N-representable one-electron reduced density matrix reconstruction with frozen core electrons.

Recent advances in quantum crystallography have shown that, beyond conventional charge density refinement, a one-electron reduced density matrix (1-RDM) satisfying N-representability conditions can be reconstructed using jointly experimental X-ray structure factors and directional Compton profiles (DCP) through semidefinite programming. So far, such reconstruction methods for 1-RDM, not constrained to idempotency, have been tested only on a toy model system (CO2). In this work, a new method is assessed on crystalline urea [CO(NH2)2] using static (0 K) and dynamic (50 K) artificial experimental data. An improved model, including symmetry constraints and frozen core-electron contribution, is introduced to better handle the increasing system complexity. Reconstructed 1-RDMs, deformation densities and DCP anisotropy are analysed, and it is demonstrated that the changes in the model significantly improve the reconstruction quality, even when there is insufficient information and data corruption. The robustness of the model and the strategy are thus shown to be well adapted to address the reconstruction problem from actual experimental scattering data.

5-Fluoro-1,2,3-triazole motif in peptides and its electronic properties.

The 5-fluoro triazole amino acid scaffold prepared by halogen exchange has been incorporated into peptides. From the X-ray diffraction of the 5-fluoro triazole motif, the main observation was an important localization on one side of the negative potential surface. The fluorine atom reveals a cylindrical shape in its deformation electron density.

Spin-resolved atomic orbital model refinement for combined charge and spin density analysis: application to the YTiO3 perovskite.

A new crystallographic method is proposed in order to refine a spin-resolved atomic orbital model against X-ray and polarized neutron diffraction data. This atomic orbital model is applied to the YTiO3 perovskite crystal, where orbital ordering has previously been observed by several techniques: X-ray diffraction, polarized neutron diffraction and nuclear magnetic resonance. This method gives the radial extension, orientation and population of outer atomic orbitals for each atom. The interaction term between Ti3+, Y3+ cations and O2- ligands has been estimated. The refinement statistics obtained by means of the orbital method are compared with those obtained by the multipole model previously published.

Inferring the one-electron reduced density matrix of molecular crystals from experimental data sets through semidefinite programming.

Constructing a quantum description of crystals from scattering experiments is of great significance to explain their macroscopic properties and to evaluate the pertinence of theoretical ab initio models. While reconstruction methods of the one-electron reduced density matrix have already been proposed, they are usually tied to strong assumptions that limit and may introduce bias in the model. The goal of this paper is to infer a one-electron reduced density matrix (1-RDM) with minimal assumptions. It has been found that the mathematical framework of semidefinite programming can achieve this goal. Additionally, it conveniently addresses the nontrivial constraints on the 1-RDM which were major hindrances for the existing models. The framework established in this work can be used as a reference to interpret experimental results. This method has been applied to the crystal of dry ice and provides very satisfactory results when compared with periodic ab initio calculations.

Spin resolved electron density study of YTiO3 in its ferromagnetic phase: signature of orbital ordering.

The present work reports on the charge and spin density modelling of YTiO3 in its ferromagnetic state (T C = 27 K). Accurate polarized neutron diffraction and high-resolution X-ray diffraction (XRD) experiments were carried out on a single crystal at the ORPHÉE reactor (LLB) and SPRING8 synchrotron source. The experimental data are modelled by the spin resolved pseudo-atomic multipolar model (Deutsch et al., 2012 ▸). The refinement strategy is discussed and the result of this electron density modelling is compared with that from XRD measured at 100 K and with density functional theory calculations. The results show that the spin and charge densities around the Ti atom have lobes directed away from the O atoms, confirming the filling of the t 2g orbitals of the Ti atom. The d xy orbital is less populated than d xz and d yz , which is a sign of a partial lift of degeneracy of the t 2g orbitals. This study confirms the orbital ordering at low temperature (20 K), which is already present in the paramagnetic state above the ferromagnetic transition (100 K).

Experimental and theoretical insights of functionalized hexavanadates on Na+/K+-ATPase activity; molecular interaction field, ab initio calculations and in vitro assays.

