Domain-averaged Fermi-hole analysis for solids

Localization and Delocalization in Solids from Electron Distribution Functions

The extent of electron localization and delocalization in molecular and condensed phases has been the subject of intense scrutiny over the years. In Chemistry, where real, instead of momentum space viewpoints are many times closer to intuition, a plethora of localization descriptors exist, including a family of indices invariant under orbital transformations that rely only on an underlying partition of the physical space into meaningful regions. These localization and delocalization indices measure the fluctuation of the electron population contained in such domains, and have been rigorously related to the insulating or conductive character of extended systems. Knowledge of the full electron population probability distribution function is also available in molecules, where it has provided many meaningful results as well as uncovered exotic interaction regimes in excited states. Electron distribution functions (EDFs), which can be seen as real space analogs of Pauling resonance structures, are now reported in periodic systems. In agreement with what is known in finite systems, ionic compounds display narrow EDFs that get wider as covalency sets in. Contrarily to conventional wisdom, most electrons delocalize over their nearest neighbors, even in quasi electron-gas metals like sodium, and it is only in the decay rate of the probability distribution where conductors and insulators can be distinguished.

Ni Oxidation State and Ligand Saturation Impact on the Capability of Octaazamacrocyclic Complexes to Bind and Reduce CO2

Two 15-membered octaazamacrocyclic nickel(II) complexes are investigated by theoretical methods to shed light on their affinity forwards binding and reducing CO2. In the first complex 1[NiIIL]0, the octaazamacrocyclic ligand is grossly unsaturated (π-conjugated), while in the second 1[NiIILH]2+ one, the macrocycle is saturated with hydrogens. One and two-electron reductions are described using Mulliken population analysis, quantum theory of atoms in molecules, localized orbitals, and domain averaged fermi holes, including the characterization of the Ni-CCO2 bond and the oxidation state of the central Ni atom. It was found that in the [NiLH] complex, the central atom is reduced to Ni0 and/or NiI and is thus able to bind CO2 via a single σ bond. In addition, the two-electron reduced 3[NiL]2- species also shows an affinity forwards CO2.

Electronic structure of Schiff-base peroxo{2,2'-[1,2-phenyl-enebis(nitrilo-methanylyl-idene)]bis-(6-meth-oxy-phenolato)}titanium(IV) monohydrate: a possible model structure of the reaction center for the theoretical study of hemoglobin

An extensive characterization of [Ti(C22H18N2O6)]·H2O was performed by topological analysis according to Bader's quantum theory of atoms in molecules (QTAIM) from the experimentally (multipole model) and theoretically (DFT) determined electron density. To the best of our knowledge, this study is the first example of an experimental electronic structure of a coordination compound in which a peroxo anion is bonded to a 3d central atom. The titanium coordination polyhedron could be described as a deformed tetrahedral pyramid if the midpoint of the peroxide O-O bond (side-on mode) is considered to be in the quasi-apical position. According to the multipole model (MM) results, the titanium atom has a positive QTAIM charge of 2.05 e- which does not correspond to the formal Ti (IV) oxidation state. On the other hand, the peroxo oxygen atoms O(1) and O(2) have MM QTAIM charges of -0.27 and -0.12, respectively. This asymmetric charge density distribution on the peroxo oxygens is in agreement with the distorted orientation of the O2 moiety with respect to the titanium atom. Despite the fact that the overall MM charge of the O2 moiety is more remote from the formal -2 charge than from neutral O2, the O-O distance remains close to that in the peroxo O2 2- anion. In the case of DFT results, the titanium atom charge is also found to be close to +2, the O2 x- moiety charge is around -1, the optimized O-O distance is shorter by only ca 0.04 Å than the experimental value of 1.5005 (16) Å, and the DFT d-populations on titanium are found to be lower than the experimental MM value. This study is the first experimental electronic structure of a transition metal peroxo complex.

Charge density of 4-methyl-3-[(tetrahydro-2H-pyran-2-yl)oxy]thiazole-2(3H)-thione. A comprehensive multipole refinement, maximum entropy method and density functional theory study

The structure of 4-methyl-3-[(tetrahydro-2H-pyran-2-yl)oxy]thiazole-2(3H)-thione (MTTOTHP) was investigated using X-ray diffraction and computational chemistry methods for determining properties of the nitrogen-oxygen bond, which is the least stable entity upon photochemical excitation. Experimentally measured structure factors have been used to determine and characterize charge density via the multipole model (MM) and the maximum entropy method (MEM). Theoretical investigation of the electron density and the electronic structure has been performed in the finite basis set density functional theory (DFT) framework. Quantum Theory of Atoms In Molecules (QTAIM), deformation densities and Laplacians maps have been used to compare theoretical and experimental results. MM experimental results and predictions from theory differ with respect to the sign and/or magnitude of the Laplacian at the N-O bond critical point (BCP), depending on the treatment of n values of the MM radial functions. Such Laplacian differences in the N-O bond case are discussed with respect to a lack of flexibility in the MM radial functions also reported by Rykounov et al. [Acta Cryst. (2011), B67, 425-436]. BCP Hessian eigenvalues show qualitatively matching results between MM and DFT. In addition, the theoretical analysis used domain-averaged fermi holes (DAFH), natural bond orbital (NBO) analysis and localized (LOC) orbitals to characterize the N-O bond as a single σ bond with marginal π character. Hirshfeld atom refinement (HAR) has been employed to compare to the MM refinement results and/or neutron dataset C-H bond lengths and to crystal or single molecule geometry optimizations, including considerations of anisotropy of H atoms. Our findings help to understand properties of molecules like MTTOTHP as progenitors of free oxygen radicals.

Domain overlap matrices from plane-wave-based methods of electronic structure calculation

Plane waves are one of the most popular and efficient basis sets for electronic structure calculations of solids; however, their delocalized nature makes it difficult to employ for them classical orbital-based methods of chemical bonding analysis. The quantum chemical topology approach, introducing chemical concepts via partitioning of real space into chemically meaningful domains, has no difficulties with plane-wave-based basis sets. Many popular tools employed within this approach, for instance delocalization indices, need overlap integrals over these domains-the elements of the so called domain overlap matrices. This article reports an efficient algorithm for evaluation of domain overlap matrix elements for plane-wave-based calculations as well as evaluation of its implementation for one of the most popular projector augmented wave (PAW) methods on the small set of simple and complex solids. The stability of the obtained results with respect to PAW calculation parameters has been investigated, and the comparison of the results with the results from other calculation methods has also been made.