GRID internal coordinate

Equation (7.19) was also obtained by Hounslow et al. (1988) after correcting the original equation proposed by Batterham et al. (1981). However, diis equation is nodiing odier than the fixed-pivot technique applied for a geometric grid with ratio equal to two and after superimposing the conservation of the zeroth- and first-order moments (with particle mass as internal coordinate). 

Both the ring puckering and the carbonyl wagging motions are needed for the description the low frequency modes of cyclobutanone. Energy points on a grid defined by selected values of the internal coordinates were obtained from fully optimized Hartree-Fock calculations with Moller Plesset corrections for electron correlation. These data points were fitted to the power series expansion... 

Zigzagging The first approach is to build a structured grid of coordinate lines without reference to the internal boundaries. The coordinate lines, in some sense nearest to the internal boundaries, are then located and the internal boundary is displaced to the lines. That is, the geometric data is itself modified. This process is called zigzagging. This is the most robust technique and can generate a grid for any object if the initial grid has sufficient resolution. 

Differential methods - in these techniques the internal grid coordinates are found via the solution of appropriate elliptic, parabolic or hyperbolic partial differential equations. 

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