Blake A.J.(ed.) Crystal Structure Analysis

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302 The presentation of results

make small rotations to reﬁne this view. It is always a good idea to

explore a range of views in case a less obvious one proves to be the best.

Most programs will allow you to do this either by continuous rotation or

in small incremental steps and, unless you have a very large structure or

a really slow computer, the default rotation speed should be acceptable.

In fact, with faster processors you may need to slow the rotation rate for

smaller molecules to prevent their spinning too rapidly.

Most drawings are composed from atoms and the bonds linkingthem.

The connectivity information, which tells the program which atoms to

drawbonds between, can be input explicitly along with theco-ordinates,

but it is more common for the program to calculate the connectivity

array using values for covalent or other radii appropriate to each atom.

For example, the program may consider that two atoms are bonded

if their separation is less than the sum of their covalent radii (plus a

‘fudge factor’ to ensure that slightly longer bonds are not missed): if

the stored default covalent radius for carbon is 0.70 Å and the default

‘fudge factor’ is 0.40 Å then any pair of carbon atoms will be deemed

to be bonded if they are within (0.70 + 0.70 + 0.40) = 1.80 Å of each

other. This approach is generally valid for organic compounds, where

covalent radii are well deﬁned, and many users may be unaware of the

default values simply because they never need to change them. With

organometallic and inorganic compounds more care must be taken to

ensure that all relevant interatomic distances are considered. It may be

necessary to edit the connectivity list in order to add or remove speciﬁc

entries. There will be limits on the numbers of atoms and bonds that

can be handled within any particular program: these limits may be set

within the program, perhaps at compilation, or they may be determined

by the memory available.

19.5 Drawing styles

Awide range of representations is possible and it is important to choose

appropriately. The simplest is a stick drawing, where bonds are repre-

sented by straight lines: atoms are implied by bond intersections or

termini (Fig. 19.1). Some programs use this representation for rapid

preliminary assessment of the best viewing direction as it is the least

demanding in terms of computing power (and is therefore faster). It

may also be the best way to display some large molecules, where draw-

ing atoms as spheres or ellipsoids would seriously obscure the features

behind them.

Fig. 19.1 A simple stick drawing.

Fig. 19.2 A ball-and-spoke model.

A more usual style (ball-and-spoke, Fig. 19.2) involves displaying

atoms as spheres (circles in projection) with the bonds shown as rods.

The user can select the radii of the spheres and the width of the bonds,

alter the bond style and add shading or other effects to the atoms:

Figure 19.3 shows the styles available in SHELXTL/PC (Sheldrick, 2001).

Such features can be used to emphasize features of importance, such as

the co-ordination sphere in a metal complex (Fig. 19.4). Different bond

19.5 Drawing styles 303

types can be used to indicate π -bonded ligands in metal complexes, or

interactions such as intramolecular hydrogen bonds.

–1

–2

–3

–4

Fig. 19.3 A range of style for atoms and

bonds.

A highly informative type of plot, colloquially referred to as an

‘ORTEP’ after its best-known implementation (Johnson, 1965, 1976),

depicts atomic displacements as displacement ellipsoids. If the program

offers a range of ellipsoid styles (e.g. those labelled –4 to –1 in Fig. 19.3)

it will be possible to represent atomic motion and (to a limited extent)

differentiate atom types in the same drawing (Fig. 19.5). The ellipsoids

can be scaled in size to represent the percentage probability of ﬁnding

within them the electrons around the atom as it vibrates: this probability

level must always be quoted in the ﬁgure caption and a value of 50%

is typical, although values such as 20% or 70% are sometimes used to

obtain reasonable views of structures with particularly high or low U

values, respectively. Ellipsoid plots are uniquely helpful in highlight-

ing possible problems such as disorder that may not be obvious from

Fig. 19.4 The use of different styles for a metal complex.

Fig. 19.5 Different style for displacement ellipsoids.

304 The presentation of results

Fig. 19.6 A space-ﬁlling model.

the numerical U

values, even when these are available. In fact, some

crystallographers are suspicious of ball-and-spoke plots because disor-

der and other potential problems such as incorrect atom assignments

can be hidden, by either accident or intent.

