Fourier Program

 

A program for Fourier maps calculations.

JGP  JRC 2004

 

Scope

The program Fourier calculates the scattering density inside the unit cell of a crystal of whatever symmetry. The GFourier allows to create and visualizate the results of Fourier program using a menu-driven interface with the help of the mouse and few keyboard input.

 

General Aspects

The program Fourier calculates the scattering density inside the unit cell of a crystal of whatever symmetry. It uses a Fast Fourier Transform (FFT) subroutine to accelerate the calculation of the following expression:

 

 

 

Where V is the volume of the unit cell. H is a reciprocal lattice vector, r is a vector position inside the unit cell, and F(H) are complex Fourier coefficients used to perform different types of Fourier syntheses. The units of  are those of F(H) divided by those of V. For instance, if F(H) are given en electron units (usual absolute units for X-ray diffraction) and V in  ,  is calculated as Number-of-Electrons/ .

 

 

Running the program

Invoking the program:

Local_Prompt> fourier [input_file]

 

where the input file is the control for the program. Also you need a file containing the hkl’s and structure factors. The extension for both files are inp and fou respectively. If Fourier runs properly il will output up to two files:

 

CODE.out       General output file

CODE.bin       Binary file containing the scattering density inside the unit cell.

 

The program GFourier allows to create from the scratch an input control file CODE.inp for Fourier using just a menu-driven interface with the help of the mouse and few keyboard input.

 

 

Input Control File

The input control file is totally free format. It is a command-driven-like file. All commands and keywords are case insensitive. Empty lines are allowed and if the symbol "!" appears as the first character, the line is considered as a comment.

There are only 13 commands that are explained below (for a sake of clarity we give here the commands and keywords in upper-case):

 

 

ATOM

e.g.  ATOM  Label X  Y  Z  [occ]

This command is optional and the maximum number that can be input at present is 500. Label is a string (of 4 characters max) representing the name of the atom and X Y Z are three real numbers representing the fractional coordinates. occ is the occupation number. This parameter is optional.

The atoms are not used inside Fourier. They are given optionally only for graphic representation purposes. Fourier put this information in the output binary file that is read by GFourier.

Example: ATOM  Ba  0.5000  0.5000  0.5000

 

 

CELL

e.g.  CELL a b c alpha beta gamma

The command CELL is followed by the six real numbers defining the metrics of the unit cell. Usually a,b,c are in angstroms and alpha,beta,gamma in degrees.

 

 

END

This command tells the program that the lines below are not to be taken into account.

 

 

FILE

e.g.  FILE  KeyWords  NameFile

The command FILE provides information about files to the program. NameFile is the name of a file. It may include the full path. The values of Keywords are:

FOU

The structure factors file name is provided in NameFile.

 

ATOM

The name of an optional atom file (only the ATOM command is recognized inside) is provided in NameFile

BIN

The name of the binary file is provided in NameFile.

 

NameFile can be absent if BIN and ATOM are given. In this case the name of the file is the same as the name of the input control file with extensions ".bin" and ".atm".

Examples:       FILE  fou  myfile.fou

FILE  ATOM  my_atoms.atm

FILE bin

 

 

FOURIER

e.g.  FOURIER KeyWords

This command tells to the program what kind of Fourier synthesis have to be calculated. At present, the possible values of KeyWords are:

PATT FOSQ

Patterson Map using observed squared structure factors  

PATT FCAL

Patterson Map using calculated squared structure factors  

FOBS

Fourier Map using observed structure factors and calculated phases  

FCAL

Fourier Map using calculated structure factors and phases  

DIFF

Difference Fourier Map  

AABB

User supplied real and imaginary parts of the Fourier coefficients  

 

Examples:       FOURIER PATT FOSQ

FOURIER DIFF

 

 

FORMAT

e.g.  FORMAT kw1  kw2  kw3  kw4 ...kw9

Where kw(i) are keywords representing one of the following items:

H:  h-index

K:  k-index

L:  l-index

A:  Real part of the structure factor (or of the user-supplied Fourier coeff.)

B:  Imaginary part

Fo:  Observed structure factor

Fc:  Calculated structure factor

Phase:  Phase of the structure factor in degrees.

SigFo:  Standard deviation  of the observed structure factor.

 

Tells the program the order in which appear the different items in the Fourier file specified by FILE FOU.

Examples:       FORMAT  h k l  A  B

FORM    h k l  Fo  Fc  Phase

Form   A B  Fo  h k l

 

 

F000

e.g.   F000 value1 [value2]

Gives the value of F(000) (value1)  and a scale factor (value2) for all map. The default values are value1=0.0000, value2=1.000

Example:        F000  822  1.0

 

 

GRID

e.g.  GRID  nx  ny  nz

User-supplied grid values for calculating the scattering density. By default the program calculates automatically the three integer values nx, ny and nz.

Example:        GRID  20 20 25

 

 

LIST

e.g.  LIST Keywords

This command tells to the program output additional information. At present, the possible values of KeyWords are:

ATOMS

List of atoms in the unit cell.

DIST value1 value2

List of distance of the peaks between value1 and value2. In default, value1 = 1.000, value2 = 2.5 Å.

 

Example:        LIST atoms

 LIST dist 1.8  2.25

 

REFLEC

e.g.  REFLEC KeyWord Value(s)

Where KeyWord is one of the items SRAN, SMIN, SMAX, SIGM and Value(s) is one or two (only for SRAN) real numbers.

This command instructs the program about the  limits of Fourier calculation.

Examples:       REFLEC  SRAN  0.0   0.88

reflec  SMAX 1.2

Reflec  SMIN 0.2

 

 

SCAN

e.g.  SCAN npeaks

This command activates the peak search subroutine. The program look for the coordinates of the highest "npeaks" peaks in the asymmetric unit of the  mapThese are repeated for the first "npeaks" peaks found. Symmetry equivalent peaks are not included.

Example:        SCAN 10

 

 

SPGR

e.g.  SPGR Space_Group

The command SPGR tells to the program that the string Space_Group is the Hermann-Mauguin symbol for the space group. The symbol must be given using a space before the symbol corresponding to a symmetry direction. Following the International Table descriptions, choice 1 can be introduced by adding “:1” to Hermann-Mauguin symbol (choice 2 is in default) and for Rhombohedral axes “:R” (hexagonal axes are in default).

Examples:       SPGR  P n m a

SPGR  P 41/m

SPGR P m m n:1

SPGR R 3:R

The program uses the symbol to generate the full set of symmetry operators that are used to expand the reflection indices. It is wise to verify that the reduced set of symmetry operators are correctly generated.

 

 

TITLE

e.g.  TITLE comment

The command TITLE tells the program that comment should be used as a title.

Example: TITLE  Fourier Difference Map for CarbaDiazepine

 

Contact

Javier Gonzalez - Platas

Instituo de Bioorgánica “Antonio González” & Dpto. de Física Fundamental II

Universidad de La Laguna, Tenerife, SPAIN

Tel: (34) 922 318317, Fax: (34) 922 318320

e-mail: jplatas@ull.es

 

Juan Rodriguez - Carvajal

Laboratoire Leon Brillouin (CEA - CNRS)

CEA / Saclay, 91191 Gif sur Yvette Cedex, FRANCE

Tel: (33) 1 6908 3343, Fax: (33) 1 6908 8261

e-mail: juan@bali.saclay.cea.fr