Union of primitive internal coordinates when connectivity changes occur between reactants and products. Solid lines denote bonds and angles that do not exist on the complementary structure, while dashed lines are coordinates that exist for both reactant and product structures. Torsions are used but not shown.
Alanine dipeptide reactant and product configurations.
Convergence of alanine dipeptide reaction path using GSM (11 nodes). Each GSM iteration consists of 2 optimization cycles in the growth phase, and 3 after growth is completed. Note that GSM-CART and GSM-LST are converged until F = 0.1. At the first iteration, GSM-CART has F = 3.8 (not shown). Spikes in the perpendicular gradient (F) occur when new nodes are added. Though F increases during the growth phase of GSM-IC, addition of each new node occurs with sufficient accuracy that spiking is nearly eliminated.
Ammonia borane reactions (top) and associated transition states: B–H addition (left) and H2 elimination (right).
Investigated reactions with ethylene and cis-butadiene: Diels-Alder (top) and ene reaction (bottom).
Reactive intermediates in the taxadiene synthesis pathway. The transferring hydrogen is highlighted in red. Cartesian coordinates for the endpoints (reoptimized at the level of theory used in this article) and labels from Ref. 82 .
Approximate TS structures from GSM-CART (F = 0.4 and F = 0.1) and the exact TS for the ene reaction, select interatomic distances in Å. Note that the H that is being transferred from butadiene to ethylene is not as stretched at F = 0.1 compared to the exact TS. The exact TS structure has the H shared between the two Cs, and this feature is present in the F = 0.4 structure but not the F = 0.1 structure. GSM-IC at F = 0.1 with climbing image (not shown) produces a structure close to the exact TS: C–C distance 2.09 Å, C–H–C distances: 1.57 Å and 1.30 Å.
Summary of test reactions and their respective activation barriers (exact TS at unrestricted B3LYP level of theory, see computational details).
Gradients required to converge GSM reaction paths to specified optimization levels.
Number of gradients required for convergence of taxadiene reaction paths with GSM.
Initial guess structure and convergence data for TS searches using GSM-CART and GSM-IC for the B–H activation and ene reactions. The eigenvector following P-RFO method is used for the local search starting with an exact Hessian.
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