In reality, of course, molecules do not consist of balls and spokes, and

these give a poor idea of the external shape and steric requirements of a

molecule. A more realistic representation is provided by a plot such as

Fig. 19.6, where the atoms are shown as spheres having van der Waals

radii rather than much smaller, arbitrary radii. These are referred to as

‘van der Waals’ or ‘space-ﬁlling’ plots and can be used to investigate

questions such as whether a central metal atom is fully enclosed by its

ligand array or exposed and therefore more likely to undergo reaction.

The program SCHAKAL (Keller, 1989) was the ﬁrst to allow you to dis-

play a composite picture of a ball-and-stick drawing of your molecule

within its van der Waals envelope.

The molecules to be included can be selected automatically by the

When adjusting the size of your graphics,

take care to not change it unequally in two

dimensions as it gives a distorted picture

that can be misleading:

Notice how much more acute the C–Si–C

angle looks above than below. To stop this

from happening, ensure that you always

have ‘Lock Aspect Ratio’ switched on:

program (using criteria such as distance from a reference point or a cer-

tain number of unit cells) but the default selection may not give the

best diagram. It is important to select and design packing diagrams in

order to bring out the points you wish to illustrate without introducing

unnecessary clutter. For this reason, the alternative approach of explic-

itly generating the required symmetry-equivalent molecules by the use

of symmetry operations and cell translations has much to recommend

it, even although it demands a higher level of understanding of crystal

symmetry and expertise in using the more advanced features of graph-

ics programs. Packing diagrams are frequently of poor quality and low

information content and suggest that to the maxim ‘one picture is worth

a thousand words’ should be added ‘but only if it is a good one’. If the

point of your packing diagram is merely to show that your molecules

form typical linear chains it may be more effective to convey this in

words. With some journals adopting a policy that only one illustration

of a structure is normally published, the ability to produce plots with

high information content is very useful. For example, it may be possible

toshow both asinglemolecule and thesalientfeaturesofits environment

in a single illustration (e.g. Fig. 19.7) rather than as two separate ones.

19.5 Drawing styles 305

H1W

H1 N1

H1W

01W

Fig. 19.7 A view of the environment of a reference molecule (labelled) showing the

hydrogen-bondingnetwork. The symmetry codes need to be deﬁned in the text or caption.

The important interactions between molecules should be made as clear

as possible, typically by the use of different bond types: for example, in a

structure containing two types of hydrogen bond these could be differ-

entiated using dashed and dotted lines while normal (intramolecular)

bonds are shown by solid lines. If your ﬁgure is to be a representation

of the packing you will probably want to include the outline of the unit

cell, with the axes labelled. The labelling of symmetry-related atoms

is a slightly difﬁcult area, as the method recommended by many jour-

nals (superscripted lower-case Roman numerals) is not easily available

in many graphics programs. Fortunately, it is usually possible to work

round this with a little ingenuity.

The captions to packing diagrams are probably one of the least

exploited ways to convey structural information. They are often limited

to ‘Fig. 2: a view of the crystal packing’ when they could contain concise

information about the view direction, the most important contacts and

distances and the resulting arrangement of molecules (see Fig. 19.8).

If you work with inorganic compounds, molecular representations

may be less appropriate than polyhedral plots in which groups of atoms

form polyhedral shapes (e.g. six oxygen atoms around a metal centre

can be linked to generate an octahedron), which are shown as opaque

solid shapes. Neighbouring polyhedra are linked through their vertices,

edges or faces to build up the structure. As with packing diagrams of

molecules the selection of suitable symmetry-equivalents is important

to the effectiveness of the illustration.

306 The presentation of results

Fig. 19.8 What would you suggest as a caption?

Fig. 19.9 A stereo pair, with separate left- and right-eye views.

19.6 Creating three-dimensional illusions

When even a simple three-dimensional structure is represented in two

dimensions there is loss of information and for more complex cases this

canbe quite misleading. Various techniques havebeendeveloped to give

an illusion of depth on the screen or on paper, including depth cueing,

the use of perspective, bond tapering, hidden-line removal and the use

of shading and highlights. Some techniques (e.g. depth cueing) work

better on a screen than on paper because of the different background

colours used. You may ﬁnd that your graphics program has the required

parameters already optimized, but conversely it may be rewarding to

adjust these so as to produce the best effects for your example. However,

bewareof overdoing effects such as perspective or bond tapering to such

an extent that the result looks ridiculous.

