Q orbital

The delocalization-polarization mechanism in the singlet state is more complicated than that in triplet. Similar to the triplet state, there also exists a cyclic - G- T - E- T - configuration or -7t-p-7t -q- (-o-p-o -q-) orbital interaction in the singlet (Fig. 6). In the singlet state, however, the radical orbital q is an electron-accepting orbital (A) for the a-spin electron (rather than the donating orbital in triplet). Thus, there is an additional path of a-spin electron delocalization, - G- T - Tj- T - or... 

In the singlet state of Jt-type 1,3-diradical (e.g., TM, 2), there may also exist the through-space interaction between radical centers, i.e., p...q interaction (Fig. 9), in addition to the previously addressed cyclic -p-o -q-o- orbital interactions (Fig. 6). The through-space interaction is indispensable for the bond formation between the radical centers. The corresponding delocalization of the a-spin electron is shown in Fig. 9a. Clearly, the involvement of the through-space p... q interaction gives rise to two cyclic orbital interactions, -p-o -q- and -p-o-q-. From Fig. 9, one can find that the cyclic -p-o -q- orbital interaction can satisfy the phase continuity requirements for the a-spin electron the electron-donating radical orbital, p (D) can... 

Furthermore, linear combinations of complex pair of eigenfunctions mi = 1 define new pjgUre 2 16- Polar functions with the same shape as pzi but directed along Q 0y 2 jor mi the X and Y axes, respectively, and dubbed px and py q orbitals. This new set of p-functions are claimed to be... 

Throughout this work, several systems are discussed and the specific theoretical level is indicated in each case. The adopted notation is given as follows. CASSCF calculations including n electrons, m orbitals and averaging k states is denoted as SA-fc-C ASSCIm). If all CAS configurations are used to build the reference space for the MRCI procedure, it is referred to simply as MRCI. On the other hand, if a different space with p electrons and q orbitals is used, it is denoted MRCI(/ , q). The Cl expansion includes either all single and double excitations (MR-CISD) or... 

In this simplified model, we therefore consider that the nr interactions with the carbonyl ligand involve only the two nr Q orbitals it is thus a double-face 7r-acceptor (3-14). 

Figure 3.5. Interaction diagram showing the perturbation of the d block of an octahedral complex (left-hand side, a interactions only) by the two jr Q orbitals of a carbonyl ligand (right-hand side). The electronic occupation shown corresponds to a complex with a d electronic configuration.

By an exactly analogous analysis, it can be shown that in the case of six carbonyl ligands, the three orbitals in the tig block are stabilized to the same extent by four bonding interactions with the tt q orbitals (3-34), though the two e orbitals are not affected. 

Both first- and second-order energetic corrections lower the energy of relative to tt a- 1 ii st- and second-order corrections work in opposite directions for the tt orbital. In most cases the first-order term dominates and both n and n levels lie lower in the AB molecule than they do in A A. I or example, the ttcq and 7t o levels of a carbonyl double bond are invariably lower than the ttcc nd ttcc levels of the comparable carbon-carbon double bond, as shown in 6.9. Because of its lower energy and larger carbon p coefficients, nucleophiles attack the 7t q orbital of carbon with greater facility than the tt c orbital in an alkcne. We focus our attention... 

Let us consider (within the RHF scheme) the simplest closed-shell qrstem with both electrons occupying the same orbital (p. The Slater determinant, called (G from the ground state) is built from two spinorbitals d> =

2 = virtual orbital (p2, corresponding to orbital energy S2, and we may form two other spinorbitals from it. We are now interested in the energies of all the possible excited states which can be formed from this pair of orbitals. These states will be represented as Slater determinants, built from (pi and (p2 orbitals with the appropriate electron occupancy. We will also assume that excitations do not deform the q> orbitals (which is, of course, only partially true). Now all possible states may be listed by occupation of the ej and S2 orbital levels, see Table 8.2. 

The results demonstrate the presence of significant a-a inteactions between the ac-Si orbital and the Oq-q orbital, which stabilizes the diaxial conformation, in a similar fashion to the anomeric effect between an oxygen p-type lone pair and a ffc x effect... 

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