2. Constructive and destructive interference (in phase and out-of-phase interaction) a. Sigma bond is achieved by head on overlap

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1 Discussion #1 Chapter 10 CH MOs TF s name: Your name: Discussion Section: 1. Atomic Orbital (s, p, d, f) vs. Molecular Orbital (σ, σ *, NB, π, π *, π nb ) a. Total Number of MO =Total Number of AO 2. Constructive and destructive interference (in phase and out-of-phase interaction) a. Sigma bond is achieved by head on overlap b. Bonding MO (σ, π) - Constructive interference in phase interaction c. Antibonding MO (σ *, π * ) - Destructive interference out-of-phase interaction d. π formed from side-by-side overlap of available p AO a. π * is out-of-phase overlap of available p AO b.π is in-phase side-by-side overlap of available p AO 3. Factors that affect the formation of MOs from AOs: S.O.E. i. Symmetry AOs must have a compatible orientation to achieve an overlap. ii. Overlap: If AO's have correct symmetry, consider how much they overlap. The greater the overlap, the greater the energy change relative to the AO energies. iii. Energy: If the pair of AO's has the correct symmetry and greatest overlap, consider

2 1. If you have two atoms that together have 5 atomic orbitals, when those atoms combine to form a molecule, how many molecular orbitals are you going to have? 2. Below on the left is an empty molecular orbital diagram of F 2. Below to the right are various molecular orbitals, with the inter-nuclear axes shown with a dotted line. You will fill in the boxes next to the molecular orbitals in part (a). You will fill in the circles on the molecular orbital diagram in part (b). Carefully follow the instructions below. A B 2p 2p C D 2s B 2s E F 2 Fluorine a. In the box to the right of the molecular orbitals formed in F 2 above, provide the proper name of each molecular orbital (e.g. σ 2s, π *, etc). b. Match each molecular orbital on the right to the molecular orbital diagram on the left. Show your answer by placing the letter in the circle beside the molecular orbital. Letter B is filled in for you. c. In the molecular orbital diagram above, populate both the atomic and molecular orbitals with electrons by putting arrows on the horizontal lines for F 2 and the fluorine atoms. All three systems are in the ground state. d. Using the diagram above to guide you, calculate the bond orders for the following species. F F 2 + : F 2 2- : e. Naturally Fluorine is a diamagnetic molecule. Let say in the planet far, far away we found a fluorine that is paramagnetic: proposed and draw the molecular orbitals that Fluorine must have to be paramagnetic. 2

3 3. (At Home) C 2 is naturally is diamagnetic and O 2 is paramagnetic. Proposed and draw the molecular orbitals that will make C2 paramagnetic. And Proposed and draw the molecular orbitals that will make O2 diamagnetic. 4. For each of the AO combinations below, draw the resulting MO. What do we call that resulting MO? a. Discuss any axes of symmetry the MO may have. b. Is this MO destructive or constructive interference (or neither or both)? c. (at home) Now draw as many other combinations of AOs that give, *, MOs as you can, using only s and p AOs. Discuss the relative energies of the resultant MOs you just drew. d. (at home ) Now draw as many other combinations of AOs that give, * MOs. 5. Which below describes the pairs of AO's in Li 2 according to increasing overlap and why? a. 1s + 1s < 2s + 2s < 1s + 2s b. 1s + 2s < 1s + 1s < 2s + 2s c. 1s + 1s < 1s + 2s < 2s + 2s 3

4 6. Draw two AO energy diagrams for the atoms in CN - one atom on the left and one atom on the right, leaving space in the middle. Draw a picture of each AO. Draw the MO energy diagram and pictures of the resulting MOs in between and fill them with the electrons for the molecule. a. Draw the MO diagram(hint : count how many AO you start with and how many valence electrons you have) b. Calculate the bond order. c. Is CN - diamagnetic or paramagnetic? d. Are the bonding electrons centered more on C or on the N? e. If an electron is removed, will this make the bond longer or shorter? 7. (At home on a separate piece of paper) Draw two AO energy diagrams for the following atoms in [C 2, N 2, O 2, F 2, HF, BF, HB +, HO + ], one atom on the left and one atom on the right, leaving space in the middle. Draw a picture of each AO. Draw the MO energy diagram and pictures of the resulting MOs in between and fill them with the electrons for the molecule. a. Calculate the bond order for each molecule. b. Discuss which of the molecular orbitals are responsible for single, double bonds, etc. c. Discuss the relative length, reactivity and strength of these bonds. d. What are the magnetic properties of these molecules? (Which one is diamagnetic and which one is paramagnetic.) 4

5 8. Atom A has a single valence electron. The ionization energy of A is 10 ev the energy of the AA bonding MO is σ AA = 13eV and of the AA antibonding MO is σ* AA = 5 Ev. -5 ev σ* 1s -10 ev -13 ev 1s 1s σ 1s a. Calculate the energy change, in ev, for the ion combination process A (g) + A(g) AA(g). Enthalpy of reaction = E f E i b. Calculate the energy change, in ev, for the ion combination process A - (g) + A(g) AA - (g). Enthalpy of reaction = E f E i 9. Atoms X and Y each have a single valence electron. The ionization energy of X is 5 ev and that of Y is 6 ev. The bond energy of XY is 5 ev. Calculate the energy of the XY bonding MO.(Answer:-8eV) 5