The influence of three functionalized hexavanadates (V6): Na2 [V6O13{(OCH2)3CCH3}2], [H2]2 [V6O13{(OCH2)3CCH2OCOCH2CH3}2] and [(C4H9)4N]2 [V6O13{(OCH2)3CCH2OOC(CH3)2-COOH}2 on Na+/K+-ATPase activity, was investigated in vitro. Including compounds already tested by Xu et al. (Journal of Inorganic Biochemistry 161 (2016) 27-36), all functionalized hexavanadates inhibit the activity of Na+/K+-ATPase in a dose-dependent manner but with different inhibitory potencies. Na2 [V6O13{(OCH2)3CCH3}2] was found to have the best inhibition properties - showing 50% inhibition IC50 = 5.50 × 10-5 M, while [(C4H9)4N]2 [V6O13{(OCH2)3CCH2OOC(CH3)2-COOH}2] showed the lowest inhibitory power, IC50 = 1.31 × 10-4 M. In order to understand the bioactivity of functionalized hexavanadates series, we have also used a combined theoretical approach: determination of electrostatic potential from ab initio theoretical calculations and computation of the molecular interaction field (MIF) surface.

Joint refinement model for the spin resolved one-electron reduced density matrix of YTiO3 using magnetic structure factors and magnetic Compton profiles data.

In this paper, we propose a simple cluster model with limited basis sets to reproduce the unpaired electron distributions in a YTiO3 ferromagnetic crystal. The spin-resolved one-electron-reduced density matrix is reconstructed simultaneously from theoretical magnetic structure factors and directional magnetic Compton profiles using our joint refinement algorithm. This algorithm is guided by the rescaling of basis functions and the adjustment of the spin population matrix. The resulting spin electron density in both position and momentum spaces from the joint refinement model is in agreement with theoretical and experimental results. Benefits brought from magnetic Compton profiles to the entire spin density matrix are illustrated. We studied the magnetic properties of the YTiO3 crystal along the Ti-O1-Ti bonding. We found that the basis functions are mostly rescaled by means of magnetic Compton profiles, while the molecular occupation numbers are mainly modified by the magnetic structure factors.

Quantum Crystallography: Current Developments and Future Perspectives.

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.

Development of a joint refinement model for the spin-resolved one-electron reduced density matrix using different data sets.

The paper describes a joint refinement model of the spin-resolved one-electron reduced density matrix using simultaneously magnetic structure factors and magnetic directional Compton profiles. The model is guided by two strategies: (i) variation of basis functions and (ii) variation of the spin population matrix. The implementation for a finite system is based on an expansion of the natural orbitals on basis sets. To show the potential benefits brought by the joint refinement model, the paper also presents the refinement results using magnetic structure factors only. The joint refinement model provides very satisfactory results reproducing the pseudo-data. In particular, magnetic Compton profiles have a strong effect not only on the off-diagonal elements of the spin-resolved one-electron reduced density matrix but also on its diagonal elements.

Reactivity of 12-tungstophosphoric acid and its inhibitor potency toward Na+/K+-ATPase: A combined 31P NMR study, ab initio calculations and crystallographic analysis.

Influence of 12-tungstophosphoric acid (WPA) on conversion of adenosine triphosphate (ATP) to adenosine diphosphate (ADP) in the presence of Na+/K+-ATPase was monitored by 31P NMR spectroscopy. It was shown that WPA exhibits inhibitory effect on Na+/K+-ATPase activity. In order to study WPA reactivity and intermolecular interactions between WPA oxygen atoms and different proton donor types (D=O, N, C), we have considered data for WPA based compounds from the Cambridge Structural Database (CSD), the Crystallographic Open Database (COD) and the Inorganic Crystal Structure Database (ICSD). Binding properties of Keggin's anion in biological systems are illustrated using Protein Data Bank (PDB). This work constitutes the first determination of theoretical Bader charges on polyoxotungstate compound via the Atom In Molecule theory. An analysis of electrostatic potential maps at the molecular surface and charge of WPA, resulting from DFT calculations, suggests that the preferred protonation site corresponds to WPA bridging oxygen. These results enlightened WPA chemical reactivity and its potential biological applications such as the inhibition of the ATPase activity.

When combined X-ray and polarized neutron diffraction data challenge high-level calculations: spin-resolved electron density of an organic radical.

