Parametrically Managed Activation Functions for Improved Global Potential Energy Surfaces for Six Coupled ⁵<i>A</i>′ States and Fourteen Coupled ³<i>A</i>′ States of O + O₂

We report new potential energy surfaces for six coupled ⁵<i>A</i>' states and 14 coupled ³<i>A</i>' states of O₃. The new surfaces are created by parametrically managed diabatization by deep neural network (PM-DDNN). The PM-DDNN method uses calculated adiabatic potential energy surfaces to discover and fit an underlying adiabatic-equivalent set of diabatic surfaces and their couplings and obtains the fit to the adiabatic surfaces by diagonalization of the diabatic potential energy matrix (DPEM). The procedure yields the adiabatic surfaces and their gradients, as well as the DPEM and its gradient. If desired one can also compute the nonadiabatic coupling due to the transformation. The present work improves on previous work by using a new coordinate to guide the decay of the neural network contribution to the many-body fit to the whole DPEM. The main objective was to obtain smoother potentials than the previous ones with better suitability for dynamics calculations, and this was achieved. Furthermore, we obtained suitably small deviations from the input reference data. For the six coupled ⁵<i>A</i>' surfaces, the 60,366 data below 10 eV are fit with a mean unsigned error (MUE) of 49 meV, and for the 14 coupled ³<i>A</i>' surfaces, the 76,733 data below 10 eV are fit with an MUE of 28 meV. The data below 5 eV fit even more accurately with MUEs of 37 meV (⁵<i>A</i>') and 20 meV (³<i>A</i>').