Transition metal complexes (TMCs) are a diverse family of compounds with applications to a range of fields, from medicinal chemistry to renewable energy. Recently, there have been growing efforts to develop graph neural network (GNN) approaches that can discover and design new TMCs with optimal properties. However, TMCs are difficult to express as graphs due to the metal d orbitals, and their representation can be ambiguous, with multiple possible graphs of different topologies or even disconnected graphs, which limits the applicability of GNNs. To address this gap, David Balcells and colleagues proposed a natural quantum graph representation (NatQG) for TMCs and its implementation into GNN models based on message-passing algorithms.
NatQG leverages electronic structure data from natural bond orbital (NBO) analysis to transform the quantum wavefunction into a set of localized molecular orbitals. Second-order perturbation analysis (SOPA) then uncovers the nature of the interactions between pairs of NBOs based on their energy differences. Together, NBO and SOPA data define the topology and inform the nodes and edges for two separate forms of NatQG graphs: a version with undirected edges and a version with edges directed along the donor–acceptor orbital interactions. These graphs are then used to develop GNNs for the prediction of TMC quantum properties: the authors embed the node and edge attributes of the NatQG graphs into existing GNNs, such as a message passing neural network (MPNN). Additionally, the authors generated a transition metal quantum mechanics graph dataset, with NatQG graphs of over 60,000 TMCs (including all thirty elements in the 3d, 4d, and 5d series) along with their density functional theory geometries and properties.
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