Molecular Structure And Bonding Mock Tests

In Hückel molecular orbital theory applied to the butadiene molecule (CH₂=CH−CH=CH₂, a linear conjugated system with 4 carbon atoms in the π system), the secular determinant yields four π molecular orbital energy levels. What is the total π-electron binding energy of butadiene in its ground state, expressed in terms of the Coulomb integral α and the resonance integral β? (Butadiene has 4 π electrons that fill the two lowest-energy MOs.)

What is the bond order and magnetic property of the superoxide ion O₂⁻ according to Molecular Orbital Theory? (Total electrons = 17)

Which of the following diatomic species has the shortest bond length? (Use molecular orbital theory to determine the bond order for each species. Higher bond order generally correlates with shorter bond length. Consider the effect of the number of electrons in bonding versus antibonding orbitals.)

According to molecular orbital theory, why is O₂ paramagnetic?

The Cramer rule is used to solve a system of linear equations arising from the LCAO-MO method. For the Hückel treatment of ethene (C₂H₄), the secular determinant is: |(α - E), β; β, (α - E)| = 0. The two π molecular orbital energies are:

The Frost circle (Frost-Musulin diagram) for benzene predicts that the π molecular orbital energy levels, in order from lowest to highest, are:

In the molecular orbital diagram of carbon monoxide (CO), a heteronuclear diatomic molecule, the highest occupied molecular orbital (HOMO) has which character? (Consider the relative orbital energies: oxygen is more electronegative than carbon, so oxygen atomic orbitals are lower in energy. The MO diagram shows that the 3σ orbital, derived primarily from carbon 2p_z and some 2s mixing, is the HOMO. Note that CO has 10 valence electrons: 4 from C and 6 from O.)

According to Molecular Orbital Theory (MOT), which species has the highest bond order and is diamagnetic?