# Homework 8

- Page ID
- 204085

Name: ______________________________

Section: _____________________________

Student ID#:__________________________

This homework is mixture of quantum calculations and group theory. We will use the cool web base *ab initio* site by Perri at Sonoma State U. Download the following paper and review the concept (http://pubs.acs.org/doi/pdf/10.1021/ed5004228). Follow the directions on this tutorial (you only need to install Avogadro).

## Q1

Create an input file for water. You can do this via the Avogadro package you installed before OR you can do it directly online in the SSU submit page ( https://chemcompute.sonoma.edu/gamessweb/submit.html). Either works. You will need to optimize the water structure before doing the quantum calculations just like with benzene and their is a clear step in the "submit page". What are the benefits of doing this?

## Q2

For the QM calculation, use these parameters:

- Do a Geometry optimization
- Do the IR add-on
- Use the 3-21G basis set
- Use the Restricted Hartree-Fock method (this is a Self-Consistant Field approach discussed in Chem 110A)
- Use no DFT Functional
- Use no (PCM) Solvent

and submit the job. This may take a minute or two.

The difference between single-point calculations and geometry optimization is that that the former calculates the electron structure for one specific and given geometry; the later will do it at a series of geometries while decreasing the total energy of the system. This is similar to the Walsh diagram if a water molecule were set at linear and then it were allowed to bend. The calculations would predict a bending based on the number of electrons in the molecular orbital. What is the underlying approximation that allows use to do such calculations?

## Q3

You will get 13 molecular orbitals in the calculation, but not all are occupied. From the molecular orbital diagram discussed in Section 10.3 for water address the following questions:

- How many of these 13 molecular are occupied?
- What is the total electronic energy of the water (hint: sum up all electron energies)?
- Did you use atomic orbitals as the basis set for your calculations?

## Q4

- Draw and describe the lowest energy molecular orbital in terms of underlying atomic orbitals.
- Draw and describe the HOMO in terms of underlying atomic orbitals.
- Draw and describe the LUMO in terms of underlying atomic orbitals.

## Q5

What is the point group for water? What are the symmetry elements associated with this point group and what are the irreducible representations (use Mullikin notation) for this point group.

## Q6

For each of the seven lowest lying molecular orbitals (occupied or not) are the orbitals symmetry or antisymmetric with respect to the four symmetry elements of the relevant point group and assign the irreducible representation associated with that molecular orbital.

## Q7

If the absorption of a photon were to promote an electron from the HOMO to the LUMO in water. What would be the photon wavelength necessary for this excitation (in nm)?

## Q8

As we will learn next week (And you were taught in gen chem), there are \(3N\) degrees fo freedom associated with a 3-D molecule. For water, this is separate into three-degrees of translation, three degrees of rotation and three degrees of vibration. The calculation calculates all nine.

- From inspection of these modes, what is the "energy" (poorly defined now and better defined later) of each mode.
- Which modes are the lowest in energy?
- Which modes are the highest?
- Which are lower than thermal energy \(k_bT\) at room temperature?