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 theMoProsoftware. 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 ofanyproperty 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 availableMoProprogram dedicated to charge-density refinement and modelling.

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On the Existence and the Classification of Critical Points for Non-Smooth Functionals

Canadian Journal of Mathematics ◽

10.4153/cjm-1995-036-9 ◽

1995 ◽

Vol 47 (4) ◽

pp. 684-717 ◽

Cited By ~ 6

Author(s):

G. Fang

Keyword(s):

Critical Point ◽

Critical Points ◽

Metric Space ◽

Critical Point Theory ◽

Complete Metric Space ◽

Point Theory ◽

Topological Properties ◽

Smooth Case ◽

Continuous Functionals

AbstractWe extend the min-max methods used in the critical point theory of differentiable functionals on smooth manifolds to the case of continuous functionals on a complete metric space. We study the topological properties of the min-max generated critical points in this new setting by adopting the methodology developed by Ghoussoub in the smooth case. Many old and new results are extended and unified and some applications are given.

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A charge density study of π-delocalization and intermolecular interactions

Physical Chemistry Chemical Physics ◽

10.1039/c5cp01575h ◽

2015 ◽

Vol 17 (21) ◽

pp. 14177-14184 ◽

Cited By ~ 6

Author(s):

L.-C. Wu ◽

W.-C. Chung ◽

C.-C. Wang ◽

G.-H. Lee ◽

S.-I. Lu ◽

...

Keyword(s):

Charge Density ◽

Intermolecular Interactions ◽

Critical Points ◽

Black Line ◽

Bond Path ◽

Π Interactions ◽

Weak Intermolecular Interactions ◽

A Charge ◽

Density Study

The location of bond critical points (red dots) and its associated bond path (black line) provide the evidence on the existence of the weak intermolecular interactions of the π–π interactions between triazole rings of atrz molecules in crystal with the close ring distance of 3.17 Å.

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A Charge Density Model of Silicon-nanowire GAA MOSFET Incoroperating the Source-drian Tunneling Effect for IC Design

10.1109/isctis51085.2021.00078 ◽

2021 ◽

Author(s):

He Cheng ◽

Chao Zhang ◽

Tiefeng Liu ◽

Chuang Xie ◽

Zhjia Yang ◽

...

Keyword(s):

Charge Density ◽

Silicon Nanowire ◽

Density Model ◽

Tunneling Effect ◽

Ic Design ◽

A Charge

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Benzenoid hydrocarbon aromaticity in terms of charge density descriptors

Canadian Journal of Chemistry ◽

10.1139/v97-141 ◽

1997 ◽

Vol 75 (9) ◽

pp. 1174-1181 ◽

Cited By ~ 105

Author(s):

S.T. Howard ◽

T.M. Krygowski

Keyword(s):

Charge Density ◽

Critical Point ◽

Critical Points ◽

Electron Distribution ◽

Stationary Points ◽

Bond Critical Point ◽

Total Density ◽

Benzenoid Hydrocarbon ◽

Hartree Fock ◽

Point Data

Hartree–Fock/6-31G** calculations on the benzenoid hydrocarbons benzene, naphthalene, phenanthrene, anthracene, pyrene, tetracene, triphenylene, chrysene, perylene, and coronene are used to investigate the link between aromaticity and the electron distribution. Topological charge density analysis is used, concentrating on the electron distribution ρ (and its Hessian) at bond and ring critical points. With regard to the bond critical point data, it is shown that ρc, [Formula: see text]ρc, and the bond "ellipticity" ε are closely correlated with the bond lengths so, as aromaticity indicators, they have little to add over and above existing indices based on structure. However, the same properties evaluated at the ring critical points in the total density, and also at the equivalent stationary points in the π and σ densities, correlate closely with two different aromaticity indices (one based on structure, the other on magnetic properties), the curvature of ρ perpendicular to the ring plane giving (marginally) the best results. Hence a ring critical point (RCP) index is proposed as a way of quantifying aromaticity, based directly on the electron distribution. Keywords: quantum chemistry, electron density, aromaticity, aromaticity index, HOMA, NICS.

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