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

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

Number or symbol

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

Label, x, y, z, and optionally occupancy and B

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

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Ca Z 20 · r_cov 1.76 Å O Z 8 · r_cov 0.66 Å C Z 6 · r_cov 0.76 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.
atom	neighbour	distance	symmetry of the neighbour
Ca	O1	2.4158	`-x+1/2,-y+3/2,z-1/2`
	O2	2.4455	`-x+1,-y+1,-z+2`
	O2	2.4455	`x-1/2,-y+1,-z+2`
	O2	2.5193	`x-1/2,y-1/2,-z+3/2`
	O2	2.5193	`-x+1,y-1/2,-z+3/2`
	O2	2.5502	`x,y,z`
	O2	2.5502	`-x+1/2,y,z`
	O1	2.6542	`x-1/2,y-1/2,-z+3/2`
	O1	2.6542	`x+1/2,y-1/2,-z+3/2`
	C	2.9052	`x,y,z`
	C	2.9385	`x-1/2,y-1/2,-z+3/2`
	C	2.9385	`x+1/2,y-1/2,-z+3/2`
C	O1	1.2784	`x,y,z`
	O2	1.2842	`x,y,z`
	O2	1.2842	`-x+1/2,y,z`
	C	2.8768	`-x+1/2,-y+3/2,z-1/2`
	C	2.8768	`-x+1/2,-y+3/2,z+1/2`
	Ca	2.9052	`x,y,z`
	Ca	2.9385	`x-1/2,y+1/2,-z+3/2`
	Ca	2.9385	`x+1/2,y+1/2,-z+3/2`
	O2	3.1065	`-x+1/2,-y+3/2,z+1/2`
	O2	3.1065	`x,-y+3/2,z+1/2`
	O2	3.1139	`-x+1/2,-y+3/2,z-1/2`
	O2	3.1139	`x,-y+3/2,z-1/2`
	O1	3.1745	`-x+1/2,-y+3/2,z+1/2`
O1	C	1.2784	`x,y,z`
	O2	2.2216	`x,y,z`
	O2	2.2216	`-x+1/2,y,z`
	Ca	2.4158	`-x+1/2,-y+3/2,z+1/2`
	Ca	2.6542	`x-1/2,y+1/2,-z+3/2`
	Ca	2.6542	`x+1/2,y+1/2,-z+3/2`
	O1	2.9805	`-x,-y+2,-z+2`
	O1	2.9805	`-x+1,-y+2,-z+2`
	O2	3.0751	`x-1/2,y+1/2,-z+3/2`
	O2	3.0751	`-x+1,y+1/2,-z+3/2`
	O2	3.1377	`-x+1/2,-y+3/2,z-1/2`
	O2	3.1377	`x,-y+3/2,z-1/2`
	C	3.1745	`-x+1/2,-y+3/2,z-1/2`
O2	C	1.2842	`x,y,z`
	O2	2.2187	`-x+1/2,y,z`
	O1	2.2216	`x,y,z`
	Ca	2.4455	`-x+1,-y+1,-z+2`
	Ca	2.5193	`x+1/2,y+1/2,-z+3/2`
	Ca	2.5502	`x,y,z`
	O2	2.7427	`-x+3/2,y,z`
	O2	3.0608	`-x+1,-y+1,-z+2`
	O2	3.0736	`x,-y+3/2,z-1/2`
	O2	3.0736	`x,-y+3/2,z+1/2`
	O1	3.0751	`x+1/2,y-1/2,-z+3/2`
	C	3.1065	`-x+1/2,-y+3/2,z-1/2`
	C	3.1139	`-x+1/2,-y+3/2,z+1/2`
	O1	3.1377	`-x+1/2,-y+3/2,z+1/2`

