exp ( -2.pi2*[ h2*(a*)2*U11 + k2*(b*)2*U22 + ... + 2hk*(a*)*(b*)*U12 ] )
for anisotropic Uij. An atom is specified as follows in the '.ins' file:
atomname sfac x y z sof [11] U [0.05] or U11 U22 U33 U23 U13 U12The atom name must be unique, except that atoms in different residues - see RESI - may have the same names; in contrast to SHELX-76 it is not necessary to pad out the atom name to 4 characters with blanks. To fix any atom parameter, add 10. Thus the site occupation factor is normally given as 11 (i.e. fixed at 1). The site occupation factor for an atom in a special position should be multiplied by the multiplicity of that position (as given in International Tables, Volume A) and divided by the multiplicity of the general position for that space group. This is the same definition as in SHELX-76 and is retained for upwards compatibility; it might have been less confusing to keep the multiplicity and occupation factor separate. An atom on a fourfold axis for example will usually have s.o.f. = 10.25.
If any atom parameter is given as (10*m+p), where abs(p) is less than 5 and m is an integer, it is interpreted as p*fv(m), where fv(m) is the mth 'free variable' (see < href=FVAR.html>FVAR). Note that there is no fv(1), since this position on an FVAR instruction is occupied by the overall scale factor, and m=1 corresponds to fixing an atom by adding 10. If m is negative, the parameter is interpreted as p*(fv(-m)-1). Thus to constrain two occupation factors to add up to 0.25 (for two elements occupying the same fourfold special position) they could be given as 20.25 and -20.25, i.e. 0.25*fv(2) and 0.25*(1-fv(2)), which correspond to p=0.25, m=2 and p=-0.25, m=-2 respectively.
In SHELX-76, it was necessary to use free variables and coordinate fixing in this way to set up the appropriate constraints for refinement of atoms on special positions. In SHELXL-93, this is allowed (for upwards compatibility) but is NOT NECESSARY: the program will automatically work out and apply the appropriate positional, s.o.f. and Uij constraints for any special position in any space group, in a conventional setting or otherwise. Thus all that is necessary is to specify atomname, sfac, x, y and z, and leave the rest to the program; when the atom is (later) made anisotropic using the ANIS command, the appropriate Uij constraints will be added. For a well-behaved structure, the list of atom coordinates (from direct methods and/or difference electron density syntheses) suffices. If the multiplicity factor (s.o.f.) is left out, it will be fixed at the appropriate value of 1 for a general position and less than 1 for a special position. Since SHELXL-93 automatically generates origin restraints for polar space groups, no atom coordinates should be fixed by the user for this purpose (in contrast to SHELX-76).
It may still be necessary to apply constraints by hand to handle disorder; a common case is that there are two possible positions for a group of atoms, in which the first set should all have s.o.f.'s of (say) 21, and the second set -21, with the result that the sum of the two occupation factors is fixed at 1, but the individual values may refine as fv(2) and 1-fv(2). Similarly if a special position with 2/m symmetry is occupied by Ca2+ and Ba2+, the two ions could be given the s.o.f.'s 30.25 and -30.25 respectively. In this case it would be desirable to use the EADP instruction to equate the Ca2+ and Ba2+ (anisotropic) displacement parameters.
If U is given as -T, where T is in the range 0.5 < T < 5, it is fixed at T times Ueq of the previous atom not constrained in this way. The resulting value is not refined independently but is updated after every least-squares cycle.
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