# Homework 2

- Page ID
- 204073

Name: ______________________________

Section: _____________________________

Student ID#:__________________________

## Q1

Normalize the following molecular orbital (on two different atoms)

\[ψ = ψ_{s,A} +λψ_{s,B}\]

where \(ψ_s\) and \(ψ_{s,B}\) are normalized and \(λ\) is a parameter. Use the notation \(S\) for overlap integral to simplify the result.

## Q2

The Cl−Sn−Cl bond angle in \(SnCl_2\) is close to 90°. What does this imply about the hybridization of the the central tin atom?

## Q3

If the unnormalized hybrid orbitals in water that that describe bonding are expressed as

\[|\psi_A \rangle = N \left( 0.61 | 2p_z \rangle + 0.79 | 2p_x \rangle - 0.5 | 2s \rangle \right)\]

\[|\psi_B \rangle = N \left( 0.61 | 2p_z \rangle - 0.79 | 2p_x \rangle - 0.5 | 2s \rangle \right)\]

- Use these expressions calculate the \(H-O-H\) bond angle in the water molecule.
- How does this compare with the experimental values?
- How would the bond angle change if the bonding wavefunction were using non-hybridized atomic orbitals?
- Calculate the s and p characters of the two wavefunctions.
- Why isn't the \( | 2p_y \rangle\) atomic orbital also mixed into the hybrid orbitals?

## Q4

What are the key aspects that separate valence bond theory from molecular orbital theory?

## Q5

Demonstrate that each of the three \(sp^2\) orbitals satisfies the orthonormality criteria for wavefunctions.

## Q6

Determine the valence electron configurations and bond orders in the following homonuclear diatomics: \(C^+_2\), \(C_2\), \(C^−_2\), \(N^+_2\), \(N_2\), \(N^−_2\), \(O^+_2\), \(O_2\), \(O^−_2\). Which species ones are paramagnetic?

## Q7

Consider the Walsh diagram for \(AH_2\) molecules:

- How many valence electrons does the \(NH_2^+\) ion have?
- According to the Walsh diagram, would you expect \(NH_2^+\) to be linear or bent?
- How many valence electrons does the \(BH_2^+\) ion have?
- According to the Walsh diagram, would you expect \(BH_2^+\) to be linear or bent?