Joint refinement of X-ray and polarized neutron diffraction data has been carried out in order to determine charge and spin density distributions simultaneously in the nitronyl nitroxide (NN) free radical Nit(SMe)Ph. For comparison purposes, density functional theory (DFT) and complete active-space self-consistent field (CASSCF) theoretical calculations were also performed. Experimentally derived charge and spin densities show significant differences between the two NO groups of the NN function that are not observed from DFT theoretical calculations. On the contrary, CASSCF calculations exhibit the same fine details as observed in spin-resolved joint refinement and a clear asymmetry between the two NO groups.

A combined crystallographic analysis and ab initio calculations to interpret the reactivity of functionalized hexavanadates and their inhibitor potency toward Na(+)/K(+)-ATPase.

In vitro influence of five synthesized functionalized hexavanadates (V6) on commercial porcine cerebral cortex Na(+)/K(+)-ATPase activity has been studied. Dose dependent Na(+)/K(+)-ATPase inhibition was obtained for all investigated compounds. Calculated half maximal inhibitory concentration IC50 values, in mol/L, for Na(+)/K(+)-ATPase were 7.6×10(-5), 1.8×10(-5), 2.9×10(-5), 5.5×10(-5) for functionalized hexavanadates (V6) with tetrabutylammonium (TBA) [V6-CH3][TBA]2, [V6-NO2][TBA]2, [V6-OH][TBA]2 and [V6-C3][TBA]2 respectively. [V6-OH][Na]2 inhibited Na(+)/K(+)-ATPase activity up to 30% at maximal investigated concentration 1×10(-3)mol/L. This reactivity has been interpreted using a study of the non-covalent interactions of functionalized hexavanadate hybrids through Cambridge Structural Database (CSD) analysis. Bibliographic searching has led to 18 different structures and 99 contacts. We have observed that C-H⋯O contacts consolidate the structures. We have also performed density functional theory (DFT) calculations and have determined electrostatic potential values at the molecular surface on a series of functionalized V6. These results enlightened their chemical reactivity and their potential biological applications such as the inhibition of the ATPase.

Deciphering the Conformational Choreography of Zinc Coordination Complexes with Standard and Novel Proton NMR Techniques Combined with DFT Methods.

The presence of water has been shown to deeply impact the stability and geometry of Zn complexes in solution. Evidence for tetra- and penta-coordinated species in a pyridylmethylamine-Zn(II) model complex is presented. Novel (1) H NMR tools such as T1 -filtered selective exchange spectroscopy and pure shifted gradient-encoded selective refocusing as well as classical 2D ((1) H-(1) H) exchange spectroscopy, diffusion-ordered spectroscopy and T1 ((1) H) measurements, in combination with density functional theory methods allow the full conformational dynamics of a pyridylmethylamine-Zn(II) complex to be revealed. Four conformers and two families of complexes depending on the hydration states are elucidated.

Modelling the experimental electron density: only the synergy of various approaches can tackle the new challenges.

Electron density is a fundamental quantity that enables understanding of the chemical bonding in a molecule or in a solid and the chemical/physical property of a material. Because electrons have a charge and a spin, two kinds of electron densities are available. Moreover, because electron distribution can be described in momentum or in position space, charge and spin density have two definitions and they can be observed through Bragg (for the position space) or Compton (for the momentum space) diffraction experiments, using X-rays (charge density) or polarized neutrons (spin density). In recent years, we have witnessed many advances in this field, stimulated by the increased power of experimental techniques. However, an accurate modelling is still necessary to determine the desired functions from the acquired data. The improved accuracy of measurements and the possibility to combine information from different experimental techniques require even more flexibility of the models. In this short review, we analyse some of the most important topics that have emerged in the recent literature, especially the most thought-provoking at the recent IUCr general meeting in Montreal.

First spin-resolved electron distributions in crystals from combined polarized neutron and X-ray diffraction experiments.

Since the 1980s it has been possible to probe crystallized matter, thanks to X-ray or neutron scattering techniques, to obtain an accurate charge density or spin distribution at the atomic scale. Despite the description of the same physical quantity (electron density) and tremendous development of sources, detectors, data treatment software etc., these different techniques evolved separately with one model per experiment. However, a breakthrough was recently made by the development of a common model in order to combine information coming from all these different experiments. Here we report the first experimental determination of spin-resolved electron density obtained by a combined treatment of X-ray, neutron and polarized neutron diffraction data. These experimental spin up and spin down densities compare very well with density functional theory (DFT) calculations and also confirm a theoretical prediction made in 1985 which claims that majority spin electrons should have a more contracted distribution around the nucleus than minority spin electrons. Topological analysis of the resulting experimental spin-resolved electron density is also briefly discussed.

