Symmetry electronic state

According to the authors, the 1,5-cyclization mode of o-diethynylbenzene (see Scheme 7.25) is determined by electron state symmetry, which is different from that of the neutral molecule of o-diethynylbenzene (Ramkumar et al. 1996). 

In certain favorable instances, one can coax the SCF equations to converge to different determinants of the same electronic state symmetry. For instance, phenylnitrenes have two different closed-shell singlet states, as re-illustrated in Figure 14.3 (cf. Section 8.5.3),... 

As an example of the former, consider the electronic states of fluorovinylidene illustrated in Figure 14.4. There are two different low lying triplet states, one having A electronic state symmetry and the other A". Furthermore, within each respective irreducible representation, the states indicated are the lowest energy triplets. Thus, wave functions for each may be determined via an SCF approach. In this case, HF theory is not particularly attractive as an... 

Various schemes exist to try to reduce the number of CSFs in the expansion in a rational way. Symmetry can reduce the scope of the problem enormously. In the TMM problem, many of the CSFs having partially occupied orbitals correspond to an electronic state symmetry other than that of the totally symmetric irreducible representation, and thus make no contribution to the closed-shell singlet wave function (if symmetry is not used before the fact, the calculation itself will determine the coefficients of non-contributing CSFs to be zero, but no advantage in efficiency will have been gained). Since this application of group theory involves no approximations, it is one of the best ways to speed up a CAS calculation. 

Spatial function Spin function Electronic state Symmetry Configuration ... 

Fig. 39 llustration of (a) a symmetry-allowed HT process and (b) a symmetry-forbidden HT process. Both reactions take place within a dimeric ethene radical cation complex. Both dimers possess C2v symmetry. For the symmetry-forbidden reaction, (a), the two ethene molecules lie in perpendicular planes consequently, the reactant and product have different electronic state symmetries, Bx and B2, respectively, and Vel is therefore zero. For the allowed process, (b), the two ethene groups lie in parallel planes and both reactant and product have identical state symmetries, Bp, thus, Vel is non-zero. For non-adiabatic HT, where Vel is very small ( 25 cm-1), the allowed and forbidden processes have nearly identical free energies of activation. 

We performed MP2/cc-pVTZ geometry optimization of cyclo-CsHs radical using Gaussian03 software [24], We have found Cs stable structure ( A electronic state) and PES saddle points of C2v ( Bi and A2 electronic states) and Cs i A" electronic state) symmetries (see Table 4 and Fig. 1) in agreement with step-by-step descent method (because the original Oh plane of the parent Dsh group is not conserved in the non-planar cyclopropenyl radical). Two symmetry descent paths of Scheme 6b may be employed ... 

Finally it may be concluded that only non-planar (A model) and planar (C model) C2v structures of B4 may be explained by JT effect. The electronic states of the remaining structures indicate that they cannot originate in a degenerate electronic state of the parent JT group. Their existence should be explained by other effects (probably also of vibronic character such as pseudo-JT effect). It has been clearly demonstrated that the treatment based on JT active coordinates may often lead to incorrect results and accounting for electronic state symmetry is necessary. 

The electronic state symmetry, transition energy (in eV), and collectivity number are given at the bottom of each image... 

The electronic state symmetry classifications described in the Introduction are contained in the properties of G and W. The intersection is symmetry required if Eqs. (6a) and (6b) are satisfied, provided only that X has the correct symmetry. The intersection is accidental symmetry-allowed, provided Eq. (6b) is satisfied when X has the correct symmetry. The intersection is accidental same-symmetry, provided symmetry does not guarantee that Eq. (6b) is satisfied. 

The Sx and Sy, Agh and Sgh describe the tilt, asymmetry and pitch of the double cone, and Sy describe the tilt of the principal axis of the cone. Agh describes the asymmetry in the pitch of the cone, which is measured by 6gh- The electronic state symmetry classification of the conical intersection is reflected in these topographical parameters. The syirmietry required double cone characteristic of the extensively studied Jahn Teller problem " has Sx = Sy = 0, and g = hhy symmetry so that q = g and Agh = 0. It is therefore a vertical (non-tilted) symmetric, Agh = 0) cone. For the accidental symmetry-allowed conical intersection only Sy... 

Once the overall electronic state symmetry of the molecule is determined, it is subject to the same rules that governed the characteristics of individual MOs. In particular, the selection rules for transitions between electronic states are dictated by the symmetry representations of the transition moment operators. 

The extension of overall electronic state symmetry to polyatomic molecules is straightforward. Individual MOs are labeled by the lowercase letters for the representations of the molecule s point group overall electronic state symmetries are labeled by the uppercase letter. Transitions between electronic states of a polyatomic molecule must obey the selection rules for the molecule s point group. 

An appreciation of electronic state symmetry is particularly useful when studying transition metal compounds. The transition metals are defined by a partially filled d subshell in the ground electronic state of the atom. The five d orbitals are degenerate in the spherically symmetric isolated atom, but that degeneracy is broken when we introduce chemical bonds. The distribution of the orbital energies that results can often be interpreted using the tools of group theory and a little chemical common sense. 

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