Least-squares Refinement Research Articles

Open versus Interpenetrated: Switchable Supramolecular Trajectories in Mechanosynthesis of a Halogen-Bonded Borromean Network

Summary Precise control over topologically intricate molecular architectures remains an open challenge for chemists due to their inherent structural complexity. We report a simple solvent-free strategy to selectively prepare two multi-component supramolecular crystalline systems based on the halogen bond, endowed with either an unknot topology or a Borromean-type entanglement. Real-time in situ monitoring of the solvent-free mechanochemical synthesis of these three-component halogen-bonded ionic co-crystals reveals that the choice of milling conditions leads to a switch in the supramolecular reaction trajectory, resulting in the selective formation of an open halogen-bonded network or a halogen-bonded Borromean-type assembly.

Synthesis, FT-IR, UV-VIS, DFT studies and SCXRD structure of 1-(tert-butyl) 3-ethyl-3-(hydroxy(thiophen-2-yl)methyl)piperidine-1,3-dicarboxylate

The crystal structure of 1-(tert-butyl) 3-ethyl 3-(hydroxy(thiophen-2-yl)methyl)piperidine-1,3-dicarboxylate (C 18 H 25 NO 5 S) I has been determined by Single Crystal X-ray Diffraction (SCXRD) techniques. It crystallizes in the orthorhombic space group Pca2 1 with unit cell parameters a = 19.4502(13)Å, b= 6.3571(4)Å, c= 15.2577(10) Å and number of molecules per unit cell, z = 4. The intensity data have been collected at room température (293 K) and the structure has been solved by direct methods. The full matrix least-squares refinement has converged the final R-value to 0.035 for 2251 observed reflections. The piperidine ring adopts a chair conformation. The structure is stabilized by two C–H…O (intermolecular interactions) and five C–H…O (intramolecular interactions). The structural and spectral studies of 1-(tert-butyl) 3-ethyl 3-(hydroxy(thiophen-2-yl)methyl)piperidine-1,3-dicarboxylate have been carried out by using both experimental and quantum chemical techniques.

"Flexible-Acceptor" General Solubility Equation for beyond Rule of 5 Drugs.

This study describes a novel nonlinear variant of the well-known Yalkowsky general solubility equation (GSE). The modified equation can be trained with small molecules, mostly from the Lipinski Rule of 5 (Ro5) chemical space, to predict the intrinsic aqueous solubility, S0, of large molecules (MW > 800 Da) from beyond the rule of 5 (bRo5) space, to an accuracy almost equal to that of a recently described random forest regression (RFR) machine learning analysis. The new approach replaces the GSE constant factors in the intercept (0.5), the octanol-water log P (-1.0), and melting point, mp (-0.01) terms with simple exponential functions incorporating the sum descriptor, Φ+B (Kier Φ molecular flexibility and Abraham H-bond acceptor potential). The constants in the modified three-variable (log P, mp, Φ+B) equation were determined by partial least-squares (PLS) refinement using a small-molecule log S0 training set (n = 6541) of mostly druglike molecules. In this "flexible-acceptor" GSE(Φ,B) model, the coefficient of log P (normally fixed at -1.0) varies smoothly from -1.1 for rigid nonionizable molecules (Φ+B = 0) to -0.39 for typically flexible (Φ ∼ 20, B ∼ 6) large molecules. The intercept (traditionally fixed at +0.5) varies smoothly from +1.9 for completely inflexible small molecules to -2.2 for typically flexible large molecules. The mp coefficient (-0.007) remains practically constant, near the traditional value (-0.01) for most molecules, which suggests that the small-to-large molecule continuum is mainly solvation responsive, apparently with only minor changes in the crystal lattice contributions. For a test set of 32 large molecules (e.g., cyclosporine A, gramicidin A, leuprolide, nafarelin, oxytocin, vancomycin, and mostly natural-product-derived therapeutics used in infectious/viral diseases, in immunosuppression, and in oncology) the modified equation predicted the intrinsic solubility with a root-mean-square error of 1.10 log unit, compared to 3.0 by the traditional GSE, and 1.07 by RFR.

