Unit V: Electronic Structure of Molecules: Bonn-Oppenheimer Approximation – Electronic structure of H2+ - Ground and Excited states of H2– LCAO-MO Theory - VB Theory – Nature of Exchange - HF-SCF Theory –Definition of Chemical bond – Correlation - Configuration interaction - Electronic structure of Homo and Hetero Diatomics of Second Row – Bonds and Lone pairs vs MOs – Bond order – sp Mixing and Avoided Crossing - MO Configuration –Electronic States and Term Symbols.
## Basic Level Prompts
- What is the Bonn-Oppenheimer approximation, and why is it a cornerstone of quantum chemistry?
- Explain how the mass difference between electrons and nuclei justifies the Bonn-Oppenheimer approximation.
- Write the total Hamiltonian for the H₂⁺ molecule and show how the Bonn-Oppenheimer approximation simplifies it.
- Why is H₂⁺ considered the simplest molecule for studying molecular bonding?
- Using the LCAO method, construct the molecular orbital for H₂⁺ from hydrogen 1s atomic orbitals.
- What distinguishes a bonding orbital from an antibonding orbital in H₂⁺?
- Compare the energy of the bonding molecular orbital in H₂⁺ to the energy of the atomic orbitals from which it is formed.
- What is the ground state electron configuration of the H₂ molecule?
- Describe how the two electrons in H₂ occupy its molecular orbitals.
- How does electron spin influence the occupancy of molecular orbitals in H₂?
- Apply the Pauli exclusion principle to explain electron pairing in the H₂ molecule.
- What is the difference between singlet and triplet electronic states in a molecule like H₂?
- Explain the LCAO-MO theory and apply it to describe the bonding in H₂.
- Derive the mathematical form of the bonding and antibonding orbitals for H₂ using LCAO.
- Define bond order and calculate it for H₂ using its molecular orbital configuration.
- Provide a quantum chemical definition of a chemical bond in terms of electron density.
- How does the electron density distribution between two nuclei indicate the presence of a chemical bond?
- What is Valence Bond (VB) theory, and how does it differ from Molecular Orbital (MO) theory in describing bonding?
- Explain the role of orbital overlap in VB theory’s description of the H₂ bond.
- Use VB theory to describe the bonding in H₂, including the concept of a sigma bond.
- What is the exchange integral in VB theory, and why is it significant?
- Define the exchange interaction and its effect on electron behavior in molecules.
- How does the exchange interaction lower the energy of the H₂ molecule in its ground state?
- What is the Hartree-Fock (HF) method, and what is its goal in quantum chemistry?
- Explain the self-consistent field (SCF) approach in HF theory and how it refines the wavefunction.
## Intermediate Level Prompts
- Describe how the HF method approximates the many-electron wavefunction for a molecule like H₂.
- Define the Fock operator and explain its role in solving the Hartree-Fock equations.
- Write the Roothaan-Hall equations and explain how they transform the HF problem into a matrix form.
- Compare the restricted and unrestricted Hartree-Fock methods for treating electron spin.
- Why does the HF method fail to fully account for electron correlation in molecules?
- Define electron correlation energy and explain its physical significance.
- What is configuration interaction (CI), and how does it address limitations of the HF method?
- Derive the energy expression for a system improved by CI, starting from the HF wavefunction.
- What is a Slater determinant, and why is it essential for describing multi-electron systems?
- Construct the MO diagram for N₂ and describe its electronic structure.
- Draw the MO diagram for O₂ and explain why it is paramagnetic.
- Compare the MO diagrams of CO and N₂, highlighting differences due to electronegativity.
- Calculate the bond order of NO and predict its bond strength relative to N₂.
- Explain sp mixing in the context of hybridization and its effect on molecular orbitals.
- What is an avoided crossing, and how does it manifest in molecular energy level diagrams?
- Analyze how sp mixing alters the MO energy levels in a molecule like BeH₂.
- Write the MO configuration for the ground state of H₂ and justify its stability.
- List the possible electronic states of H₂ arising from its ground and first excited configurations.
- Derive the term symbol for the ground state of H₂ using its MO configuration.
- Explain the role of the total spin quantum number (S) in determining molecular term symbols.
- Differentiate between Σ, Π, and Δ electronic states in diatomic molecules with examples.
- Contrast the electronic structures of homonuclear (e.g., N₂) and heteronuclear (e.g., CO) diatomic molecules.
- How does molecular symmetry influence the classification of electronic states?
- Describe how VB theory accounts for lone pairs in a molecule like H₂O.
- Use VSEPR theory to predict the geometry of H₂O based on its bonds and lone pairs.
## Advanced Level Prompts
- Compare how VB and MO theories describe bonds and lone pairs in a molecule like NH₃.
- Derive the relationship between bond order and bond length for second-row diatomic molecules.
- Explain how bond order influences the vibrational frequency of a diatomic molecule like O₂.
- What is multi-reference configuration interaction, and when is it necessary?
- Analyze the limitations of the HF method in describing the dissociation of H₂.
- How does density functional theory (DFT) improve upon HF in treating electron correlation?
- Construct the MO configuration for an excited state of H₂ and predict its properties.
- Differentiate between vertical and adiabatic excitation energies with a diagram for H₂.
- Derive the dissociation energy of H₂ using its MO energy levels and compare it to experimental values.
- Explain how potential energy surfaces arise from the Bonn-Oppenheimer approximation.
- What are non-adiabatic effects, and how do they impact molecular dynamics?
- Discuss how the electronic structure of CO influences its reactivity as a ligand.
- Define frontier molecular orbitals (HOMO and LUMO) and their role in chemical reactions.
- Calculate the HOMO-LUMO gap for O₂ and relate it to its stability.
- Explain charge transfer in a heteronuclear diatomic molecule like HCl.
- How does electronegativity difference affect the ionic character of bonds in hetero diatomic molecules?
- Relate the dipole moment of CO to its electronic structure and bonding.
- Analyze the electronic structure of CO and its implications for its triple bond strength.
- How do unpaired electrons in O₂ contribute to its magnetic properties?
- Distinguish between diamagnetic and paramagnetic behavior using N₂ and O₂ as examples.
- Define spin-orbit coupling and its effect on molecular electronic states.
- Explain how spin-orbit coupling splits energy levels in the spectrum of a molecule like NO.
- State the selection rules for electronic transitions in diatomic molecules and justify them.
- Apply the Franck-Condon principle to explain the intensity of vibrational transitions in H₂.
- Interpret the rotational fine structure in the electronic spectrum of a diatomic molecule.
पिछ्ला सुधार: शुक्रवार, 11 जुलाई 2025, 11:21 AM