Due to the form of commonly used basis sets, SCF wave functions are often not easily interpretable in terms of their atomic orbital (AO) basis functions. Especially for large basis sets it is not possible to achieve an unambiguous association of a basis function’s contribution to the wave function with the atom it is centered on. An expansion of the molecular orbitals over a minimal basis (of free-atom AOs), on the other hand, does allow for a simple interpretation of the wave function. However, free-atom atomic orbitals cannot yield a qualitatively correct minimal basis expansion as these AOs do not account for the polarization due to the molecular environment. The approach by Knizia overcomes this drawback by determining a set of polarized AOs , termed intrinsic atomic orbitals (IAOs)575, which exactly express the occupied space of the wave function . As a consequence, atomic properties, such as partial charges, become accessible through IAOs. The IAO-derived atomic charges of a closed-shell system are then given by
where is the nuclear charge of atom and represents the closed-shell SCF density matrix .
The resulting IAOs in conjunction with an orbital localization scheme can be used to construct bonding orbitals, termed intrinsic bond orbitals (IBOs). The applied localization scheme is similar to the Pipek-Mezey approach897 and effectively minimizes the number of atoms on which an orbital is centered by maximizing the functional
with respect to unitary orbital rotations. In the above equation, is the number of electrons from rotated orbital located on the IAOs of atom A:
Intrinsic bond orbitals exactly represent the occupied molecular orbitals and can thus be used to interpret the electronic molecular structure.
Calculation of intrinsic bond orbitals is controlled by the following $rem variable:
Additional control parameters for the IBO procedure can be declared in the $loco input section and are listed below.
$molecule 0 1 O 0.0000000000 0.0000000000 0.1172309766 H -0.7626482594 0.0000000000 -0.4685977726 H 0.7626482594 0.0000000000 -0.4685977726 $end $rem method = wB97M-V basis = def2-TZVP mem_total = 4000 mem_static = 500 scf_convergence = 9 thresh = 14 gui = 2 do_ibo = true $end $loco min_basis = autosad export_molden = true $end