Errors in electron density maps and the use of integrated densities in the study of charge density distributions

1968 ◽  
Vol 24 (7) ◽  
pp. 925-929 ◽  
Author(s):  
P. Coppens ◽  
W. C. Hamilton
1996 ◽  
Vol 74 (6) ◽  
pp. 1253-1262 ◽  
Author(s):  
Jordi Mestres ◽  
Miquel Duran ◽  
Juan Bertrán

A comparative electronic analysis of the generally termed hydrogen transfers between CH4 and the CH3+, CH3•, and CH3− fragments is presented. These systems are taken as simple models of hydride (H−), hydrogen (H•), and proton (H+) transfers between two carbon fragments (in these simple cases being modelized by two CH3+, CH3•, and CH3− fragments, respectively). The study is mainly focused on analysis of the electronic nature of the type of hydrogen being transferred in each system, and for this reason a topological analysis of charge density distributions was performed. Computation of Bader atomic charges and construction of the charge density, gradient vector field, and Appalachian of the charge density maps reveal the specific features of the electronic nature of the transferring H−, H•, and H+. Moreover, characterization of the bond critical points on the charge density surface permits clarification of the differences in atomic interactions between H−, H•, and H+ and the carbon belonging to each CH3+, CH3•, and CH3− fragment, respectively. A charge density redistribution analysis is also performed to quantify the reorganization of the electron density when going from the reactant complex to the transition state. Finally, effects of inclusion of the correlation energy at the MP2 and CISD levels are also discussed. Key words: electron density, hydrogen transfer, topological density analysis, molecular similarity, Bader density analysis.


2015 ◽  
Vol 44 (1) ◽  
pp. 2-9 ◽  
Author(s):  
Isabelle L. Kirby ◽  
Mateusz B. Pitak ◽  
Simon J. Coles ◽  
Philip A. Gale

2002 ◽  
Vol 58 (3) ◽  
pp. 519-529 ◽  
Author(s):  
Miroslav Slouf ◽  
Antonin Holy ◽  
Václav Petříček ◽  
Ivana Cisarova

The crystal structure and charge density of hydrogen (2,4-diaminopyrimidin-1-io)methyl]phosphonate monohydrate, C5H9N4O3P·H2O, have been determined by means of single-crystal X-ray diffraction. Diffraction data were collected at 105 K with Mo Kα radiation to a resolution of sin θ/λ = 1.08 Å−1. A four-circle diffractometer equipped with a CCD area detector was used to collect 50 161 reflections over 3 d. 6082 unique reflections with I > 3σ(I) were used in the multipole model to map the deformation electron density and gave the final statistical factors R(F) = 0.0329, wR(F) = 0.0235 and g.o.f. = 1.37. Structure determination revealed that two O atoms in the crystal structure of the title compound act as hydrogen-bond acceptors for more than one hydrogen bond. Examination of deformation electron density maps showed preferential polarization of the lone-pair electron density of the two O atoms into the shortest hydrogen bonds.


Author(s):  
Ayoub Nassour ◽  
Maciej Kubicki ◽  
Jonathan Wright ◽  
Teresa Borowiak ◽  
Grzegorz Dutkiewicz ◽  
...  

The experimental charge-density distribution in 2-methyl-1,3-cyclopentanedione in the crystal state was analyzed by synchrotron X-ray diffraction data collection at 0.33 Å resolution. The molecule in the crystal is in the enol form. The experimental electron density was refined using the Hansen–Coppens multipolar model and an alternative modeling, based on spherical atoms and additional charges on the covalent bonds and electron lone-pair sites. The crystallographic refinements, charge-density distributions, molecular electrostatic potentials, dipole moments and intermolecular interaction energies obtained from the different charge-density models were compared. The experimental results are also compared with the theoretical charge densities using theoretical structure factors obtained from periodic quantum calculations at the B3LYP/6-31G** level. A strong intermolecular O—H...O hydrogen bond connects molecules along the [001] direction. The deformation density maps show the resonance within the O=C—C=C—OH fragment and merged lone pair lobes on the hydroxyl O atom. This resonance is further confirmed by the analysis of charges and topology of the electron density.


2003 ◽  
Vol 02 (06) ◽  
pp. 487-494
Author(s):  
V. A. SABLIKOV ◽  
S. V. POLYAKOV

We report the correlated charge and spin density distributions in a quantum wire coupled to electron reservoirs. It is found that charging the wire because of the electron density redistribution between the wire and reservoirs results in the increase of the critical electron density, below which the spontaneous spin polarization appears. The distributions of the electron densities with spin up and spin down along the wire have components oscillating in opposite phases with the wave vector 2kF, kF being the Fermi wave vector. As a result the antiferromagnetic spin order appears, with one of the spin components spontaneously predominating. The charge density distribution is close to the Wigner order with the small amplitude of the 4kF charge-density waves.


2021 ◽  
Vol 16 (9) ◽  
pp. 2343-2346
Author(s):  
Shota Yamamoto ◽  
Shunsuke Kamei ◽  
Kosuke Tomita ◽  
Chikara Fujita ◽  
Kazuyuki Endo ◽  
...  

Author(s):  
Zhijie Chua ◽  
Bartosz Zarychta ◽  
Christopher G. Gianopoulos ◽  
Vladimir V. Zhurov ◽  
A. Alan Pinkerton

A high-resolution X-ray diffraction measurement of 2,5-dichloro-1,4-benzoquinone (DCBQ) at 20 K was carried out. The experimental charge density was modeled using the Hansen–Coppens multipolar expansion and the topology of the electron density was analyzed in terms of the quantum theory of atoms in molecules (QTAIM). Two different multipole models, predominantly differentiated by the treatment of the chlorine atom, were obtained. The experimental results have been compared to theoretical results in the form of a multipolar refinement against theoretical structure factors and through direct topological analysis of the electron density obtained from the optimized periodic wavefunction. The similarity of the properties of the total electron density in all cases demonstrates the robustness of the Hansen–Coppens formalism. All intra- and intermolecular interactions have been characterized.


1956 ◽  
Vol 52 (4) ◽  
pp. 703-711 ◽  
Author(s):  
R. A. Ballinger ◽  
N. H. March

ABSTRACTAn attempt is made to calculate the first few angular terms in an expansion of the electron density for the phosphine molecule in Legendre polynomials. Such an expansion is appropriate for a model in which the three hydrogen nuclei are smeared to form a circular line charge. The Thomas–Fermi approximation has been used in conjunction with the variational method. The variational density employed includes p and f angular terms. An approximate charge density map is constructed for a plane containing the molecular axis in order to demonstrate the effect of the angular terms.


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