), special heterocycles (Sect. 6), and supramolecular and macrocycles (Sect. 7). 

The OOA is not designed for and cannot consider temperature dependence of any observable of the bulk crystal. The main goal of the OOA is determining the low-temperature (0 K) symmetry pattern of the orbitally ordered ground state. 

Figure 3. (a) The ordered ground state of an AB alloy on a square lattice, with white and black circles representing the two types of atom, (b) A disordered, high-temperature, arrangement of the same alloy. 

When f) 7 g), the matrix element in the middle will equal the one-photon transition moment between the two excited states /) and ). On the other hand, when I/) = g) the same matrix element will equal the difference between the dipole moment of the excited state /) and the ground state 0). This provides a first example of the possibility of extracting lower-order properties of molecular excited states from higher-order ground state properties. 

TABLE III Spin Ordering of the Various Charge Order Ground States. 

Pol shin et al. (1972a,b) were the first to study the temperature variation of quadrupole splitting in biotite, followed by Annersten (1974), Royer (1991) and Christie et al. (1992a,b). Christie et al. (1992a) examined the magnetically ordered ground state of synthetic annite at Tc 58K. Other Mossbauer spectra of trioctahedral micas are reported... 

Employing a Multiconfigurational Zeroth-Order Ground State.58... 

Number of configurations in zeroth-order ground state Order of perturbation expansion for ground-state wave function <0 0> Operator basis Lowest S excitation energy (eV)... 

The second problem centers about the use of an approximate ground-state wave function that eminates from a multiconfigurational zeroth-order approximation. The N2 calculations in Section III.C suggest that the restriction to a single configuration zeroth-order ground state imposes a fundamental limitation on the quality of the calculated EOM ionization potentials for that system. 

Partial wave contributions (a.u.) to the second-order ground-state energy in helium. 

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