Homework Assignments and Solutions from Spring 2007 Semester

Week 12

Recommendation:  Chapter 12: 3, 5, 6, 11

Chapter 13: 1, 2, 5, 6

Exam 2 Solutions: img007.pdf: First 2 pages of exam 2 solutions

img008.pdf: Pages 3 and 4 of exam 2 solutions

img009.pdf: Last page of exam 2 solutions

Week 11

Assignment

1.  Use H2C? =CH2 as a model system to understand pi-orbitals and pi-bond energy.    For this problem, use  the DFT method at the B3LYP? /6-31G(d,p) level of theory.

a) Find the optimized structure of ethene, IR spectrum and compared to the experimental gas-phase spectrum from NIST database, plot pi and pi* orbitals. 

b) calculate the LUMO and HOMO gap and compared to the result from Huckel theory.

c) pi-bond energy can be calculated by rotate one H2C? group by 90 degrees, i.e. breaking the pi-bond.  Optimize this structure.  The difference in the energy of this structure and that of ethene gives a good estimate of the pi-bond energy.

2) Delocalization energy in butadiene.  Use the same B3LYP? /6-31G(d,p) level of theory.

a) Optimize its structure, calculate the IR spectrum and compare to the experimental data.  

b) Plot the orbitals and orbital energy diagram.  Compare these to those from Huckle theory.

c) Delocalization energy can be estimated by rotating the --CH=CH2 90 degrees with repesting to the other group.   Perform just an energy calculation with this structure and plot the pi orbitals.   The difference in the energy of this structure with that of butadiene gives a good estimation of the delocalization energy.  Compare this result to that from Huckle theory.

Week 10

Assignment

1.  Calculate the total electronic energy of He atom using HF/STO-3G,  HF/3-21G, HF/3-21( p), MP2/STO-3G, MP2/3-21G, and MP2/3-21G(p) level of theory and compare your results with the 'exact' value of -2.9033 au.

2. Using Koopman's theory at the HF/6-31G(d,p) level to predict ionization energies of Ne and Ar atoms.  Compare your results with experimental data and other calculations shown in Table 8.3.

3. Calculate the orbital energy diagram for Kr at the HF/STO-3G.   From this result, write down the electronic configuration for Kr.  Plot and identify each orbital.

4.  Calculate the geometries of BH2 and H2O? at HF/STO-3G.  Plot the orbital energy diagrams.  Write the electronic configurations.  Explain the differences between the two.

5. Repeat problem 4 but for BH3 and NH3 molecules.

6. Chapter 11, problems:  19, 25, 26, 27, and 28.

Week 9:

Recommendation:  Chapter 9: 14, 17, 19, 25, 30, 31

Assigment: 

A.  For Li2, Be2, B2, C2, N2, O2, and F2 molecules, using the MolDesign? tool to calculate at the MP2/6-31G(d) level the following: 

1. Bond lengths

2. Frequencies

3.  orbital energies for the MO energy-diagrams.  Compare with Figure 9.13.

4. From the MO energy diagram, write the electronic configurations for these molecules and compare your results to Table 9.2.

5. Plot the orbitals and compare your results with Figure 9.20.

(select runtype = Opt & Freq)  Note that B2 and O2 are triplet ground-state while others are singlet.

B.  Repeat the same calculation for HF molecule and compare your results to Figs. 18 and 19.

Week 8:

Recommendation:  Chapter 8:  26-33

Assignment:  Textbook chapter 8:  34-37

Week 7:

Recommendation: Chapter 7: 20, 21, 24, 26

Assignment: Homework6.doc

Solutions to Exam1: exam1.pdf

Week 6:

Recommendation:  Chapter 7:  5, 6, 7

Assignment:  Chapter 7 of the textbook:  Problems 17 and  18

Week 5:

Recommendation: Chapter 6: 16, 17, 20,21, 24, 27, 29

Assignment: Homework_Set_5.doc

HW_5_solutions.pdf

This is a project for your benefit only:

• physchem_table.doc: Compare and Contrast Several Models

Week 4

Recommendation: Chapter 5: 13,16, 19, 23,30, 37

Assignment: Homework_Set_4.doc

HW_4_Solutions.pdf

chart1_physchem.doc: Potentially useful information

Week 3

Recommendation: Chapter 3: 16, 20, 21, 22 Chapter 4: 7, 16, 17, 26

Assignment: Homework_Set_3.doc

HW_3_Solutions.pdf

Week 2

Recommendation: Chapter 3: 2, 3, 6, 7, 11, 12, 17, 27

Assignment:

Problem #1: Which of the following wavefunctions are 'acceptable' wavefunctions: a) Ax**2 ( x**2 = xx) b) cos (Ax) c) exp(-Ax) where A is a constant.

Problem #2: Show that the wavefunctions f1 = Sin (n pi x/a) and f2 = Cos (n pi x/a) where n and a are constants, pi is the pi constant, are orthogonal in the region 0 <= x <= a ( <= is the less than or equal sign).

Problem #3: Show that exp(ax) is an eigenfunction of the operator d/dx and find the corresponding eigenvalue. Show that exp(ax**2) is not an eigenfunction of d/dx.

Problem #4: An electron is confined to a molecule of length 1.0 nm which is about 5 atoms long.

(a) What is its minimum energy, i.e. the ground-state energy?

(b) What is the minimum excitation energy from the ground-state?

(c) What is the probability of locating the electron between x = 0 and x= 0.2 nm in the box?

physchem_HW2.pdf: Solutions to HW2

Week 1 :

Recommendation: (No grade) Textbook Chapter 1: Problems 2, 6, 11, 16, 18, 20, 22, 25, 33.

For Grade

Problem #1: Determine the kinetic energy of a photoemitted electron from the surface of Cs if the wavelength of the incident light is 525 nm. The work function for Cs is 2.14 eV. What is the velocity of the electron?

Problem #2: The following data were collected for the photoelectric emission of an electron from Ca:

a) Determine the work function

b) What is the minimum frequency of light (the threshold frequency) that will eject an electron from Ca?

Problem #3: Using Bohr theory, determine the ionization energy of atomic H, i.e. energy required to remove an electron from a H atom.

Problem #4: Derive Bohr formula for a nucleus of atomic number Z.

Physchem_HW1.pdf: Solutions to problems 1, 3, and 4 in HW1

HW_1_prob_2.xls: Solution to problem 2 HW1

-- ThanhTruong - 24 Aug 2007