Measurement of partial atomic charges by least-squares refinement of variable electron density crystallographic models

Measurement of partial atomic charges by least-squares refinement of variable electron density crystallographic models

From structure topology to chemical composition. XXVIII. Titanium silicates: Jinshajiangite from the Oktyabr'skii Massif, Donetsk Region, Ukraine, a new occurrence

ABSTRACTHere we report electron-microprobe data and unit-cell parameters for jinshajiangite, ideally NaBaFe2+4Ti2(Si2O7)2O2(OH)2F, from a new locality: the Oktyabr'skii massif in the coastal area of the Azov Sea, Donetsk region, Ukraine. Chemical analysis by electron microprobe gave Nb2O5 1.59, ZrO2 0.61, TiO2 17.07, SiO2 27.60, Al2O3 0.08, Fe2O3 2.04, FeO 16.42, BaO 9.81, ZnO 0.76, MnO 12.97, CaO 1.82, MgO 0.07, K2O 2.05, Na2O 2.51, F 2.48, H2O 1.92, O = F –1.04, sum 98.76 wt.%; H2O was determined in accord with the required number of monovalent anions for the Ti-dominant perraultite-type minerals: OH + F = 3 pfu; the Fe3+/Fe2+ ratio was assigned in accord with Mössbauer-spectroscopy results for jinshajiangite from a different locality. The empirical formula calculated on the basis of 19 (O + F) is (Na0.71Ca0.28□0.01)Σ1(Ba0.56K0.38□0.06)Σ1(Fe2+1.99Mn1.59Fe3+0.22Zn0.08Mg0.02Al0.01□0.09)Σ4 (Ti1.86Nb0.10Zr0.04)Σ2(Si4.00O14)O2[(OH)1.86F0.14]Σ2F1.00, Z = 4. Unit-cell parameters from the single-crystal data were determined by least-squares refinement of 9807 reflections with I > 10σI and are as follows: a = 10.726(8), b = 13.834(10), c = 11.065(8) Å, α = 108.172(5), β = 99.251(7), γ = 90.00(1)°, V = 1537.5(3.4) Å3, space group C .

Object-based incremental registration of terrestrial point clouds in an urban environment

Registration of terrestrial point clouds is essential for large-scale urban applications. The robustness, accuracy, and runtime are generally given the highest priority in the design of appropriate algorithms. Most approaches that target general scenarios can only fulfill some of these factors, that is, robustness and accuracy come at the cost of increased runtime and vice versa. This paper proposes an object-based incremental registration strategy that accomplishes all of these objectives without the need for artificial targets, aiming at a specific scenario, the urban environment. The key is to decompose the degrees of freedom for the SE(3) transformation to three separate but closely related steps, considering that scanners are generally leveled in urban scenes: (1) 2D transformation with matches from line primitives, (2) vertical offset compensation by robust least-squares optimization, and (3) full SE(3) least-squares refinement using uniformly selected local patches. The robustness is prioritized in the whole pipeline, as structured first by a primitive-based registration and two least-squares optimizations with robust estimations that do not require specific keypoints. An object-based strategy for terrestrial point clouds is used to increase the reliability of the first step by the line primitives, which significantly reduces the search space without affecting the recall ratio. The least-squares optimization contributes to achieve a global optimum for the accurate registration. The three coupling steps are also more efficient than segregated coarse-to-fine registration. Experimental evaluations for point clouds acquired in both a metropolis and in old-style cities reveal that the proposed methods are superior to or on par with the state-of-the-art in robustness, accuracy, and runtime. In addition, the methods are also agnostic to the primitives adopted.

Substitutions of Amino Acid Residues in the Substrate Binding Site of Horse Liver Alcohol Dehydrogenase Have Small Effects on the Structures but Significantly Affect Catalysis of Hydrogen Transfer.

Previous studies showed that the L57F and F93W alcohol dehydrogenases catalyze the oxidation of benzyl alcohol with some quantum mechanical hydrogen tunneling, whereas the V203A enzyme has diminished tunneling. Here, steady-state kinetics for the L57F and F93W enzymes were studied, and microscopic rate constants for the ordered bi-bi mechanism were estimated from simulations of transient kinetics for the S48T, F93A, S48T/F93A, F93W, and L57F enzymes. Catalytic efficiencies for benzyl alcohol oxidation (V1/EtKb) vary over a range of ∼100-fold for the less active enzymes up to the L57F enzyme and are mostly associated with the binding of alcohol rather than the rate constants for hydride transfer. In contrast, catalytic efficiencies for benzaldehyde reduction (V2/EtKp) are ∼500-fold higher for the L57F enzyme than for the less active enzymes and are mostly associated with the rate constants for hydride transfer. Atomic-resolution structures (1.1 Å) for the F93W and L57F enzymes complexed with NAD+ and 2,3,4,5,6-pentafluorobenzyl alcohol or 2,2,2-trifluoroethanol are almost identical to previous structures for the wild-type, S48T, and V203A enzymes. Least-squares refinement with SHELXL shows that the nicotinamide ring is slightly strained in all complexes and that the apparent donor-acceptor distances from C4N of NAD to C7 of pentafluorobenzyl alcohol range from 3.28 to 3.49 Å (±0.02 Å) and are not correlated with the rate constants for hydride transfer or hydrogen tunneling. How the substitutions affect the dynamics of reorganization during hydrogen transfer and the extent of tunneling remain to be determined.

