problem 1: Based on their ground state electron configurations alone, rank these molecule in order of bond length from smallest to greatest:

A = N₂
B = O₂
C = NO

problem 2: Sketch for yourself the molecular orbital energy level diagram for KrF and deduce its ground state electron configurations. Is KrF likely to have a shorter or longer or same bond length as KrF⁺?

problem 3: Use the electron configurations of NO and N₂ to predict which is likely to have the shorter bond length.

NO has a ............... length.

problem 4: prepare down for yourself the secular determinant for the hypothetical molecule linear H₃ making the Huckel approximation, using the 1s atomic orbitals from each atom as the basis set. Given that α= -2.00 eV and β= -2 eV, what is the total electronic energy in eV?

problem 5: prepare down the secular determinant for the hypothetical molecule cyclic H₃ making the Huckel approximation, using the 1s atomic orbitals from each atom as the basis set. Given that α= -2.00 eV and β = -2 eV, what is the total electronic energy in eV?

problem 6: Suppose you don't know the solution to the ground state particle in a box. The function ψ = x(L-x) can be used as a trial wavefunction for the n = 1 state of a particle with mass m in a 1-D box of length L, since it satisfies the boundary conditions, etc? Using Variational Theory, find the energy of this trial wavefunction and express its energy as a multiple of the known exact energy for the 1-D box (ground state). That multiple is..............

problem 7: Suppose you don't know the solution to the ground state particle in a box. The function ψ = cx(L-x) can be used as a trial wavefunction for the n = 1 state of a particle with mass m in a 1-D box of length L, since it satisfies the boundary conditions, etc. Normalize this trial wavefunction by finding the value of c in SI units, given a value of L = 40.0nm.

The value of the normalization constant c = ..............

problem 8: Use the Huckel Molecular Orbital method to estimate the total π electron binding energy for (a) the cyclopentadienyl cation, (b) cyclopentadienyl anion. Express each in terms of the coefficients of the α and β terms.

(a) cyclopentadienyl cation;  .............α + ........... β
(b) cyclopentadienyl anion;  ..........α + .......... β.

problem 9: Using the simple HMO program, treat planar napthalene making the Huckel approximation, using the perpendicular C2p atomic orbitals from each atom as the basis set. Given that α= -2.00 eV and β= -2 eV,

what is the total π electron binding energy in eV?

What is the wavenumber in cm-1 for the HOMO to LUMO transition?

problem 10: Using the AM1 semiempirical method in HyperChem, treat planar napthalene. First build the molecule, choose SemiEmpirical methods and AM1, and perform a Geometry Optimization. Look in the "Compute>Orbitals" menu to determine the energies of the HOMO and LUMO.

What is the wavenumber in cm^-1 for the HOMO to LUMO transition predicted by AM1?

Think about what region of the spectrum this would occur in.

What value of β can you infer, that would bring the HMO method into agreement with the more advanced AM1 method?

problem 11: Use the ab initio 3-21G* method in HyperChem to compute the various properties of the water molecule.

OH bond length  ,................Angstroms

HOH bond angle  ............degrees

dipole moment magnitude  ..................Debye

(You are graded with only a 1% tolerance on this problem). To build a water molecule in HyperChem is easy: choose the "Draw" tool button on the tool bar, choose the red "O" button meaning oxygen, and Left-click once. That drops an oxygen atom in the display. Then go to the "Build" menu and Add Hydrogens and Model build. Then you have a water molecule in the display. Then go to "Setup" and choose the ab initio method. Perform a Geometry Optimization under the Compute menu. Measure the bond length and angle using the Select tool button and clicking on a Hydrogen then an Oxygen to get bond length (see lower left of screen) and then select the other hydrogen to get the angle. Go under the Compute>Properties menu to get the dipole moment.

problem 12: Use the AM1 semiempirical quantum method in HyperChem to predict whether the molecule biphenyl is planar or nonplanar. (Hint: build the molecule and then run a short Molecular Dynamics simulation of the molecule before Geometry Optimizing). Enter 0 if planar, and 1 if nonplanar ............
 
What is the C-C bond length of the central C-C bond in Angstroms to four significant figures?

How many atomic orbitals are included in the basis set, knowing that AM1 only uses AO's in the valence shell for each atom?

How many molecular orbitals are produced?

How many of those MO's are filled with electrons?

How many weighting coefficients need to be find outd to solve this problem?

problem 13: Using the PM3 semiempirical method in HyperChem, compute the C-C bond length of the central single bond in 1,3 butadiene.

C-C single bond length = ......................Angstroms

Considering how it compares to the single, double and triple C-C bond lengths of the previous problem, what can you infer about the nature of the central bond in butadiene?

problem 14: Using the AM1 semiempirical method in HyperChem, compute the C-C bond lengths in ethane, ethene, and ethyne. For each, first build the molecule, choose SemiEmpirical methods and AM1, and perform a Geometry Optimization. Use the selection tool to pick each C in succession to display bond length in the lower left of the window.

Ethane ,,,,,,,,,,,,,,,,,,,,,,,,,Angstroms
ethene ,,,,,,,,,,,,,, Angstroms
ethyne ,,,,,,,,,,,,,,,,,,,,,,Angstroms

Look up the experimental values for these bond lengths in the literature. They are:

ethane,,,,,,,,,,,,,,,,,,,, Angstroms
ethene,,,,,,,,,,,,,,,,,,,,, Angstroms
ethyne,,,,,,,,,,,,,,,,,,,,,,,,,,Angstroms