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

Fournier, Bertrand; Guillot, B.; Lecomte, Claude; Escudero‐Adán, Eduardo C.; Jelsch, Christian

doi:10.1107/s2053273318004308

Cited by 20 publications

(23 citation statements)

References 38 publications

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“…[68] Atomic charges are often unreliable to be calculated and depend moreover on the charge definition. [69] An estimation of atomic charges uncertainty can be computed according to the sample standard deviation method described in Fournier et al [70]…”

Section: Methodsmentioning

confidence: 99%

Partially Covalent Two-Electron/Multicentric Bonding between Semiquinone Radicals

Molčanov

Jelsch

Landeros

et al. 2018

Crystal Growth & Design

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X-ray charge density was determined and analyzed for two polymorphs of the Nmethylpyridinium salt of the tetrachlorosemiquinone radical anion and its analogous closed-shell relatives, tetrachloroquinone (chloranil) and tetrachlorohydroquinone. The study, which was combined with calculations of electron delocalization, electrostatic potentials, and aromaticity, presents details of electronic structure of the semiquinoid ring. This comparative study reveals that the negative charge is delocalized over the entire semiquinone radical, and that the chlorine substituents play a crucial role in its stabilization through induction effect. In general, the semiquinoid ring has partially delocalized π-electrons and is approximately halfway between a quinoid and an aromatic ring. In the orthorhombic polymorph with stacks of equidistant radicals electron density between the rings of almost 0.05 e Å-3 and four (3,-1) saddle points between the contiguous rings were found. In the diamagnetic triclinic polymorph, comprising strongly bound radical dimers (with significant covalent character-'pancake bond'), maximum electron density between the rings exceeds 0.095 e Å-3 and multiple (3,-1) critical points are found. However, only negligible electron density is observed between the dimers. Thus, in the radical anion stacks spin coupling, along with dispersive and polarization effects, defines interplanar distance and magnetic behaviour, whereas intermolecular electrostatic potential determines the ring offset.

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Section: Methodsmentioning

confidence: 99%

Partially Covalent Two-Electron/Multicentric Bonding between Semiquinone Radicals

Molčanov

Jelsch

Landeros

et al. 2018

Crystal Growth & Design

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“…[64] ESDs of the charge density properties were estimated by the recently published method. [65] Geometry, charge-density and electrostatic properties calculations were performed by MoPro; [59] molecular graphic were prepared using MoProViewer [66] and ORTEP-3. [67] Crystallographic and refinement data are shown in Table 5; additional details on refinement are deposited as Supporting Information.…”

Section: Experimental Preparationmentioning

confidence: 99%

Malleable Electronic Structure of Chloranilic Acid and Its Species Determined by X-ray Charge Density Studies

Vuković

Molčanov

Jelsch

et al. 2019

Crystal Growth & Design

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Electronic structure of five species of chloranilic acid (neutral molecule, mono-and dianion, and two chelating modes-bidendate and (bis)bidentate) is determined by X-ray charge density studies. Electron density at the bond critical points yields an accurate measure of bond order and therefore electron delocalisation. π-electron system of chloranilic acid is especially malleable, so it can adopt various degrees of delocalisation, depending on ionisation and molecular environment. 2 ABSTRACT Herein, we present a detailed X-ray charge density study of the electron delocalisation in five species of the chloranilic acid: neutral molecule, mono-and dianion, and two chelating modes-bidendate and (bis)bidentate. The experiments provide the electron density at the bond critical points, which yields an accurate measure of bond order (and therefore electron delocalisation), and complements previous literature and our data on bond lengths extracted from crystal structures and infrared spectra. Mapping of the electrostatic potential indicates electronrich and electron-poor areas in the molecule, corresponding to single (electron-poor), double and delocalised bonds (electron-rich) that can explain stacking interactions of quinoid rings in crystal packing.

