Symmetry adapted lone pair

Carbonyl compounds also have two nonbonding lone pairs on the oxygen atom. In organic chemistry texts, these are sometimes shown as two equivalent sp2-hybridized lobes (rabbit s ears). While hybridization has no effect on the total energy, the two degenerate nsp2 orbitals are inappropriate as a basis set to discuss one-electron properties such as ionization potentials or n,jt transitions. Rather, the symmetry-adapted lone pairs... 

For example, the three NH bonding and three NH antibonding orbitals in NH3, when symmetry adapted within the C3V point group, cluster into ai and e mos as shown in the Figure below. The N-atom localized non-bonding lone pair orbital and the N-atom Is core orbital also belong to ai symmetry. 

An example will help illustrate these ideas. Consider the formaldehyde molecule H2CO in C2v symmetry. The configuration which dominates the ground-state waveflinction has doubly occupied O and C 1 s orbitals, two CH bonds, a CO a bond, a CO n bond, and two 0-centered lone pairs this configuration is described in terms of symmetry adapted orbitals as follows (Iai22ai23ai2lb2 ... 

Molecular orbitals are not unique. The same exact wave function could be expressed an infinite number of ways with different, but equivalent orbitals. Two commonly used sets of orbitals are localized orbitals and symmetry-adapted orbitals (also called canonical orbitals). Localized orbitals are sometimes used because they look very much like a chemist s qualitative models of molecular bonds, lone-pair electrons, core electrons, and the like. Symmetry-adapted orbitals are more commonly used because they allow the calculation to be executed much more quickly for high-symmetry molecules. Localized orbitals can give the fastest calculations for very large molecules without symmetry due to many long-distance interactions becoming negligible. 

A T structure with the strongest ct-donor D trans to the empty site (I in Scheme 1) is preferred in the case of three pure cr-donor ligands. The presence of a ir-acceptor ligand also makes the T structure more stable. When one of the ligands is a tt-donor, X, a Y structure of type II (Scheme 1) is observed. This structure permits the formation of a w bond between the empty metal d orbital and the lone pair of X. No such tt bond is present in the T structure since all symmetry adapted d orbitals are filled. This partial M—X multiple bond stabilizes Y over T. 

A very similar approach can be used to interpret the UPS of bis-chelate complexes of acac, hfa, and related monothio and bisthio analogues (45, 51). Monomeric Ni(acac)2 has been found to possess D2h symmetry in the vapor phase (258), and this geometry is assumed here for the other bis-chelates. In D2d symmetry the rr3, +, and n- MOs of each 0-diketonate ligand combine to afford the symmetry-adapted combinations shown in Fig. 44. Introduction of the metal d orbitals, which transform as ag(d2 ), ag(dx> yz), blg(dxy), bigidxz), and b2g(dyz), completes the scheme. By analogy with the tris-chelates, the strongest interaction anticipated is that between the dxy orbital and the antisymmetric lone pair combination of b g symmetry. 

The HMO frontier orbitals of azulene (1) and cycl[3.3.3]azine44,45 (2) are shown in Figure 4.24. For 2 (bottom) they can be constructed simply by considering the interaction of the central nitrogen lone pair with the symmetry-adapted (Section 4.4) NBMOs of [12]annulene. The parameter for the central N atom is Sa N= 1.5/3 (Table 8.5 S/3C N = 0 is assumed because 1 is planar). 

The two bonds must be considered together. Their sum and difference are S5nnmetry adapted linear combinations. These are now shown in Fig. 2 as localized MO s corresponding to bonds between O and H. In the Czv point group, the symmetries are clearly a and i>i. The sum and difference of lone pair orbitals concentrated on O would correspond to a and h% symmetries. For convenience F. 3 shows the S3mametry species of the Cse point group. Only the behavior with respect to two mirror planes is necessary to classify all four species. There is also a two-fold axis at the intersection of the two planes. 

Electronically speaking, these four orbitals are doubly occupied, since they are formed from atomic orbitals that describe r-type lone pairs on each of the chloride ligands. They therefore provide a delocalized description of these lone pairs, which is adapted to the symmetry of the complex. 

Construct the four symmetry-adapted orbitals that characterize the TT-type lone pairs on the Cl ligands, and give their symmetries with respect to Pi and Pz-... 

As an example, let us consider the two lone pair levels in diazabicyclooctane 11.36. The direct, througli-space interaction between the hybrid lone pairs of nitrogen lead to the symmetry-adapted levels and shown in 11.37. Because of the... 

We shall again develop the molecular orbitals for a 04 ML4 complex in a generalized way where the ligands, L, as before represent two-electron, a donors. Figure 16.1 constructs the molecular orbitals for this system. On the left side of the figure are the metal 5, p, and d levels. On the right side are presented the symmetry-adapted combinations of the four ligand lone pairs. These were developed in some depth for the D4/, H4 system (Section 5.4). Basically the b g lone-pair combination is stabilized by metal - y and by metal x and y (see the coordinate system at... 

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