Intrinsic bond orbitals

They are obtained by unitary transformation and form an orthogonal set of orbitals localized on a minimal number of atoms.

IBOs present an intuitive and unbiased interpretation of chemical bonding with naturally arising Lewis structures.

[1] For this reason IBOs have been successfully employed for the elucidation of molecular structures[1] and electron flow along the intrinsic reaction coordinate (IRC).

This allows for a chemically intuitive orbital picture as opposed to the commonly used large and diffuse basis sets for the construction of more complex molecular wavefunctions.

[4] IAOs are constructed from tabulated free-atom AOs of standard basis-sets under consideration of the molecular environment.

[1] IBOs are constructed as a linear combination over IAOs with the condition of minimizing the number of atoms over which the orbital charge is spread.

[1] The process of IBO construction is performed by unitary tranfomation of canonical MOs, which ensures that the IBOs remain an exact and physically accurate representation of the molecular wavefunction due to the invariance of Slater determinant wavefunctions towards unitary rotations.

The product is a set of localized IBOs, closely resembling the chemically intuitive shapes of molecular orbitals, allowing for distinction of bond types, atomic contributions and polarization.

IBO analysis was used to explain the stability of electron rich gold-carbene complexes, mimicking reactive intermediates in gold catalysis.

IBO analysis was thus able to negate the double bond character of the gold-carbene complexes and provided deep insight into the electronic structure of Cy3P-Au-C(4-OMe-C6H4)2) (Cy = cyclohexyl).

This was attributed to the geometric inability of aromatic vinylidene substituents to compete with Au for π-interactions since the respective orbitals are perpendicular to each other.

[6] Making use of the low computational cost, a Cloke-Wilson rearrangement catalyzed by [Fe(CO)3NO]– was investigated by constructing the IBOs for every stationary point along the IRC.

IBO analysis has been employed in main group chemistry to elucidate oftentimes non-trivial electronic structure.

[11] Further application was found for confirming the distonic nature of a phosphorus containing radical cation reported by Chen et al. (see figure).

Three π bonding IBOs were found between the basal C5Me5 plane and the apical C, reminiscent of Cp* coordination complexes.

IBO analysis showed, that the unusual stability of the neutral ZrB12 cluster stems from several multicenter σ bonds.

Valence virtual IBOs (vvIBOs) were introduced with the investigation of high valent formal Ni(IV) complexes.

[15] In 2015, Knizia and Klein introduced the analysis of electron flow in reactions with IBO as a non-empirical and straight-forward method of evaluating curly arrow mechanisms.

Since IBOs are exact representations of Kohn-Sham wavefunctions, they can provide physical conformation for curly arrows mechanisms based on first-principles.

[2] Examples of IBO analysis along the IRC included the investigation of C-H bond activation by gold-vinylidene complexes.

The previously thought single step C-H activation reaction was in this case revealed to consist of three distinct phases: i) hydride transfer, ii) C-C bond formation and iii) sigma to pi rearrangement of the lone pair coordinated to Au.

Other reports of IBO analysis along the IRC include the elucidation and confirmation of a previously proposed mechanism for a [3,3]-sigmatropic rearrangement of a Au(I)-vinyl species[19] or the epoxidation of alkene by peracids.

IBO of the 3-center-2-electron-bond in B 2 H 6 visualized using IBOView. Recreated from reference [ 1 ] .
IBO of acrylic acid visualized using IBOview. Recreated from reference [ 1 ] .
IBOs of benzene visualized using IBOview. Recreated from reference [ 1 ] .
IBOs of Cy 3 P-Au-C(4-OMe-C 6 H 4 ) 2 ), visualized using IBOview. Recreated from reference. [ 4 ]
Structures of phosphaaluminirene [ 9 ] (1) and distonic radical ion [ 10 ] (2).
IBOs of the hexamethyl dication visualized using IBOview. Recreated from reference. [ 13 ]
IBOs along the reaction coordinate of the S N 2 -type self-exchange reaction of H 3 CCl and Cl – . Recreated from reference [ 2 ] .
Comparison of four curly arrow textbook mechanism (left) and seven curly arrow IBO derived mechanism (right) of an epoxidation with a peracid. [ 18 ]
C-H activation by a gold-vinylidene complex. IBO enables distinction of three distinct phases: i) hydride transfer, ii) C-C bond formation and iii) sigma to pi rearrangement of the lone pair coordinated to Au. [ 17 ]
Schematic representation of hydrogen atom transfer (HAT) versus proton coupled electron transfer (PCET). [ 22 ]