The optical properties of molecules are closely related to their electronic excited states. When a molecule absorbs or emits light, it undergoes a transition between different electronic states. These electronic transitions are responsible for various optical phenomena such as absorption, fluorescence, and phosphorescence. The energy difference between the initial and final electronic states determines the wavelength of the absorbed or emitted light.Quantum chemistry methods can be used to calculate the electronic excited states and their corresponding transition energies. These calculations provide valuable information about the optical properties of molecules, such as absorption spectra, emission spectra, and transition probabilities. Some common quantum chemistry methods used for these calculations include Time-Dependent Density Functional Theory TD-DFT , Configuration Interaction Singles CIS , and Coupled Cluster Singles and Doubles CCSD .Let's consider some specific examples of molecules and their electronic transitions:1. Ethylene C2H4 : Ethylene is a simple organic molecule with a double bond between the two carbon atoms. The lowest energy electronic transition in ethylene is the * transition, where an electron is promoted from the highest occupied molecular orbital HOMO to the lowest unoccupied molecular orbital LUMO . This transition is responsible for the absorption of ultraviolet light in the range of 150-200 nm.2. Benzene C6H6 : Benzene is an aromatic molecule with a conjugated system of six carbon atoms. The lowest energy electronic transition in benzene is also a * transition, but due to the extended conjugation, the transition energy is lower than that of ethylene. This results in the absorption of ultraviolet light in the range of 200-300 nm.3. -carotene: This molecule is responsible for the orange color of carrots and is an example of a conjugated polyene. The extended conjugation in -carotene leads to a series of electronic transitions in the visible region of the spectrum, resulting in strong absorption in the blue and green regions 400-500 nm and weak absorption in the red region 600-700 nm . This selective absorption gives -carotene its characteristic orange color.In summary, the optical properties of molecules are determined by their electronic excited states, and quantum chemistry methods can be employed to calculate these states and their corresponding transition energies. By understanding the relationship between electronic transitions and optical properties, chemists can design molecules with specific optical characteristics for various applications, such as solar cells, sensors, and light-emitting devices.