The relationship between the electronic excited states and the optical properties of a molecule is based on the fact that when a molecule absorbs or emits light, its electrons can be excited to higher energy levels or relax to lower energy levels. This process is responsible for the optical properties of the molecule, such as absorption and emission spectra, fluorescence, and phosphorescence.In quantum chemistry, electronic excited states can be described by the molecular orbitals, which are mathematical functions that describe the spatial distribution and energy of electrons in a molecule. When a molecule absorbs a photon, an electron is promoted from a lower-energy occupied molecular orbital HOMO to a higher-energy unoccupied molecular orbital LUMO . The energy difference between these orbitals corresponds to the energy of the absorbed photon and determines the wavelength of the absorbed light.To calculate the electronic excited states and optical properties of a molecule using quantum chemistry methods, several steps are involved:1. Construct the molecular geometry: The first step is to determine the three-dimensional structure of the molecule, which can be obtained from experimental data or by using computational methods such as molecular mechanics or quantum mechanical calculations.2. Calculate the molecular orbitals: Using quantum chemistry methods like Hartree-Fock, Density Functional Theory DFT , or post-Hartree-Fock methods e.g., Configuration Interaction, Coupled Cluster , the molecular orbitals and their corresponding energies can be calculated.3. Determine the electronic transitions: By analyzing the molecular orbitals, the possible electronic transitions between the occupied and unoccupied orbitals can be identified. These transitions correspond to the absorption or emission of light at specific wavelengths.4. Calculate the transition probabilities: The probability of each electronic transition can be calculated using the oscillator strength, which is a measure of the intensity of the absorption or emission. This can be computed using the dipole moment of the transition, which is related to the change in the electron distribution upon excitation.5. Obtain the optical properties: By combining the transition energies and probabilities, the absorption and emission spectra can be simulated. Other optical properties, such as fluorescence and phosphorescence lifetimes, can also be calculated using additional quantum mechanical methods, like time-dependent DFT or multi-reference methods.In summary, the relationship between electronic excited states and optical properties of a molecule is based on the electronic transitions between molecular orbitals upon absorption or emission of light. Quantum chemistry methods can be used to calculate these properties by determining the molecular orbitals, identifying the possible electronic transitions, and computing the transition probabilities.