AFIX Command

AFIX mn d [#] sof [11] U [10.08]

AFIX applies constraints and/or generates idealized coordinates for all atoms until the next AFIX instruction is read. The digits mn of the AFIX code control two logically quite separate operations. Although this is confusing for new users, it has been retained for upwards compatibility with SHELX-76, and because it provides a very concise notation. m refers to geometrical operations which are performed before the first refinement cycle (hydrogen atoms are idealized before every cycle), and n sets up constraints which are applied throughout the least-squares refinement. n is always a single digit; m may be two, one or zero digits (the last corresponds to m = 0).

The options for idealizing hydrogen atom positions depend on the connectivity table which is set up using CONN, BIND, FREE and PART; with experience, this can also be used to generate hydrogen atoms attached to disordered groups and to atoms on special positions. d determines the bond lengths in the idealized groups, and sof and U OVERRIDE the values in the atom list for all atoms until the next AFIX instruction. U is not applied if the atom is already anisotropic, but is used if an isotropic atom is to be made anisotropic using ANIS. Any legal U value may be used, e.g. 31 (a free variable reference) or -1.2 (1.2 times U_eq of the preceding normal atom). Each AFIX instruction must be followed by the required number of hydrogen or other atoms. The individual AFIX options are as follows; the default X-H distances depend on both the chemical environment and the temperature (to allow for librational effects) which is specified by means of the TEMP instruction.