Angles

Angles at each atom, in degrees.
at	between	angle
Ca	O1 and O2	144.574
	O1 and O2	144.574
	O1 and O2	93.612
	O1 and O2	93.612
	O1 and O2	81.217
	O1 and O2	81.217
	O1 and O1	71.838
	O1 and O1	71.838
	O1 and C	75.392
	O1 and C	86.266
	O1 and C	86.266
	O2 and O2	68.216
	O2 and O2	112.129
	O2 and O2	76.481
	O2 and O2	75.535
	O2 and O2	103.774
	O2 and O1	143.439
	O2 and O1	75.820
	O2 and C	93.638
	O2 and C	127.198
	O2 and C	69.987
	O2 and O2	76.481
	O2 and O2	112.129
	O2 and O2	103.774
	O2 and O2	75.535
	O2 and O1	75.820
	O2 and O1	143.439
	O2 and C	93.638
	O2 and C	69.987
	O2 and C	127.198
	O2 and O2	65.957
	O2 and O2	171.382
	O2 and O2	121.006
	O2 and O1	50.779
	O2 and O1	112.655
	O2 and C	145.624
	O2 and C	25.779
	O2 and C	91.064
	O2 and O2	121.006
	O2 and O2	171.382
	O2 and O1	112.655
	O2 and O1	50.779
	O2 and C	145.624
	O2 and C	91.064
	O2 and C	25.779
	O2 and O2	51.573
	O2 and O1	120.724
	O2 and O1	72.407
	O2 and C	26.207
	O2 and C	146.040
	O2 and C	95.447
	O2 and O1	72.407
	O2 and O1	120.724
	O2 and C	26.207
	O2 and C	95.447
	O2 and C	146.040
	O1 and O1	138.337
	O1 and C	94.994
	O1 and C	25.789
	O1 and C	132.660
	O1 and C	94.994
	O1 and C	132.660
	O1 and C	25.789
	C and C	119.895
	C and C	119.895
	C and C	115.175
C	O1 and O2	120.205
	O1 and O2	120.205
	O1 and C	91.301
	O1 and C	96.448
	O1 and Ca	159.628
	O1 and Ca	64.587
	O1 and Ca	64.587
	O1 and O2	84.025
	O1 and O2	84.025
	O1 and O2	79.244
	O1 and O2	79.244
	O1 and O1	120.190
	O2 and O2	119.502
	O2 and C	87.870
	O2 and C	88.228
	O2 and Ca	61.276
	O2 and Ca	159.537
	O2 and Ca	58.558
	O2 and O2	112.629
	O2 and O2	76.572
	O2 and O2	112.214
	O2 and O2	76.265
	O2 and O1	76.659
	O2 and C	87.870
	O2 and C	88.228
	O2 and Ca	61.276
	O2 and Ca	58.558
	O2 and Ca	159.537
	O2 and O2	76.572
	O2 and O2	112.629
	O2 and O2	76.265
	O2 and O2	112.214
	O2 and O1	76.659
	C and C	172.251
	C and Ca	68.327
	C and Ca	71.860
	C and Ca	71.860
	C and O2	158.492
	C and O2	158.492
	C and O2	24.344
	C and O2	24.344
	C and O1	148.509
	C and Ca	103.924
	C and Ca	111.551
	C and Ca	111.551
	C and O2	24.400
	C and O2	24.400
	C and O2	158.548
	C and O2	158.548
	C and O1	23.742
	Ca and Ca	106.888
	Ca and Ca	106.888
	Ca and O2	114.880
	Ca and O2	114.880
	Ca and O2	81.734
	Ca and O2	81.734
	Ca and O1	80.182
	Ca and Ca	115.175
	Ca and O2	87.247
	Ca and O2	123.705
	Ca and O2	47.554
	Ca and O2	85.792
	Ca and O1	119.564
	Ca and O2	123.705
	Ca and O2	87.247
	Ca and O2	85.792
	Ca and O2	47.554
	Ca and O1	119.564
	O2 and O2	41.846
	O2 and O2	134.685
	O2 and O2	163.268
	O2 and O1	41.410
	O2 and O2	163.268
	O2 and O2	134.685
	O2 and O1	41.410
	O2 and O2	41.741
	O2 and O1	152.279
	O2 and O1	152.279
O1	C and O2	29.972
	C and O2	29.972
	C and Ca	119.833
	C and Ca	89.624
	C and Ca	89.624
	C and O1	113.414
	C and O1	113.414
	C and O2	134.084
	C and O2	134.084
	C and O2	77.160
	C and O2	77.160
