Source Function applied to experimental densities reveals subtle electron-delocalization effects and appraises their transferability properties in crystals

Aromaticity Concepts Derived from Experiments

Aromaticity, a very important term in organic chemistry, has never been defined unambiguously. Various ways to describe it come from different phenomena that have been experimentally observed. The most important examples related to some theoretical concepts are presented here.

A fast approximate extension of the interacting quantum atoms energy decomposition to excited states

An approach is developed for the fast calculation of the interacting quantum atoms energy decomposition (IQA) from the information contained in the first order reduced density matrix only. The proposed methodology utilizes an approximate exchange-correlation density from Density Matrix Functional Theory without the need to evaluate the correlation-exchange contribution directly. Instead, weight factors are estimated to decompose the exact V_xc into atomic and pairwise contributions. In this way, the sum of the IQA contributions recovers the energy obtained from the electronic structure calculation. This method can, hence, be applied to obtain atomic contributions in excited states on the same footing as in their ground states using any method that delivers the reduced first-order density matrix. In this way, one can locate chromophores from first principles quantum chemical calculations. Test calculations on the ground and excited states of a set of small molecules indicate that the scaled atomic contributions reproduce vertical electronic transition energies calculated exactly. This approach may be useful to extend the applicability of the IQA approach in the study of large photochemical systems especially when the calculations of the second order reduced density matrices is prohibitive or not possible.

Benzene and Borazine, so Different, yet so Similar: Insight from Experimental Charge Density Analysis

Although benzene and borazine are isoelectronic and isostructural, they have very different electronic structures, mainly due to the polar nature of the B-N bond. Herein, we present an experimental study of the charge density distribution obtained from the multipole model formalism and Hirshfeld atom refinement (HAR) based on high-resolution X-ray diffraction data of borazine B₃N₃H₆ (1) and B,B',B″-trichloroborazine (2) crystals. These data are compared to those obtained from HAR for benzene (4) and 1,3,5-trichlorobenzene (5) and further compared with values obtained from density functional theory calculations in the gas phase, where N,N',N″-trichloroborazine (3) was also included. The results confirm that, unlike benzene, borazines are only weakly aromatic with an island-like electronic delocalization within the B₃N₃ ring involving only the nitrogen atoms. Furthermore, delocalization indices and interacting quantum atom energy for bonded and non-bonded atoms were found to be highly suitable indicators capable of describing the origin of the discrepancies observed when the degree of aromaticity in 2 and 3 is evaluated using common aromaticity indices. Additionally, analysis of intermolecular interactions in the crystals brings further evidence of a weakly aromatic character of the borazines as it reveals surprising similarities between the crystal packing of borazine and benzene and also between B,B',B″-trichloroborazine and 1,3,5-trichlorobenzene.

Anharmonic motions versus dynamic disorder at the Mg ion from the charge densities in pyrope (Mg3Al2Si3O12) crystals at 30 K: six of one, half a dozen of the other

The possible occurrence of static/dynamic disorder at the Mg site in pyrope (Mg₃Al₂Si₃O₁₂), with or without anharmonic contribution to the thermal vibrations even at low temperatures, has been largely debated but conclusions were contrasting. Here a report is given on the experimental charge density distribution, ρ_EXP, of synthetic pyrope at T = 30 K, built through a Stewart multipolar expansion up to l = 5 and based on a very precise and accurate set of in-home measured single-crystal X-ray diffraction amplitudes with a maximum resolution of 0.44 Å. Local and integral topological properties of ρ_EXP are in substantial agreement with those of ρ_THEO, the corresponding DFT-grade quantum charge density of an ideal pyrope crystal, and those derived from synchrotron investigations of chemical bonding in olivines. Relevant thermal atomic displacements, probably anharmonic in nature, clearly affect the whole structure down to 30 K. No significant (> 2.5σ) residual Fourier peaks are detectable from the ρ_EXP distribution around Mg, after least-squares refinement of a multipole model with anharmonic thermal motion at the Mg site. Experimental findings were confirmed by a full analysis of normal vibration modes of the DFT-optimized structure of the perfect pyrope crystal. Mg undergoes wide displacements from its equilibrium position even at very low temperatures, as it is allocated in a ∼ 4.5 Å large dodecahedral cavity and involved in several soft phonon modes. Implications on the interplay among static/dynamic disorder of Mg and lattice vibrational degrees of freedom are discussed.

Insights on spin delocalization and spin polarization mechanisms in crystals of azido copper(II) dinuclear complexes through the electron spin density Source Function

The Source Function (SF) tool was applied to the analysis of thetheoreticalspin density in azido CuIIdinuclear complexes, where the azido group, acting as a coupler between the CuIIcations, is linked to the metal centres either in an end-on or in an end–end fashion. Results for only the former structural arrangement are reported in the present paper. The SF highlights to which extent the magnetic centres contribute to determine the local spin delocalization and polarization at any point in the dimetallic complex and whether an atom or group of atoms of the ligands act in favour or against a given local spin delocalization/polarization. Ball-and-stick atomic SF percentage representations allow for a visualization of the magnetic pathways and of the specific role played by each atom along these paths, at given reference points. Decomposition of SF contributions in terms of a magnetic and of a relaxation component provides further insight. Reconstruction of partial spin densities by means of the Source Function has for the first time been introduced. At variance with the standard SF percentage representations, such reconstructions offer a simultaneous view of the sources originating from specific subsets of contributing atoms, in a selected molecular plane or in the whole space, and are therefore particularly informative. The SF tool is also used to evaluate the accuracy of the analysed spin densities. It is found that those obtained at the unrestricted B3LYP DFT level, relative to those computed at the CASSCF(6,6) level, greatly overestimate spin delocalization to the ligands, but comparatively underestimate magnetic connection (spin transmission) among atoms, along the magnetic pathways. As a consequence of its excessive spin delocalization, the UB3LYP method also overestimates spin polarization mechanisms between the paramagnetic centres and the ligands. Spin delocalization measures derived from the refinement of Polarized Neutron Diffraction data seem in general superior to those obtained through the DFT UB3LYP approach and closer to the far more accurate CASSCF results. It is also shown that a visual agreement on the spin-resolved electron densities ραand ρβderived from different approaches does not warrant a corresponding agreement between their associated spin densities.

A first-prototype multi-determinant X-ray constrained wavefunction approach: the X-ray constrained extremely localized molecular orbital–valence bond method

All the current variants of Jayatilaka's X-ray constrained wavefunction (XCW) approach work within the framework of the single-determinant wavefunctionansatz. In this paper, a first-prototype multi-determinant XCW technique is proposed. The strategy assumes that the desired XCW is written as a valence-bond-like expansion in terms of pre-determined single Slater determinants constructed with extremely localized molecular orbitals. The method, which can be particularly suitable to investigate systems with a multi-reference character, has been applied to determine the weights of the resonance structures of naphthalene at different temperatures by exploiting experimental high-resolution X-ray diffraction data. The results obtained have shown that the explicit consideration of experimental structure factors in the determination of the resonance structure weights may lead to results significantly different compared with those resulting only from the simple energy minimization.

Expanding the usage of the Source Function to experimental electron densities

The Source Function provides unique information about chemical bonding in the solid state, from theory as well as from experiment. It is now established that the concept of electronic delocalization in aromatic systems can be accurately studied using X-ray derived electron densities, and even more importantly the contributions are transferable between similar systems.