Abstract
Structural complexity measures based on Shannon information entropy are widely used for inorganic crystal structures. However, the application of these parameters for molecular crystals requires essential modification since atoms in inorganic compounds usually possess more degrees of freedom. In this work, a novel scheme for the calculation of complexity parameters (HmolNet, HmolNet,tot) for molecular crystals is proposed as a sum of the complexity of each molecule, the complexity of intermolecular contacts, and the combined complexity of both. This scheme is tested for several molecular crystal structures.
Highlights
Nowadays, the most widespread method of assessment of the amount of information contained in a symbolic message is the calculation of so-called information entropy, introduced by Claude Shannon [1]
The calculation of complexity measures based upon Shannon information entropy has become a routine procedure for inorganic crystal structures [2,11,12,17]
A simple method of dividing atoms into equivalence classes with respect to their occupied orbits is of limited usefulness, especially for molecular crystals with a high symmetry of molecular constituents
Summary
The most widespread method of assessment of the amount of information contained in a symbolic message is the calculation of so-called information entropy, introduced by Claude Shannon [1]. Translational degrees of freedom and np is the total number of atoms in the reduced unit cell, along with the value of V*, characterizes the stability of a crystal structure Along this line, it was proposed recently to complement the informational complexity of a crystal structure by its coordinational complexity [15], which considers the number of degrees of freedom of atoms, depending on their site-symmetry group. It was proposed recently to complement the informational complexity of a crystal structure by its coordinational complexity [15], which considers the number of degrees of freedom of atoms, depending on their site-symmetry group This measure utilizes the classical entropy functional according to Shannon: H=. The 32 crystal classes are distributed over 18 abstract classes with a definite complexity (Table 1)
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