Interpretation of Experimental Electron Densities by Combination of the QTAMC and DFT

What is it about?

Interpretation of the experimental multipole-modelled electron densities by combination of the quan-tum theory of atoms in molecules and crystal (QTAMC) and orbital-free formulae of the density func-tional theory (DFT) is considered. It is demonstrated that approximate kinetic energy density calculat-ed using the second-order gradient expansion reproduces the main features of this quantity in the mo-lecular or crystal position space, at that the quantitative agreement is achieved for closed-shell and in-termediate atomic interactions. Combination of DFT-approximated kinetic energy density and the local virial theorem provides an appropriate approximation for potential energy density and electronic energy density, also based on the experimental electron density and its derivatives. Consideration of these functions as well as exchange and correlation energy densities provides a comprehensive characteriza-tion of bonding in molecules and crystals based on electron density. Integration of the local functions over atomic basins defined by the zero-flux condition allows expressing the electronic energy of mole-cules and crystals in terms of atomic contributions derived directly from X-ray diffraction experiment, the total electronic energy is in reasonable agreement with direct quantum-chemistry calculation.

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Why is it important?

It is a challenge to work out the real-space energy analysis of bonding based on the experimental ED. Fortunately, there is a theory, which establishes the interconnection between the electron density and the energy densities of different kind. This is the density functional theory (DFT) which exploits ED as a main variable and determines all the properties of atoms, molecules and crystals in the ground electronic state. Thus, DFT provides a basis for a quantitative characteriza-tion of bonding in terms of energy densities and other functions related to electron density. Therefore, it is attractive to combine the formalism of the DFT with experimental electron density to analyze the nature of atomic and molecular interactions in molecules and solids in terms of the local energies. In principle, it might be done in two different ways. The exact functionals connecting ED and the energy densities of electrons - the kinetic, potential, exchange and correlation densities - are, in general, unknown. Therefore, the DFT methods use either Kohn and Sham orbital scheme or approximate functionals with explicit (but non-unique) dependence of these functions on ED and its derivatives. The former approach might be realized using idempotent one-electron density matrix iteratively reconstructed from the experimental electron density or by the Hartree-Fock calculations, which are constrained to obtain the wave functions that reproduce experimental X-ray structure factors. The latter approach is closer to the Hohenberg-Kohn formulation of the DFT: it is orbital-free and allows to avoid the variational determination of wave functions. This is the approach which is considered in this work: we aim to demonstrate here that it allows a more comprehensive extraction of the information on the chemical bonding containing in the experimental electron density.