Matthias Hofmann, Henry F. SchaeferIII, in Encyclopedia of Physical science and modern technology (Third Edition), 2003

II.A.1 power Terms


Advanced force fields distinguish several atom species for each facet (depending top top hybridization and also neighboring atoms) and introduce various power contributions to the complete force ar energy, EFF:


where Estr and Ebend are power terms because of bond stretching and angle bending, respectively; Etors relies on torsional angles describing rotation about bonds; and also EvdW and also Eelst define (nonbonded) van der Waals and electrostatic interactions, dong (Fig. 2). In enhancement to these simple terms typical to all empirical force fields there might be extra state to improve the performance for certain tasks. Every term is a role of the nuclear coordinates and also a number of parameters. Once the parameters have been defined, the complete energy, EFF, can be computed and also subsequently lessened with respect to the coordinates.

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Clemens Simbrunner, Helmut Sitter, in Handbook of crystal Growth: slim Films and Epitaxy (Second Edition), 2015

11.1.2.2 The influence of the Substrate surface ar Symmetry top top the molecular Adsorption


The the contrary of every substrate surface deserve to be explained by one of 17 possible 2D space- or wallpaper-groups <22–24>. All groups can be created by a combination of 3 symmetry elements, namely (1) glide reflections, (2) winter planes, and also (3) rotation centers. Come visualize the affect of this operations, representative substrate surfaces have been chosen and also are depicted in Figure 11.4.



FIGURE 11.4. Visualization concerning the affect of mirror planes and also rotational centers top top the molecule adsorption. Polar plots, suggested in the peak panel, reflect the adsorption power of 6T top top muscovite mica (001) (left) and also p-6P ~ above KCl (100) (right) together a function of adsorption angle φ. The zero top top the power scale is collection to the power of the the very least favorable angle. As 6T have the right to adsorb in two various geometries, 2 curves room depicted, one equivalent to left-handed (red) and also the various other to right-handed (blue) enantiomer. Experimental observed adsorption geometries are shown by gray one <19–21> and corresponding regional adsorption web page are depicted in the bottom panel. In general, mirror-reflections command to point chirality, i beg your pardon is characterized by the generation of two different but energetically indistinguishable adsorption sites. The affect of rotational centers is demonstrated because that p-6P/KCl, whereby symmetry in general leads to 4 different, however energetically equivalent, adsorption sites. (For translate of the references to color in this number legend, the leader is referred to the online variation of this book.)


Force-field simulations have been performed because that the adsorption the a strict all-trans 6T molecule top top a muscovite mica (001) surface and a p-6P molecule ~ above KCl (100). Molecules the are inherently achiral but acquire a type of 2D chirality as soon as adsorbed on a substrate surface ar are additionally named prochiral <25>. As all-trans 6T to represent a prochiral conformation, simulations have been performed because that left- and also right-handed enantiomers, and corresponding data are suggested by blue and also red curves. For each molecular adsorption angle (φ), the preferred adsorption site has been determined, and also its adsorption power is depicted in terms of a polar plot in the height panel that Figure 11.4. Together sketched in Figure 11.4, φ characterizes the azimuthal orientation that the lengthy molecular axis (LMA) family member to <110> of muscovite mica (001) and also <01¯1¯> that KCl (100). The zero top top the power scale is set to the power of the the very least favorable angle.

Mirror Plane/Glide Plane: for example, the molecule adsorption of 6T on muscovite mica has actually been chosen and obtained adsorption energies are shown in the left panel of Figure 11.4 together a polar plot. Experimentally deduced molecular adsorption angles are suggested by gray circles <2>. Energetically preferable adsorption geometries, i m sorry are also found from speculative data, are suggested below. Simulated adsorption web page are populated either through the left- (red, φ = 60°) or right-handed (blue, φ = −60°) enantiomer and also can be constructed by winter operation. Moreover, due to C2 allude symmetry that both species, energetically identical adsorption geometries can be acquired by rotating the molecules by 180°. It can be concluded the mirror- and glide-reflection in general lead to the generation of 2 energetically tantamount adsorption website <2,24>. In the instance of prochiral molecules, resulting adsorption sites are not energetically tantamount for both enantiomers yet are populated either by a left- or right-handed molecule. Consequently, 2 energetically identical long molecule axis orientations are developed in the general case, i m sorry reduces the worldwide anisotropy. Moreover, it must be stated that the derived molecule–surface combination does not have any kind of mirror facets in general. Consequently, the generated geometry is additionally called point chirality, and can it is in induced also by very symmetric adsorbates, e.g., p-6P <26,27>. The only way to stop the development of neighborhood chiral motifs through adsorption occasions is listed if the winter planes of an achiral-molecule and also -substrate surface overlap. Exemplary, together an particularly configuration deserve to be accomplished if the LMA of p-6P is oriented parallel or common to the mirror plane of muscovite mica (001) <2>. Importantly, it must be stated that point-, pro-, organizational- and conformational-chirality created by intrinsic achiral molecules deserve to only it is in expressed top top a neighborhood level, e.g., over a restricted surface area. ~ above a global level, e.g., when incorporated over the entire surface, chirality disappears as result of an equal generation of both enantiomorphs <27>.

Rotational Center: To analyze the affect of rotational symmetry, the adsorption of p-6P molecule on KCl (100) has actually been simulated. The acquired adsorption energies are gift in hatchet of a polar plot in the height right dashboard of Figure 11.4. As an adsorbed p-6P molecule is defined by two mirror the contrary planes and consequently have the right to be described by a C2v point group, simulations have only to be performed because that a single molecular configuration. Again, gray one represent experimental data <19,20> describe an energetical desired LMA orientation follow me the 〈011〉 crystallographic directions. An analogous molecule alignment has also been deduced for 6T <28> and also can be described by the existence of strong surface corrugations on the KCl (100) surface <29>. Moreover, simulated adsorption data reflect mirror- (mirror planes along 〈001〉 and also 〈011〉 are indicated by bold solid lines) and fourfold rotational-symmetry, which can be explained by the p4m space group the the KCl (100) surface. As shown in the bottom best panel of Figure 11.4, energetically identical adsorption sites deserve to be created by a 90° rotation in ~ a fourfold symmetry point.

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Based top top the latter discussion, it have the right to be concluded the the number of energetically identical adsorption sites increases with the visibility of rotational-, glide- and also mirror-symmetry on the substrate surface. An introduction for each wallpaper group is provided in Table 11.1 <24>.


Equivalent SitesWallpaper Group
1p1
2p2, pm, pg, cm
3p3
4pmm, pmg, pgg, cmm, p4
6p31m, p3m1, p6
8p4m, p4g
12p6m