Significant progress has been made by Chinese Scientists studied on development of fast and effective theoretical calculation approach for the excited-state Hessian in complex system.

Nowadays, the theoretical calculation for the excited-state Hessian in complex system.is one of cutting-edge research in chemistry. Most recently, the Chinese theoretical chemists made remarkable progress towards the development of fast and effective theoretical calculation approach for the excited-state Hessian in time-dependent density functional theory（TDDFT).

Under the financial support of National Nature Science of Foundation (NNSF) (Grant #: 21073168, 21290193), Concerned with the poor computational accuracy and numerical efficiency of the finite difference method, Prof. Wan-Zhen Liang's group in the USTC and XMU successfully realized computational first-order or second-order energy derivatives of electronic excited states with respect to nuclear coordinates or external electronic field within the framework of TDDFT. The successful realization of the analytical calculation on the excited-state Hessian within TDDFT has made the large-scale numerical calculations on the excited-state vibrational frequencies and other related physical quantities, such as the geometrical derivatives of the transition dipole moment, and photophysics process, become feasible for the medium-sized systems or large molecules. The computational program has been published in the quantum chemical software package so called Q-Chem. Their related works have been also published in such International Journals as (J. Chem. Phys. 135, 18411 (2011); J. Chem. Phys. 135, 18411 (2011); J. Chem. Phys. 134, 044114 (2011); J. Chem. Theory Comput. 8, 4474, (2012). )

Because the photochemistry and photophysics processes often occur in a certain environment, interactions between system and surrounding environment exist and result in energy, materials or information exchange, and thus have a non-negligible effect on system properties. Therefore, Liang’s research group developed hybrid system in complex environment, and accurate and efficient calculation methods and procedures, through combining of electronic structure methods and solvation model with molecular dynamics. The realization of these methods and procedures will further promote the theoretical study of excited-state dynamic process occurred in the solution and protein environment.