The traditional way to restore some depth to a ﬂat molecular plot is

by inducing stereopsis. A ‘stereo pair’ (Fig. 19.9) consists of two draw-

ings, one for each eye, with a suitable separation and slightly different

19.8 Textual information in drawings 307

rotations. When viewed, the two drawings should merge to give a com-

plete three-dimensional effect. Such pairs are not universally effective,

as a substantial proportion of the population literally cannot see the

point of them (they cannot get the two images to merge) and the effec-

tiveness should be compared with that of a ‘mono’ plot occupying a

similar area.

19.7 The use of colour

In the last few years colour plots of crystal structures have become

much more accessible, due to the wider availability of suitable soft-

ware, the falling price of high-quality colour printers and the greater

readiness with which many journals will publish colour plots, often at

no charge but only where referees are convinced that they enhance the

presentation signiﬁcantly. The use of colour is most effective where it

illuminates features that could not otherwise be easily identiﬁed: for

example, in a polymeric structure two different metal atoms may have

similar-looking high co-ordination and it might be impossible to ﬁnd

room for adequately sized labels to differentiate them. Colour codes

can be deﬁned in the ﬁgure caption or by means of a key panel. Other

applications include colour coding of different bonds or atoms; high-

lighting of important features; colour coding of different molecules or

structural motifs such as planes in packing diagrams; and sometimes

just because colour looks wonderful on a poster. As with many good

things, there are advantages in moderation: overuse of colour can be

distracting and, if all or most of the atoms are coloured, many of the

beneﬁts of its use may be lost. Note that there are certain loose conven-

tions about atom colours that you can use to convey more information:

orange for B, black for C, light blue for N, red for O, light green for F,

brown for Si, yellow for S, a darker green for Cl, and blue, green or red

for metals. You are under no obligation to use these colours, but using

other colour schemes will confuse at least some of those looking at the

plot. Colour is probably least effective if only thin atom outlines are

coloured and the colours are weak (yellow can be particularly problem-

atic): it is better to ﬁll the atom with a strong, vibrant colour. The use of

colour opens up the possibility of using variations in intensity to convey

depth information (depth cueing).

19.8 Textual information in drawings

Although the main constituents of a molecular plot will be atoms and

bonds, it is normal (but not always essential) to include text, most com-

monly atom labels such as C1, N2 or O(3), or atom types (C/N/O).

Unless colour or shading has been used to identify atom types, a draw-

ing consisting only of chemically indistinguishable atoms and bonds

is of limited use. Make sure that any labels are of a sufﬁcient size that

they will be legible at their ﬁnal reduced size (but not so huge that they

308 The presentation of results

overwhelm the structure) and placed so that they will not overlap or

merge with any atoms or bonds. Obviously, make sure the labels refer

to the correct atoms and do not leave any ambiguity. If the graphics pro-

gram inserts them automatically, do checktheir placement. One decision

is whether to have parentheses in your atom labels or not [e.g. C24 or

C(24)]: the latter require more space but in some circumstances can help

to avoid confusion [e.g. using some fonts the labels C11 and Cl1 may

look very similar, while C(11) and Cl(1) are clearly distinguished]. If the

program really cannot provide the text you need, you may be able to

transfer the plot into a graphical manipulation program (e.g. Adobe Pho-

toshop,Corel Paint Shop Pro).Journals now refuse to transfer hand-written

labels onto an unlabelled copy of the plot. It is not always necessary to

label every last atom, but any atoms referred to in the text or in a table

of selected molecular geometry parameters should be identiﬁed: for

example, in a co-ordination compound labelling the central metal and

the ligand donor atoms may sufﬁce. (You can always include a fully

labelled version for the referees and possibly for deposition.) Unless

they are of special signiﬁcance (e.g. involved in H-bonding) hydrogen

atoms are not normally labelled.

Other text may be included: this can be excellent on large posters,

but where ﬁgures will undergo reduction it is likely to become hard

to read. For example, adding bond lengths and angles to a drawing

may help interpretation, but only if they are legible. To avoid cluttered

drawings, some journals expressly forbid these additions and insist that

you relegate such text to the ﬁgure caption.

