Grid point

The probes themselves could be fitted with a button, like a computer mouse, for clicking when over a grid point. This would allow one-hand operation and make sampling in... 

This expression, in combination with (A3.11.122), detemiines the action of the kinetic energy operator on the wavefiinction at each grid point. The action of Vis just at each grid point. 

Here H fonns an A x A matrix, where A is the dimensionality of the space and is generally much smaller than the number of grid points. 

Note that equation (A3.11.1881 includes a quantum mechanical trace, which implies a sum over states. The states used for this evaluation are arbitrary as long as they form a complete set and many choices have been considered in recent work. Much of this work has been based on wavepackets [46] or grid point basis frmctions [47]. 

But we emphasize that more general forces may be applied [81,91]. The grid points follow the trajectory and are defined through... 

Determine the dielectric constants for each of the faces between the grid points. 

Assign A value of 1 or 0 to each grid point to identify points that are or are not accessible to mobile ions, respectively. 

To display properties on molecular surfaces, two different approaches are applied. One method assigns color codes to each grid point of the surface. The grid points are connected to lines chicken-wire) or to surfaces (solid sphere) and then the color values are interpolated onto a color gradient [200]. The second method projects colored textures onto the surface [202, 203] and is mostly used to display such properties as electrostatic potentials, polarizability, hydrophobidty, and spin density. 

A cubic lattice is superimposed onto the solute(s) and the surrounding solvent. Values of the electrostatic potential, charge density, dielectric constant and ionic strength are assigned to each grid point. The atomic charges do not usually coincide with a grid point and so the... 

The reaction coordinate is one specific path along the complete potential energy surface associated with the nuclear positions. It is possible to do a series of calculations representing a grid of points on the potential energy surface. The saddle point can then be found by inspection or more accurately by using mathematical techniques to interpolate between the grid points. 

Once the molecules are aligned, a molecular field is computed on a grid of points in space around the molecule. This field must provide a description of how each molecule will tend to bind in the active site. Field descriptors typically consist of a sum of one or more spatial properties, such as steric factors, van der Waals parameters, or the electrostatic potential. The choice of grid points will also affect the quality of the final results. 

The grid of computed values for the variable used in defining the contour is a grid of exactly the size of the current working area subdivided evenly such that the total number of grid points is as the user specifies. 

Finite Difference Method To apply the finite difference method, we first spread grid points through the domain. Figure 3-49 shows a uniform mesh of n points (nonuniform meshes are possible, too). The unknown, here c(x), at a grid point x, is assigned the symbol Cj = c(Xi). The finite difference method can be derived easily by using a Taylor expansion of the solution about this point. Expressions for the derivatives are ... 

The solution is known at each of these grid points (Y(Xrt)). First the Fourier transform is taken. 

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