The energy of an excited state in a molecule is higher than that of the ground state. In a ground state, the electrons in a molecule occupy the lowest possible energy levels, while in an excited state, one or more electrons are promoted to higher energy levels. This promotion of electrons to higher energy levels requires energy, which is typically provided by absorption of light or through a chemical reaction. As a result, the energy of an excited state is always greater than the energy of the ground state.There are several methods used in quantum chemical calculations to determine the energy of excited states. Some of the most common methods include:1. Time-Dependent Density Functional Theory TD-DFT : TD-DFT is an extension of the widely used Density Functional Theory DFT that allows for the calculation of excited state energies. It involves solving the time-dependent Kohn-Sham equations, which describe the time evolution of the electron density in response to an external perturbation, such as an electromagnetic field.2. Configuration Interaction CI : CI is a post-Hartree-Fock method that involves the linear combination of Slater determinants, which represent different electronic configurations of the molecule. By including more and more Slater determinants in the calculation, the CI method can provide increasingly accurate estimates of the excited state energies.3. Coupled Cluster CC theory: CC is another post-Hartree-Fock method that involves the exponential ansatz for the wavefunction. It accounts for the electron correlation effects by considering the many-body interactions between electrons. The equation-of-motion coupled cluster EOM-CC approach is used to calculate excited state energies within the CC framework.4. Multi-reference methods: These methods, such as Complete Active Space Self-Consistent Field CASSCF and Multi-Reference Configuration Interaction MRCI , are particularly useful for systems where the ground and excited states are close in energy or have significant multi-configurational character. They involve the use of multiple reference wavefunctions to describe the ground and excited states, allowing for a more accurate description of the electronic structure.5. Quantum Monte Carlo QMC methods: QMC methods, such as Variational Monte Carlo VMC and Diffusion Monte Carlo DMC , involve the use of stochastic sampling techniques to approximate the ground and excited state wavefunctions. These methods can provide highly accurate results, but they are computationally expensive compared to other methods.Each of these methods has its own advantages and limitations, and the choice of the method depends on the specific system being studied and the level of accuracy required for the excited state energy calculations.