Normalization of the integrated intensities

Normalization of the integrated intensities (%normal command)

In the normalization procedure the diffraction intensities are normalized using the Wilson method (Wilson, 1942). Statistical analysis of the intensities is made in order to suggest the presence or absence of the inversion center, to identify the possible presence and type of pseudotranslational symmetry (Cascarano et al. 1988 a,b; Fan, Yao et al. 1988) and to detect preferred orientation effects (Altomare et al. 1994; Altomare et al. 1996). Possible deviations (of displacive type) from ideal pseudotranslational symmetry are also detected. Information about the presence of pseudo symmetry, can be used as prior information for a new integrated intensities extraction process.

Directives in the %normal command

The following directives must be added after the command %normal in the input file to activate specific non-default procedures:

bfactor x
Temperature factor if the user wants to supply it. (The scale factor is assumed equal to 1).

nopreferred
The program does not apply the correction for preferred orientation (if detected).

yespseudo
The program recycles the information about pseudotranslational symmetry for a new extraction process (see Example 1 for its use).

nreflections n
Number of active reflections with the largest E-values subject to a minimum value of E(obs) = 1.0.

Default = 4 * number of independent atoms + 50 if centrosymmetric + 50 if triclinic + 150 to a maximum of 499. If pseudo directive is on, the program tries to use all the |E|’s down to 1.0.

nzro n
Number of the smallest E-values (maximum E-value=0.3) to calculate psi-zero triplets (used in the calculation of the figures of merit in the phasing process). The default (and the maximum) is 1/3 of the strong reflections. (The directive allows to decrease that number).

npla n
n is the number of candidate planes for preferred orientation analysis (default 10; maximum 30).

The number includes the equivalent planes which will be not considered.

plane h k l G
Preferred orientation direction supplied by the user; G is the correction factor.

pseudotranslation n(1,1) n(2,1) n(3,1) n(4,1) n(1,2) . . . n(4,3)
If parameters are equal to zero, or omitted, the normalization routine performs statistics for the pseudotraslation effects and renormalizes the reflections on assuming the most probable pseudotranslation as prior information.

If user wants to supply a specific pseudotranslational symmetry, and this corresponds to a class given in Table 1, n(1,1) can be set to the class number and the other values must be omitted.
If the pseudotranslation is more complex, it should be specified by up to 3 sets of 4 values n(i,j) so that:

[n(1,j)*h + n(2,j)*k +n(3,j)*l = n(4,j)*m]       j=1,..,3

where m is an integer number.

thrp x
Threshold value of the mean fractionary scattering power to recycle the pseudotranslational symmetry information for a new extraction process.

Patterson map calculation (%patterson command)

In this module the Patterson map can be calculated by using the normalized (or non-normalized) structure factor moduli as coefficients. By using the directive inversion, it is possible to exploit the information of positivity of the electron density (in the direct space) in the extraction routine: the Patterson map is modified and inverted, providing a set of structure factor moduli values to use for a new extraction process.

Directives in the %patterson command

The following directives must be added after the command %patterson in the input file to activate specific non-default procedures:

e*f (or f*e)
Coefficients to be used in the Patterson synthesis (e**2 is the default).

f**2 (or f*f)
Coefficients to be used in the Patterson synthesis (e**2 is the default).

inverse
To activate the procedure of calculating the |F| values from an inverted suitably modified Patterson map (Altomare et al., 1998). The values are then used as starting point in the Le Bail algorithm for extracting new structure factor moduli from the experimental pattern (see Example 2 for its application).

map, layx, layy, layz, peaks, limit, grid
See the corresponding directives in the %fourier command.

npat n
The number of cycles of successive inversions of the Patterson map. (Default values: 6 for X-ray data, 5 for neutron data).

Examples

Example 1
Use of the pseudotranslational symmetry (if it is present) as prior information for a new extraction process.

