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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

bP at 0, 0.4669, 0.1667Al at 0.5339, 0.5339, 0O2 at 0.257, 0.4164, 0.1186O1 at 0.1235, 0.7078, 0.2677O1 at 0.8765, 0.5843, 0.0657aO2 at 0.743, 0.1594, 0.2147Al at 0.4661, 0, 0.3333P at 1, 0.4669, 0.1667Al at 0.4661, 1, 0.3333O1 at 0.4157, 0.2922, 0.399O2 at 0.5836, 0.8406, 0.4519Al at 0, 0.4661, 0.6667P at 0.5331, 0.5331, ½O1 at 0.2922, 0.4157, 0.601O2 at 0.8406, 0.5836, 0.5481O2 at 0.1594, 0.743, 0.7853O1 at 0.7078, 0.1235, 0.7323P at 0.4669, 0, 0.8333Al at 1, 0.4661, 0.6667P at 0.4669, 1, 0.8333O2 at 0.4164, 0.257, 0.8814O1 at 0.5843, 0.8765, 0.9343cAl at 0.5339, 0.5339, 1
drag to rotate · scroll to zoomLook along

P Z 15 · rcov 1.07 Å Al Z 13 · rcov 1.21 Å O Z 8 · rcov 0.66 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.

Distances

Interatomic distances, in Å.
atomneighbourdistancesymmetry of the neighbour
AlO11.7390x,y,z
O11.7390x-y,-y,-z+2/3
O21.7610-y+1,x-y,z-2/3
O21.7610-x+1,-x+y,-z+4/3
P3.0836-y,x-y-1,z-2/3
P3.0836-x+y+1,-x+1,z-1/3
P3.0867-y+1,x-y,z-2/3
P3.0867-x+y+1,-x,z-1/3
PO21.5065x,y,z
O21.5065x-y,-y,-z+5/3
O11.5120-y+1,x-y,z+1/3
O11.5120-x+1,-x+y,-z+4/3
Al3.0836-y+1,x-y,z+1/3
Al3.0836-x+y+1,-x,z+2/3
Al3.0867-y,x-y-1,z+1/3
Al3.0867-x+y+1,-x+1,z+2/3
O1P1.5120-x+y+1,-x+1,z-1/3
Al1.7390x,y,z
O12.4511y,x,-z+1
O22.4742-x+1,-x+y+1,-z+4/3
O22.4745-x+y+1,-x+1,z-1/3
O22.8033-x+1,-x+y,-z+4/3
O22.8598-y+1,x-y,z-2/3
O12.8852x-y,-y,-z+2/3
O2P1.5065x,y,z
Al1.7610-x+y+1,-x+1,z+2/3
O22.4388x-y,-y,-z+5/3
O12.4742-x+1,-x+y,-z+4/3
O12.4745-y+1,x-y,z+1/3
O12.8033-x+1,-x+y+1,-z+4/3
O12.8598-x+y+1,-x+1,z+2/3
O22.9335y,x,-z+2

Angles

Angles at each atom, in degrees.
atbetweenangle
AlO1 and O1112.101
O1 and O2109.587
O1 and O2106.435
O1 and P126.739
O1 and P17.174
O1 and P92.717
O1 and P119.336
O1 and O2106.435
O1 and O2109.587
O1 and P17.174
O1 and P126.739
O1 and P119.336
O1 and P92.717
O2 and O2112.792
O2 and P91.572
O2 and P109.062
O2 and P17.656
O2 and P114.860
O2 and P109.062
O2 and P91.572
O2 and P114.860
O2 and P17.656
P and P142.693
P and P106.450
P and P91.407
P and P91.407
P and P106.450
P and P122.489
PO2 and O2108.078
O2 and O1110.124
O2 and O1110.105
O2 and Al90.956
O2 and Al123.240
O2 and Al123.989
O2 and Al20.765
O2 and O1110.105
O2 and O1110.124
O2 and Al123.240
O2 and Al90.956
O2 and Al20.765
O2 and Al123.989
O1 and O1108.306
O1 and Al19.854
O1 and Al112.166
O1 and Al90.805
O1 and Al111.158
O1 and Al112.166
O1 and Al19.854
O1 and Al111.158
O1 and Al90.805
Al and Al122.508
Al and Al106.450
Al and Al91.418
Al and Al91.418
Al and Al106.450
Al and Al142.656
O1P and Al142.973
P and O135.847
P and O234.876
P and O234.866
P and O2109.025
P and O2131.161
P and O1162.882
Al and O1137.448
Al and O2153.859
Al and O2108.887
Al and O237.052
Al and O235.461
Al and O133.950
O1 and O260.315
O1 and O260.304
O1 and O2102.796
O1 and O2158.972
O1 and O1129.537
O2 and O259.053
O2 and O2138.864
O2 and O2119.884
O2 and O1159.923
O2 and O279.871
O2 and O2100.717
O2 and O1139.966
O2 and O262.386
O2 and O160.344
O2 and O158.410
O2P and Al141.579
P and O235.961
P and O135.019
P and O135.010
P and O1155.469
P and O1107.650
P and O2135.692
Al and O2157.712
Al and O1108.204
Al and O1133.135
Al and O136.513
Al and O134.953
Al and O233.604
O2 and O160.480
O2 and O160.468
O2 and O1160.475
O2 and O1138.270
O2 and O2126.286
O1 and O159.381
O1 and O1138.864
O1 and O177.919
O1 and O2103.531
O1 and O1122.254
O1 and O1102.229
O1 and O2157.773
O1 and O161.246
O1 and O259.752
O1 and O257.862

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.