Are you certain? A word on similarity indices.

Daniel Tchoń, 1.07.2022

The difference between displacement parameters of individual atoms can be compared using a metric called similarity index. This index was introduced by Whitten & Spackman as S12 = 100 (1 – R12), where R12 is a measure of the overlap between the probability density functions described by two ADPs, U1 and U2, in the Cartesian frame.

Formula for R12

For two identical ADPs R12 = 1 and S12 = 0. The smaller the value of S12, the better the agreement between U1 and U2. When the similarity index is calculated for each pair of compared ADPs, the mean overall similarity index can be calculated. In hikari this averaging is performed both for all atoms, denoted as avg(*), as well as for all hydrogen atoms only, denoted as avg(H).

Animation presenting similarity index as a function of ellipsoid growing in all directions by a factor of 1.2
Animation presenting similarity index as a function of ellipsoid growing in all directions by a factor of 2.0
Animation presenting similarity index as a function of ellipsoid growing in one direction by a factor of 2.0
Animation presenting similarity index as a function of ellipsoid growing in one direction by a factor of 2.0
Animation presenting similarity index as a function of ellipsoid rotating
Animation presenting similarity index as a function of ellipsoid rotating
Structure of 2''AP-delta under 9kbar Structure of 2''AP-delta under 10kbar
Structure of 2''AP-gamma under 12kbar Structure of 2''AP-gamma under 17kbar
Structure of QOSZON after HAR Structure of QOSZON after HAR using NoMoRe
Structure of 2°AP-alpha under 0kbar Structure of 2°AP-alpha under 5kbar
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