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“…0.04 e Å À3 (2%) in the electron density and to max. 0.42 e Å À5 (3%) in its Laplacian (Fournier et al, 2018). The error of the topological charge of heteroatoms reported is 0.03 e. However, this standard deviation estimate below 5% does not change the MM electron density topology in a qualitative way.…”

Section: Introductionmentioning

confidence: 78%

“…We will present the estimated errors (standard deviations) in the experimentally refined MM electron density topology in terms of contributions from the multipole populations as implemented in the XD package (Volkov et al, 2016). The error estimation in the MM-refined electron density has been considered in several studies (Grabowsky et al, 2008;Kamiń ski et al, 2014;Krause et al, 2017;Fournier et al, 2018). Most recently, a method which can be automatically used for the error estimation is given by Fournier (Fournier et al, 2018), as implemented in the MoPro package (Guillot et al, 2001;Jelsch et al, 2005).…”

Section: Introductionmentioning

confidence: 99%

“…The error estimation in the MM-refined electron density has been considered in several studies (Grabowsky et al, 2008;Kamiń ski et al, 2014;Krause et al, 2017;Fournier et al, 2018). Most recently, a method which can be automatically used for the error estimation is given by Fournier (Fournier et al, 2018), as implemented in the MoPro package (Guillot et al, 2001;Jelsch et al, 2005). Therein reported sample standard deviations in the midbond region (bond critical points, see below) were estimated to max.…”

Section: Introductionmentioning

confidence: 99%

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Charge density of 4-methyl-3-[(tetrahydro-2H-pyran-2-yl)oxy]thiazole-2(3H)-thione. A comprehensive multipole refinement, maximum entropy method and density functional theory study

Vénosová

Kožíšková

Kožı́šek

et al. 2020

Acta Crystallogr Sect B

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The structure of 4-methyl-3-[(tetrahydro-2H-pyran-2-yl)oxy]thiazole-2(3H)thione (MTTOTHP) was investigated using X-ray diffraction and computational chemistry methods for determining properties of the nitrogen-oxygen bond, which is the least stable entity upon photochemical excitation. Experimentally measured structure factors have been used to determine and characterize charge density via the multipole model (MM) and the maximum entropy method (MEM). Theoretical investigation of the electron density and the electronic structure has been performed in the finite basis set density functional theory (DFT) framework. Quantum Theory of Atoms In Molecules (QTAIM), deformation densities and Laplacians maps have been used to compare theoretical and experimental results. MM experimental results and predictions from theory differ with respect to the sign and/or magnitude of the Laplacian at the N-O bond critical point (BCP), depending on the treatment of n values of the MM radial functions. Such Laplacian differences in the N-O bond case are discussed with respect to a lack of flexibility in the MM radial functions also reported by Rykounov et al. [Acta Cryst. (2011), B67, 425-436]. BCP Hessian eigenvalues show qualitatively matching results between MM and DFT. In addition, the theoretical analysis used domain-averaged fermi holes (DAFH), natural bond orbital (NBO) analysis and localized (LOC) orbitals to characterize the N-O bond as a single bond with marginal character. Hirshfeld atom refinement (HAR) has been employed to compare to the MM refinement results and/or neutron dataset C-H bond lengths and to crystal or single molecule geometry optimizations, including considerations of anisotropy of H atoms. Our findings help to understand properties of molecules like MTTOTHP as progenitors of free oxygen radicals.

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

Abstract: Errors on molecular properties including the topology of electron density and electrostatics are estimated from a sample of deviating models generated using the variance–covariance matrix issued at the end of the charge-density refinement.

Cited by 20 publications

References 38 publications

Partially Covalent Two-Electron/Multicentric Bonding between Semiquinone Radicals

Partially Covalent Two-Electron/Multicentric Bonding between Semiquinone Radicals

Malleable Electronic Structure of Chloranilic Acid and Its Species Determined by X-ray Charge Density Studies

Charge density of 4-methyl-3-[(tetrahydro-2H-pyran-2-yl)oxy]thiazole-2(3H)-thione. A comprehensive multipole refinement, maximum entropy method and density functional theory study

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