SHELXL-93 provides a bewildering selection of (AFIX and HFIX) options for positioning and refining hydrogen atoms, as detailed in the section atom lists and least-squares constraints. For routine refinement, however, the riding model is a good choice for tertiary CH (HFIX 13), secondary CH2 (HFIX 23), ethylenic =CH2 (HFIX 93), acetylenic CH (HFIX 163), BH in polyhedral boranes (HFIX 153), and aromatic CH or amide NH (HFIX 43). The hydrogen coordinates are re-idealized before each cycle, and 'ride' on the atoms to which they are attached (i.e. the coordinate shifts are the same for both). In this riding model, the C-H vector remains constant in magnitude and direction, but its origin, i.e. the position of the carbon atom in the unit-cell, may move. Both C and H contribute to the derivative calculations which improves convergence. Alternatively AFIX (or HFIX) 14 etc. performs a similar riding refinement but allows the C-H distance to vary as well (keeping the C-H distances equal within a CH2 or CH3 group). It is possible to use SADI or DFIX to restrain chemically equivalent C-H distances involving different carbons to be equal.
Methyl and hydroxyl groups are more difficult to position accurately. If good (low-temperature) data are available the method of choice is HFIX 137 for -CH3 and HFIX 147 for -OH groups; in this approach, a difference electron density synthesis is calculated around the circle which represents the loci of possible hydrogen positions (for a fixed X-H distance and Y-X-H angle). The maximum electron density (in the case of a methyl group after local threefold averaging) is then taken as the starting position for the hydrogen atom(s). In subsequent refinement cycles (and in further least-squares jobs) the hydrogens are re-idealized at the start of each cycle, but the current torsion angle is retained; the torsion angles are allowed to refine whilst keeping the X-H distance and Y-X-H angle fixed. If unusually high quality data are available, AFIX 138 would allow the refinement of a common C-H distance for a methyl group but not allow it to tilt; a variable metric rigid group refinement (AFIX 9 for the carbon followed by AFIX 135 before the first H) would allow it to tilt as well, but still retain tetrahedral H-C-H angles and equal C-H distances within the group.
If the data quality is less good, then the refinement of torsion angles may not converge very well. In such cases the hydrogens can be positioned geometrically and refined using a riding model by HFIX 33 for methyl and HFIX 83 for hydroxyl groups. This staggers the methyl groups, and -OH groups attached to saturated carbons, as well as possible; -OH groups attached to aromatic rings are placed in one of the two positions in the plane. In either -OH case the choice of hydrogen position is then determined by best hydrogen bond (to an N, O, Cl or F atom) which can be created. For disordered methyl groups (with two sites rotated by 60 degrees from one another) HFIX 123 is recommended, possibly with refinement of the corresponding site occupation factors via a 'free variable' so that their sum is unity (e.g. 21 and -21).
The choice of a suitable (default) O-H distance is very difficult. O-H internuclear distances for isolated molecules in the gas phase are about 0.96 Angstroms (cf. 1.10 for C-H), but the appropriate distance to use for X-ray diffraction must be appreciably shorter to allow for the displacement of the center of gravity of the electron distribution towards the oxygen atom, and also for librational effects. Although the (temperature dependent) value assumed by the program fits reasonably well for O-H groups in predominantly organic molecules, appreciably longer O-H distances are appropriate for low temperature studies of strongly (cooperatively) hydrogen bonded systems - short H..O distances are always associated with long O-H distances. If there are many such O-H groups and good quality data are available, HFIX 88 (or 148) plus SADI restraints to make all the O-H distances approximately equal (with an esd of say 0.01) is a good approach.
Hydrogen atoms may also 'ride' on atoms in rigid groups (unlike SHELX-76); for example HFIX 43 could reference carbon atoms in a rigid phenyl ring. In such a case further geometrical restraints (SADI, SAME, DFIX, FLAT) are not permitted on the hydrogen atoms; this is the only exception to the general rule that any number of restraints may be applied to any atom, whatever constraints are also being applied to it. This is much more general than in SHELX-76.
If the hydrogen atoms are generated using HFIX, the standard option is to set the isotropic U's to -1.2 (-1.5 for methyl and hydroxyl) which is interpreted as 1.2 (or 1.5) times the equivalent isotropic displacement parameter of the last atom which did not use this facility. A good alternative is to use 'free variables' to constrain the U values of chemically equivalent hydrogens to be equal.
Hydrogen atoms are identified as such by their scattering factor numbers, which must correspond to a SFAC name H (or $H). Other elements which need to be specifically identified (e.g. so that HFIX 43 can use different default C-H and N-H distances) are defined similarly. However for the output of the PLAN instruction, hydrogen atoms are identified as those atoms with a radius of less the 0.4 Angstroms (this is not as illogical as it may sound; the PLAN output is concerned with potential hydrogen bonds etc., not with the scattering power of an atom, and SHELXL-93 has to handle neutron as well as X-ray data).
OMIT $H (or OMIT_* $H if residues are employed) combined with L.S. 0, FMAP 2 and PLAN -100 enables an 'omit map' to be calculated, which is a convenient way of checking whether there are actually electron density peaks close to the calculated hydrogen positions. In this omit map, the hydrogen atoms are retained but do not contribute to Fc; if a non-zero electron density appears in the 'Peak' column for one of these hydrogens in the Fourier output, then there was an actual peak in the difference electron density synthesis within 0.31 Angstroms of the expected hydrogen position.
There are a number of operations in SHELXL-93 in which hydrogen atoms are treated specially, for example in the connectivity array, in atom lists defined using the '>' and '<' symbols, in the atoms following the SAME, ANIS and AFIX instructions, and in the output generated by PLAN. This approach is very convenient for the vast majority of structure refinements. However it may be useful to know how the program decides which atoms are 'hydrogens' in order to be able to treat hydrogens as normal atoms. The program scans the SFAC instructions (either format) for an element named 'H', and if one is found, treats all atoms with this scattering factor number specially. If two or more scattering factors are named 'H', only the last one gets this special treatment, which provides a way of tricking the program into allowing both 'normal' and 'special' hydrogens. Similarly for neutron data, where an SFAC instruction is needed for each element anyway, one could if desired suppress the special treatment of hydrogens by labeling their SFAC instruction 'Hyd' or even 'D'.
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