When a hybrid functional is used in TDDFT, the contribution to the eigenvalue (excitation energy) is

(8) |

The response kernel for the hybrid PBE0 approximation has been implemented and tested. In doing so we came across a numerical instability that seems to occur only for systems with so-called `spurious' excited states [5]. The problem manifests in the production of negative eigenvalues.^{7} The instability appears to arise from a subtle interplay or the Hartree-Fock response and the PBE exchange-correlation response when the response density is very small, but non-zero. The problem is circumvented by increasing the granularity of CASTEP's fine grid (to `fine_grid_scale=4.0`

), which improves the quality of the numerical derivatives in the GGA response term.

While preparing for the implementation of the response terms for the B3LYP hybrid, it was discovered that the existing code used an incorrect calling sequence for the Becke 88 and LYP correlation routines. These routines are key components for the B3LYP implementation. The code was fixed and will be released in CASTEP version 5.5. The implementation of the B3LYP response terms is in progress.

Using purely Hartree-Fock exchange for TDDFT in the Tamm-Dancoff approximation is equivalent to CIS (configuration interaction with single substitutions). This function is also implemented.