Orbital shapes
Note: Examples of most of these are included in the example subdirectory of the download distribution. Most of these were discussed in detail in the Intrinsic Atomic Orbitals (IAOs) paper.
![sigma bonds](img/acrylic_acid-sigma.png)
![sigma bonds](img/re2me8-dianion-sigma-bond.png)
![sigma bonds](img/so3-sigma-bond.png)
Usually highly localized (98% of charge on two atoms)
Can be unpolarized (e.g., C-C sigma bonds, if bonding atoms have same electro-negativities) or polarized (e.g., C-O bonds, best seen in orbital charge composition).
Different shapes result from different AO sizes/hybrid forms making up the bonds (e.g., d-d-sigma in Re-Re bond, or s-s-sigma in C-H)
In higher elements, valence bonds often have visible „
dents “ where the inner-shell electrons of the atom reside (e.g., S-O bond on the S side)
![pi bonds](img/acrylic_acid-pi-bond.png)
![pi bonds](img/acrylic_acid-pi-bond-O.png)
![pi bonds](img/acrylic_acid-pi-lone-pair-O.png)
![pi bonds](img/re2me8-dianion-pi-bond.png)
π-bonds come in a variety of shapes and sizes. Unlike σ-bonds, which usually are highly localzied, both π-bonds and π-lone pairs are often de-localized to neighboring atoms. (e.g., delocalized C-C-π-bond, localized C-O-π-bond, mostly localized O-π-lone pair)
In C≡C triple bonds in conjugated systems, the two π-bond components are often delocalized differently, and to different sides.
![aromatic bonds](img/pi-bond-4-center.png)
![aromatic bonds](img/pi-bond-3-center.png)
C≃C: Aromatic bonds effectively come in two degenerate shapes, which are mathematically equivalent. One is primarily localized on three centers, the other on four centers.
IBOs normally prefer the three-center version. But, especially in reaction paths, the type of the pi bonds can change.
![banana bonds](img/c3h6-banana-bond.png)
Banana bonds are most often seen in cyclopropyl groups. They can be viewed as hybrids between regular σ- and π-bonds. While they are often highly-localized, their increased π-character still predestines them for π-bond like reactivity patterns.
Normally we write double bonds as one σ- and one π-bond, but they can also be written as two equivalent banana bonds. Both descriptions are
physically equivalent . IBOs normally produce the former description, because they prefer a pair of one highly localized and one semi-delocalized orbital to an equivalent description of two equivalent somewhat delocalized orbitals. In other localization methods (e.g., Boys localization) this is different.- A variation of this pattern is also commonly seen in Boranes. Here a very similar orbital shape occurs and is used to bridge a two-electron (2e) chemical bond over three centers (3c). These bonds are electronically
simple (i.e., well described by mean field theory), but cannot be easily written as Lewis structures. - While the borane 2e3c-bond is the most well known, a different, but also common 2e3c bond is often formed by CO ligands in tetrahedral coordination. This is a two-electron three-center p-d-p bond. The one shown here is from The Electronic Ground State of [Fe(CO)3(NO)]−: A Spectroscopic and Theoretical Study
![banana bonds](img/banana-pi-hybrid.png)
Commonly seen in cationic systems involving cyclopropyl groups (e.g., carbo-cations) and reaction paths involving cyclopropyl ring opening or closing reactions.
The example is taken from The Stabilizing Effects in Gold Carbene Complexes, where such bonds are shown to play a major role in stabilizing carbo-cation sites (instead of pi-backbonds from Gold, as one might imagine).