19.9 Some hints for effective drawings

(a) Decide on the content: this is usually obvious for a single molecule

but there is much more choice for packing diagrams. In some cases

the hydrogen atoms make it impossible to see the rest of the structure

and can be omitted, although you may wish to include those on O or N

atoms, for example.You can sometimes reduce clutter by devices such as

drawing a single bond (in a different style) from the metal to the centroid

of a co-ordinated benzene (or cyclopentadiene) ring rather than the six

(or ﬁve) bonds to the individual carbon atoms. Sometimes you need to

omit peripheral groups, or show only the ipso carbon of an aryl ring,

before you can see the salient parts of the molecule (you must state in

the ﬁgure caption that you have done this). In some cases you may ﬁnd

it impossible to show all the important features in a single view.

(b) Invest some time looking for the best viewing direction with the

minimum of overlap, especially where important atoms are concerned.

If an atom really cannot be manoeuvred into view you could add a

phrase such as ‘C8 is wholly obscured by C7’ to the ﬁgure caption.

size them by using a distinct style for the atoms or bonds involved?

For example, you can identify a metal’s co-ordination sphere by having

19.10 Tables of results 309

a distinct style for the ligand–metal bonds. If an atom has additional

co-ordination at a greater distance, the bonds involved can be shown

differently.

(d) If colour is effective use it in moderation to draw attention to

selected features of the structure.

(e) Choose the most effective representation to convey the informa-

tion you want, bearing in mind that some journals may have speciﬁc

requirements. Displacement ellipsoid plots certainly contain a lot of

information, but it may not be the information you want to convey.

Often, the most signiﬁcant atoms appear smallest because they have

higher atomic and co-ordination numbers and consequently have lower

displacement parameters. Furthermore, there is limited scope for differ-

entiating atom types (but see Fig. 19.5), whereas a ball-and-spoke model

allows more freedom to assign atomic radii and drawing styles. Avoid

theuseof similar styles for differentatoms as faraspossible:forexample,

styles 7, 8 and 9 in Fig. 19.3 may look identical if the circle representing

the atom is very small (e.g. in a packing diagram) or after reduction.

(f) Avoid clutter. In some cases you have to add atom labels but it

may be possible to be selective. Omitting parentheses may help, as will

calling the only phosphorus atom in the structure P1 or even P rather

than P01 or P001. Also, you may be able to label the carbon atoms using

only their numbers (i.e. omitting the atom type and any parentheses). If

there is no room to place a label close enough to an atom to identify it

uniquely, consider placing the label some distance away with a line or

arrow pointing to the atom.

(g) Take particular care with stereo views. Do they constitute a

good view? Most importantly, are they better than a larger mono view

occupying the same space?

(h) As mentioned earlier, different criteria apply for different publica-

tion formats. Are you preparing an illustration for a journal, a thesis, a

poster, a web page, or an overhead transparency? Do not unthinkingly

transfer a ﬁgure between formats without assessing its suitability. For

example, a web graphic that is so complex that it takes a long time to

download, or that is effective only on a very high resolution monitor, is

unlikely to reach a wide audience.

(i) If you are submitting results to a journal that allows only a limited

number of views (e.g. one) of any single structure, consider whether

ﬁgures can be combined without loss of information.

(j) Be creative and have fun – this part of crystallography allows you

more choice than any other. The original ORTEP manual (Johnson, 1965)

exhorted users to improve on the standard views produced from the

program – that is now easier than ever.

19.10 Tables of results

The main tables produced at the end of the structure reﬁnement will

comprise all or most of the following:

310 The presentation of results

• fractional atomic co-ordinates (with s.u.s) – and possibly U

or B

values – for the non-H atoms: the values may be multiplied by a conve-

nient factor (given in the table heading) to give integers, or expressed

as decimal numbers;

• atomic displacement parameters – normally as U

or B

– with s.u.s;

• fractional atomic co-ordinates – and possibly U

iso

or B

iso

values –

for H atoms that have not been reﬁned freely (those that have could

either be given here, with s.u.s, or moved into the ﬁrst table);

• molecular geometry parameters (bond lengths, valence angles, tor-

sion angles, intermolecular contacts, least-squares mean plane data, etc.)

