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Interatomic Distances and Angles

The first thing anybody asks of a solved structure: how far apart are the atoms, and at what angles. Give a cell, a space group and the asymmetric unit — the page expands them by the symmetry, finds every neighbour inside a radius you choose, and names each one by the operation that produced it.

You supply
A unit cell, a space group and one atom per line of the asymmetric unit. Any constant or coordinate may carry its standard uncertainty in brackets, as a CIF writes it, and those are what the uncertainties below are propagated from.
Reading it
Uncertainties are propagated as if the parameters were uncorrelated, because a CIF does not carry the refinement’s variance–covariance matrix. That is not what a refinement program prints: for two atoms of one rigid group the correlation is usually positive, which makes the figure here larger. It is not an upper limit either.

Worked examples: Quartz, with uncertainties supplied · NaCl · Cu · α-Fe · CsCl · ZnS · quartz · cristobalite · berlinite · rutile · aragonite · ZrO2 · albite

Unit cell
Å
Å
Å
°
°
°

A constant may carry its standard uncertainty in brackets, exactly as a CIF writes it — 4.9137(2). That is what the uncertainties below are built from.

Space group

Conditions belong to a setting, not to a space group number. Pnma, Pbnm and Pmcn are one space group with its axes labelled three ways, and the three tables differ: the mirror that empties hk0 in one of them empties 0kl in another. Every setting in the International Tables is here with its own operations, so P21/n and P21/a answer for themselves.

Atoms in the asymmetric unit

One atom per line, for example Si 0.4697(1) 0 1/6. This is the same notation the structure factor page reads, so a list works on either — and a coordinate may carry its uncertainty, which only this page uses. A coordinate written as a fraction is one the symmetry fixes, and carries no uncertainty by definition.

How far to look
Å

Every neighbour inside this radius is listed. The angle table grows as the square of the neighbour count, so a small increase here is a large one there.

These are distances and angles, not bonds. Every neighbour inside the radius is listed; whether two atoms are bonded is a chemical judgement this page does not make. Contacts are found through every symmetry operation of the space group and across cell boundaries, so the list is the full environment and not only what lies inside one cell.

The cell, filled

Cu at 0, 0, 0Cu at 0, 1, 0bCu at ½, ½, 0Cu at 1, 0, 0Cu at 0, ½, ½aCu at ½, 0, ½Cu at 0, 0, 1Cu at 1, 1, 0cCu at ½, 1, ½Cu at 1, ½, ½Cu at 0, 1, 1Cu at ½, ½, 1Cu at 1, 0, 1Cu at 1, 1, 1
drag to rotate · scroll to zoomLook along

Cu Z 29 · rcov 1.32 Å

Hover an atom to name it. Click one to pin it and mark every copy of that site.

Every atom of the cell is drawn, including the symmetry-equivalent ones. An atom lying on a face, an edge or a corner belongs to each cell it touches and is drawn in all of them, so counting the spheres overcounts the contents of one cell. Colours are the standard CPK ones, and spheres are drawn at half the covalent radius (Cordero et al., 2008), reduced further only if that would make two of them run into each other — at full size two bonded atoms touch by definition. These are not ionic radii: in a salt the cation is drawn larger than the anion, which is the opposite of the ionic picture. No bonds are drawn, because which contacts are bonds is a chemical judgement this page does not make.

The symmetry the atoms obey

The atoms obey exactly the 192 operations of the space group given, and no others that this cell would permit.

Distances

Interatomic distances, in Å.
atomneighbourdistancesymmetry of the neighbour
CuCu2.5561x,y-1/2,z-1/2
Cu2.5561x,y-1/2,z+1/2
Cu2.5561x,y+1/2,z-1/2
Cu2.5561x,y+1/2,z+1/2
Cu2.5561x-1/2,y,z-1/2
Cu2.5561x-1/2,y,z+1/2
Cu2.5561x+1/2,y,z-1/2
Cu2.5561x+1/2,y,z+1/2
Cu2.5561x-1/2,y-1/2,z
Cu2.5561x-1/2,y+1/2,z
Cu2.5561x+1/2,y-1/2,z
Cu2.5561x+1/2,y+1/2,z

Angles

Angles at each atom, in degrees.
atbetweenangle
CuCu and Cu90.000
Cu and Cu90.000
Cu and Cu180.000
Cu and Cu60.000
Cu and Cu120.000
Cu and Cu60.000
Cu and Cu120.000
Cu and Cu60.000
Cu and Cu120.000
Cu and Cu60.000
Cu and Cu120.000
Cu and Cu180.000
Cu and Cu90.000
Cu and Cu120.000
Cu and Cu60.000
Cu and Cu120.000
Cu and Cu60.000
Cu and Cu60.000
Cu and Cu120.000
Cu and Cu60.000
Cu and Cu120.000
Cu and Cu90.000
Cu and Cu60.000
Cu and Cu120.000
Cu and Cu60.000
Cu and Cu120.000
Cu and Cu120.000
Cu and Cu60.000
Cu and Cu120.000
Cu and Cu60.000
Cu and Cu120.000
Cu and Cu60.000
Cu and Cu120.000
Cu and Cu60.000
Cu and Cu120.000
Cu and Cu60.000
Cu and Cu120.000
Cu and Cu60.000
Cu and Cu90.000
Cu and Cu90.000
Cu and Cu180.000
Cu and Cu60.000
Cu and Cu60.000
Cu and Cu120.000
Cu and Cu120.000
Cu and Cu180.000
Cu and Cu90.000
Cu and Cu60.000
Cu and Cu60.000
Cu and Cu120.000
Cu and Cu120.000
Cu and Cu90.000
Cu and Cu120.000
Cu and Cu120.000
Cu and Cu60.000
Cu and Cu60.000
Cu and Cu120.000
Cu and Cu120.000
Cu and Cu60.000
Cu and Cu60.000
Cu and Cu90.000
Cu and Cu90.000
Cu and Cu180.000
Cu and Cu180.000
Cu and Cu90.000
Cu and Cu90.000

About the uncertainties

No uncertainties are quoted, because none were given. Nothing in the cell or the coordinates above carries a bracket, so there is nothing to propagate. An absent uncertainty is not a zero one.

Write a constant as 4.9137(2) or a coordinate as 0.4697(1) and every distance and angle below will carry its own, split into the part that comes from the cell and the part that comes from the coordinates.

Contacts were searched out to 3.2 Å. A neighbour is named by the operation that produces it from the atom in the list above, written out in full rather than as a numbered code.

Where this comes from