# VECSUM (CCP4: Unsupported Program)

## NAME

vecsum - program to deconvolute a Patterson function and solve the structure.

## SYNOPSIS

vecsum MAPIN foo_in.map MAPOUT foo_out.map
[control data in fixed order]

## DESCRIPTION

The purpose of this program is to deconvolute a Patterson function and solve the structure. Although it was designed for heavy-atom difference Pattersons (isomorphous and FHLE) there is no reason why it could not be used to solve structures of small molecules.

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 expected

```
Then 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 1/8

```
7. 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)
The harmonic mean is strongly biased towards the minimum, yet takes some account of the higher values, and is a reasonable compromise between the Minimum and Sum functions.

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)
END

```
The 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.

## Control data for the VECSUM program.

```
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

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.

```

## INPUT AND OUTPUT FILES

### Input

MAPIN
Patterson map prepared by FFT.

### Output

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

RSPS - alternative program
FFT - prepare Patterson function for MAPIN
PEAKMAX - look for sites in MAPOUT

## Example of control data.

```
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

```