6 10. Below is a molecular orbital diagram for the hypothetical molecule XY. a) What is the first ionization energy of atom Y? IE Y = ev b) What is the first ionization energy of XY? IE XY = ev c) What is the bond energy of the reaction: XY + X + + Y (Answer: 4eV) d) What is the bond order of XY, XY +, XY 2+, XY? e) Arrange the following in order of decreasing of the bond dissociation energy XY, XY +, XY 2+, XY. 11. For a single-electron atom X, E σ1s = 12 ev, E σ1s* = 7 ev, and E 1s = 10 ev. What is ΔE for the reaction: X 2 X + X? (Answer: 1eV) 6

7 12. Consider the Ionization energies for H, Na, and F. Assume z is along the bond axis. Draw the correlation diagram for NaF and HF: HF: NaF: An Element: IE H 1s 13.6 ev F 2s 25.0 ev F 2p z 17.4 ev Na 3s 5.1eV a. Discuss the relative ionic and covalent character of NaF verses HF. [Hint: It might help if you look at the picture you just drew.] b. Which pair of AOs in HF will interact most strongly? a. H 1s + F 1s b. H 1s + F 2s c. H 1s + F 2p z d. H 1s + F 2p y e. C and D equally c. The bond pair in NaF is in the Na 3s + F 2p z MO. The bond pair in HF is in the H 1s + F 2p z MO. Which of the following is true? a. The bond pair is almost entirely on the F of HF b. The bond pair is almost entirely on the H of HF. c. The bond pair is almost entirely on the F of NaF. d. The bond pair is almost entirely on the Na of NaF e. (a) and (d) 13. Generally, the valence electrons on different atoms, rather than the core electrons, interact with one another. Choose the best explanation. A. Adjacent valence electron waves have the greatest overlap. B. Adjacent valence electron waves have the same energy. C. Core electron clouds have the wrong symmetry. D. Core electron clouds move with the wrong frequency. 14. How can one decide which diagram represents compound with the most ionic characteristic? 7

8 15. Atoms A and B each have a single valence electron. The ionization energy of A is 4 ev and that of B is 6 ev. The energy of the AB bonding MO is σ AB = 9 ev and of the AB antibonding MO is σ* AB = 2 ev Calculate the energy change, in ev, for the ion combination process A(g) + B (g) AB - (g).(answer:-4ev) 16. AO 1 and AO 2 are going to form MOs. Assume AO 1 and AO 2 have correct symmetry, greatest overlap, and are closest in energy. AO 1 has IE = 7 ev and AO 2 has IE = 9 ev. Draw a picture of this, clearly indicating the relative energies of all AOs and MOs. For each MO, discuss which AO contributes more to it. 17. AO 1 and AO 2 are going to form MOs. Assume AO 1 and AO 2 have correct symmetry, greatest overlap, and are closest in energy. AO 1 has IE =2 ev and AO 2 has IE =13 ev. Draw a picture of this, clearly indicating the relative energies of all AOs and MOs. For each MO, discuss which AO contributes more to it.!!! In Preparation for next week: 1. Review Lewis Structures!!!!!!! 2. SN is a steric number it represent number of atoms + number of lone pairs attached to the center atom. 3. Hybridized atomic orbital (sp 3 (SN=4), sp 2 (SN=3), sp (SN=2)) Example 1, of a σ frame with sp 3 hybridized atomic orbitals: CH 4 1s + 3 p orbitals = Four of sp 3 hybridized AOs (SN=4, with angle) Example 2: Using hybridized atomic orbitals above, sketch the σ frame for the MO structure for C 2 H 6 (Hint: first draw a Lewis structure, and determine steric number (SN) of the center atoms) 8

9 Example 3, of a σ frame with sp 2 hybridized atomic orbitals: 1s + 2 porbilas = Three sp 2 hybridized AOs and one free p AO perpendicular to the plane of the molecule. (SN=3, with 120 angle) Using the sp 2 hybrid orbitals shown Sketch σ frame structure for H 2 CCH 2 π frame correlation diagram will look like that: Example 4 of a σ frame with sp hybridized atomic orbitals: 1s + 1 p orbital = Two sp hybridized AOs and two free p AO perpendicular to the plane of the molecule and perpendicular to each other. (SN=2, with 180 angle) Using the sp hybrid orbitals shown, try to sketch MO structure for HCCH. (Sketch σ frame and π frame, draw π correlation diagram) 9

10 Example 5. Draw correlation diagram for H 2 O using hybridized AOs. (For help look at the example of CH 4 shown below.) Molecular Orbital Instructions: 1. Making correlation diagrams for π framework of polyatomic molecules a. Draw Lewis Structure and any resonance structures. i. Count the number of valence electrons ii. Assign hybridization of all the atoms A. Determine hybridization of the center atom(s) B. Terminal atoms will have the same hybridization of the center atom. b. Identify framework i. Identify number of bonds in the molecule and the number of e - involved ii. Identify number of lone pairs and the number of e - involved c. Identify π framework i. Determine the number of electrons involved in the π bonds A. # π(electrons)=#valence e - - (electrons)- lone pair(electrons) ii. Count the p AO s not involved in hybridization. iii. Sketch the corresponding π MO. iv. Rank them in terms of increasing energy (depending on number of loops) v. Fill the π MO s with the electrons involving in π bonds vi. Label the π MO s as bonding, antibonding and /or nonbonding Useful links: Bonding in diatomic molecules, Questions on Symmetry, Overlap, Energy, "Li bonding 1s and 2s electron clouds" "XY 2s correlation diagram" "XY 2s correlation diagram, bonding electron cloud, and dipolemoment" 10

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