To determine the HOMO highest occupied molecular orbital and LUMO lowest unoccupied molecular orbital energies of the ethylene molecule C2H4 , we can use a simple molecular orbital MO calculation based on the linear combination of atomic orbitals LCAO method. Ethylene has a double bond between the two carbon atoms, which consists of a sigma bond formed by the overlap of sp2 hybrid orbitals and a pi bond formed by the overlap of unhybridized p orbitals. The hydrogen atoms are bonded to the carbon atoms through sigma bonds formed by the overlap of sp2 hybrid orbitals on carbon and 1s orbitals on hydrogen.The molecular orbitals of ethylene can be described as follows:1. C-C : formed by the overlap of sp2 orbitals on each carbon atom.2. C-H : formed by the overlap of sp2 orbitals on carbon and 1s orbitals on hydrogen.3. C=C : formed by the overlap of unhybridized p orbitals on each carbon atom.The HOMO in ethylene is the C=C orbital, which is the highest energy occupied molecular orbital. The LUMO is the * C=C orbital, which is the lowest energy unoccupied molecular orbital and is the antibonding counterpart of the C=C orbital.To determine the energies of the HOMO and LUMO, we can use quantum chemistry software packages like Gaussian or GAMESS to perform a molecular orbital calculation. However, without performing the actual calculation, we can only provide a qualitative description of the HOMO and LUMO energies.As for the potential for conjugation, ethylene itself does not have any conjugated system. However, if ethylene is part of a larger molecule with alternating single and double bonds such as in polyenes or aromatic compounds , it can participate in conjugation. Conjugation involves the delocalization of electrons across the pi orbitals of the conjugated system, which can lead to increased stability and unique chemical properties.