Excited State degenerate

Frozen orbital analysis Excited state Degenerate system Ab initio... 

Figure 5. A cut across the ground state (GS) and the excited state (ES) potential surfaces of the H4 system. The parameter Qp is the phase preserving nuclear coordinate connecting the H(lll) with the transition state between H(I) and H(1I) (Fig, 4). Keeping the phase of the electronic wave function constant, this coordinate leads from the ground to the excited state. At a certain point, the two surfaces must touch. At the crossing point, the wave function is degenerate.

An example that is closely related to organic photochemishy is the x e case [70]. A doubly degenerate E term is the ground or excited state of any polyatomic system that has at least one axis of symmetry of not less than third order. It may be shown [70] that if the quadratic tenn in Eq, (17) is neglected, the potential surface becomes a moat around the degeneracy, sometimes called Mexican hat, The polar coordinates p and <(>, shown in Figure 20, can be used to write an expression for the energy ... 

CIS=(NState =n) Specifies how many excited states are to be predicted. The default is 3. Note that if you are searching for some specific number of excited states, especially in conjunction with spectroscopic data, you will want to set NStales to a somewhat higher number to take into account the forbidden and degenerate states that are very likely to be interspersed within the states you are looking for. 

Since we need to find both triplet and singlet excited states, we ve included the 50-50 option to the CIS keyword. We ve asked for two states of each type, the exact number we require for this well-studied system. When examining new systems, however, it s often a good idea to request slightly more states than you initially want to. allow for degenerate states and other unexpected results. 

The search for a conical intersection is also successful. The predicted structure is at the left. The predicted energies of the two states—the ground state and the first excited state—differ by about 0.00014 Hartrees, confirming that they are degenerate at these points on the two potential energy surfaces. ... 

If we apply the Mulak model of a pseudoaxial, D, symmetry (14), using a ratio c/a = 0.95, we find indeed a singlet ground state 0> and a first excited state 1> causing the observed TIP. Deviation from Di symmetry will affect to first order only the excited degenerate states and will not alter this simple... 

Figure 3. Molecular-orbital diagrams as obtained by the ROHF method. Dashed lines indicate MOs dominated by the metal d-orbitals, the solid lines stand for doubly occupied or virtual ligand orbitals. Orbitals which are close in energy are presented as degenerate the average deviation from degeneracy is approximately 0.01 a.u. In the case of a septet state (S=3), the singly occupied open-shell orbitals come from a separate Fock operator and their orbital energies do not relate to ionization potentials as do the doubly occupied MOs (i.e. Koopmann s approximation). For these reasons, the open-shell orbitals appear well below the doubly occupied metal orbitals. Doubly occupying these gives rise to excited states, see text.

Azulene (XI) possesses a transannular bond which has the same effect as those of bowtiene (Fig. 3). The splittings of the top filled and bottom empty degenerate orbitals of cyclododecapentaene in this case are half the corresponding splitting in the case of bowtiene, and are not large enough to produce an effective vibronic interaction between the ground and lowest excited states of the resultant azulene molecule. 

If the full molecular symmetry is assumed, the ground states of the cation radical of fulvalene and the anion radical of heptafulvalene are both predicted to be of symmetry by using the semiempirical open-shell SCF MO method The lowest excited states of both radicals are of symmetry and are predicted to be very close to the ground states in the framework of the Hiickel approximation these states are degenerate in both cases (Fig. 4). Therefore, it is expected that in both these radicals the ground state interacts strongly with the lowest excited state through the nuclear deformation of symmetry ( — with the result that the initially assumed molecular... 

On the other hand, in the anion radical of fulvalene and the cation radical of heptafulvalene, the energy gaps between the ground and lowest excited state (which is in both cases doubly degenerate in the Hiickel approximation (Fig. 4)) are predicted to be reasonably large (1.4 and 1.7 eV, respectively), so that these radicals would not suffer a symmetry reduction. 

The effect of electric quadrupole interaction for Fe is exemplified in Fig. 4.6. The ground state remains unsplit because of the lack of quadrupole moment for 7 = 1/2. The excited state with 7 = 3/2 splits into two doubly degenerate substates 3/2, 3/2) and 3/2, 1/2) due to the w/ dependence of the quadrupole energies ... 

Fig. 4.6 Quadrupole splitting of the excited state of Fe with I = 3/2 and the resulting Mossbauer spectrum. Quadrupole interaction splits the spin quartet into two degenerate sublevels 7, OT/) with energy separation A q = 2 q. The ground state with I = 1/2 remains unsplit. The nuclear states are additionally shifted by electric monopole interaction giving rise to the isomer shift 8...

As a consequence of the Hohenberg-Kohn theorem [14], a non-degenerate ground state electron density p(r) determines the Hamiltonian H of the system within an additive constant, implying that the electron density p(r) also determines all ground state and all excited state properties of the system. 

Frequency degenerate 2PA is a third order, y° nonlinear optical process whereby two photons of equal energy are simultaneously absorbed to raise a system into an excited state of energy equal to that of the sum of the two photons. The propagation... 

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