E states

At this stage we may distinguish between excitation involving different electronic states and excitation occurring within the same electronic (ground) state. Wlien the spectroscopic states are located in different electronic states, say the ground (g) and excited (e) states, one frequently assumes the Franck-Condon approximation to be applicable ... 

Figure 20, The potential surface near the degeneracy point of a degenerate E state that distorts along two coordinates and Q. The parameter is the stabilization energy of the ground state (the depth of the moat ), [Adapted from [70]].

Similar to the case without consideration of the GP effect, the nuclear probability densities of Ai and A2 symmetries have threefold symmetry, while each component of E symmetry has twofold symmetry with respect to the line defined by (3 = 0. However, the nuclear probability density for the lowest E state has a higher symmetry, being cylindrical with an empty core. This is easyly understand since there is no potential barrier for pseudorotation in the upper sheet. Thus, the nuclear wave function can move freely all the way around the conical intersection. Note that the nuclear probability density vanishes at the conical intersection in the single-surface calculations as first noted by Mead [76] and generally proved by Varandas and Xu [77]. The nuclear probability density of the lowest state of Aj (A2) locates at regions where the lower sheet of the potential energy surface has A2 (Ai) symmetry in 5s. Note also that the Ai levels are raised up, and the A2 levels lowered down, while the order of the E levels has been altered by consideration of the GP effect. Such behavior is similar to that encountered for the trough states [11]. 

Recently, several QSPR solubility prediction models based on a fairly large and diverse data set were generated. Huuskonen developed the models using MLRA and back-propagation neural networks (BPG) on a data set of 1297 diverse compoimds [22]. The compounds were described by 24 atom-type E-state indices and six other topological indices. For the 413 compoimds in the test set, MLRA gave = 0.88 and s = 0.71 and neural network provided... 

The and 72 states are broadened as a result of slight variations in the crystal field. The 72 and E states are sharper but the E state is split into two components, 29 cm apart, because of the slight distortion of the octahedral field. Population inversion and... 

Fig. 51. Zeeman splitting of the lowest AE octet of the CHj group. Levels of the E state with m = +1/2 are twice degenerate.

ELEMENT z OUTER ELECTRON CONFIGURATION OXIDATION E° states M — - M+3 + 3e +3 ION RADIUS... 

The vanishing of this matrix element is, in fact, independent of the assumption of current conservation, and can be proved using the transformation properties of the current operator and one-partic e states under space and time inversion, together with the hermiticity of jn(0). By actually generating the states q,<>, from the states in which the particle is at rest, by a Lorentz transformation along the 3 axis, and the use of the transformation properties of the current operator, essentially the entire kinematical structure of the matrix element of on q, can be obtained.15 We shall, however, not do so here. Bather, we note that the right-hand side of Eq. (11-529) implies that... 

When the parameters deduced from the calculations on AI2 and AI3 are applied to bulk Al, the cohesive energy is too small and the bond length is too large. The small cohesive energy is expected because our computed AI2 at the TZ2P-CPF level is only 71% of the experimental value (42.46). The bulk values are in much better agreement with experiment if the model is parameterized using the experimental and r values for the E state. Hence, the... 

Contrera JF, Matthews EJ, Benz RD. Predicting the carcinogenic potential of pharmaceuticals in rodents using molecular structural similarity and E-state indices. Regul Toxicol Pharmacol 2003 38 243-59. 

The aim of this work is to obtain the four lowest E curves and wavefunctions of BH at the same level of accuracy and to bring out the interplay of ionic, Rydberg and valence states at energies and internuclear distances which were not previously investigated. We have therefore made use of a method, already put forward by us [16,17] to determine at once quasi-diabatic and adiabatic states, potential energy cnrves and approximate nonadiabatic couplings. We have analogously determined the first three E+ states, of which only the lowest had been theoretically studied... 

The third column of table 1 contains the spectroscopic constants of the four E states, based on the corrected adiabatic potentials. Apart from the Dc, Tg and energies, which are bound to coincide with the experimental values, we observe a remarkable improvement in the computed vibrational levels of the state. The... 

AE and R values here presented for the barrier and outer minimum of this potential curve are probably the best estimates available to date. The vibrational levels belonging to the C E state are much less accurately determined, the energy differences AE(calc. — exp.) ranging from -58 to -280 cm. The only previous determination of this potential energy curve leads to overestimate the same levels by 200-600 cm (the same holds for the lowest electronic states, and may be partly due to a poor interpolation, i.e. to an insufficient number of points on the potential curves). No comparison with previous determinations is possible for the state. 

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