Last Name or Student ID

Transcription

1 11/05/18, Chem433 Exam # 2 Last ame or Student ID 1. (2 pts) 2. (9 pts) 3. (2 pts) 4. (2 pts) 5. (2 pts) 6. (2 pts) 7. (2 pts) 8. (4 pts) 9. (14 pts) 10. (10 pts) 11. (26/31 pts) 12. (25/27 pts) Extra Total: (100/107 pts) The exam consists of two parts. The first part is close book/ close notes with mostly conceptual problems. Give a brief explanation for maximum credit. You can submit corrections to your answers either online before midnight 11/5/18. If answered correctly, corrections will get you 50% of the face value. The second part is take-home. You should bring it to class on Wednesday, 11/7/18, to be submitted at the beginning of the class.

2 Part I. In class and collected after 1 hour. It is close book close notes portion with mostly conceptual problems. Give a brief explanation for a full credit. 1. (2 pts) How many radial and angular nodes can be found in 6f orbital? 2. (9 pts) Consider the ground state of H2 molecule a) (3 pts) Identify which of the wavefunctions below correspond to the ground state of H2 molecule in the MO and VB description, respectively. Be aware that one function represents neither. a) = (1sA(1)1sB(2) + 1sB(1)1sA(2)) ( (1) (2) - (1) (2)) b) = (1sA(1) + 1sB(1)) (1sA(2) + 1sB(2)) ( (1) (2) - (1) (2)) c) = (1sA(1) + 1sB(2)) (1sA(2) + 1sB(1)) ( (1) (2) - (1) (2)) b) (4 pts) Comment on what is the main difference between the MO and VB description. You may illustrate it by comparing the two functions you identified above. c) (2 pts) Can the states in answers for a) be characterized by certain values of the overall spin? If yes, what is the spin state for each of the two functions you identified? 3. (2 pts) Place the energies of the following orbitals in the order of increasing for carbon atom: a) E(1s) < E (2s) = E(2p) < E (3s) = E(3p) = E (3d) b) (E(1s) > E (2s) = E(2p) > E (3s) = E(3p) = E (3d) c) E(1s) < E (2s) < E(2p) < E (3s) < E(3p) < E (3d) d) E(1s) > E (2s) > E(2p) > E (3s) > E(3p) > E (3d) 4. (2 pts) Identify all alternant hydrocarbons among those shown below. a) b) c) d)

3 5. (2 pts) Bosons are particles that : a) have half an integer spin b) have an integer spin c) their multiparticle wavefunction is symmetric with respect to exchanging any two of them, (1,2) = (2,1) d) their multiparticle wavefunction is antisymmetric with respect to exchanging any two of them, (1,2) = - (2,1) e) a and c f) b and d g) a and d h) b and c 6. (2 pts) Homogeneous line broadening: a) explains doppler broadening b) explains lifetime broadening c) is described by a Lorentzian lineshape d) is described by a Gaussian lineshape e) b and c f) a and d 7. (2 pts) Identify the quantum numbers n, l and ml for an orbital sketched below. What is the name of this orbital? Different colors represent different signs of the wavefunction. 8. (4 pts) Calculate the portion of light transmitted through a 1.0 cm cell filled with M solution of tetraphenyl porphyrin at the 416 nm, where its extinction coefficient is = M -1 cm -1. Provide your answer in % of transmitted light.

4 9. (14 pts) Consider SiO molecule. a) (6 pts) Sketch its molecular orbital energy level diagram with the electrons placed in these orbitals for the ground electronic state. What is the ground state electron configuration? b) (2 pts) What is the bond order for the ground state? c) (2 pts) What is the spin of the lowest energy term for this configuration? d) (2 pts) Will its cation SiO have longer or shorter bond length? e) (2 pts) What is the degeneracy of rotational J = 5 state of SiO?

