Resources for the first map

Here is the Fourier series that gives the first electron-density map 

In words, the desired electron-density function is a Fourier series in which term hkl has amplitude IFobsl, which equals (7/, /)1/2, the square root of the measured intensity Ihkl from the native data set. The phase ot hkl of the same term is calculated from heavy-atom, anomalous dispersion, or molecular replacement data, as described in Chapter 6. The term is weighted by the factor whU, which will be near 1.0 if ct hkl is among the most highly reliable phases, or smaller if the phase is questionable. This Fourier series is called an Fobs or Fo synthesis (and the map an Fo map) because the amplitude of each term hkl is iFobsl for reflection hkl. 

The first term in this Fourier series, the F000 term, should contain (f0oo)1/2 where /000 is the intensity of reflection 000, which lies at the origin of the reciprocal lattice. Recall that this reflection is never measured because it is obscured by the direct beam. Examination of Eq. (7.3) reveals that F000 is a 

I will consider the latter case, in which the first map defines a molecular envelope, with perhaps a little additional detail. If more detail can be discerned, the crystallographer can jump ahead to later stages of the map-improvement process I am about to describe. If the molecular envelope cannot be discerned, then more data collection is required. 

The crude molecular image seen in the F0 map, which is obtained from the original indexed intensity data (IFobsI) and the first phase estimates (a calc), serves now as a model of the desired structure. A crude electron density function is devised to describe the unit-cell contents as well as they can be observed in the first map. Then the function is modified to make it more realistic in the light of known properties of proteins and water in crystals. This process is called, depending on the exact details of procedure, density modification, solvent leveling, or solvent flattening. 

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