Making excited state MD faster: Extrapolation of transition densities for TD-DFT calculations

Excited state molecular dynamics simulations are a powerful computational tool for the study of photoinduced phenomena. These are often used in conjunction with linear response TD-DFT to get the excited state energy and its gradients. At each step of molecular dynamics simulation, the new molecular geometry is relatively close to the previous ones, suggesting that some extrapolation strategy can be applied, such that the results of the previous calculations, which are available for free, can be used to predict the result of the upcoming calculation. The prediction can then be used as a guess for the iterative solver to lower the number of iterations and thus the cost. In this contribution, we present an extension of the Grassmann extrapolation scheme to linear response TD-DFT, in which the knowledge about the manifold structure to which the solutions belong is used to make the extrapolation more accurate. The new extrapolation strategy is then tested on four systems, showing a significant acceleration of the excited state molecular dynamics.