Molecular Structure And Bonding Mock Tests

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 Cramer rule is used to solve the Hückel secular determinants. For butadiene (CH₂=CH-CH=CH₂), the Hückel secular determinant gives four π molecular orbital energies. The total π-electron binding energy (in units of β, where β < 0) for the ground state of butadiene (4 π electrons) is:

According to molecular orbital theory, which of the following species has the highest bond order? (Atomic numbers: N = 7, O = 8)

According to molecular orbital theory, why is O₂ paramagnetic?

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.)

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.)

The HOMO of 1,3-butadiene (in its ground state) has how many nodes between carbon atoms?

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