Triplet configurations

Singlet and Triplet Configurations. Let us first consider an interaction which involves just the ground-state determinant Aq and the four singly excited deter-mJna-n+e which Can bc deiivcd from an orbital... 

Fig. 4. Determinants used to derive singlet and triplet configurations...

Fig. 8. Block form of the triplet configuration interaction problem involving 25 singly excited configurations Ag 6 Big 6 B2n 8 B3a 5). The symmetry classification refers to the space part of the triplet functions...

In the case of carbenonitrenes, the nitrene subunit has an intrinsic preference for a triplet configuration, and, thus, for a A" ground state, a carbene with a very strong preference for a closed-shell singlet ground state is required. Such a case has not been realized yet. On the other hand, if both subunits are carbenes, then. 

The rearrangement of /1-diketones is most simply explained assuming the involvement of an n,n excited reactive state. Its triplet configuration was demonstrated by the quenching effect of 1,3-pentadiene on the rearrangement 176 - 175.109 The nature of the excited state of enol lactone is not... 

Comparison of the chemical reactions of various carbenes with those of methylene itself is also very interesting. Both diphenylcarbene52 and propargylene,52 which possess triplet configurations in their ground states, add nonstereospecifically to olefins. Moreover, diphenylcarbene reacts with oxygen54 to form an excited state of benzophenone.50... 

FIGURE 32. (a) A schematic configuration mixing diagram for the insertion of MR2 into XH . A is the energy gap between the singlet and triplet configurations of the reactants. Adapted from Reference 440. (b) Dominant orbital interactions in the transition state of the insertion reactions of MR2 into a X—H bond. Based on the discussion in Reference 431... 

We consider either singlet perturbations or triplet perturbations, which in Eq. (14) correspond to the + and - signs, respectively. In Eq. (15) the same distinction corresponds to interpreting A ) as a singlet or a triplet configuration state function (CSF). 

The reaction of C with NH3 might lead preferentially to HNC via the isomer HjNC (Allen et al. (1980), Brown, (1977)) which lies 2eV above the linear isomer HNCH. The stable triplet configuration HaNC might radiatively decay into singlet HjNC" rather than isomerize to the linear form. 

Fig. 14. A loop update for two antiferromagneticaUy coupled spins in a magnetic field with J = g iBh. (a) Starting from the triplet configuration ), (b) a loop is constructed, proposing to go to (c), the intermediate configuration ), which has an exponentially small acceptance rate, and finally into configurations like (d) which represent the singlet state l/ /2( Ti) I it))- As in the previous figure a thick line denotes an up-spin and a thin line a down-spin...

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