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One of the well‐established methods of modern quantum crystallography is undoubtedly the X‐ray constrained wavefunction (XCW) approach, a technique that enables the determination of wavefunctions which not only minimize the energy of the system under examination, but also reproduce experimental X‐ray diffraction data within the limit of the experimental errors. Initially proposed in the framework of the Hartree–Fock method, the strategy has been gradually extended to other techniques of quantum chemistry, but always remaining limited to a single‐determinant ansatz for the wavefunction to extract. This limitation has been recently overcome through the development of the novel X‐ray constrained spin‐coupled (XCSC) approach [Genoni et al. (2018). Chem. Eur. J.24, 15507–15511] which merges the XCW philosophy with the traditional spin‐coupled strategy of valence bond theory. The main advantage of this new technique is the possibility of extracting traditional chemical descriptors (e.g. resonance structure weights) compatible with the experimental diffraction measurements, without the need to introduce information a priori or perform analyses a posteriori. This paper provides a detailed theoretical derivation of the fundamental equations at the basis of the XCSC method and also introduces a further advancement of its original version, mainly consisting in the use of molecular orbitals resulting from XCW calculations at the Hartree–Fock level to describe the inactive electrons in the XCSC computations. Furthermore, extensive test calculations, which have been performed by exploiting high‐resolution X‐ray diffraction data for salicylic acid and by adopting different basis sets, are presented and discussed. The computational tests have shown that the new technique does not suffer from particular convergence problems. Moreover, all the XCSC calculations provided resonance structure weights, spin‐coupled orbitals and global electron densities slightly different from those resulting from the corresponding unconstrained computations. These discrepancies can be ascribed to the capability of the novel strategy to capture the information intrinsically contained in the experimental data used as external constraints. [ABSTRACT FROM AUTHOR]

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 molecular orbital theory and, consequently, provide only pictures of the "experimental" electronic structures that are far from the traditional chemical perception. Here a new strategy is proposed that, by combining the XCW philosophy with the spin‐coupled method of valence bond theory, enables direct extraction of 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. From X‐ray diffraction to resonance structures weights. A new quantum crystallographic method that enables taking into account the X‐ray diffraction data in full Valence Bond calculations is proposed. Exploiting the new technique, insights into the electron distributions around each atomic center and, particularly, into the weights of resonance structures can be directly obtained from usual X‐ray diffraction measurements. [ABSTRACT FROM AUTHOR]

Orbitals that are extremely localized on molecular fragments represent a powerful tool for a number of purposes: to cite a few examples, they allow to reduce strongly the complexity of calculations on large systems and are easily transferable from one molecule to another, providing a suitable and efficient way to build up the electronic structure of large molecules. Recently, we have developed efficient algorithms to determine extremely localized molecular orbitals (ELMOs), which will be reviewed in this paper. As a rigorous localization is strictly connected to a reduction in the number of variational parameters, which reflects into an increased value of the associated energy with respect to the Hartree Fock value, we have developed a number of strategies to relax the wavefunction built up using transferred localized orbitals. The extreme localization has also been exploited in connection with the “Divide and Conquer” technique to determine the electron densities of large polypeptides assembled from orbitals computed on small model molecules. Moreover, we will discuss the recent application of the ELMOs in the framework of the hybrid QM/MM methods to describe the frontier region. We will also show that the ELMOs can be used to extract chemical interpretations from numerical results. A variety of applications will be presented. [ABSTRACT FROM AUTHOR]

Abstract: The ‘nearsightedness’ of electronic structure is an underlying principle in many of the linear scaling methods recently developed to study large systems. Among them, there are strategies based on the transfer of orbitals strictly localized on molecular fragments, such as the extremely localized molecular orbitals (ELMOs). Unfortunately, due to the non-orthogonal nature of these orbitals, the density matrix calculation is computationally demanding, so preventing a straightforward application to very large molecules. In this Letter, we show how this problem can be overcome by a proper application of the ‘Divide and Conquer’ strategy to the ELMO approach. [Copyright &y& Elsevier]

Abstract: A new method to compute high-quality electron densities of polypeptides is proposed. The method is based on the transferability properties of extremely localized molecular orbitals, which can be used to describe with great accuracy the different functional groups of a molecule. It is therefore possible to generate a database of such orbitals, each of them associated with specific amino acids or with the peptide bond. A new program, DENPOL, has been written in order to build up the electron density of a generic polypeptide using this database. Due to both the large number of orbitals required to describe a polypeptide and the non-orthogonal nature of these orbitals, a Divide & Conquer strategy has been used to assemble the final electron density. The application of this approach is particularly efficient thanks to the extreme localization of the orbitals. The comparison with the corresponding electron densities generated by the Hartree–Fock method, shows the accuracy of the proposed approach and indicates that the electron densities generated by DENPOL are very close to those generated by an ab initio approach. [Copyright &y& Elsevier]