The relationship between the structure and the properties of a drug or material is a key concept of chemistry. Knowledge of the three-dimensional structure is considered to be of such...

Quantum crystallography combines quantum chemistry and experimental diffraction or scattering to provide both enhanced wavefunctions and charge densities.

Crystallography and quantum mechanics have always been tightly connected because reliable quantum mechanical models are needed to determine crystal structures. Due to this natural synergy, nowadays accurate distributions of electrons in space can be obtained from diffraction and scattering experiments. In the original definition of quantum crystallography (QCr) given by Massa, Karle and Huang, direct extraction of wavefunctions or density matrices from measured intensities of reflections or, conversely, ad hoc quantum mechanical calculations to enhance the accuracy of the crystallographic refinement are implicated. Nevertheless, many other active and emerging research areas involving quantum mechanics and scattering experiments are not covered by the original definition although they enable to observe and explain quantum phenomena as accurately and successfully as the original strategies. Therefore, we give an overview over current research that is related to a broader notion of QCr, and discuss options how QCr can evolve to become a complete and independent domain of natural sciences. The goal of this paper is to initiate discussions around QCr, but not to find a final definition of the field.

The fast and reliable determination of wave functions and electron densities of macromolecules has been one of the goals of theoretical chemistry for a long time and, in this context, several linear scaling techniques have been successfully devised over the years. Different approaches have been adopted to tackle this problem and one of them exploits the fact that, according to the traditional chemical perception, molecules can be seen as constituted of recurring units (e.g., functional groups) with well-defined chemical features. This has led to the development of methods in which the global wave functions or electron densities of macromolecules are obtained by simply transferring density matrices or fuzzy electron densities associated with molecular fragments. In this context, we propose an alternative strategy that aims at quickly reconstructing wave functions and electron densities of proteins through the transfer of extremely localized molecular orbitals (ELMOs), which are orbitals strictly localized on small molecular units and, for this reason, easily transferable from molecule to molecule. To accomplish this task we have constructed original libraries of ELMOs that cover all the possible elementary fragments of the twenty natural amino acids in all their possible protonation states and forms. Our preliminary test calculations have shown that, compared to more traditional methods of quantum chemistry, the transfers from the novel ELMO-databanks allow to obtain wave function and electron densities of large polypeptides and proteins at a significantly reduced computational cost. Furthermore, notwithstanding expected discrepancies, the obtained electron distributions and electrostatic potentials are in very good agreement with those obtained at Hartree-Fock and density functional theory (DFT) levels. Therefore, the results encourage to use the new libraries as alternatives to the popular pseudoatom-databases of crystallography in the refinement of

Despite more and more remarkable computational ab initio results are nowadays continuously obtained for large macromolecular systems, the development of new linear-scaling techniques is still an open and stimulating field of research in theoretical chemistry. In this family of methods, an important role is occupied by those strategies based on the observation that molecules are generally constituted by recurrent functional units with well-defined intrinsic features. In this context, we propose to exploit the notion of extremely localized molecular orbitals (ELMOs) that, due to their strict localization on small molecular fragments (e.g., atoms, bonds, or functional groups), are in principle transferable from one molecule to another. Accordingly, the construction of orbital libraries to almost instantaneously build up approximate wave functions and electron densities of very large systems becomes conceivable. In this work, the ELMOs transferability is further investigated in detail and, furthermore, suitable rules to construct model molecules for the computation of ELMOs to be stored in future databanks are also defined. The obtained results confirm the reliable transferability of the ELMOs and show that electron densities obtained from the transfer of extremely localized molecular orbitals are very close to the corresponding Hartree-Fock ones. These observations prompt us to construct new ELMOs databases that could represent an alternative/complement to the already popular pseudoatoms databanks both for determining electron densities and for refining crystallographic structures of very large molecules.

The subdivision of protein structures into smaller and independent structural domains has a fundamental importance in understanding protein evolution and function and in the development of protein classification methods as well as in the interpretation of experimental data. Due to the rapid growth in the number of solved protein structures, the need for devising new accurate algorithmic methods has become more and more urgent. In this paper, we propose a new computational approach that is based on the concept of domain as a compact and independent folding unit and on the analysis of the residue-residue energy interactions obtainable through classical all-atom force field calculations. In particular, starting from the analysis of the nonbonded interaction energy matrix associated with a protein, our method filters out and selects only those specific subsets of interactions that define possible independent folding nuclei within a complex protein structure. This allows grouping different protein fragments into energy clusters that are found to correspond to structural domains. The strategy has been tested using proper benchmark data sets, and the results have shown that the new approach is fast and reliable in determining the number of domains in a totally ab initio manner and without making use of any training set or knowledge of the systems in exam. Moreover, our method, identifying the most relevant residues for the stabilization of each domain, may complement the results given by other classification techniques and may provide useful information to design and guide new experiments.

Embedding strategies currently provide the best compromise between accuracy and computational cost in modeling chemical properties and processes of large and complex systems. In this framework, different methods have been proposed all over the years, from the very popular QM/MM approaches to the more recent and very TOC GRAPHICS KEYWORDS. Embedding methods, QM/QM' techniques, extremely localized molecular orbitals, Local Self-Consistent Field approach.

Due to both technical and methodological difficulties, determining and analyzing charge densities of very large molecular systems represents a serious challenge that, in the crystallographers community, has been mainly tackled by observing that the so-called pseudoatoms of the electron density multipole expansions are reliably transferable from molecule to molecule. This has led to the construction of pseudoatoms databanks that have allowed successful refinements of crystallographic structures of macromolecules, while taking into account their corresponding reconstructed electron distributions. A recent alternative/complement to the previous approach is represented by techniques based on extremely localized molecular orbitals (ELMOs) that, due to their strict localization on small molecular fragments (e.g., atoms, bonds, and functional groups), are also in principle exportable from system to system. The ELMOs transferability has been already tested in detail, and, in this work, it has been compared to the one of the pseudoatoms. To accomplish this task, electron distributions obtained both through the transfer of pseudoatoms and through the transfer of extremely localized molecular orbitals have been analyzed, especially taking into account topological properties and similarity indexes. The obtained results indicate that all the considered reconstruction methods give completely reasonable and similar charge densities, and, consequently, the new ELMOs libraries will probably represent new useful tools not only for refining crystal structures but also for computing approximate electronic properties of very large molecules.