[control data in fixed order]

The main features of the program are as follows :

1. It is completely space-group general.

2. It takes as input a Patterson function produced by the Fast Fourier Transform FFT program in the standard format. Like the FFT program it works with a user specified array to optimise use of memory.

3. The Patterson function must comprise at least one asymmetric unit of the appropriate point group. However, for high symmetry cases it is advisable to compute as many asymmetric units as the available memory and disk space will allow in order to minimise searching for equivalent positions, although there is probably no advantage in computing more than one half of the cell. This will mean generating equivalents for and computing the Patterson in P1 bar. This incidentally simplifies the problem of unique axis orientation as no permutation of axes is required. It is recommended that the sampling interval in the Patterson be about dmin/4, i.e. in FFT NX = 4*hmax etc.

4. The program requires an estimate of the expected number of major sites. This is could be 1 to start with, and increased as more sites are found. The value is used to calculate an upper thresholding level :

Pmax = ( P(0,0,0) + Pooo ) / (Ngep * Nexp)where

P(0,0,0) = origin value e.g. 1000 Pooo = Fooo contribution, typically 5 to 10 for P(0,0,0) = 1000 Ngep = Number of general equivalent positions (not counting centring) Nexp = Number of major sites expectedThen if P(u,v,w) + Pooo > Pmax , the value is truncated to Pmax. Also if P(u,v,w) + Pooo < 0 , the value is truncated to 0.

5. The program can calculate a "symmetry function" or a "superposition function" or a combination of the two (see Stout & Jensen, X-ray structure determination, chapter 14). The user can control which Harker vectors, if any, are combined with the superposition function.

6. The program produces a map of the possible sites in the structure very much like an electron density map. The symmetry function, which is normally calculated first, uses only Harker vectors and therefore has higher symmetry than the true space group.

e.g. : P21 has asymmetric unit : x = 0 to 1, y = 0 to 1/2, z = 0 to 1 equivalent origins : x = 0 or 1/2, y = any, z = 0 or 1/2 symmetry function : x = 0 to 1/2, y = 0, z = 0 to 1/2 (i.e. only 1 section.) P41212 has asymmetric unit : x = 0 to 1, y = 0 to 1, z = 0 to 1/8 equivalent origins : (x,y) = (0,0) or (1/2,1/2), z = 0 or 1/2 symmetry function : x = 0 to 1/4, y = 0 to 1, z = 0 to 1/87. Each point in the map produced is a combination of the values found for the calculated vectors in the Patterson function. At present there are 3 modes of combination :

- a)
- Minimum
- b)
- Arithmetic mean (equivalent to sum)
- c)
- Harmonic mean (reciprocal of mean of reciprocals)

8. The user is recommended to proceed in a stepwise fashion by first choosing a site in the symmetry function. Experience suggests that apparent sites lying on true rotation (as opposed to screw) axes are more likely than not to be wrong; these can be eliminated by opting to ignore Harker vectors falling on the Patterson origin; however the possibility that one or more sites do lie on rotation axes should be borne in mind. Having chosen a site with high density, the coordinates are added to the input data, and a second site chosen. This process is repeated until the site densities fall off significantly compared with the rms noise level printed at the end of the output.

9. The option to print a list of the vectors between the input sites should be used to monitor the fit with the Patterson; it is important to realise that it is not enough just to find sites which have vectors falling on peaks in the Patterson; unexplained peaks of high density almost certainly indicate a wrong or at best incomplete solution.

10. The user supplies a "discrimination" which simply truncates the lower values in the output map. A value of 0.2 will cause map values < 0.2*Pmax not to be printed. Use a higher value to get more discrimination, but run the risk of missing weak sites.

11. The user supplies a "tolerance" (in grid units). The effect of this is to search the local area of each vector in the Patterson function within a sphere of the specified radius and return the maximum value to the combination function. The program will stop if no grid points are found, e.g., if you give a site with coordinates (1.5, 10.5, 0) (in grid units) and a tolerance of 0.5, there will be no points on the Patterson grid within this distance of the site, the closest being 0.707 grid units away. Also beware of giving too large a value for the tolerance (i.e. > 1.5), as this will require a large amount of searching and hence an inordinate amount of cpu time.

12. The user supplies a REAL array to the FFT program and an INTEGER*2 array to the VECSUM program e.g. :

INTEGER*2 MAP COMMON MAP(70000) CALL VECSUM(70000) ENDThe size of this array must be greater than the number of grid points in the Patterson function calculated by FFT. The VECSUM program reports the size actually used. Note size of array required = (Number of Patterson sections +2) * Number of points per section.

