{'fraction_non_alphanumeric': 0.017133066818960593, 'fraction_numerical': 0.001142204454597373, 'mean_word_length': 5.84375, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Molecular packing and symmetry of two-dimensional crystals.

Periodic arrangements on surfaces resulting from monolayer formation are critical in determining the electronic structure of thin films, the adhesion of surface coatings, the properties of lubricants, and the polymorphic form of heteronucleated crystals. Unlike substrate-directed chemisorption, the process of physisorption is highly responsive to molecular structure and stands out as a controllable method of creating variable surface patterns with periodicities on the low end of the nanoscale. Despite decades of study focused upon such ordered structures, the principles guiding the formation of these two-dimensional crystals have been obscured by the lack of a systematic and critical compilation. Thus, prediction of two-dimensional structure based upon the composition of the individual building blocks remains in its infancy. Here we demonstrate through the compilation and analysis of a database of two-dimensional structures that molecular-scale patterns are dictated by the same factors that determine bulk crystal structure, but these factors give rise to different preferred packing symmetries. In marked contrast to three-dimensional systems, achiral molecules in two-dimensional crystals are likely to adopt chiral structures, and racemic mixtures are expected to produce enantiopure domains. The determination of plane group frequencies allowed experimental verification of Kitaigorodskii's 50-year old theory of close packing as applied to two-dimensional tiling. This fundamental comparison between bulk crystals and physisorbed monolayers provides new tools and directions for future exploration in the engineering of surfaces with prescribed two-dimensional patterns.