Angle-dependent line-of-centers

Janssen, M.H.M. and Stolte, S. (1987) Calculation of steric effects in reactive collisions employing the angle-dependent line of centers model. J. Phys. Chem. 91, 5480-5486. 

Connor, J.N.L., Whitehead, J.C. and Jakiibetz, W (1987) Orientation dependence of the F + H2 reaction - analysis of the angle-dependent line-of-centers model. J. Chem. Soc., Faraday Tram. 83. 1703-1718. 

This model, generally referred to as the angle-dependent line-of-centers (ADLOG)... 

Figure 3.11 Orientation dependence of the cross-section for the reaction H + D2(v= /= 0) HD + D at the two indicated values of the collision energy Ej- The ordinate is dff R/dcos y = 2ctr(cos y). The solid curves were calculated from the angle-dependent line-of-centers model, Eq. (3.34), and the (open and filled) points represent dynamical computations (these are quasi-classical trajectory results that have statistical error bars as discussed in Chapter 5) on the ab initio potential surface referred to in Figure 3.10 [adapted from N. C. Blais, R. B. Bernstein, and R. D. Levine, J. Phys. Chem. 89, 20 (1985)].

COS 0 47re0x2 ix = dipole moment, d = angle between line of centers and axis of dipole length of dipole small compared to x (sign depends on z and orientation) Coulomb 2... 

M. The line-of-centers model with a steric requirement, (a) Derive the result (3.35) for the energy dependence of the reaction cross-section when the barrier depends on the approach angle. The point is that you will have to be care fid about the limits of integration and this will make you think in detail about the energy dependence of the cone of acceptance. See Smith (1980). (b) Derive the results... 

This projection has the area preservation property, i.e. the relative sizes of surface elements are preserved in the image plane and do not depend on the proximity of the cylinder axis to the surface. On the other hand, a distortion is introduced with respect to the h and a-direction, so the angles are not preserved anymore. There is no distortion at the vertical center line of the image, but the distortion increases progressively when moved to the left and right. 

View Factor. The view factor of a point on a plane surface located at a distance L from the center of a sphere (fireball) with radius r depends not only on L and r, but also on the orientation of the surface with respect to the fireball. If 2 is the view angle, and 0 is the angle between the normal vector to the surface and the line connecting the target point and the center of the sphere (see Figure 6.9), the view factor (F) is given by... 

Here, V(R, )) is the interaction potential depending on the distance R from the atom to the center of mass of the molecule and on the angle l) between the molecular axis and the line connecting the atom with the center of mass of the molecule, NA is Avogadro s constant, and V,(R) are the radial coefficients in the expansion of the potential in Legendre polynomials Ph... 

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