The Fractional Occupation Number Weighted Density as a Versatile Analysis Tool for Molecules with a Complicated Electronic Structure

Abstract

The fractional occupation number weighted density (FOD) analysis is explored as a general theoretical diagnostic for complicated electronic structures. Its main feature is to provide robustly and quickly the information on the localization of "hot" (strongly correlated and chemically active) electrons in a molecule. We demonstrate its usage in four different prototypical applications: 1) As a new and fast measure of the biradical character of polycyclic aromatic hydrocarbons, 2) for the selection of active orbital spaces in multiconfigurational or complete active space self consistent field (MCSCF/CASSCF) treatments, 3) as a possibility to describe molecular-energy landscapes consistently in regions with varying biradical character, as exemplified by partial double-bond torsions, and 4) as a powerful visualization method for static electron correlation effects in large biomolecules in connection with an efficient semi-empirical tight-binding molecular orbital scheme. The last application opens a full quantum-mechanical, unbiased route to the automatic detection of errors in experimental protein X-ray structures, such as false protonation states or misplaced atoms. In the first example, the complete (unfragmented) quantum-chemical calculation of the FOD for an entire metalloprotein with more than 7500 atoms is described.

Density functional theory and ab initio studies on hyperfine coupling constants of phosphinyl radicals

“…Monoradicals do not necessarily have a large static electron correlation, but such situations are not uncommon, and the cyano, ethynyl, and cysteine thiyl radicals are cases in point . Recently a versatile tool to measure static electron correlation was introduced: the fractional occupation number weighted electron density (FOD) . In this approach, the special density ρ FOD is obtained by performing a computationally attractive finite‐temperature DFT calculation in which the electrons are self‐consistently smeared over the molecular orbitals according to the Fermi‐Dirac distribution .…”

“…The ρ FOD plots can be considered as a computationally cheap but robust way to identify the strongly correlated electrons in molecular systems and to choose an appropriate quantum chemical method for the intended computational study. It is also possible to integrate ρ FOD over all space to obtain a single number ( N FOD ) which can be used to measure static electron correlation or to quantify the biradical character of organic molecules such as polycyclic aromatic hydrocarbons …”

Exploiting the Ring Strain of Diphosphetanes: A Synthetic and Computational Approach towards 1,2,5‐Selenadiphospholanes

“…Calculated bond lengths and angles are in good agreement with the solid‐state structures (see the Supporting Information). In addition, FOD analyses were performed (Figure ) ,. For 2‐ meso , an N FOD value of 0.12 was obtained, indicating just minor multireference character of its electronic structure.…”

“…Hereby, higher configuration state functions contribute with 6.4 % to the ground‐state wave function of 4‐ meso whilst in 2‐ meso the contributions just amount to 1.5 %. In both compounds, the FOD is dominantly localised at the selenium atoms which together with their N FOD values indicates that DFT functionals with little or no Hartree‐Fock (HF) exchange are suitable for the proper description of their wave functions ,. As a consequence, the TPSS family of functionals (TPSS, TPSSh and TPSS0; 0 %, 10 % and 25 % HF exchange, respectively) was chosen to describe the electronic structure and to investigate the reactivity of 2‐ meso and 4‐ meso .…”

Spectroscopic and Electronic Properties of Molybdacarborane Complexes with Non‐innocently Acting Ligands

“…Scalar relativistic effects were taken into account by using the zeroth-order regular approximation (ZORA) [65] for which the ORCA implementation follows the model potential approximation of van Wüllen. [66] For the frequency calculations the same settings as for the geometry optimisation were used as it was performed on the optimised geometry.C AS-SCF/def2-TZVPP calculations with SC-NEVPT2 [67] correction on 1a were carried out with an active space of eight/ten electrons and nine/ten orbitals, respectively.A ctive space choices were derived from analysis of the FOD calculations [68] and ap receding CAS-SCF(10,10) calculation. Images of the molecular orbitals, natural orbitals, transition densities and FOD results of the op-timised structures were rendered with the UCSF Chimera program package.…”