Time-Dependent Density Functional Theory TDDFT is a quantum mechanical method used to investigate the electronic excited states and optical properties of molecules and materials. It is an extension of Density Functional Theory DFT , which is a widely used method for studying the ground-state properties of systems.TDDFT calculates electronic excited states and optical properties by solving the time-dependent Kohn-Sham equations. These equations describe the time evolution of the electron density in response to an external perturbation, such as an electromagnetic field. By solving these equations, TDDFT can determine the excitation energies and transition dipole moments of the system, which are related to the absorption and emission spectra.The main difference between TDDFT and other methods like Configuration Interaction CI and Coupled Cluster CC lies in the way they treat electron correlation. TDDFT is a single-reference method, meaning that it starts from a single Slater determinant usually the ground-state Kohn-Sham determinant and calculates the excited states by considering the response of the electron density to an external perturbation. This approach is computationally less demanding than CI and CC methods, which are multi-reference methods that explicitly consider the mixing of multiple electronic configurations to describe the excited states.CI and CC methods are generally more accurate than TDDFT, especially for systems with strong electron correlation effects. However, they are also more computationally expensive, making them less suitable for large systems or high-throughput calculations. TDDFT, on the other hand, provides a good balance between accuracy and computational cost, making it a popular choice for studying the electronic excited states and optical properties of a wide range of systems.In summary, TDDFT calculates electronic excited states and optical properties by solving the time-dependent Kohn-Sham equations, which describe the response of the electron density to an external perturbation. It is different from CI and CC methods in terms of its treatment of electron correlation and computational cost, offering a more efficient approach for studying the excited states of large systems.