Projection-operator calculations for molecular shape resonances: TheΣu+2resonance in electron-hydrogen scattering

1985 ◽  
Vol 31 (2) ◽  
pp. 641-651 ◽  
Author(s):  
Michael Berman ◽  
Claus Mündel ◽  
Wolfgang Domcke
Author(s):  
S. Cusack ◽  
J.-C. Jésior

Three-dimensional reconstruction techniques using electron microscopy have been principally developed for application to 2-D arrays (i.e. monolayers) of biological molecules and symmetrical single particles (e.g. helical viruses). However many biological molecules that crystallise form multilayered microcrystals which are unsuitable for study by either the standard methods of 3-D reconstruction or, because of their size, by X-ray crystallography. The grid sectioning technique enables a number of different projections of such microcrystals to be obtained in well defined directions (e.g. parallel to crystal axes) and poses the problem of how best these projections can be used to reconstruct the packing and shape of the molecules forming the microcrystal.Given sufficient projections there may be enough information to do a crystallographic reconstruction in Fourier space. We however have considered the situation where only a limited number of projections are available, as for example in the case of catalase platelets where three orthogonal and two diagonal projections have been obtained (Fig. 1).


2019 ◽  
Author(s):  
Adam Al-Janabi ◽  
Richard Mandle

<p>The nematic twist-bend (N<sub>TB</sub>) liquid crystal phase possesses a local helical structure with a pitch length of a few nanometres and is the first example of spontaneous symmetry breaking in a fluid system. All known examples of the N­<sub>TB­</sub> phase occur in materials whose constituent mesogenic units are aromatic hydrocarbons. It is not clear if this is due to synthetic convenience or a <i>bona fide</i> structural requirement for a material to exhibit this phase of matter. In this work we demonstrate that materials consisting largely of saturated hydrocarbons could also give rise to this mesophase. Furthermore, replacement of 1,4-disubstituted benzene with <i>trans</i> 1,4-cyclohexane or even 1,4-cubane does not especially alter the transition temperatures of the resulting material nor does it appear to impact upon the heliconical tilt angle, suggesting the local structure of the phase is unperturbed. Calculating the probability distribution of bend angles reveals that the choice of isosteric group has little impact on the overall molecular shape, demonstrating the shape-driven nature of the N<sub>TB</sub> phase. </p>


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