caa a22 4500 60548788X CHVBK 20210128100453.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s00214-015-1720-9 doi (NATIONALLICENCE)springer-10.1007/s00214-015-1720-9 Benchmarks of graph invariants for hydrogen-bond networks in water clusters of different topology [Elektronische Daten] [Andrey Tokmachev, Andrei Tchougréeff, Richard Dronskowski] The diversity of the various forms of water stems from systems of hydrogen bonds. Cooperative behaviour of hydrogen-bond networks gives rise to unique properties of water systems. A number of approaches to understand and model the collective behaviour of hydrogen bonds and predict their properties on the basis of a small number of calculations have been put forward. Among them, the concept of graph invariants provides most general descriptors for hydrogen-bond networks, which are routinely used to predict properties of water systems. In the present work, we examine the formalism of graph invariants and propose its modification which may be beneficial for water structures with defects. To benchmark graph invariants, we carried out quantum-chemical calculations of more than $$10^7$$ 10 7 water clusters with different hydrogen-bond configurations. The quality of the approximation is studied as a function of the type of graph invariant and its order. The results demonstrate that the method is applicable only to cage-like structures without significant strains. Springer-Verlag Berlin Heidelberg, 2015 Water clusters nationallicence Hydrogen bonds nationallicence Graphs nationallicence Invariants nationallicence APSG nationallicence Tokmachev Andrey NBICS Centre, NRC Kurchatov Institute, Kurchatov Sq. 1, 123182, Moscow, Russia aut Tchougréeff Andrei Moscow Center for Continuous Mathematical Education, Bol'shoy Vlas'evskiy 11, 119002, Moscow, Russia aut Dronskowski Richard Institut für Anorganische Chemie, RWTH Aachen University, Landoltweg 1, 52056, Aachen, Germany aut Theoretical Chemistry Accounts Springer Berlin Heidelberg 134/10(2015-10-01), 1-8 1432-881X 134:10<1 2015 134 214 https://doi.org/10.1007/s00214-015-1720-9 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00214-015-1720-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Tokmachev Andrey NBICS Centre, NRC Kurchatov Institute, Kurchatov Sq. 1, 123182, Moscow, Russia aut NATIONALLICENCE 700 1- Tchougréeff Andrei Moscow Center for Continuous Mathematical Education, Bol'shoy Vlas'evskiy 11, 119002, Moscow, Russia aut NATIONALLICENCE 700 1- Dronskowski Richard Institut für Anorganische Chemie, RWTH Aachen University, Landoltweg 1, 52056, Aachen, Germany aut NATIONALLICENCE 773 0- Theoretical Chemistry Accounts Springer Berlin Heidelberg 134/10(2015-10-01), 1-8 1432-881X 134:10<1 2015 134 214