The degree of conjugation in a -system has a significant impact on the energy levels of the Highest Occupied Molecular Orbital HOMO and the Lowest Unoccupied Molecular Orbital LUMO of a molecule. Conjugation refers to the overlapping of p-orbitals across alternating single and double bonds in a molecule, which allows for the delocalization of -electrons. This delocalization stabilizes the molecule and lowers the energy levels of its molecular orbitals.As the degree of conjugation increases, the energy gap between the HOMO and LUMO orbitals decreases. This is because the delocalization of -electrons across a larger conjugated system leads to a more significant stabilization effect, which lowers the energy of both the HOMO and LUMO orbitals. The reduced energy gap between these orbitals has several implications, including:1. Lower excitation energy: A smaller HOMO-LUMO gap means that less energy is required to excite an electron from the HOMO to the LUMO. This can result in the molecule having a lower energy absorption band and a longer wavelength of absorption in the UV-visible spectrum.2. Increased chemical reactivity: A smaller HOMO-LUMO gap can make the molecule more susceptible to nucleophilic and electrophilic attacks, as the energy barrier for these reactions is lowered.To obtain information about the HOMO and LUMO energies and the degree of conjugation from quantum chemical calculations, one can perform computational studies using methods such as Density Functional Theory DFT or Time-Dependent Density Functional Theory TD-DFT . These methods allow for the calculation of molecular orbital energies, including the HOMO and LUMO, as well as the excitation energies and oscillator strengths for the excited states.By analyzing the calculated molecular orbital energies and the energy gap between the HOMO and LUMO, one can gain insights into the degree of conjugation in the -system and its effect on the molecule's properties. Additionally, the calculated excitation energies and oscillator strengths can be used to simulate the UV-visible absorption spectrum of the molecule, providing further information about the impact of conjugation on the molecule's electronic transitions.