scholarly journals Failure of the interaction energy approximation

Author(s):  
Phillip Hudson ◽  
Henry L Woodcock ◽  
Stefan Boresch
2020 ◽  
Author(s):  
Phillip Hudson ◽  
Henry L Woodcock ◽  
Stefan Boresch

Author(s):  
B. R. Ahn ◽  
N. J. Kim

High energy approximation in dynamic theory of electron diffraction involves some intrinsic problems. First, the loss of theoretical strictness makes it difficult to comprehend the phenomena of electron diffraction. Secondly, it is difficult to believe that the approximation is reasonable especially in the following cases: 1) when accelerating voltage is not sufficiently high, 2) when the specimen is thick, 3) when the angle between the surface normal of the specimen and zone axis is large, and 4) when diffracted beam with large diffraction angle is included in the calculation. However, until now the method to calculate the many beam dynamic electron diffraction without the high energy approximation has not been proposed. For this reason, the authors propose a method to eliminate the high energy approximation in the calculation of many beam dynamic electron diffraction. In this method, a perfect crystal with flat surface was assumed. The method was applied to the calculation of [111] zone axis CBED patterns of Si.


Author(s):  
Philip Isett

This chapter presents the equations and calculations for energy approximation. It establishes the estimates (261) and (262) of the Main Lemma (10.1) for continuous solutions; these estimates state that we are able to accurately prescribe the energy that the correction adds to the solution, as well as bound the difference between the time derivatives of these two quantities. The chapter also introduces the proposition for prescribing energy, followed by the relevant computations. Each integral contributing to the other term can be estimated. Another proposition for estimating control over the rate of energy variation is given. Finally, the coarse scale material derivative is considered.


2019 ◽  
Author(s):  
Prasanth Babu Ganta ◽  
Oliver Kühn ◽  
Ashour Ahmed

The phosphorus (P) immobilization and thus its availability for plants are mainly affected by the strong interaction of phosphates with soil components especially soil mineral surfaces. Related reactions have been studied extensively via sorption experiments especially by carrying out adsorption of ortho-phosphate onto Fe-oxide surfaces. But a molecular-level understanding for the P-binding mechanisms at the mineral-water interface is still lacking, especially for forest eco-systems. Therefore, the current contribution provides an investigation of the molecular binding mechanisms for two abundant phosphates in forest soils, inositol hexaphosphate (IHP) and glycerolphosphate (GP), at the diaspore mineral surface. Here a hybrid electrostatic embedding quantum mechanics/molecular mechanics (QM/MM) based molecular dynamics simulation has been applied to explore the diaspore-IHP/GP-water interactions. The results provide evidence for the formation of different P-diaspore binding motifs involving monodentate (M) and bidentate (B) for GP and two (2M) as well as three (3M) monodentate for IHP. The interaction energy results indicated the abundance of the GP B motif compared to the M one. The IHP 3M motif has a higher total interaction energy compared to its 2M motif, but exhibits a lower interaction energy per bond. Compared to GP, IHP exhibited stronger interaction with the surface as well as with water. Water was found to play an important role in controlling these diaspore-IHP/GP-water interactions. The interfacial water molecules form moderately strong H-bonds (HBs) with GP and IHP as well as with the diaspore surface. For all the diaspore-IHP/GP-water complexes, the interaction of water with diaspore exceeds that with the studied phosphates. Furthermore, some water molecules form covalent bonds with diaspore Al atoms while others dissociate at the surface to protons and hydroxyl groups leading to proton transfer processes. Finally, the current results confirm previous experimental conclusions indicating the importance of the number of phosphate groups, HBs, and proton transfers in controlling the P-binding at soil mineral surfaces.


1978 ◽  
Vol 72 (1) ◽  
pp. 125-139 ◽  
Author(s):  
J.C. Le Bosse ◽  
J. Lopez ◽  
J. Rousseau-Violet

2021 ◽  
Author(s):  
Thufail M. Ismail ◽  
Neetha Mohan ◽  
P. K. Sajith

Interaction energy (Eint) of hydrogen bonded complexes of nitroxide radicals can be assessed in terms of the deepest minimum of molecular electrostatic potential (Vmin).


Author(s):  
Sehrish Naz ◽  
Sajda Ashraf ◽  
Mohammad K. Parvez ◽  
Mohammed S. Al-Dosari ◽  
Zaheer Ul-Haq

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