Question

What is the symmetry of the bonding molecular orbital formed by a linear combination of the p_x or p_y atomic orbitals in a homonuclear diatomic molecule?

Answer 1

The Molecular Orbital method uses linear combinations of symmetry-related orbitals of bonded atoms, to form molecular orbitals that will contain all the electrons present in a molecule. The molecular orbitals should be considered as energy levels of the molecule. A corresponding energy level diagram is constructed. Electrons are introduced into the diagram and a net bond order is determined. The magnitude of the bond order depends on the number of electrons in the molecule and the type of molecular orbitals they occupy. Consider the MO analysis of bonding in hydrogen molecule as formed from two separated hydrogen atoms: Each separated hydrogen atom has one electron in its vs and it is in a 1s atomic orbital. Both electrons have the same energy, and this feature is represented by placing them at the same vertical level in the diagram. Next consider the shapes and trigonometric signs of s atomic orbitals. They are spherical in shape and have a positive trigonometric sign. Orbitals can overlap if they have the same symmetry and trigonometric sign. ONE linear combination is the SUM of their functions [y1s(H atom a) +y1s(H atom b) ] which can be diagrammed as shown to the right. The result INCREASES electron density directly between the two nuclei, and is a SIGNA BOND ( s ) The OTHER is the DIFFERENCE of their functions y 1s y 1s (H atom a) (H atom b) - This result decreases electron density directly between the two nuclei and is called a SIGMA ANTIBOND ( s * ) The sigma bonding MO ( s ) is MORE stable than the separated atoms and is represented on a LOWER level in the energy diagram, relative to the two separated hydrogen atoms. The sigma antibonding MO ( s * ) is LESS stable than the separated atoms and is represented on a HIGHER level in the energy diagram, relative to the two separated hydrogen atoms. The resulting molecular orbital energy diagram has three sections. The CENTER section displays energy levels for the molecule. Left and right sections display energies of separated atoms + + plus SUM Combination of two 1s atomic orbitals The signs are trignometric, NOT CHARGES. + + - DIFFERENCE Combination of two 1s atomic orbitals The signs are trignometric, NOT CHARGES. MINUS + - s * 1s