Symmetrized fragment orbital

Employing a C2 symmetry in the case of the thiirene 1-dioxide and remembering that the spiro-operator that mixes the fragment orbitals gives nonzero matrix elements only if these orbitals are symmetric to the C2 operation53, the net result is stabilizing. On the other hand, thiirene 1-oxide suffers a homoconjugative destabilization. 

It is important to explicitly account for the possibility that the metal surface atoms coordinated to the adsorbate can also be metal surface nearest-neighbor atoms. It appears to be essential to incorporate this feature in the chemisorption model, and we will discuss it for the particular case of the threefold coordination. If the adsorbate orbital o has a s-symmetry, it will coordinate with a surface fragment orbital that is a symmetric combination of surface s-atomic orbitals 1, 2 and 3, located on the coordinating surface atoms. If the adsorbate orbital has p-symmetry, it will coordinate with an antisymmetric fragment orbital. The surface orbital fragment... 

The PDOSs of the threefold adsorbed C atom in Figure 10.3c shows a bonding contribution of a symmetric surface fragment orbitals at the lower value of—11 eV. 

The PDOSs of the jr-symmetric surface orbital fragments show also a stronger interaction in the threefold adsorption site. The bonding density of states is shifted to lower energies, which will give a larger contribution to the attractive interaction. 

It is now helpful to introduce the concept of a local axis set. When the LGOs for a Y group in an XY molecule involve orbitals other than spherically symmetric i orbitals, it is often useful to define the axis set on each Y atom so that the axis points towards X. Diagram 5.9 illustrates this for the Fg fragment. 

In order to produce the closed shell singlet, the molecule has to bend in the zx plane, as shown in (a) of Fig. 9.5, so the N2 fragment departs at an angle to the molecular axis. In order to form the triplet, one electron from the uppermost singlet geminal (61) of the reactant moves to an orbital of CH2 with the same irrep the other is obliged to go to the totally symmetric a orbital of methylene. 

However, the shift from threefold to atop position can only be understood by also considering the LDOS j(E) of the surface-fragment orbitals that interact with the adsorbed hydrogen atoms. For atop-adsorbed hydrogen, one has to compute the LDOS i(E) of the atomic orbital (pi of the metalatom bonded to hydrogen for three-coordinated hydrogen symmetrically coordinated to three surface metalatoms, it is the LDOS f(E) of the grouporbital /]/3>i(Pi + (P2 + (P )-... 

Returning to Figure 18.8 notice that if the ethylene were rotated by 90° so that it lies in the PtCl3 plane, the interaction between n and 2o remains the same. The 2o fragment orbital is cylindrically symmetric. Now n interacts with b rather than b2-The overlap of the two metal orbitals with tt is similar. The same situation applies to (ethylene)Cr(CO)s. Rotation of ethylene by 45° causes tt to interact with a combination of the two members of the e set. However, in both cases the ji orbital interacts with a filled metal orbital [36] upon rotation. Therefore, the most stabile orientations are those shown in Figure 18.8. 

In both conformations, l0 and 2o interact with the ethylene tt level. That produces three molecular orbitals the lower two shown in Figure 19.4 are filled. The middle level can be identified with the e set in a trigonal bipyramidal splitting pattern and the lowest level is mainly ethylene tt with some l0 and 2oi character mixed into it in a bonding fashion. It is important that the overlap between these three fragment orbitals is essentially invariant to rotation. In other words, all are cylindrically symmetrical with respect to the Fe—olefin axis. Therefore, energies of the three molecular orbitals must also be constant as a function of rotation. The 02 Fe(CO)4... 

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