The excited state dynamics of a molecule differ from its ground state in several ways. In the ground state, a molecule is in its lowest energy configuration, with electrons occupying the lowest energy orbitals. When a molecule is excited, one or more electrons are promoted to higher energy orbitals, leading to changes in the electronic structure, geometry, and reactivity of the molecule. These changes can result in various phenomena, such as fluorescence, phosphorescence, and photochemical reactions.To study and quantify the differences between the excited state and ground state dynamics of a molecule, ab initio calculations can be employed. Ab initio methods are computational chemistry techniques based on quantum mechanics, which solve the Schrödinger equation for a molecular system without relying on empirical data. These methods can provide highly accurate results, but they can be computationally demanding.Here are some ways ab initio calculations can be used to study excited state dynamics:1. Vertical excitations: By calculating the energy difference between the ground state and excited states, one can determine the vertical excitation energies. These energies correspond to the energy required to promote an electron from the ground state to an excited state without any change in the nuclear geometry.2. Adiabatic excitations: In contrast to vertical excitations, adiabatic excitations take into account the changes in nuclear geometry upon excitation. By optimizing the geometry of both the ground and excited states, one can calculate the adiabatic excitation energies and compare the structural differences between the two states.3. Potential energy surfaces PES : Ab initio calculations can be used to map out the potential energy surfaces of both ground and excited states. By analyzing the PES, one can gain insights into the reaction pathways, transition states, and conical intersections that govern the excited state dynamics.4. Time-dependent density functional theory TD-DFT : TD-DFT is an extension of density functional theory DFT that allows for the calculation of excited state properties. By solving the time-dependent Schrödinger equation, one can obtain information about the excited state dynamics, such as excitation energies, oscillator strengths, and transition dipole moments.5. Non-adiabatic molecular dynamics NAMD : NAMD simulations can be performed using ab initio methods to study the excited state dynamics of a molecule in real-time. These simulations can provide information about the relaxation pathways, energy transfer processes, and photochemical reactions that occur in the excited state.In summary, the excited state dynamics of a molecule differ from its ground state in terms of electronic structure, geometry, and reactivity. Ab initio calculations can be employed to study and quantify these differences, providing valuable insights into the behavior of molecules in their excited states.