Table 3. Number of TLS groups with ADP matrices that are reproducible by explicit group motions (R _U ≤ 0.05).

PDB content (November 2016): 32 162 entries containing TLS records, 260 353 TLS groups in total. For 263 TLS groups all three matrices were zero and these groups were excluded from further work. Decomposition of TLS matrices into parameters of elemental motions was performed using (9), (10) and (11). The ‘Extracted groups’ column shows the total number of TLS groups for which parameter extraction was possible and ‘Extracted entries’ shows the number of PDB entries for which this was possible for all of the groups. ‘Wrong content’ shows the number of groups for which random-model generation was impossible for technical reasons and ‘Libration undefined’ shows the number of groups for which all libration matrices were zero. Other columns: overall motion (5), overall libration (6), conditions verified for each of the three librations of the group including their screw components (7) and conditions verified for each of the three pure librations of the group (8).

Method	Extracted entries	Extracted groups	Wrong content	Overall motion	Libration undefined	Overall libration	Individual screw	Individual libration
Equation (9)
Total	4290	88434	314	88120	167	87953	87953	87953
R U ≤ 0.05				45093		23042	6107	87908
Equation (10)
Total	4826	95152	332	94820	167	94653	94653	94653
R U ≤ 0.05				46627		24163	7478	94596
Equation (11)
Total	4826	95150	332	94818	167	94651	94651	94651
R U ≤ 0.05				57463		31395	11238	94590