SAR Interferometric Baseline Refinement Based on Flat-Earth Phase without a Ground Control Point

Interferometric baseline estimation is a key procedure of interferometric synthetic aperture radar (SAR) data processing. The error of the interferometric baseline affects not only the removal of the flat-earth phase, but also the transformation coefficient between the topographic phase and elevation, which will affect the topographic phase removal for differential interferometric SAR (D-InSAR) and the accuracy of the final generated digital elevation model (DEM) product for interferometric synthetic aperture (InSAR). To obtain a highly accurate interferometric baseline, this paper firstly investigates the geometry of InSAR imaging and establishes a rigorous relationship between the interferometric baseline and the flat-earth phase. Then, a baseline refinement method without a ground control point (GCP) is proposed, where a relevant theoretical model and resolving method are developed. Synthetic and real SAR datasets are used in the experiments, and a comparison with the conventional least-square (LS) baseline refinement method is made. The results demonstrate that the proposed method exhibits an obvious improvement over the conventional LS method, with percentages of up to 51.5% in the cross-track direction. Therefore, the proposed method is effective and advantageous.

Electrocatalytic activity and chemical sensor application of Mn-MOF: synthesis, crystal structure and photo luminescent properties

A solvothermal method was used to synthesize a Manganese metal-organic framework (Mn-MOF), [Mn(Tpa)(Mi)(DMF)] (Tpa = Terephthalic acid, Mi = Methylimidazole, DMF = Dimethylformamide). The Mn-MOF molecule has a three dimensional network in which the θ ranges from 5.942–50 with monoclinic I2/a space group. The final full matrix least-squares refinement over F2 is converged on R1 = 0.0558, wR2 = 0.1696 through GOF = 1.095. Mn-MOF shows a strong luminescence along with red-shift, which indicates that these are the potential candidates for various luminescent applications. Electro catalytic activities of Mn-MOF electrode have also been tested for in 5 mM K4FeCN6 and K3FeCN6 in 0.5 M KCl solution. The electrochemical sensor detection of ascorbic acid (AA) in Mn-MOF was used as a buffer solution (pH-7.0). The ascorbic acid peak potential is a great deal nearer to the Mn-MOF electrode peak potential is ΔEp = 0.062 V. These results indicate that Mn-MOF electrode exhibits a very good electro catalytic activity and good chemical sensor by a quick reply in favor of ascorbic acid detection.

Single crystal investigation of the YbAl2 compound

A sample of nominal composition Yb33,3Al66,7 was synthesized from high-purity elements (Yb ≥ 98.9 wt.% and Al ≥ 99.999 wt.%) by arc-melting under a purified argon atmosphere, using Ti as a getter and a tungsten electrode. To achieve high efficiency of the interaction between the components, the sample was melted twice. The ingot was annealed at 500°C in an evacuated quartz ampoule for 720 h and subsequently quenched in cold water. The weight loss during the preparation of the sample was less than 1 % of the total mass, which was 2 g. The chemical composition of the selected crystals was checked with a field-emission scanning electron microscope (FEINovaNanoSEM 230) equipped with an EDS analyzer.
 Laue and rotation diffraction patterns of selected single crystals showed cubic symmetry. Integrated intensities measured with graphite-monochromatized Мо Kα radiation (l = 0.71073 Å) on an Xcalibur Atlas CCD diffractometer confirmed the cubic lattice. The structure type MgCu2 was assigned and the structure was refined using the program SHELXL (full-matrix least-squares refinement on F2)] with anisotropic displacement parameters for all of the atoms: Pearson symbol cF24, space group Fd-3m, a = 7.7011(4) Å, V = 456.73(7) Å3, Z = 8, R = 0.0261, Rw = 0.0726 for 42 reflections.
 It is well-known that the trivalent state is usual one for the rare earth metals. The dependence of the mean atomic volume of the RAl2 binary showed of the so-called “valence” fluctuation state for Eu and Yb.

