Gaussian planes

Figure 6.26 Representation in the Gaussian plane of the phase relationships between the structure factor of a pure protein, FP, a heavy atom, FH and an isomorphic heavy atom derivative of the protein,...

Figure 6.27 Representation in the Gaussian plane of the phase relationships derived by single isomorphous replacement, SIR, in a protein. The structure factor of the protein vector, FP, lies on a circle of radius FP centred at O. The structure factor of the heavy metal derivative, FPH, lies on a circle of radius Fph, with centre at the tip of the vector -Fh- The intersection of the two circles represents the two solutions to equation (6.6). The resulting vector FP can be drawn in two positions, corresponding to two different phase angles...

The computational problem is formally the same whether a Gaussian, plane wave or polynomial basis is used - calculate matrix elements of quantum mechanical operators over basis functions and solve the variational problem by an iterative procedure - but the nature of the functions results in some differences. With a GTO basis the matrix elements are calculated directly, while with a plane wave basis the matrix elements involving the potential energy can be generated by simple multiplication, as long... 

In general. F(hkl) is a complex number when plotted in the Gaussian plane (Fig. 34). it has not only a modulus IF I but also a phase angle (p. 

It is apparent from the ray diagram of Fig. 3.3 that there is a plane, A-A, nearer to the lens than the geometrical or Gaussian focus plane, where the resolution is improved. It is called the plane of least confusion or Scherzer focus [3, 4, 7], and it is close to where the rays from the outermost parts of the lens intersect the axis. From Fig. 3.3 the distance 6Z between this plane and the Gaussian image plane is approximately the radius of the image disc in the Gaussian plane divided by a. The radius is Ma C and a = ajM, so... 

Fig. 3.3 the distance 6Z between this plane and the Gaussian image plane is approximately the radius of the image disc in the Gaussian plane divided by a. ... 

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