Analytical derivative techniques for TDDFT excited-state properties: Theory and application

We review our recent work on the methodology development of the excited-state properties for the molecules in vacuum and liquid solution. The general algorithms of analytical energy derivatives for the specific properties such as the first and second geometrical derivatives and IR/Raman intensities are demonstrated in the framework of the time-dependent density functional theory (TDDFT). The performance of the analytical approaches on the calculation of excited-state energy Hessian has also been shown. It is found that the analytical approaches are superior to the finite-difference method on the computational accuracy and efficiency. The computational cost for a TDDFT excited-state Hessian calculation is only 2-3 times as that for the DFT ground-state Hessian calculation. With the low computational complexity of the developed analytical approaches, it becomes feasible to realize the large-scale numerical calculations on the excited-state vibrational frequencies, vibrational spectroscopies and the electronic-structure parameters which enter the spectrum calculations of electronic absorption and emission, and resonance Raman spectroscopies for medium-to large-sized systems.