Orbital contours

Figure 2.7. Simplified energy diagram of copper and copper-oxo sites (BP/DNP), showing relative positions of the triplet and singlet states, along with the relevant Kohn-Sham orbital contours.

As we have seen in earlier sections, wave functions can be used to perform useful calculations to determine values for dynamical variables. Table 2.2 shows the normalized wave functions in which the nuclear charge is shown as Z (Z = 1 for hydrogen) for one electron species (H, He+, etc.). One of the results that can be obtained by making use of wave functions is that it is possible to determine the shapes of the surfaces that encompass the region where the electron can be found some fraction (perhaps 95%) of the time. Such drawings result in the orbital contours that are shown in Figures 2.3, 2.4, and 2.5. 

Figure 2.16 Orbital contours comparing nc —(2s)u (right) and n0-(2s)Li (left) overlap, with each Li+ at R = 2.0 A (cf. Fig. 2.15).

The strength of the Fajb interaction and its variations with distance and orientation can be conveniently visualized in terms of the overlap of 7ra and 7tb NBOs, on the basis of a Mulliken-type approximation (cf. Eq. (1.34)). As an example, the top two panels of Fig. 3.38 compare the overlapping 7ta-7tb orbital contours for trails 1 and cis 2 isomers of butadiene. As shown in Fig. 3.38, the overlap in the cis isomer 2 (S = 0.2054) is slightly weaker than that in the trans isomer 1 (S = 0.2209), due to the unfavorable orientation of the 7ta across the nodal plane of the 7tb in the latter case. Consistently with the weaker 7ta-7tb overlap, the JtA F nh ) interaction is less, namely 0.0608 in 1 versus 0.0564 in 2. The delocalization tail of the 7fa NEMO is correspondingly less than its value in the trans isomer... 

In contrast to benzene, the pi-conjugative stabilizations of D4h-symmetric cyclobutadiene, 18, are found to be exactly zero. The absence of conjugative stabilization may also be judged from the 7ta—7rb orbital contours in Fig. 3.44. Indeed, it is... 

Figure 3.49 Orbital contours for hyperconjugative interactions in propene (a)

Table 3.23 summarizes the rotation barriers and leading vicinal cr-cr interactions for methyl rotors CH3—X(X = CH3, NH2, OH) as well as higher group 14 congeners H3M—MH3(M = Si, Ge). Figure 3.59 shows orbital contour diagrams for syn and anti orientations of selected vicinal donor-acceptor NBOs in these species. We now discuss some qualitative trends of torsion barrier potentials in terms of these examples. 

Figure 3.59 Leading vicinal c-c donor-acceptor interactions for molecules in Table 3.23 (cf. Fig. 3.55 for ethane), comparing orbital contours in anti (left) and syn (right) orientations of (a) methylamine, (b) methanol, (c) disilane, and (d) digermane.

Figure 3.64 Torsion-barrier interactions of NH2CH2F. Left panel the torsional potential (solid line) and leading nN-oCF+ stabilization (dashed line) in the range 4> = 0-150°, where the amine group does not spontaneously undergo inversion. Right panel orbital contours of the strong nN-uCF+ interaction at = 0°.

The authors are particularly grateful to Kenneth Sundberg for plotting the pi-orbital contours. 

Figure 2. Orbital contour plots for the global minima isomers (a) of Na(3p)Ar clusters.

Figure 4. Wave function contour maps for ReH 2 molecular orbitals. Contour values and sign convention as in Figure 1. Interior contours close to the rhenium atom center have been omitted. Hatom centers are marked by%.

Fig. 5 Molecular orbital contour plots of the occupied orbital 14a1 (a) and the virtual orbital 16a (b) of dioxetanone. Full and broken lines refer to different phases of the orbitals...

Figure 27. Molecular orbital contour of the HOMO for [Ni(mnt)2]. [Adapted from (389).]...

Figure 30. Molecular orbital contour for the b2g orbital of [Ni(S2C2Me2)2] at 0.8 A above the NiS. plane. [Adapted from (328).]...

FIGURE 3. Orbital energy levels for the [Ni(Me2C2S2)2], z = 2—, 1—, 0 redox series and orbital contour plots for z = 0. The MO of the ligands are divided in n (out-of-plane, along the z-axis) and a (in-plane, in the xy-plane) types. Reprinted with permission from Reference 13. Copyright 2003 American Chemical Society... 

Figure 3. 3-dimensional orbital contours of the [( j5-C5HS)Mn(CO)2] fragment with respect to a vacant ligand on the z-axis, with the dominant metal orbital contribution shown next to the contours. The 3a correlates with the dz2 o acceptor, the a" correlates with the dyz it donor, the 2a correlates with the dxz ir donor, and the la correlates with the dx2-y2 S donor. 

Formation of bent bonds is also reflected in diagrams of orbital contours using the spin density as a probe (Figure 19-4) spin density accumulates on H - one of each NH3 that becomes more coplanar with the MN4 plane. The transfer of spin density from the metal to atoms from the second coordination sphere, induced by bent bonding, might have important consequences for the reactivity in macrocyclic compounds. 

Figure 19-11. MO energy diagram for complex I (Figure 19-10) calculated with LFDFT the energies of LFDFT orbitals are compared with those resulting from the average-of-configuration KS calculation. Orbital contours (pertaining to values of the density of 0.05 a.u.) are plotted, but atoms are omitted for clarity (see color plate section)...

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