Lindemann index

The Lindemann index is a simple measure of thermally driven disorder in atoms or molecules. The local Lindemann index is defined as:

${\displaystyle q_{i}={\frac {1}{N-1}}\sum _{j\neq i}{\frac {\sqrt {\langle r_{ij}^{2}\rangle -\langle r_{ij}\rangle ^{2}}}{\langle r_{ij}\rangle }}}$

Where angle brackets indicate a time average. The global Lindemann index is a system average of this quantity.

Care must be taken if the molecule possesses globally defined dynamics, such as about a hinge or pivot, because these motions will obscure the local motions which the Lindemann index is designed to quantify. An appropriate tactic in this circumstance is to sum the r_ij only over a small number of neighbouring atoms to arrive at each q_i. A further variety of such modifications to the Lindemann index are available and have different merits, e.g. for the study of glassy vs crystalline materials.

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