Where metal atoms are coordinated by ligands, or take part in interactions with other metals, when is it correct to consider that interaction as a covalent bond ? Is there some distance criterion that one can use ? Should one consider bonds to metal ions ? Unfortunately, throughout the history of structure determinations, there has been little or no consistency in how these questions have been answered.

The connectivity of entries in the CSD is usually stored as defined by the author of the paper in which the structure was reported. Different authors have used different criteria to decide whether a particular interaction should be considered covalent. An interatomic distance between, say, a copper atom and an oxygen atom of 2.8Å may be considered as a covalent bond by one person, or as a close approach or non-bonded interaction by another. The metals of Groups Ia and IIa are particularly difficult to treat consistently; in the case of ions, no formal covalent bonds may have been assigned at all.

Up to now, this has caused serious problems for those people who use the CSD to study the occurrence and geometries of metal coordination. The latest release of QUEST addresses this. It contains a new facility for the user to set their own distance criteria for which particular atoms in a structure should be assigned as coordinated to metal atoms, to calculate that coordination - selectively recalculating connectivity - as a QUEST search proceeds, and to display and tabulate accordingly.

New Commands

 The new facilities are not visible on the QUEST interface - they take the form of commands which may be entered using the MANUAL-MODE function in the 3D-CONSTRAIN sub-menu. The set values for MERAD, MECALC and MEXP are displayed in orange when SUMMARY is active, and they may be deleted in the normal way using DELETE-INSTRUCTIONS.

MERAD

The form of this command is:

 MERAD  atom-type   radius

e.g.      MERAD  Pb  1.8

This will set the elemental radius for lead to be used in the recalculation of connectivity initiated by the MECALC command (see below) during the subsequent QUEST search to 1.8Å, i.e. overwriting the default that would otherwise be used.
 
 

MECALC

The form of this command is:

 MECALC  atom-type-1   atom-type-2   tolerance

e.g.  MECALC  Pb    O    0.4

This means that during the recalculation of connectivity, any Pb-O distance that is less than the sum of lead and oxygenÆs elemental radii, plus the tolerance (in this case 0.4Å) will be assigned, displayed, and if required tabulated as a single covalent bond. The elemental radius used will be the default value for the CSD (see Appendix A) unless MERAD has been used to reset it for one or both of the elements involved.

The symbols used may be for single elements or for groups, using the default symbols used in the CSD (e.g. 1A, 2A, 7A, AA for any atom, etc.) or any set using the ELDEF commands.

Tolerances may be negative:

e.g. MECALC   Pb    C    -2.0

will not assign anything longer than the sum of lead and carbonÆs elemental radii MINUS 2Å as a bond. This is a method of removing unwanted bonds between specified elements.
 

MEXP

Many structures containing coordinated metal atoms are polymeric, and recalculation of connectivity using MECALC will add a large number to these as formally ionic atoms become connected. Recalculated polymeric structures are, by default, displayed in QUEST simply as the asymmetric unit with one polymeric link. This can cause problems during searching, as the ligand shells may be incomplete. The MEXP command forces the polymer to be expanded for search and display purposes to include complete ligands around all symmetry independent metal centres.

A warning is given in the QUEST journal file if this expansion produces too many atoms or bonds to generate the connectivity or diagram:

 <REFCOD> omitted: errors in new chemical/crystal connectivity

The MEXP command should therefore only be used if complete ligands are being searched for or displayed; if only the first coordination shell is important, omission of MEXP will enable the maximum number of hits to be retained.
 

DEFINE

Three new DEFINE commands have been introduced, to carry forward existing and recalculated connectivity information through for analysis in VISTA. They are analogous to the existing DEFINE LABname/number atom_number and DEFINE RADname/number atom_number commands, and take the same form. When set, they are displayed in green in the summary area :

DEFINE TCNname/number atom_number

 This can be used to tabulate the total coordination number for particular atoms in the structures found, whether existing or recalculated using MECALC (this is recommended for polymeric structures), allowing analysis in VISTA to take this into account.

DEFINE ANOname/number atom_number

 This command tabulates the atomic number of atoms found in the search, allowing the results to be selectively analysed in VISTA on the basis of element type. This is useful to sift out the individual elementsÆ structures found when using a group symbol as the central metal atom.

DEFINE VDWname/number atom_number

 This allows the tabulation of the atomsÆ van der WaalsÆ radius, either the default value for the element type or a user-defined value particular to the substructure test, set using the VDW command.
 

Matched and Unmatched Entries

 Use of the above commands is straightforward in the majority of CSD entries where the existing crystal connectivity (the 3D diagram) and the chemical connectivity (the 2D diagram) are perfectly matched. All the existing bond types, atomic charges etc. are retained in the recalculated connectivity, with any new bonds assigned as single.

