An efficient implementation of analytical nuclear gradients for linear-response time-dependent density functional theory in the plane wave basis

We present an efficient implementation of the analytical nuclear gradient of linear-response time-dependent density functional theory (LR-TDDFT) with the frozen core approximation (FCA). This implementation is realized based on the Hutter’s formalism and the plane wave pseudopotential method. Numerical results demonstrate that the LR-TDDFT/FCA method using a small subset of Kohn–Sham occupied orbitals are accurate enough to reproduce the LR-TDDFT results. Here, the FCA remarkably reduces the computational cost in solving the LR-TDDFT eigenvalue equation. Another challenge in the calculations of analytical nuclear gradients for LR-TDDFT is the solution of the Z-vector equation, for which the Davidson algorithm is a popular choice. While, for large systems the standard Davidson algorithm exhibits a low convergence rate. In order to overcome this problem, we generalize the two-level Davidson algorithm to solve linear equation problems. A more stable performance is achieved with this new algorithm. Our method should encourage further studies of excited-state properties with LR-TDDFT in the plane wave basis.