(a) Interpretation: The approximate energies of the real system are to be evaluated if H 12 = H 21 = − 0.50 (arbitrary energy units). Concept introduction: The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equal to zero.

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Answer 1

Question

Chapter 12, Problem 12.49E

Interpretation Introduction

(a)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−0.50 (arbitrary energy units).

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equal to zero.

Interpretation Introduction

(b)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−5.0 (arbitrary energy units). The difference between the calculated energies and the energies from part a is to be stated.

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equals to zero.

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C This question shows how molecular orbital (MO) theory can be used to understand the chemical properties of elemental oxygen O₂ and its anionic derivative superoxide Oz. a) Draw the MO energy diagram for both O2 and O2. Clearly label your diagram with atomic orbital names and molecular orbital symmetry labels and include electrons. Draw the Lewis structure of O2. How does the MO description of O2 differ from the Lewis structure, and how does this difference relate to the high reactivity and magnetic properties of oxygen? ) Use the MO diagram in (a) to explain the difference in bond length and bond energy between superoxide ion (Oz, 135 pm, 360 kJ/mol) and oxygen (O2, 120.8 pm, 494 kJ/mol).

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-Page: 8 nsition metal ions have high-spin aqua complexes except one: [Co(HO)₁]". What is the d-configuration, oxidation state of the metal in [Co(H:O))"? Name and draw the geometry of [Co(H2O)]? b) Draw energy diagrams showing the splitting of the five d orbitals of Co for the two possible electron configurations of [Co(H2O)]: Knowing that A = 16 750 cm and Пl. = 21 000 cm, calculate the configuration energy (.e., balance or ligand-field stabilization energy and pairing energy) for both low spin and high spin configurations of [Co(H2O)]. Which configuration seems more stable at this point of the analysis? (Note that 349.76 cm = 1 kJ/mol) Exchange energy (IT) was not taken into account in part (d), but it plays a role. Assuming exchange an occur within t29 and within eg (but not between tz, and ea), how many exchanges are possible in the low in configuration vs in the high spin configuration? What can you say about the importance of exchange energy 07

Answer 2

Question

Chapter 12, Problem 12.49E

Interpretation Introduction

(a)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−0.50 (arbitrary energy units).

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equal to zero.

Interpretation Introduction

(b)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−5.0 (arbitrary energy units). The difference between the calculated energies and the energies from part a is to be stated.

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equals to zero.

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Answer 3

Question

Chapter 12, Problem 12.49E

Interpretation Introduction

(a)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−0.50 (arbitrary energy units).

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equal to zero.

Interpretation Introduction

(b)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−5.0 (arbitrary energy units). The difference between the calculated energies and the energies from part a is to be stated.

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equals to zero.

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Answer 4

Question

Chapter 12, Problem 12.49E

Interpretation Introduction

(a)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−0.50 (arbitrary energy units).

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equal to zero.

Interpretation Introduction

(b)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−5.0 (arbitrary energy units). The difference between the calculated energies and the energies from part a is to be stated.

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equals to zero.

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Answer 5

Chapter 12, Problem 12.49E

Interpretation Introduction

(a)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−0.50 (arbitrary energy units).

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equal to zero.

Interpretation Introduction

(b)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−5.0 (arbitrary energy units). The difference between the calculated energies and the energies from part a is to be stated.

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equals to zero.

Answer 6

Chapter 12, Problem 12.49E

Interpretation Introduction

(a)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−0.50 (arbitrary energy units).

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equal to zero.

Answer 7

Chapter 12, Problem 12.49E

Interpretation Introduction

(a)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−0.50 (arbitrary energy units).

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equal to zero.

Answer 8

Interpretation Introduction

(b)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−5.0 (arbitrary energy units). The difference between the calculated energies and the energies from part a is to be stated.

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equals to zero.

Answer 9

Interpretation Introduction

(b)

Interpretation:

The approximate energies of the real system are to be evaluated if H12=H21=−5.0 (arbitrary energy units). The difference between the calculated energies and the energies from part a is to be stated.

Concept introduction:

The secular determinant is used to solve the linear variation theory. The secular determinant is formed by the energy, overlap integrals and the energy eigenvalues. The energy of a given system is minimized by taking the secular determinant equals to zero.

Answer 10

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Answer 11

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Answer 12

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Answer 13

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Solution Summary: The author explains that the secular determinant is used to solve the linear variation theory.

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