Structure-specific restraints for least-squares refinement from tight binding quantum chemistry

Structure-specific restraints for least-squares refinement from tight binding quantum chemistry

PDB2INS: bridging the gap between small-molecule and macromolecular refinement.

The open-source Python program PDB2INS is designed to prepare a .ins file for refinement with SHELXL [Sheldrick (2015). Acta Cryst. C71, 3-8], taking atom coordinates and other information from a Protein Data Bank (PDB)-format file. If PDB2INS is provided with a four-character PDB code, both the PDB file and the accompanying mmCIF-format reflection data file (if available) are accessed via the internet from the PDB public archive [Read et al. (2011). Structure, 19, 1395-1412] or optionally from the PDB_REDO server [Joosten, Long, Murshudov & Perrakis (2014). IUCrJ, 1, 213-220]. The SHELX-format .ins (refinement instructions and atomic coordinates) and .hkl (reflection data) files can then be generated without further user intervention, appropriate restraints etc. being added automatically. PDB2INS was tested on the 23 974 X-ray structures deposited in the PDB between 2008 and 2018 that included reflection data to 1.7 Å or better resolution in a recognizable format. After creating the two input files for SHELXL without user intervention, ten cycles of conjugate-gradient least-squares refinement were performed. For 96% of these structures PDB2INS and SHELXL completed successfully without error messages.

Discreditation of the pyroxenoid mineral name ‘marshallsussmanite’ with a reinstatement of the name schizolite, NaCaMnSi3O8(OH)

AbstractSchizolite, originating from the type locality, Tutop Agtakôrfia, in the Ilímaussaq alkaline complex, Julianehåb district, South Greenland, was described initially by Winther (1901) with additional data being supplied by Bøggild (1903). Recently, a proposal for the new mineral ‘marshallsussmanite’ was submitted to, and approved by, the International Mineralogical Association Commission on New Minerals, Nomenclature and Classification (IMA2013-067) by Origlieri et al. (2013). Results from the detailed examination of two schizolite cotype samples presented here, using single-crystal and powder X-ray diffraction, and optical properties, confirms it to be equivalent to ‘marshallsussmanite’. Historical precedence sets a priority for discrediting the name ‘marshallsussmanite’ in favour of the original, more-than-a century-old name, schizolite. The two schizolite samples investigated vary slightly in physical and chemical properties but are consistent overall. The prismatic crystals are pale red or pink to brownish. Schizolite is brittle with a splintery aspect. It is biaxial (+), with average optical parameters: α = 1.626 ± 0.003, β = 1.630 ± 0.002, γ = 1.661 ± 0.002, 2Vmeas = 71(4)° and 2Vcalc = 40°; there is no pleochroism. Electron microprobe analysis shows both samples have nearly identical compositions (differences <0.4 wt.% oxide), with the mean values of: SiO2 52.6(4); Al2O3 0.005(1); FeO 2.54(2); MnO 13.86(9); CaO 17.9(4); Na2O 8.9(1); and H2O 2.59(2) wt.% oxide; this corresponds to a mean formula of: Na1.00(2)Ca1.11(7)Mn0.68(1)Fe0.12(0)Si3.041(1)O8(OH). Final least-squares structure refinements for both samples converged at R1 values ≤2.0%; H atoms were located in all refinements.

Redox-Active 1D Coordination Polymers of Iron-Sulfur Clusters.

Here we describe the combination of an archetypal redox-active metal sulfide cluster, Fe4S4, with an organic linker, 1,4-benzenedithiolate, to prepare coordination polymers containing infinite chains of Fe4S4 clusters. The crystal structures of two solid materials have been solved from synchrotron X-ray powder diffraction data using simulated annealing and refined by a least-squares Rietveld refinement procedure. The electronic properties of these chains have also been characterized by UV-visible and Mössbauer spectroscopies. Additional experiments demonstrated that these chains can be solubilized by variation of the countercation and that the chain structure is maintained in solution. The redox-activity of the Fe4S4 clusters can be accessed with chemical reagents. Introduction of charge carriers by reduction of the Fe4S4 clusters is found to increase the electrical conductivity of the materials by up to 4 orders of magnitude. These results highlight the utility of Fe4S4 clusters as redox-active building blocks in preparing new classes of coordination polymers.

