HKLF Instruction

HKLF n [0] s [1] r11...r33 [1 0 0 0 1 0 0 0 1] wt [1] m [0]


The HKLF command tells the program which format has been chosen for this file, and allows the indices to be transformed using the 3x3 matrix r11...r33, so that the new h is r11*h + r12*k + r13*l etc. The program will not accept matrices with negative or zero determinants. It is essential that the cell, symmetry and atom coordinates in the '.ins' file correspond to the indices AFTER transformation using this matrix.

n is negative if reflection data follow, otherwise they are read from the '.hkl' file. The data are read in FORMAT(3I4,2F8.2,I4) (except for |n| < 3) subject to FORTRAN-77 conventions. The data are terminated by a record with h, k and l all zero (except |n| = 1, which contains a terminator and a checksum). In the reflection formats given below, BN stands for batch number. If BN is greater than one, Fc^2 is multiplied by the (BN-1)'th coefficient specified by means of BASF instructions (see below). If BN is zero or absent, it is reset to one. The multiplicative scale s multiplies both Fo^2 and sigma(Fo^2) (or Fo and sigma(Fo) for n = 1 or 3). The multiplicative weight wt multiplies all 1/sigma^2 values and m is an integer 'offset' needed to read 'condensed data' (HKLF 1); both are included for compatibility with SHELX_76. Negative n is also only retained for upwards compatibility; it is much better to keep the reflection data in the 'name.hkl' file, otherwise the data can easily get lost when editing 'name.res' to 'name.ins' for the next job.

n = 1:
SHELX_76 condensed data (BN is set to one). 'Condensed data' impose unnecessary index restrictions and can introduce rounding errors; although they still have their uses (email!), SHELXL_93 cannot generate condensed data and their use is discouraged.

n = 2:
h k l Fo^2 sigma(Fo^2) BN [1] lambda [#] in FORMAT(3I4,2F8.2,I4,F8.4) for refinement based on singlet reflections from Laue photographs. The data are assumed to be scaled for source intensity distribution and geometric factors and (if necessary) corrected for absorption. If lambda is zero or absent the value from the CELL instruction is used. n = 2 switches off the merging of equivalent reflections BEFORE l.s. refinement (i.e. sets MERG 0); equivalents and measurements of the same reflections at different wavelengths are merged after least-squares refinement and the subsequent application of a dispersion correction, but before Fourier calculations.

The remaining options (n > 2) all require FORMAT(3I4,2F8.2,I4); as is normal for a FORTRAN program, other formats (e.g. F8.0) may be used for the floating point numbers provided that eight columns are used in all and a decimal point is present.

n = 3:
h k l Fo sigma(Fo) BN [1] (if BN is absent or zero it is set to 1). The use of data corresponding to this format is NOT RECOMMENDED, since the generation of Fo and sigma(Fo) from Fo^2 and sigma(Fo^2) is a tricky statistical problem and could introduce bias.

n = 4:
h k l Fo^2 sigma(Fo^2) BN [1] for the standard reflection data file. Since Fo^2 is obtained as the difference of the experimental peak and background counts, it may be positive or (occasionally) negative.

n = 5:
h k l Fo^2 sigma(Fo^2) m where m is the twin component number. Each measured Fo^2 value is fitted to the sum of k[|m|]*Fc[|m|]^2 over all contributing components, multiplied by the overall scale factor. m should be given as positive for the last contributing component and negative for the remaining ones (if any). The values of Fo^2 and sigma(Fo^2) are taken from the last ('prime') reflection in a group, and may simply be set equal for each component, but the indices h,k,l will in general take on different values for each component. The starting values of the twin factors k[2]..k[max(m)] are specified on BASF instruction(s); k[1] is given by one minus the sum of the other twin factors. Note that many simple forms of twinning can also be handled with HKLF 4 and a TWIN instruction to generate the indices of the remaining twin component(s); HKLF 5 is required if the reciprocal space lattices of the components cannot be superimposed exactly. HKLF 5 sets MERG 0.

n = 6:
h k l Fo^2 sigma(Fo^2) m as for n = 5, there may be one or more sets of reflection indices corresponding to a single Fo^2 value. The last reflection in a group has a positive m value and the previous members of the group have negative m. The values of Fo^2 and sigma(Fo^2) are taken from the last ('prime') reflection in a group, and may simply be set to the same values for the others. m is here the reflection MULTIPLICITY, and is defined as the number of equivalent permutations of the given h, k and l values, not counting Friedel opposites. This is intended for fitting resolved powder data for high symmetry crystal systems. For example, in a powder diagram of a crystal in the higher cubic Laue class (m3m) the reflections 3 0 0 (with multiplicity 3) and 2 2 1 (multiplicity 12) would contribute to the same measured Fo^2. HKLF 6 sets MERG 0. HKLF 6 may not be used with BASF.

THERE MAY ONLY BE ONE HKLF INSTRUCTION AND IT MUST COME LAST except when HKLF -n is followed by reflection data in the .INS file, in which case the file is terminated by the end of the reflection data. Negative n is retained for compatibility with SHELX_76 but is not recommended!