5 10. (10 pts) Hybrid sp 2 orbitals are constructed as linear combinations of an s, px, and py orbitals of the same atom. If one of the hybrid orbitals (not normalized) is h1 = (s + 2 ½ px) identify the other two. a) (3 pts) ormalize h1. Hint: Remember that s and px, py orbitals represent an orthonormal set. Calculate the norm, = <h1 h1> and renormalize to get h1 = h1/ ½ b) (7 pts) Identify h2 and h3. Make sure that these hybrid orbitals are orthogonal to h1 and each other and the same relative contribution p vs s. To achieve that, take each remaining hi = (s + aipx+ bipy)/ 1/2 with the norm the same as calculated above for h1.

6 11. (26/31 pts) Consider Ti 2+ ion. a) (2 pts) What is its ground electron configuration? b) (3 pts) What is its ground state term and its degeneracy? c) (3 pts) What are the possible states for this term and their degeneracies? d) (2 pts) Which one is of the lowest energy state? e) (2 pts) Explain why [Ar]3d 1 4s 1 is likely the lowest energy excited electron configuration. f) (3 pts) What is the lowest energy term for this configuration? Hint: Draw the orbital diagrams for all unfilled subshells and follow the Hund s rules for electron placement. g) (2 pts) What are the possible states for this term?

7 h) (2 pts) Transitions between which states in g) and c) are allowed? i) (2 pts) List all possible terms for [Ar]3d 1 4p 1 excited electron configuration. i) (2 pts) List all states for [Ar]3d 1 4p 1 excited electron configuration to which optical transitions are dipole allowed and identify the lowest energy one out of them. j) (Honors, 5 pts) Identify all other possible terms for the ground electron configuration of Ti 2+.

8 Part II. Take home and collected on Wednesday in class. You should be answering these questions without any help. If submitted in class, each correct answer gets 1.5 times of its face value. 12. (25/27 pts total) Consider a series of aromatic molecules (all satisfy the 4n+2 rule): benzene, pyridine, pyrazine, pyrimidine, and 1,3,5 triazine. Using Hückel approximation calculate the energies of their molecular orbitals and analyze them as suggested below. The values of the coulomb and resonance integrals for nitrogen with one p electron, like in these molecules, equal = C +0.5 CC and C = CC = 2.4 ev, respectively benzene pyridine pyrazine pyrimidine 1,3,5-triazine a) (5 pts) Compare it with that calculated using particle on a ring (POR) approximation with the assumption of identical C-C bond lengths of LCC = 1.39 Å and C- bond lengths of LC = 1.37 Å. For the estimate of ring diameter use R = 3 ½ /12 Li What are the shortcomings of this model as applied to these molecules and how can it be improved? Molecule R, A LUMO-HOMO max, nm benzene Pyridine Pyrazine Pyrimidine 1,3,5-triazine b) (10 pts) Calculate the wavelengths of the lowest energy transitions for all these molecules using the Hückel approximation with the above parameters. Hint: Construct the Hamiltonian matrices and calculate the energy eigen values. Identify HOMO and LUMO and calculate the energy differences for the transitions and the corresponding wavelengths of these transitions. You may use any software to identify the eigen values; for example, the one from the class web site. Molecule HOMO LUMO LUMO-HOMO max, nm benzene Pyridine Pyrazine pyrimidine 1,3,5-triazine

9 c) (5 pts) From the above found energies of the states, identify the electron affinity (EA) for each molecule d) (5 pts) From the above found energies of the states, identify the ionization energies (IP) for each molecule Molecule IP, ev EA, ev benzene Pyridine Pyrazine pyrimidine 1,3,5-triazine e) (2 pts, Honors) What is wrong with assigning the ionization energy to the HOMO energy in this case?

10 Extra Credit.1 (up to 15 pts) you would have to show it to me in person. Perform an analysis based on Hückel approximation for regioselectivity in electrophilic substitution for different substituent groups in benzene. For simplicity, let us use CH2 + as electron ( ) withdrawing group and CH2 as electron ( ) donating group. Does the analysis of only HOMO orbital automatically lead to the corresponding ortho/para and metha directing? - H 2 C + H 2 C