m = 0: No action.
m = 1: Idealized tertiary C-H with all X-C-H angles equal. There must be three and only three other bonds in the connectivity table to the immediately preceding atom, which is assumed to be carbon. m = 1 is often combined with a riding model refinement (n = 3).
m = 2: Idealized secondary CH₂ with all X-C-H and Y-C-H angles equal, and H-C-H determined by X-C-Y (i.e. approximately tetrahedral, but widened if X-C-Y is much less than tetrahedral). This option is also suitable for riding refinement (n = 3).
m = 3: Idealized CH₃ group with tetrahedral angles. The group is staggered with respect to the shortest other bond to the atom to which the -CH₃ is attached. If there is no such bond (e.g. an acetonitrile solvent molecule) this method cannot be used (but m = 13 is still viable).
m = 4: Aromatic C-H or amide N-H with the hydrogen atom on the external bisector of the X-C-Y or X-N-Y angle. m = 4 is suitable for a riding model refinement, i.e. AFIX 43 before the H atom.
m = 5: Next five non-hydrogen atoms are fitted to a regular pentagon, default d = 1.42 A.
m = 6: Next six non-hydrogen atoms are fitted to a regular hexagon, default d = 1.39 A.
m = 7: Identical to m = 6 (included for upwards compatibility from SHELX-76). In SHELX-76 only the first, third and fifth atoms of the six-membered ring were used as target atoms; in SHELXL-93 this will still be the case if the other three are given zero coordinates, but the procedure is more general because any one, two or three atoms may be left out by giving them zero coordinates.
m = 8: Idealized OH group, with X-O-H angle tetrahedral. If the oxygen is attached to a saturated carbon, all three staggered positions are considered for the hydrogen. If it is attached to an aromatic ring, both positions in the plane are considered. The final choice is based on forming the 'best' hydrogen bond to a nitrogen, oxygen, chlorine or fluorine atom. The algorithm involves generating a potential position for such an atom by extrapolating the O-H vector, then finding the nearest N, O, F or Cl atom to this position, taking symmetry equivalents into account. If another atom which, (according to the connectivity table) is bonded to the N, O, F or Cl atom, is nearer to the ideal position, the N, O, F or Cl atom is not considered. Note that m = 8 had a different effect in SHELX-76 (but was rarely employed).
m = 9: Idealized terminal X=CH₂ or X=NH₂+ with the hydrogen atoms in the plane of the nearest substituent on the atom X. Suitable for riding model refinement (AFIX 93 before the two H atoms).
m = 10: Idealized pentamethylcyclopentadienyl (Cp*). This AFIX must be followed by the 5 ring carbons and then the 5 methyl carbons in cyclic order, so that the first methyl group (atom 6) is attached to the first carbon (atom 1). The default d is 1.42 A, with the C-CH₃ distance set to 1.063d. A variable-metric rigid group refinement (AFIX 109) would be appropriate, and would allow for librational shortening of the bonds. Hydrogen atoms (e.g. with AFIX 37 or 127) may be included after the corresponding carbon atoms, in which case AFIX 0 or 5 (in the case of a rigid group refinement) must be inserted before the next carbon atom.
m = 11: Idealized naphthalene group with equal bonds (default d = 1.39 A). The atoms should be numbered as a symmetrical figure of eight, starting with the alpha C and followed by the beta, so that the first six atoms (and also the last six) describe a hexagon in cyclic order. m = 11 is also appropriate for rigid group refinement (AFIX 116).
m = 12: Idealized disordered methyl group; as m = 3 but with two positions rotated from each other by 60 degrees. The corresponding occupation factors should normally be set to add up to one, e.g. by giving them as 21 (i.e. 1*fv(2) ) and -21 ( 1*(1-fv(2)) ). If HFIX is used to generate an AFIX instruction with m=12, the occupation factors are fixed at 0.5. AFIX 12n is suitable for a para methyl on a phenyl group with no meta substituents, and should be followed by 6 half hydrogen atoms (first the three belonging to one -CH₃ component, then the three belonging to the other, so that hydrogens n and n+3 are opposite one another). Disordered -CF₃ groups may also be generated in this way (with d=1.32).
m = 13: Idealized CH₃ group with tetrahedral angles. If the coordinates of the first hydrogen atom are non-zero, they define the torsion angle of the methyl group. Otherwise (or if the AFIX instruction is being generated via HFIX) a structure-factor calculation is performed (of course only once, even if many hydrogens are involved) and the torsion angle is set which maximizes the sum of the electron density at the three calculated hydrogen positions. Since even this is not an infallible method of getting the correct torsion angle, it should normally be combined with a rigid or rotating group refinement for the methyl group (e.g. mn = 137 before the first H). In subsequent least- squares cycles the group is re-idealized retaining the current torsion angle. -CF₃ groups may be generated in the same way (with d = 1.32).
m = 14: Idealized OH group, with X-O-H angle tetrahedral. If the coordinates of the hydrogen atom are non-zero, they are used to define the torsion angle. Otherwise (or if HFIX was used to set up the AFIX instruction) the torsion angle is chosen which maximizes the electron density (see m = 13). Since this torsion angle is unlikely to be very accurate, the use of a rotating group refinement is recommended (i.e. mn = 147 before the H atom).
m = 15: BH group in which the boron atom is bonded to either four or five other atoms as part of an polyhedral fragment. The hydrogen atom is placed on the vector which represents the negative sum of the unit vectors along the four or five other bonds to the boron atom.
m = 16: Acetylenic C-H, with X-C-H linear. Usually refined with the riding model, i.e. AFIX 163.
m > 16: A group defined in a FRAG...FEND section with code = m is fitted, usually as a preliminary to rigid group refinement. The FRAG...FEND section MUST precede the corresponding AFIX instruction in the '.ins' file, but there may be any number of AFIX instructions with the same m corresponding to a single FRAG...FEND section.

When a group is fitted (m = 5, 6, 10 or 11, or m > 16), atoms with non-zero coordinates are used as target atoms with equal weight. Atoms with all three coordinates zero are ignored. Any three or more non-colinear atoms may be used as target atoms.

'Riding' (n = 3, 4) and 'rotating' (n = 7, 8) hydrogen atoms, but not other idealized groups, are re-idealized (if m is 1, 2, 3, 4, 8, 9, 12, 13, 14, 15 or 16) before each refinement cycle (after the first cycle, the coordinates of the first hydrogen of a group are always non-zero, so the torsion angle is retained on reidealizing). For n = 4 and 8, the angles are reidealized but the (refined) X-H bond length is retained, unless the hydrogen coordinates are all zero, in which case d (on the AFIX instruction) or (if d is not given) a standard value which depends on the chemical environment and temperature (TEMP) is used instead.

n = 0

No action.

