On the interpretation of domain averaged Fermi hole analyses of correlated wavefunctions

Abstract

Few methods allow for a physically sound analysis of chemical bonds in cases where electron correlation may be a relevant factor. The domain averaged Fermi hole (DAFH) analysis, a tool firstly proposed by Robert Ponec in the 1990's to provide interpretations of the chemical bonding existing between two fragments Ω and Ω' that divide the real space exhaustively, is one of them. This method allows for a partition of the delocalization index or bond order between Ω and Ω' into one electron contributions, but the chemical interpretation of its parameters has been firmly established only for single determinant wavefunctions. In this paper we report a general interpretation based on the concept of excluded density that is also valid for correlated descriptions. Both analytical models and actual computations on a set of simple molecules (H2, N2, LiH, and CO) are discussed, and a classification of the possible DAFH situations is presented. Our results show that this kind of analysis may reveal several correlated assisted bonding patterns that might be difficult to detect using other methods. In agreement with previous knowledge, we find that the effective bond order in covalent links decreases due to localization of electrons driven by Coulomb correlation.

One‐electron images in real space: Natural adaptive orbitals

“…These functions describe n ‐center bonds in real space (or cores and lone pairs, if n = 1) much as general multicenter NBOs do in Weinhold's prescription. We have also given a physically sound interpretation of NAdOs in the n = 1 case (Ponec's domain natural orbitals, domain natural orbitals (DNOs)) for correlated wavefunctions, showing how genuinely new bonding scenarios, not available in the absence of correlation, may arise in its presence. NAdOs resemble conceptually the hierarchical adaptive natural density partitioning framework proposed by Boldyrev and coworkers .…”

“…Our goal is then to construct intuitive chemical bonding indices from real space RDs, valid for general correlated electronic structure descriptions, that retain, as much as possible, the one‐electron language used by chemists. We have embarked on such a project in the last years , …”

“…It is the purpose of this article to take one further step in our project, and show how two‐center NAdOs behave in correlated and noncorrelated descriptions of simple molecules. We will briefly discuss on their interpretation, following the ideas already outlined for one‐center NAdOs or DNOs, and we will then focus on how they closely reproduce the standard MO paradigm in simple cases. Our aim is to show that most of the chemical bonding toolbox available in textbooks may be directly extracted from these new objects when the IPM is a good approximation, but that provide truly new insight when this is not true.…”

Toward deformation densities for intramolecular interactions without radical reference states using the fragment, atom, localized, delocalized, and interatomic (FALDI) charge density decomposition scheme

“…[50] If we vary r 1 over all space, it then gives the total, molecular-wide density distribution of the electrons which can be found in a volume element dr 2 . Since the hole calculates the origin (r 2 ) of the excluded electron (at r 1 ), plotting eq.…”

Revisiting the carbonyl n → π* electronic excitation through topological eyes: expanding, enriching and enhancing the chemical language using electron number distribution functions and domain averaged Fermi holes

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The theory of chemical bonding is underdeveloped in electronic excited states, even in small molecules. [15] The information that can be extracted from these electron recovering techniques is extremely wide and, as previously indicated, it can be used to close (or at least decrease) the predictive gap of many QCT analyses. The statistics of the electron populations, through a fruitful combination of electron distribution functions (EDFs) and domain averaged Fermi holes (DAFHs), was used to enlighten our chemical knowledge of a paradigmatic process: the n → π * excitation in formaldehyde.

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