Accurate empirical rovibrational energies and transitions of H216O.

Several significant improvements are proposed to the computational molecular spectroscopy protocol MARVEL (Measured Active Rotational-Vibrational Energy Levels) facilitating the inversion of a large set of measured rovibrational transitions to energy levels. The most important algorithmic changes include the use of groups of transitions, blocked by their estimated experimental (source segment) uncertainties, an inversion and weighted least-squares refinement procedure based on sequential addition of blocks of decreasing accuracy, the introduction of spectroscopic cycles into the refinement process, automated recalibration, synchronization of the combination difference relations to reduce residual uncertainties in the resulting dataset of empirical (MARVEL) energy levels, and improved classification of the lines and energy levels based on their accuracy and dependability. The resulting protocol, through handling a large number of measurements of similar accuracy, retains, or even improves upon, the best reported uncertainties of the spectroscopic transitions employed. To show its advantages, the extended MARVEL protocol is applied for the analysis of the complete set of highly accurate H216O transition measurements. As a result, almost 300 highly accurate energy levels of H216O are reported in the energy range of 0-6000 cm-1. Out of the 15 vibrational bands involved in accurately measured rovibrational transitions, the following three have definitely highly accurate empirical rovibrational energies of 8-10 digits of accuracy: (v1v2v3) = (0 0 0), (0 1 0), and (0 2 0), where v1, v2, and v3 stand for the symmetric stretch, bend, and antisymmetric stretch vibrational quantum numbers. The dataset of experimental rovibrational transitions and empirical rovibrational energy levels assembled during this study, both with improved uncertainties, is considerably larger and more accurate than the best previous datasets.

Aspherical scattering factors for SHELXL - model, implementation and application.

A new aspherical scattering factor formalism has been implemented in the crystallographic least-squares refinement program SHELXL. The formalism relies on Gaussian functions and can optionally complement the independent atom model to take into account the deformation of electron-density distribution due to chemical bonding and lone pairs. Asphericity contributions were derived from the electron density obtained from quantum-chemical density functional theory computations of suitable model compounds that contain particular chemical environments, as defined by the invariom formalism. Thanks to a new algorithm, invariom assignment for refinement in SHELXL is automated. A suitable parameterization for each chemical environment within the new model was achieved by metaheuristics. Figures of merit, precision and accuracy of crystallographic least-squares refinements improve significantly upon using the new model.

Structural investigations on bredigite from the Hatrurim Complex

Bredigite, Сa7Mg(SiO4)4, is an indicator mineral of metasomatic rocks of the sanidinite facies formed at high temperatures (>800 °C) and low pressures (<1–2 kbar). Bredigite samples from ternesite-gazeevite-larnite pyrometamorphic rocks of the Hatrurim Complex (Negev Desert, Israel) have been studied by electron probe micro analysis and single-crystal diffraction using synchrotron radiation. They are characterized by a relatively uniform composition. The empirical formula calculated on the basis of 16 O atoms per formula unit is: (Ca7.006Na0.015Ba0.014)Σ7.035Mg0.938(Si4.000P0.014)Σ4.014O16. Basic crystallographic data of a sample studied by X-ray diffraction are as follows: orthorhombic symmetry, space group Pnnm, a = 18.38102(17) Å, b = 6.74936(7) Å, c = 10.90328(11) Å, V = 1352.66(2) Å3, Z = 4. Structure solution and subsequent least-squares refinements resulted in a residual of R(|F|) = 0.023 for 2584 independent observed reflections with I > 2σ(I) and 149 parameters. To the best of our knowledge this is the first detailed structural investigation on natural bredigite. In contrast to previous studies on samples retrieved from metallurgical slags there was no need to describe the structure in the acentric space group Pnn2. Furthermore, the problem of Ba incorporation into the bredigite structure is discussed. Data on the composition of Ba-bearing bredigites from pyrometamorphic rocks of the Hatrurim Complex from Jordan with simplified formula Ba0.7Ca13.3Mg2(SiO4)8 (based on 32 oxygen atoms) are provided for the first time, pointing out perspectives of finding new Ba-bearing minerals isostructural with bredigite in nature.

