Cutting comers

The main approximation of such one-dimensional corrections is that the tunnelling is assumed to occur along the MER This may be a reasonable assumption for reactions having either early or late (close to either reactant or product) transition states. For reactions where both bond breaking and formation are significant at the TS (as is usually the case), the dominant tunnel effect is comer cutting (Figure 16.5), i.e. the favoured... 

Figure 16.S A contour plot illustration of the comer cutting tunneling path...

Fig. 6.3 Skewed coordinate potential surfaces for some hydrogen transfer reactions, (a) Top HH+ H = H + HH. (b, upper) CH + C = C + HC. (b, lower) HF + H = H + FH. (c) C1H + Cl = C1+HC1 (schematic). The mass dependence of the skew angle is apparent. The MEP s are indicated as the line Q(/ in Fig. 6.3a and the heavier lines in Fig. 6.3b. The path in Fig. 6.3a marked PP is discussed later in the text, as is the comer cutting path in Fig. 6.3c shown as the dotted line (Figure 6.3ais from Marcus, R. A. and Coltrin, M. E., J. Chem. Phys. 67, 2609 (1977) Figure 6.3b and c are From Agmon, N., Chem. Phys. 76, 203 (1983))...

Fong, C.Y. and Poon, A.W., 2004, Planar comer-cut square microcavities ray optics and FDTD analysis. Opt Express 12(20) 4864-4874. 

Figure 6.8 Similar to Fig. 6.6, but showing a set of images from an elastic band calculation that exhibits comer cutting. ... 

The instanton method takes into account only the dynamics of the lowest energy doublet. This is a valid description at low temperature or for high barriers. What happens when excitations to higher states in the double well are possible And more importantly, the equivalent of this question in the condensed phase case, what is the effect of a symmetrically coupled vibration on the quantum Kramers problem The new physical feature introduced in the quantum Kramers problem is that in addition to the two frequencies shown in Eq. (28) there is a new time scale the decay time of the flux-flux correlation function, as discussed in the previous Section after Eq. (14). We expect that this new time scale makes the distinction between the comer cutting and the adiabatic limit in Eq. (29) to be of less relevance to the dynamics of reactions in condensed phases compared to the gas phase case. 

Chain-of-states methods have also been used for finding classical dynamical paths.4 A2 Gillilan and Wilson" suggested using an object function similar to equation 1 for finding saddle points, but this suffers from the comer-cutting and down-sliding problems discussed above. 

Cadmium rhenium(V) oxide is deep violet in color. Its crystalline habit is roughly octahedral with the triangular faces (111) having their comers cut. It is stable in air and attacked slowly in strongly oxidizing media. The crystals are treated with dilute nitric acid to ensure a pure product since the impurities are soluble in this acid. 

To make cut stars, the damp mixture is spread out in a shallow pan, pressed down evenly, cut into cubes, say % to % inch on the side, allowed to dry, and broken apart. Because of their comers, cut stars take fire very readily and are well suited for use in rockets and small aerial bombshells. Cylindrical stars are preferred for Roman candles. 

The NEB method recognized that the issues with the elastic band technique arose from specific components of the force. The issues with comer cutting arise from components of the force perpendicular to the path, which tend to pull images away from the path. Image sagging can be attributed to components of the tme force parallel to the path the spacing between images becomes uneven to balance out the net force. The simple solution to these issues is to minimize the elastic band with these force components projected out. The NEB force is... 

Readiness reviews are important because projects frequently fall behind schedule and/or run over budget, thus creating pressure on the project team to eliminate or postpone the installation of any items that are not absolutely necessary for the start-up. If not controlled properly, this can lead to comer-cutting—either intentional or inadvertent—which may in turn jeopardize the safety or operabihty of the modified facility. The review gives the operations department the authority to refuse to accept care, custody, and control of a facility that they judge to be unsafe or difficult to operate. In effect, a PSR provides a breathing space for everyone to make sure that the plant that they are about to start is safe. 

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