Nondirect-Product\nLocal Diabatic Representation with\nSmolyak Sparse Grids

Modeling nonadiabatic conical intersection dynamics is\ncritical\nfor understanding a wide range of photophysical, photochemical, and\nbiological phenomena. Here we develop a nonadiabatic conical intersection\nwave packet dynamic method in the local diabatic representation using\nSmolyak sparse grids. Employing sparse grids avoids the direct-product\ngrids in configuration space and alleviates the exponential scaling\nof computation costs with the molecular size. Numerical demonstrations\nare first performed for a two-dimensional vibronic model of pyrazine,\nwhere the results using sparse grids are in excellent agreement with\nthose using direct-product grids, with sparse grids being much faster.\nMoreover, we demonstrate that for a four-dimensional pyrazine model,\nwhere direct-product grids are computationally infeasible, sparse\ngrids can provide almost exact results. The sparse grid local diabatic\nrepresentation method is further applied to a realistic model system\nof phenol photodissociation with much more complex potential energy\nsurfaces; the results using sparse grids still agree very well with\nthe direct-product grids. Finally, by combining with electronic structure\ncalculations, we apply our method to the Shin–Metiu model without\nquasi-diabatization. The sparse grid and direct-product grid results\nare in good agreement, with the sparse grid computational cost being\nhalf of the full grid.