A rigorous identification of all metastable polymorphs for better and safer drugs

近几十年来，已知晶体结构的数量以及为晶体结构预测等目的而创建的模拟结构呈指数级增长。晶体通常按对称群分类，然而鉴于它们是有限的和离散的，许多不同的晶体被分类在一起，几乎相同的结构可以被分类为不同的。这项研究的目的是开发一个周期结构的“连续”分类，其中所有晶体都生活在一个严格可参数化的“晶体等距空间”中。一个关键的公理是，由于晶体是刚性物体，“刚性运动”（平移+旋转）不会改变晶体，因此我们的晶体描述符也不应该在刚性运动下改变。这项工作考虑了更广泛的“等距”变换（刚性运动+反射）。在等距下不改变的晶体描述子称为“等距不变量”。与离散对称群相反，我们的“连续”等距不变量保证原子位置的微小变化会导致不变量的微小变化。本论文的贡献是晶体的连续等距不变量的集合，每个晶体都具有晶体学或几何学感兴趣的各种性质。我们将展示这些不变量的快速比较如何能够在剑桥结构数据库和晶体学开放数据库之间产生广泛的交叉条目列表，我们如何在这些数据库中发现错误条目，以及我们如何证明“晶体等距原理”：所有已知的非无序有机晶体都是由其原子中心的几何形状唯一决定的。

The number of known crystal structures, as well as simulated structures created for purposes such as crystal structure prediction, has risen exponentially in recent decades. Crystals are often classified by symmetry groups, however given they are finite and discrete, many otherwise distinct crystals are classified together, and nearly identical structures can be classified as different. The aim of this research is to develop a 'continuous' classification of periodic structures, where all crystals live in a rigorously parameterisable 'Crystal Isometry Space'.A key axiom is that since crystals are rigid objects, 'rigid motion' (translation + rotation) does not change a crystal, and therefore our crystal descriptors should not change under rigid motion either. This work considers the wider class of transformations 'isometry' (rigid motion + reflection). A crystal descriptor which does not change under isometry is called an 'isometry invariant'. As opposed to discrete symmetry groups, our 'continuous' isometry invariants guarantee that small changes in atomic positions result in small changes in the invariant.The contribution of this thesis is a collection of continuous isometry invariants of crystals each with various properties of interest to crystallography or geometry. We will show how fast comparisons of these invariants were able to produce an extensive list of cross-entries between the Cambridge Structural Database and Crystallography Open Database, how we discovered erroneous entries in these databases, and how we demonstrated the 'Crystal Isometry Principle': all known non-disordered organic crystals are determined uniquely by the geometry of its atomic centres alone.