n = 1

The coordinates, s.o.f. and U or U_ij are fixed.

n = 2

The s.o.f. and U (or U_ij) are fixed, but the coordinates are free to refine.

n = 3

The coordinates, but not the s.o.f. or U (or U_ij) 'ride' on the coordinates of the previous atom with n not equal to 3. The same shifts are applied to the coordinates of both atoms, and both contribute to the derivative calculation. The atom on which riding is performed may not itself be a riding atom, but it may be in a rigid group (m = 5, 6 or 9).

n = 4

This constraint is the same as n = 3 except that the X-H distance is free to refine. The X-H vector direction does not change. This constraint requires better quality reflection data than n = 3, but allows for variations in apparent X-H distances caused by libration and bonding effects. If there is more than one equivalent hydrogen, the same shift is applied to each equivalent X-H distance (e.g. to all three C-H bonds in a methyl group). n = 4 may be combined with DFIX or SADI restraints (to restrain chemically equivalent X-H distances to be equal) or embedded inside a rigid (n = 6) group, in which case the next atom (if any) in the same rigid group must follow an explicit AFIX instruction with n = 5. Note that n = 4 had a different effect in SHELX-76.

n = 5

The next atom(s) are 'dependent' atoms in a rigid group. Note that this is automatically generated for the atoms following an n = 6 or n = 9 atom, so does not need to be included specifically unless m has to be changed (e.g. AFIX 35 before the first hydrogen of a rigid methyl group with AFIX 6 or 9 before the preceding carbon).

n = 6

The next atom is the 'pivot atom' of a NEW rigid group, i.e. the other atoms in the rigid group rotate about this atom, and the same translational shifts are applied to all atoms in the rigid group.

n = 7

The following (usually hydrogen) atoms (until the next AFIX with n not equal to 7) are allowed to ride on the immediately preceding atom X and rotate about the Y-X bond; X must be bonded to one and only one atom Y in the connectivity list, ignoring the n = 7 atoms (which, if they are F rather than H, may be present in the connectivity list). The motion of the atoms of this 'rotating group' is a combination of riding motion (c.f. n = 3) on the atom X plus a tangential component perpendicular to the Y-X and X-H bonds, so that the X-H distances, Y-X-H and H-X-H angles remain unchanged. This constraint is intended for -OH, -CH₃ and possibly -CF₃ groups. X may be part of a rigid group, which may be resumed with an AFIX n = 5 following the n = 7 atoms.

n = 8

This constraint is similar to n = 7 except that the X-H distances may also vary, the same shifts being applied along all the X-H bonds. Thus only the Y-X-H and H-X-H angles are held constant; the relationship of n = 8 to n = 7 corresponds to that of n = 4 to n = 3. DFIX and SADI restraints may be useful for the X-H distances. This constraint is useful for -CF₃ groups or for -CH₃ groups with good data.

n = 9

The first (pivot) atom of a new 'variable metric' rigid group. Such a group retains its 'shape' but may shrink or expand uniformly. It is useful for C5H5 and BF4 groups, which may show appreciable librational shortening of the bond lengths. Subsequent atoms of this type of rigid group should have n = 5, which is generated automatically by the program if no other AFIX instruction is inserted between the atoms. Riding atoms are not permitted inside this type of rigid group. Only the pivot atom coordinates may be fixed (by adding 10) or tied to free variables, and only the pivot atom may lie on a special position (for the automatic generation of special position constraints).

Although there are many possible combinations of m and n, in practice only a small number is used extensively, as discussed in the section on hydrogen atoms. Rigid group fitting and refinement (e.g. AFIX 66 followed by six atoms of a phenyl ring or AFIX 109 in front of a Cp* group) is particularly useful in the initial stages of refinement; atoms not found in the structure solution may be given zero coordinates, in which cases they will be generated from the rigid group fit.

A rigid group or set of dependent hydrogens must ALWAYS be followed by 'AFIX 0' (or another AFIX instruction)! Leaving out 'AFIX 0' by mistake is a common cause of error; the program is able to detect and correct some obvious cases, but in many cases this is not logically possible.

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