Accelerating ab-initio calculations using semiempirical methods.

We report a general strategy to speedup the Time-Dependent Density Functional Theory (TDDFT) calculations of molecular response properties by leveraging semiempirical models. Instead of replacing expensive ab-initio methods with cheap semiempirical methods,  we use the semiempirical methods to accelerate the ab-initio calculations. As an example, we use a semi-empirical preconditioner in the iterative Davidson algorithm to accelerate the TDDFT excitation energy calculation, acquiring a cost reduction of 37-70%. The crucial advantage of using the semi-empirical preconditioner is that the converged result is unchanged, so there is no tradeoff between accuracy and speedup. Moreover,  the preconditioner can be further improved by tuning the empirical parameters that define the semiempirical model, leading to an additional cost reduction of 10 to 20%. A promising application of our work is non-adiabatic molecular dynamics, where significant cost reduction should be expected since excitation energies are computed millions of times.