International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2010 
International Tables for Crystallography (2010). Vol. B, ch. 1.3, pp. 7374

Structure factors may be calculated from a list of symmetryunique atoms by Fourier transformation of the orbit decomposition formula for the motif given in Section 1.3.4.2.2.4:i.e. finally:
In the case of Gaussian atoms, the atomic transforms areor equivalently
Two common forms of equivalent temperature factors (incorporating both atomic form and thermal motion) are
In the first case, does not depend on , and therefore:In the second case, however, no such simplification can occur:These formulae, or special cases of them, were derived by Rollett & Davies (1955), Waser (1955b), and Trueblood (1956).
The computation of structure factors by applying the discrete Fourier transform to a set of electrondensity values calculated on a grid will be examined in Section 1.3.4.4.5.
References
Rollett, J. S. & Davies, D. R. (1955). The calculation of structure factors for centrosymmetric monoclinic systems with anisotropic atomic vibration. Acta Cryst. 8, 125–128.Trueblood, K. N. (1956). Symmetry transformations of general anisotropic temperature factors. Acta Cryst. 9, 359–361.
Waser, J. (1955b). The anisotropic temperature factor in triclinic coordinates. Acta Cryst. 8, 731.