	C and C	64.957
	O2 and O2	59.915
	O2 and Ca	116.350
	O2 and Ca	117.113
	O2 and Ca	61.466
	O2 and O1	139.960
	O2 and O1	86.237
	O2 and O2	144.783
	O2 and O2	111.815
	O2 and O2	88.311
	O2 and O2	67.506
	O2 and C	67.656
	O2 and Ca	116.350
	O2 and Ca	61.466
	O2 and Ca	117.113
	O2 and O1	86.237
	O2 and O1	139.960
	O2 and O2	111.815
	O2 and O2	144.783
	O2 and O2	67.506
	O2 and O2	88.311
	O2 and C	67.656
	Ca and Ca	108.162
	Ca and Ca	108.162
	Ca and O1	57.796
	Ca and O1	57.796
	Ca and O2	98.187
	Ca and O2	98.187
	Ca and O2	153.997
	Ca and O2	153.997
	Ca and C	175.210
	Ca and Ca	138.337
	Ca and O1	50.366
	Ca and O1	156.624
	Ca and O2	52.232
	Ca and O2	102.775
	Ca and O2	49.082
	Ca and O2	90.339
	Ca and C	71.040
	Ca and O1	156.624
	Ca and O1	50.366
	Ca and O2	102.775
	Ca and O2	52.232
	Ca and O2	90.339
	Ca and O2	49.082
	Ca and C	71.040
	O1 and O1	112.672
	O1 and O2	64.534
	O1 and O2	108.200
	O1 and O2	98.349
	O1 and O2	137.201
	O1 and C	121.222
	O1 and O2	108.200
	O1 and O2	64.534
	O1 and O2	137.201
	O1 and O2	98.349
	O1 and C	121.222
	O2 and O2	52.967
	O2 and O2	59.020
	O2 and O2	78.498
	O2 and C	77.543
	O2 and O2	78.498
	O2 and O2	59.020
	O2 and C	77.543
	O2 and O2	41.411
	O2 and C	23.469
	O2 and C	23.469
O2	C and O2	30.249
	C and O1	29.823
	C and Ca	129.759
	C and Ca	95.663
	C and Ca	92.518
	C and O2	149.751
	C and O2	123.202
	C and O2	79.789
	C and O2	79.448
	C and O1	136.424
	C and C	67.729
	C and C	67.428
	C and O1	79.872
	O2 and O1	60.043
	O2 and Ca	124.108
	O2 and Ca	122.979
	O2 and Ca	64.214
	O2 and O2	180.000
	O2 and O2	94.910
	O2 and O2	90.000
	O2 and O2	90.000
	O2 and O1	116.484
	O2 and C	69.077
	O2 and C	69.129
	O2 and O1	69.295
	O1 and Ca	124.702
	O1 and Ca	67.755
	O1 and Ca	119.614
	O1 and O2	119.957
	O1 and O2	150.065
	O1 and O2	70.595
	O1 and O2	73.300
	O1 and O1	142.040
	O1 and C	70.934
	O1 and C	73.646
	O1 and O1	94.165
	Ca and Ca	103.244
	Ca and Ca	104.465
	Ca and O2	55.892
	Ca and O2	53.782
	Ca and O2	145.872
	Ca and O2	52.841
	Ca and O1	89.754
	Ca and C	162.390
	Ca and C	62.458
	Ca and O1	55.098
	Ca and Ca	135.626
	Ca and O2	57.021
	Ca and O2	141.132
	Ca and O2	50.679
	Ca and O2	95.984
	Ca and O1	91.046
	Ca and C	73.862
	Ca and C	116.812
	Ca and O1	137.870
	Ca and O2	115.786
	Ca and O2	50.683
	Ca and O2	88.485
	Ca and O2	128.388
	Ca and O1	55.361
	Ca and C	69.260
	Ca and C	106.604
	Ca and O1	86.503
	O2 and O2	85.090
	O2 and O2	90.000
	O2 and O2	90.000
	O2 and O1	63.516
	O2 and C	110.923
	O2 and C	110.871
	O2 and O1	110.705
	O2 and O2	129.744
	O2 and O2	91.993
	O2 and O1	61.509
	O2 and C	117.807
	O2 and C	82.452
	O2 and O1	59.471
	O2 and O2	138.080
	O2 and O1	71.643

13 further angles are not shown — the table stops at 300. An angle table grows as the square of the neighbour count, so a small reduction in the radius removes a great many.

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.