Nondirect-Product Local Diabatic Representation with Smolyak Sparse Grids

Modeling nonadiabatic conical intersection dynamics is critical for understanding a wide range of photophysical, photochemical, and biological phenomena. Here we develop a nonadiabatic conical intersection wave packet dynamic method in the local diabatic representation using Smolyak sparse grids. Employing sparse grids avoids the direct-product grids in configuration space and alleviates the exponential scaling of computation costs with the molecular size. Numerical demonstrations are first performed for a two-dimensional vibronic model of pyrazine, where the results using sparse grids are in excellent agreement with those using direct-product grids, with sparse grids being much faster. Moreover, we demonstrate that for a four-dimensional pyrazine model, where direct-product grids are computationally infeasible, sparse grids can provide almost exact results. The sparse grid local diabatic representation method is further applied to a realistic model system of phenol photodissociation with much more complex potential energy surfaces; the results using sparse grids still agree very well with the direct-product grids. Finally, by combining with electronic structure calculations, we apply our method to the Shin-Metiu model without quasi-diabatization. The sparse grid and direct-product grid results are in good agreement, with the sparse grid computational cost being half of the full grid.