Experimental determination of spin-dependent electron density by joint refinement of X-ray and polarized neutron diffraction data.

New crystallographic tools were developed to access a more precise description of the spin-dependent electron density of magnetic crystals. The method combines experimental information coming from high-resolution X-ray diffraction (XRD) and polarized neutron diffraction (PND) in a unified model. A new algorithm that allows for a simultaneous refinement of the charge- and spin-density parameters against XRD and PND data is described. The resulting software MOLLYNX is based on the well known Hansen-Coppens multipolar model, and makes it possible to differentiate the electron spins. This algorithm is validated and demonstrated with a molecular crystal formed by a bimetallic chain, MnCu(pba)(H(2)O)(3)·2H(2)O, for which XRD and PND data are available. The joint refinement provides a more detailed description of the spin density than the refinement from PND data alone.

d-Orbital orientation in a dimer cobalt complex: link to magnetic properties?

The experimental charge-density distribution of the dinuclear cobalt(II) complex [Co(2)(sym-hmp)(2)](BPh(4))(2)·2H(2)O·2C(3)H(6)O was determined at 100 K. When decreasing the temperature, the magnetic susceptibility of this complex deviates from Curie law because of anti-ferromagnetic exchange interactions, but the susceptibility increases sharply at low temperature (< 20 K). To explain this magnetic behaviour a tilt angle between the Co-atom environments was previously theoretically predicted. The structure and experimental charge density determined in this study show a tilt angle. The calculated value, based on the 100 K experimental d-orbital model, is in agreement with the theoretical one.

Determination of a one-electron reduced density matrix using a coupled pseudo-atom model and a set of complementary scattering data.

A possible model of one-electron reduced density matrices is presented, adapted from the Hansen-Coppens pseudo-atomic description of electron density [Hansen & Coppens (1978). Acta Cryst. A34, 909-913]. Potential benefits from a joint refinement of the model from X-ray diffraction and deep inelastic scattering data are illustrated.

Experimental/theoretical electrostatic properties of a styrylquinoline-type HIV-1 integrase inhibitor and its progenitors.

We have established that polyhydroxylated styrylquinolines are potent inhibitors of HIV-1 integrase (IN). Among them, we have identified (E)-8-hydroxy-2-[2-(4,5-dihydroxy-3-methoxyphenyl)-ethenyl]-7-quinolinecarboxylic acid (1) as a promising lead. Previous molecular dynamics simulations and docking procedures have shown that the inhibitory activity involves one or two metal cations (Mg2+), which are present in the vicinity of the active center of the enzyme. However, such methods are generally based on a force-field approach and still remain not as reliable as ab initio calculations with extended basis sets on the whole system. To go further in this area, the aim of the present study was to evaluate the predictive ability of the electron density and electrostatic properties in the structure-activity relationships of this class of HIV-1 antiviral drugs. The electron properties of the two chemical progenitors of 1 were derived from both high-resolution X-ray diffraction experiments and ab initio calculations. The twinning phenomenon and solvent disorder were observed during the crystal structure determination of 1. Molecule 1 exhibits a planar s-trans conformation, and a zwitterionic form in the crystalline state is obtained. This geometry was used for ab initio calculations, which were performed to characterize the electronic properties of 1. The electron densities, electrostatic potentials, and atomic charges of 1 and its progenitors are here compared and analyzed. The experimental and theoretical deformation density bond peaks are very comparable for the two progenitors. However, the experimental electrostatic potential is strongly affected by the crystal field and cannot straightforwardly be used as a predictive index. The weak difference in the theoretical electron densities between 1 and its progenitors reveals that each component of 1 conserves its intrinsic properties, an assumption reinforced by a 13C NMR study. This is also shown through an excellent correlation of the atomic charges for the common fragments. The electrostatic potential minima in zwitterionic and nonzwitterionic forms of 1 are discussed in relation with the localization of possible metal chelation sites.