 In cases where the entry is flagged as unmatched or partially matched, however, the crystal connectivity is used as the starting point where present, and the chemical connectivity is removed and recalculated, including new bonds introduced by MECALC, using the same algorithm as that employed in PreQuest. If the crystal connectivity is not present in the entry but atomic coordinates are, then connectivity is calculated for the whole structure using the default radii given in Appendix A and a tolerance of 0.4Å, before MECALC adjustments are made.
The results in some unmatched cases may not be chemically sensible due to any misplaced atoms or unresolved disorder. A warning message is displayed in the journal file:

 <REFCOD> not fully matched: reassigning bond types and charges
 

Output Formats

 Recalculated connectivities may be saved and output in MODEL, CIF, FDAT, GLIST and OUTPUT COORD. FDAT provides a means of visualising the new connectivity in PLUTO. PostScript output from QUEST shows the new 2D and 3D connectivity.

 The other output formats, MOL2, FCON, ASER, FSER and BCCAB, report the original, unchanged connectivity.

 In order to save a list of connections to metals with recalculated connectivity, the option SAVE MCOR must be used. This can be typed in the SEARCH sub-menu. A file <jobname>.mcor is produced, which includes fractional coordinates, ORTEP symmetry operator codes for all included atoms, and metal-ligand bond distances. An example is given in Appendix B.
 
 

Example

The effects of the above commands are best illustrated using a simple example. A search is set up to look for ligands coordinated to lead via the commonly coordinated atoms O, N, P and S, as part of a study into coordination numbers of lead. In QUEST, a substructure is sketched as shown above and the search is run (element symbol QA is a defined group meaning O,N, P or S).

The first hit is refcode AMBOPB, which is displayed as shown:

i.e. the lead atom is shown to have a coordination number of 2. If the search is allowed to proceed to completion, there are 294 hit entries (October 1998 release).

If the search is then repeated with the identical substructure, but with new commands as follows:

MERAD  Pb  1.8
MECALC  Pb   QA   0.4
MEXP
DEFINE TCN1 1

... the first hit is once again AMBOPB, this time displayed differently;
 

It can be seen that the lead atom now has a coordination number of 6 - a "bond" is now clear to one of the oxygen atoms in the nitrate ion, and coordination to oxygen and nitrogen atoms in neighbouring ligands make the structure a 3D framework.

Input of the .tab file produced to VISTA shows the total coordination number for the lead atom has been retained, allowing separation of different coordination numbers and study of different coordination geometries. In this simple example, bond and other geometries have not been tabulated, but it is possible in VISTA to plot a histogram of coordination numbers for lead.

Use of the save .mcor facility produces the file shown as Appendix B, with the central lead atom and the six atoms in the first coordination shell included.

If this search is allowed to proceed to completion, there are now 296 hits (October 1998 release). Thus with the slight expansion of coordination around the lead atoms, more structures have been brought into the study.
 
 

Appendix A: Default Covalent Radii in the CSD
 
 

EL R (Å) EL R (Å) EL R (Å) EL R (Å)
Ac 1.88 Er 1.73 Na 0.97 Sb 1.46
Ag 1.59 Eu 1.99 Nb 1.48 Sc 1.44
Al 1.35 F 0.64  Nd 1.81 Se 1.22
Am 1.51 Fe 1.34 Ni 1.50 Si 1.20
As 1.21 Ga 1.22 Np 1.55 Sm 1.80
Au 1.50 Gd 1.79 O  0.68 Sn 1.46
B  0.83 Ge 1.17 Os 1.37 Sr 1.12
Ba 1.34 H  0.23 P  1.05 Ta 1.43
Be 0.35 Hf 1.57 Pa 1.61 Tb 1.76
Bi 1.54 Hg 1.70 Pb 1.54 Tc 1.35
Br 1.21 Ho 1.74 Pd 1.50 Te 1.47
C  0.68 I  1.40 Pm 1.80 Th 1.79
Ca 0.99 In 1.63 Po 1.68 Ti 1.47
Cd 1.69 Ir 1.32 Pr 1.82 Tl 1.55
Ce 1.83 K  1.33 Pt 1.50 Tm 1.72
Cl 0.99 La 1.87 Pu 1.53 U  1.58
Co 1.33 Li 0.68 Ra 1.90 V  1.33
Cr 1.35 Lu 1.72 Rb 1.47 W  1.37
Cs 1.67 Mg 1.10 Re 1.35 Y  1.78
Cu 1.52 Mn 1.35 Rh 1.45 Yb 1.94
D  0.23 Mo 1.47 Ru 1.40 Zn 1.45
Dy 1.75 N  0.68 S  1.02 Zr 1.56
        X  0.00

The element symbol X is used occasionally when a site is (equally) occupied by two elements. The radius assigned to X is then often the mean of the two elemental radii.
 
 

Appendix B: An example .mcor file
 

AMBOPB
Pb1       0.326800  0.144900  0.166700
O1        0.374000 -0.343000  0.147000  1555   2.790
O4        0.335000  0.326000  0.356000  1555   2.456
O4A       0.165000 -0.174000  0.144000  2545   2.836
O5        0.339000 -0.046000  0.357000  1555   2.484
O5B       0.161000  0.454000  0.143000  2555   2.846
N1        0.510000  0.222000  0.222000  1555   2.564