The "jump" between direct and reciprocal
spaces, mediated by a Fourier transform represented by the electron
density function
Moreover,
the number of points in the
unit cell, where the ρ function has to be calculated, is very
high. In a cell of about 100 x 100 x 100 Angstrom^{3},
it
would be necessary to calculate at least 1000 points in every unit cell
direction to obtain a resolution of 100/1000, which equals 0.1
Angstrom in each
direction. This means calculating at least 1000 x 1000 x 1000 =
1,000,000,000 points (one billion points) and at each point to
"add" several
thousand
(or hundreds
of thousands)
structure factors F(hkl).
It should therefore be clear that, regardless of the difficulties of
the phase problem, solving a crystal structure implies the use of
computers.
Finally, the analysis of a crystal or molecular structure also implies
calculating many geometric parameters that define interatomic
distances, bond angles, torsional angles, molecular surfaces,
etc., using the atomic coordinates (xyz).