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X-ray Constrained Spin-Coupled Wavefunction: a New Tool to Extract Chemical Information from X-ray Diffraction Data

Abstract : The X-ray constrained wavefunction (XCW) approach is a reliable and widely used method of Quantum Crystallography that allows the determination of wavefunctions compatible with X-ray diffraction data. So far, all the existing XCW techniques have been developed in the framework of the Molecular Orbital theory and, consequently, provide only pictures of the "experimental" electronic structures that are far from the traditional chemical perception. Here we propose a new strategy that, by combining the XCW philosophy with the Spin-Coupled method of the Valence Bond theory, enables to directly extract traditional chemical information (e.g., weights of resonance structures) from X-ray diffraction measurements. Preliminary results have shown that the new technique is really able to efficiently capture the effects of the crystal environment on the electronic structure and can be considered as a new useful tool to perform chemically sound analyses of the X-ray diffraction data. Besides the well-known multipolar model, [1] one of the new pillar-methods of the emerging field of Quantum Crystallography [2] is Jayatilaka's X-ray constrained wavefunction (XCW) approach, [3] which is the most widely used strategy among the techniques that aim at extracting wavefunctions or density matrices from experimental X-ray diffraction or scattering data. [4] It consists in determining wavefunctions that not only minimize the energy of the investigated systems, but that also maximize the agreement between calculated and experimental structure factors amplitudes. So far, the approach has been mainly proposed within the Molecular Orbital theory, especially in the framework of the Hartree-Fock formalism, [3] but also including relativistic corrections. [5] Therefore, in its original form, the Jayatilaka strategy provides completely delocalized pictures of electronic structures that can be rationalized in terms of traditional chemical concepts (e.g., local bonds, hybridization, Lewis structures, resonance structures, etc.) by only applying a posteriori Quantum Chemical Topology methods [6,7] or other bonding-analysis techniques, such as the Natural Bond Orbitals strategy and the Natural Resonance Theory. [7] The only attempts to recover the traditional chemical perception in the context of the XCW approach without resorting to a posteriori methods are the more recent XC-ELMO [8] and XC-ELMO-VB [9] techniques. Nevertheless, in the former, Extremely Localized Molecular Orbitals) [10] (ELMOs) corresponding to atoms, bonds and functional groups are directly extracted from X-ray diffraction data, but a localization scheme is actually imposed a priori on the electronic structure before starting the calculations. In the latter, only the weights of resonance structures are determined from the experimental data, while the Slater determinants used for the expansion of a pseudo Valence Bond wavefunction are obtained by means of preliminary ELMO calculations and are strictly kept frozen during the minimization-fitting process. Here we present a novel XCW method that allows the extraction of usual chemical information from X-ray diffraction data without performing a posteriori analyses or introducing a priori information. To accomplish this task we have coupled the XCW philosophy to the Spin-Coupled (SC) approach, [11] a Valence Bond [12] technique that provides a fully correlated description of the electronic structure, but still interpretable in terms of one-particle functions and close to the traditional chemical perception. In fact, from the shapes of the SC orbitals it is generally possible to draw conclusions on the spatial arrangements of the electronic clouds and the hybridization of atoms. Furthermore, from the weights associated with the different spin-coupling modes, one can get insights into the relative importance of the resonance structures for the system under exam. In the new X-ray constrained Spin-Coupled (XCSC) technique, the wavefunction ansatz assumes the analytical form of a traditional SC wavefunction for a system of N electrons in the spin-state (,):
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Contributor : Alessandro Genoni <>
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Alessandro Genoni, Davide Franchini, Stefano Pieraccini, Maurizio Sironi. X-ray Constrained Spin-Coupled Wavefunction: a New Tool to Extract Chemical Information from X-ray Diffraction Data. Chemistry - A European Journal, Wiley-VCH Verlag, 2018, 24 (58), pp.15507-15511. ⟨10.1002/chem.201803988⟩. ⟨hal-02196487⟩



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