Crystal and Molecular Structure and DFT Calculations of the Steroidal Oxime 6E-Hydroximino-androst-4-ene-3,17-dione (C19H25NO3) a Molecule with Antiproliferative Activity

The single crystal X-ray structure of the novel steroid derivative, 6E-hydroximino-androst-4-ene-3,17-dione (C19H25NO3) (code name RB-499), possessing antiproliferative activity against various cell lines is presented. The analysis produced the following results: chemical formula C19H25NO3; Mr = 315.40; crystals are orthorhombic space group P212121 with Z = 4 molecules per unit cell with a = 6.2609(2), b = 12.5711(4), c = 20.0517(4) Å,Vc = 1578.18(7) Å3, crystal density Dc = 1.327 g/cm³. Structure determination was performed by direct methods, Fourier and full-matrix least-squares refinement. Hydrogens were located in the electron density and refined in position with isotropic thermal parameters. The final R-index was 0.0324 for 3140 reflections with I > 2σ and 308 parameters. The Absolute Structure Parameter − 0.07(5) confirms the correct allocation of the absolute configuration. The presence of the double bond C=O at position 3 in Ring A has caused a distortion from the usual chair conformation and created an unusual distorted sofa conformation folded across an approximate m-plane through C(1)–C(4). Ring B is a distorted chair, its conformation being influenced by the presence of the C(6)=N(6)–O(6)H group in position 6. Ring C is a symmetrical chair. Ring D exhibits both a distorted mirror symmetry conformation [influenced by the C(17)=O(17) group] and a distorted twofold conformation. DFT calculations indicated some degree of flexibility in rings A, C and D with ring A showing the greatest variation in torsion angles. The crystal packing is governed by H-bonds involving O(3), O(6) and O(17). DFT calculations of bond distances and angles, optimized at the B3LYP/6–31++G(d,p) level, were in good agreement with the X-ray structure.Graphical Ring A conformations: (a) Experimental and (b) Calculated. The differences in torsion angle values indicate a degree of flexibility in the ring. The ring conformations are shown in Figures (ii) and (iv) respectively (drawn with BIOVIA [12]. Regions A1 and A2 are approximately planar in both, being planar within 0.048 Å and 0.105 Å respectively.

X-ray molecular orbital analysis. I. Quantum mechanical and crystallographic framework.

Molecular orbitals were obtained by X-ray molecular orbital analysis (XMO). The initial molecular orbitals (MOs) of the refinement were calculated by the ab initio self-consistent field (SCF) MO method. Well tempered basis functions were selected since they do not produce cusps at the atomic positions on the residual density maps. X-ray structure factors calculated from the MOs were fitted to observed structure factors by the least-squares method, keeping the orthonormal relationship between MOs. However, the MO coefficients correlate severely with each other, since basis functions are composed of similar Gaussian-type orbitals. Therefore, a method of selecting variables which do not correlate severely with each other in the least-squares refinement was devised. MOs were refined together with the other crystallographic parameters, although the refinement with the atomic positional parameters requires a lot of calculation time. The XMO method was applied to diformohydrazide, (NHCHO)2, without using polarization functions, and the electron-density distributions, including the maxima on the covalent bonds, were represented well. Therefore, from the viewpoint of X-ray diffraction, it is concluded that the MOs averaged by thermal vibrations of the atoms were obtained successfully by XMO analysis. The method of XMO analysis, combined with X-ray atomic orbital (AO) analysis, in principle enables one to obtain MOs or AOs without phase factors from X-ray diffraction experiments on most compounds from organic to rare earth compounds.

A method to estimate statistical errors of properties derived from charge-density modelling.

Estimating uncertainties of property values derived from a charge-density model is not straightforward. A methodology, based on calculation of sample standard deviations (SSD) of properties using randomly deviating charge-density models, is proposed with the MoPro software. The parameter shifts applied in the deviating models are generated in order to respect the variance-covariance matrix issued from the least-squares refinement. This `SSD methodology' procedure can be applied to estimate uncertainties of any property related to a charge-density model obtained by least-squares fitting. This includes topological properties such as critical point coordinates, electron density, Laplacian and ellipticity at critical points and charges integrated over atomic basins. Errors on electrostatic potentials and interaction energies are also available now through this procedure. The method is exemplified with the charge density of compound (E)-5-phenylpent-1-enylboronic acid, refined at 0.45 Å resolution. The procedure is implemented in the freely available MoPro program dedicated to charge-density refinement and modelling.