# 2: ab initio Calculations - Diatomic Molecular Orbitals (Dry Lab)


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This homework is a little different. 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 will not need to install Avogadro for this HW). We will use this package multiple times in this class so make sure you can complete the online tutorial if you are confused.

To start the calculations

• click "student mode"
• click on red/blue molecular orbital (under GAMESS)
• click on "submit" on top right

## Calculations

Run the geometry optimization calculations on five fluorine dimer species and fill in the below table. You will need to pay careful attention to the occupied molecular orbitals (the ones with negative energies) in each calculation to fill in the table. To do this, you will need to address the spin and charge of the system explicitly (see previous Homework #7B for details on multiplicity in quantum calculations).

• If the spin multiplicity of the atom is not 1, then use the UHR (Unrestricted Hartree-Fock) method,
• If the spin multiplicity of the atom is 1, you can use either the RHF (Restricted Hartree-Fock) or UHR method (should give the same results).

Use the 6-311G** basis set for each calculation. If you select the RHF method and have a non-unity spin multiplicity, the program will give you an error.

Also select the IR option so you can get the rotational (rigid rotor) and vibrational constants (harmonic oscillator).

Species Spin
Multiplicity $$2S+1$$
Charge Predicted
Electronic
Configuration
(from Calculation)
Bond
Order
Bond
Length
Rotational
Constants
(cm-1)
Vibrational
Constants
(cm-1)
$$F_2^{+2}$$ 3 +2
$$F_2^{+}$$       3/2
$$F_2$$     $$\sigma_{2s}^2 {\sigma^*_{2s}}^2 \sigma_{2p_z}^2 \pi_{2p}^4 {\pi^*_{2p}}^4$$
$$F_2^{-1}$$
$$F_2^{-2}$$

To calculate the bondlength, you have to extract the output file and find the XYZ coordinates of each atom (atom 1 and atom 2) in the optimized geometry. Then you use

$d = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2 + (z_1-z_2)^2}$

## Submit for Credit the Following Items or Answers

Submit the above table filled out for the total binding electronic energy of each atom. (Do not copy from others as we will compare tables.)

• Does the order of the molecular orbitals in the predicted electron configuration from the calculations for your species follow the "true" order discussed in class and the text? If not, explain why this may be the case.
• Plot the vibrational constant vs. bond order using your favorite software (e.g., Excel or Matlab or Plot2 for mac users). Justify this trend with a quantum description.
• Plot the bond length vs. bond order using your favorite software (e.g., Excel or Matlab or Plot2 for mac users). Justify this trend with a quantum description.
• How would you calculate the bond energies (or enthalpies) for the species above?
• How many rotational constants did you extract? Is that the correct number? Why or Why not?
• How many vibrational constants did you extract? Is that the correct number? Why or Why not?
• How many translational constants did you extract? Is that the correct number? Why or Why not?
• For the $$F_2$$ species, confirm that the rotational constant predicted from the calculation is similar to that predicted from the bond length and reduced mass of the molecule.

2: ab initio Calculations - Diatomic Molecular Orbitals (Dry Lab) is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.