%structure agpz
%job AGPZ - data from home diffractometer
%data
    pattern agpz.pow
    cell 6.526 20.059 6.464 90.000 90.000 90.000
    spacegroup p b c a
    content Ag 8 N 16 C 24 H 24
    wavelength 1.54056 
%extraction
%normal
    yespseudo
%continue

Example 2
Use of the Patterson map inversion as prior information for a new extraction process.

%structure lasi
%job lasi - Neutron data
%data 
       pattern lasi.pow 
       cell 5.4059 8.7934 14.2754 90.000 112.731 90.00 
       content La 8 Si 8 O 8 
       spacegroup p 21/c 
       wavelength 2.3400 
       neutron
%extraction
%normal 
%patterson 
       inverse
%continue

Table 1
Classes of reflections corresponding to the low index pseudotranslational symmetry.

1)

h+k+l= 1n

2)

h= 2n

3)

k= 2n

4)

l= 2n

5)

h+k+l= 2n

6)

h+k= 2n

7)

h+l= 2n

8)

k+l= 2n

9)

h= 3n

10)

k= 3n

11)

l= 3n

12)

h+k= 3n

13)

h+l= 3n

14)

k+l= 3n

15)

h+k+l= 3n

16)

h+k+2l= 3n

17)

h+2k+l= 3n

18)

2h+k+l= 3n

19)

h+2k= 3n

20)

h+2l= 3n

21)

k+2l= 3n

22)

l= 4n

23)

k= 4n

24)

h= 4n

25)

h+k= 4n

26)

h+l= 4n

27)

k+l= 4n

28)

h+k+l= 4n

29)

2h+2k+l= 4n

30)

2h+k+2l= 4n

31)

h+2k+2l= 4n

32)

2h+k+l= 4n

33)

h+2k+l= 4n

34)

h+k+2l= 4n

35)

h+2k= 4n

36)

h+2l= 4n

37)

k+2l= 4n

38)

2h +k= 4n

39)

2h+l= 4n

40)

2k+l= 4n

41)

3h+3k+l= 4n

42)

3h+k+3l= 4n

43)

h+3k+3l= 4n

44)

h+2k+3l= 4n

45)

h+3k+2l= 4n

46)

3h+k+2l= 4n

47)

h+3k= 4n

48)

h+3l= 4n

49)

k+3l= 4n

50)

3k+2l= 6n

51)

2k+3l= 6n

52)

2h+3k= 6n

53)

3h+2k= 6n

54)

3h+2l= 6n

55)

2h+3l= 6n

56)

2h+2k+3l= 6n

57)

3h+2k+3l= 6n

58)

3h+3k+2l= 6n

59)

4k+3l=12n

60)

4h+3l=12n

61)

4h+3k=12n

62)

3k+4l=12n

63)

3h+4k=12n

64)

3h+4l=12n

65)

h = 2n & k = 2n

66)

h = 2n & l = 2n

67)

k = 2n & l = 2n

68)

h = 2n & k+l = 2n

69)

k = 2n & h+l = 2n

70)

l = 2n & h+k = 2n

71)

h+k = 2n & h+l = 2n

72)

h = 2n & k= 2n & l= 2n

References

Altomare A., Cascarano G., Giacovazzo C., Guagliardi A., Burla M.C., Polidori G. & Camalli M. (1994). J. Appl. Cryst. 27, 435 – 436.
Altomare A., Burla M.C., Cascarano G., Giacovazzo C., Guagliardi A., Moliterni, A.G.G. & Polidori, G. (1996). J. Appl. Cryst. 29, 341-345.
Altomare A., Foadi J., Giacovazzo C., Moliterni A.G.G., Burla M.C. and Polidori G. (1998). J. Appl. Cryst. 31, 74 – 77.
Cascarano G., Giacovazzo C. & Luic’ M. (1988a). Acta Cryst. A44, 176-183.
Cascarano G., Giacovazzo C. & Luic’ M. (1988b). 
Acta Cryst. A44, 183-189.
Fan H., Yao J. & Qian J. (1988). 
Acta Cryst. A44, 688-691.
Wilson, A. J. C. (1942). Nature, 152.