Record 1. Title Record 2. JU JV JW Sort order for output map. JU = fastest (across page) axis on output with 1 for x JV = medium (down page) . . 2 for y JW = slowest (section) . . 3 for z For map output in standard orientation (2nd setting monoclinic, y sections), JU JV JW = 1 3 2 For map output with z sections (1st setting monoclinic), JU JV JW = 2 1 3 Record 3. LX MX LY MY LZ MZ limits in x, y, z for output. Record 4. Pooo DISC TOL COSA COSB COSG Pooo = Fooo contribution ( 5 to 10 for Patterson origin of 1000). DISC = discrimination (e.g. 0.2) TOL = tolerance (e.g. 1.1) COSA, COSB, COSG are cosines of unit cell angles, used to calculate distances in the local search, but the values are not critical. Record 5. NLINE LATT NGEP NHAR NUSE NEXP NSIT IFUN NLINE = Maximum number of columns per line in printed map. If 0 defaults to normal width (64). If < 0 suppresses printing and produces a map on disk in standard format. LATT = lattice type, 1 = P, 2 = I, 3 = R, 4 = F, 5 = A, 6 = B, 7 = C. NGEP = number of general equivalent positions (g.e.p.'s) in space group counting any centrosymmetrically related, but not related by centring translations (minus 1 if identity omitted). NHAR = number of different Harker vectors to use. NUSE = number of g.e.p.'s to use to generate half a primitive cell from the Patterson input (0 if the input Patterson is already half a cell). NEXP = number of major sites expected. If negative, the Patterson origin peak will be removed. This effectively eliminates spurious sites that fall on pure rotation axes (if the space group has any), but of course should not be used if it is suspected that there are 1 or more sites that really do lie on a rotation axis. NSIT = number of sites input, or 0 to produce a symmetry function. If both NHAR and NSIT are zero, the program outputs the truncated Patterson function. If NSIT is negative, the program only produces a list of all vectors between the input sites and their equivalent positions, with the corresponding value in the Patterson. IFUN = type of combination function, 1 = Minimum, 2 = Arithmetic mean (equivalent to Sum), 3 = Harmonic mean. If IFUN is positive, the combination value for all Harker and cross-vectors is calculated; if IFUN is negative, the combination values are calculated for the two types of vectors are calculated separately and then combined as a Minimum function (makes no difference if IFUN = 1). The latter option may give improved discrimination. Omit record 6 if NGEP = 0. Record 6. General equivalent positions as in International Tables, Vol 1. The identity may be omitted. This record to be given NGEP times. Omit records 7 and 8 if NHAR = 0. Record 7. Serial numbers of g.e.p.'s to use for Harker vectors (NHAR numbers). If all Harker vectors are to be used this will be just the integers from 1 to NGEP (omitting the identity if present). In some space groups some Harker vectors are equivalent and in such cases some time will be saved if only the unique ones are given, and the appropriate multiplicities are given on the next record. If in doubt give all g.e.p. numbers except the identity and give the multiplicities all 1. Record 8. Multiplicities of Harker vectors (NHAR numbers). Omit record 9 if NUSE = 0. Record 9. Serial numbers of g.e.p.'s to be used to generate Patterson symmetry (NUSE numbers). The translation components are not used. Omit record 10 if NSIT = 0. Record 10. Site coordinates in grid units. This record to be given NSIT times.

- MAPIN
- Patterson map prepared by FFT.

- MAPOUT
- Map of the "symmetry function" or "superposition function".

RSPS - alternative program

FFT - prepare Patterson function for MAPIN

PEAKMAX - look for sites in MAPOUT

GC2 ETHGCL ANOMALOUS/LOCAL SCALED 5.5A FHLE, GRID = 40 40 72. P41212 2 1 3 0 39 0 39 0 9 10 .2 1.1 0 0 0 0 0 7 6 0 3 5 3 -X,-Y,1/2+Z 1/2-Y,1/2+X,1/4+Z 1/2+Y,1/2-X,3/4+Z Y,X,-Z -Y,-X,1/2-Z 1/2-X,1/2+Y,1/4-Z 1/2+X,1/2-Y,3/4-Z 1 2 4 5 6 7 1 2 1 1 1 1 .5 29.5 0 24.1 15.6 2.5 .8 9.7 5 4 26.5 6.7 33 20 7