Anisotropy, of potential

On the theoretical side the H20-He systems has a sufficiently small number of electrons to be tackled by the most sophisticated quantum-chemical techniques, and in the last two decades several calculations by various methods of electronic structure theory have been attempted [77-80]. More recently, new sophisticated calculations appeared in the literature they exploited combined symmetry - adapted perturbation theory SAPT and CCSD(T), purely ab initio SAPT [81,82], and valence bond methods [83]. A thorough comparison of the topology, the properties of the stationary points, and the anisotropy of potential energy surfaces obtained with coupled cluster, Moller-Plesset, and valence bond methods has been recently presented [83]. 

Luckhaus D and Quack M 1993 The role of potential anisotropy in the dynamics of the CH chromophore in CHXg (Cg ) symmetric tops Chem. Phys. Lett. 205 277-84... 

Surface SHG [4.307] produces frequency-doubled radiation from a single pulsed laser beam. Intensity, polarization dependence, and rotational anisotropy of the SHG provide information about the surface concentration and orientation of adsorbed molecules and on the symmetry of surface structures. SHG has been successfully used for analysis of adsorption kinetics and ordering effects at surfaces and interfaces, reconstruction of solid surfaces and other surface phase transitions, and potential-induced phenomena at electrode surfaces. For example, orientation measurements were used to probe the intermolecular structure at air-methanol, air-water, and alkane-water interfaces and within mono- and multilayer molecular films. Time-resolved investigations have revealed the orientational dynamics at liquid-liquid, liquid-solid, liquid-air, and air-solid interfaces [4.307]. 

The dipole density profile p (z) indicates ordered dipoles in the adsorbate layer. The orientation is largely due to the anisotropy of the water-metal interaction potential, which favors configurations in which the oxygen atom is closer to the surface. Most quantum chemical calculations of water near metal surfaces to date predict a significant preference of oxygen-down configurations over hydrogen-down ones at zero electric field (e.g., [48,124,141-145]). The dipole orientation in the second layer is only weakly anisotropic (see also Fig. 7). 

The orientational structure of water near a metal surface has obvious consequences for the electrostatic potential across an interface, since any orientational anisotropy creates an electric field that interacts with the metal electrons. Hydrogen bonds are formed mainly within the adsorbate layer but also between the adsorbate and the second layer. Fig. 3 already shows quite clearly that the requirements of hydrogen bond maximization and minimization of interfacial dipoles lead to preferentially planar orientations. On the metal surface, this behavior is modified because of the anisotropy of the water/metal interactions which favors adsorption with the oxygen end towards the metal phase. 

Connor J. N. L., Sun H., Hutson J. M. Exact and approximate calculations for the effect of potential anisotropy on integral and differential cross-sections Ar-N2 rotationally inelastic scattering, J. 

As has been noticed by Gelbart and Gelbart [7], the predominant orientational interaction in nematics results from the isotropic dispersion attraction modulated by the anisotropic molecular hard-core. The anisotropy of this effective potential comes from that of the asymmetric molecular shape. The coupling between the isotropic attraction and the anisotropic hard-core repulsion is represented by the effective potential... 

Rotational state distributions of the OH(A) product for v = 0 to 3 have also been determined. Highly rotationally excited OH(A,v = 0,1) products are dominant as in the ground state, indicating that the angular anisotropy of the potential is also very important to the production of these product states on the H2O B lA state surface. The vibrational distribution... 

Another potential vertical medium is not a continuous thin film, but rather an assembly of metal particles deposited in well defined pores in an alumina film on Al [109-117]. The shape anisotropy of the particles gives the desired vertical anisotropy. In producing such structures, the proper conditions for the anodization of the Al disk and for the subsequent control of pore size are as important as the conditions of metal deposition. The structures of such disks are discussed in detail below. 

The previous approach is valid as long as the molecular reorientation can be described by a single correlation time. This excludes molecules involving internal motions and/or molecular shapes which cannot, to a first approximation, be assimilated to a sphere. Due to its shape, the molecule shown in Figure 15 cannot evidently fulfil the latter approximation and is illustrative of the potentiality of HOESY experiments as far as carbon-proton distances and the anisotropy of molecular reorientation are concerned.45 58... 

A larger number of examples of 5f- 3d systems are known, and have been recently reviewed [43]. We reiterate here only the potentially enormously beneficial effect of sizable 5f-3d exchange couplings exploiting the large magnetic moments of first row transition metal ions and the anisotropy of actinides. Examples are the previously discussed U-Mn wheel and chain [36, 38]. 

As expected from the anisotropy of chemical etching of Si in alkaline solutions, the electrochemical dissolution reaction shows a strong dependence on crystal orientation. For all crystal orientations except (111) a sweep rate independent anodic steady-state current density is observed for potentials below PP. For (111) silicon electrodes the passivation peak becomes sweep rate dependent and corresponds to a constant charge of 2.4 0.5 mCcm-2 [Sm6]. OCP and PP show a slight shift to more anodic potentials for (111) silicon if compared to (100) substrates, as shown in Fig. 3.4. 

The apparently statistical distribution observed in the calculations for low J arose from several kinds of trajectories that combined to produce the observed distribution. The existence, position and magnitude of the rotational rainbow is sensitive to the orientational anisotropy of the attractive interaction potential (washed out by averaging), and does not result from anisotropies in the repulsive interaction region. 

The origin of stereofacial selectivity in electrophilic additions to methylene-cyclohexanes (2) and 5-methylene-l,3-dioxane (3) has been elucidated experimentally (Table 2) and theoretically. Ab initio calculations suggest that two electronic factors contribute to the experimentally observed axial stereoselectivity for polarizable electrophiles (in epoxidation and diimide reduction) the spatial anisotropy of the HOMO (common to both molecules) and the anisotropy in the electrostatic potential field (in the case of methylenedioxane). The anisotropy of the HOMO arises from the important topological difference between the contributions made to the HOMO by the periplanar p C-H a-bonds and opposing p C—O or C—C cr-bonds. In contrast, catalytic reduction proceeds with equatorial face selectivity for both the cyclohexane and the dioxane systems and appears to be governed largely by steric effects. ... 

Hereafter, we will assume uniaxial anisotropy, of easy-axis type, given by Eq. (3.4) (if not otherwise indicated), since it is the simplest symmetry that contains the basic elements (potential minima, barriers) responsible for the important role of magnetic anisotropy in superparamagnets. Experimental evidence for uniaxial anisotropy is given in Refs. 15 and 16. 

Periodic surface profiles on vicinal surfaces have received considerable attention in the past, both from a continuum as well as an atomistic point of view [8-18], Here we describe briefly some recent work for surfaces of miscut a (about 3-10°) based on continuum mechanics specifically designed to take the anisotropy of y(0) into account [18], The approach is based on eq. (1) and the excess chemical potential given by [2]... 

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