– there will usually be two versions of these tables, a shorter list of

selected parameters for publication and a fuller listing (of the bonds

and angles at least) for refereeing and deposition;

• structure-factor tables.

It is also possible to tabulate crystal data and details of the structure

determination, although this is not efﬁcient in terms of space unless

you can combine data for at least two or three structures in one table.

Journals may have particular requirements, but if none are speciﬁed

(perhapsbecausethejournal rarelypublishescrystal structures),those of

the journals of the Royal Society of Chemistry or theAmerican Chemical

Society seem to be widely accepted.

Journals still vary enormously in their policies on crystallographic

data – what they will publish, what they require as supplementary data

and what they will deposit. Before you start to prepare a submission,

studythe relevantinstructions for authors(traditionallypublishedin the

ﬁrst issue of each year but now available on the journal’s web pages)

and follow them closely. There is, however, a strong trend towards pub-

lishing less, and many journals stopped publishing structure factors,

displacement parameters, fractional co-ordinates and full molecular

geometry (more or less in that chronological order) so that the selec-

tion of results for publication assumes greater importance (see below).

Many journals will require supplementary data in CIF format rather

than hard-copy, although for a time some remained a little suspicious

of electronic data and demanded both! Some reﬁnement programs will

produce tables of results automatically and, although these are useful,

they almost always beneﬁt from critical inspection and sometimes man-

ual adjustment of content and format, but you must exercise extreme

care not to introduce numerical or other errors.

19.11 The content of tables

19.11.1 Selected results

Selection almost always involves molecular geometry parameters as

co-ordinate data are usually complete – it is deﬁnitely not permissible

to include only the co-ordinates of what you consider the ‘interesting’

atoms. The selection of geometry parameters depends on the chemical

nature of the compound and the structural features that you want to

emphasize. These are often obvious: in a co-ordination compound you

19.11 The content of tables 311

might want to include only bonds involving a central metal and angles

subtended at it (torsion angles involving such metals may be produced

automatically but in most cases are not even worth archiving), but each

structure should be considered individually. There is no point in trying

to publish bond lengths that have been constrained during reﬁnement,

or that are unreliable because they fall in a region affected by disorder.

Extensive listing of the internal molecular geometry of typical benzene

rings, whether constrained or not, is useful only for refereeing purposes

and deposition. In many organic compounds there are no interesting

or unusual bond lengths or angles that merit publication, but a selec-

tion of torsion angles might be worth including. Mean values or ranges

may usefully supplant large numbers of individual values for similar

parameters.

19.11.2 Redundant information

Where a molecule lies on a crystallographic symmetry element, some

of its molecular geometry parameters will be equal or simply related

to each other and therefore not all need to be given. Strictly speaking,

only the unique set should be given and automatic table-generating rou-

tines may not be able to cope with this requirement. It may, however,

be sensible to include some redundant information to make the situa-

tion clearer, especially for a non-crystallographic audience. For example,

molecules of doubly bridged dinuclear metal complexes M

(μ − L)

contain four-membered rings and these are often found lying across

crystallographic inversion centres: by symmetry, the opposite M–Lbond

lengths are equal; the two M–L–M angles are equal; the two L–M–L

angles are equal; the MLML rings are strictly planar; and adjacent pairs

of M–L–M and L–M–L angles add up to exactly 180

◦

. The independent

parameters are two adjacent M–L bond lengths and one angle within the

ring. A mirror plane or a two-fold rotation axis instead of an inversion

centre will involve different relationships among the parameters, and

theserelationshipswill depend on the orientation of these symmetry ele-

ments. Similar arguments apply to the more common situation where a

structure contains a central, often metal, atom on a special position. For

example, a four-co-ordinate palladium atom on an inversion centre has

only two independent bond lengths and one independent angle.

When tables contain atoms that are related by symmetry to those

in the original asymmetric unit, for example in order to give a bond

lengthbetweentwoatomsrelated by a mirrorplane, these atoms must be

clearly identiﬁed (e.g. C5



, C5* and C5

could be symmetry-equivalents

of atom C5) and the symmetry operations denoted by



,*or

deﬁned in

a footnote.

19.11.3 Additional entries

Not all entries required for a molecular geometry table are necessarily

produced automatically. ‘Long’ bonds may be missed and have to be

inserted manually; short contacts such as those in hydrogen bonding