# Rotation of Ethane

Characterize the potential energy surface for the rotation of ethane

This exercise will guide you through determining the rotational energy for ethane. Read the overview for the energy profile for the rotation of ethane (see Section 1.1.5).

## Setup and Run

In a molecular modeling program (such as Avogadro), build the staggered and eclipsed conformers of ethane in symmetry. Save each set of Cartesian coordinates to a separate Gaussian input file. I have chosen to use the B3LYP/cc-pVDZ level of theory for these computations. Below are the two input files. You can copy this data into your own input files.

Be sure that your files end with a blank line otherwise Gaussian will immediately terminate. Place the input files in an appropriate set of directories on sequoia. Name your files as 1.inp. Be sure to include a g09.pbs file in each directory.

I have placed my files in the following directories:

• ~/chem/ethane/staggered/b3lyp/dz
• ~/chem/ethane/eclipsed/b3lyp/dz

WATCH: Setup the staggered ethane input file into the directory listed above.

Commands:

• mkdir -p ~/chem/ethane/staggered/b3lyp/dz to make the directory from your HOME directory
• cd ~/chem/ethane/staggered/b3lyp/dz to change into the directory
• vi 1.inp to create the input file
• i to enter Insert Mode
• right click (or middle click) to paste
• Enter to insert a blank line at the end of the file
• ESC to enter Command Mode
• :wq to save and close the file

To run the jobs, type:

% qsub g09.pbs

Your job should now be in the queue. To check if it has been queued up, type

% qstat | grep \$USER

This will only show your jobs that are in the queue. Once the job completes, it will no longer be in the queue. A 1.out file should be in your directory if the job ran.

## Analyze the Output File

The output file contains a plethora of information. For now, we want to pull the final electronic energy from the output file of each ethane conformer.

% grep "SCF Done:" 1.out

Staggered Conformer:

Here is the result of typing the above command on the output file of the staggered conformer:

 SCF Done:  E(RB3LYP) =  -79.8285304741     A.U. after    9 cycles
SCF Done:  E(RB3LYP) =  -79.8292682271     A.U. after    9 cycles
SCF Done:  E(RB3LYP) =  -79.8292865564     A.U. after    6 cycles
SCF Done:  E(RB3LYP) =  -79.8292865564     A.U. after    1 cycles

WATCH: Pull the electronic energies from the output file.

Commands:

• grep "SCF Done:" 1.out will print to the screen every line in 1.out that contains the string “SCF Done:”.

The last energy is what we want. Another command to type to simply get the last energy is

% grep "SCF Done:" 1.out | tail -1
SCF Done:  E(RB3LYP) =  -79.8292865564     A.U. after    1 cycles

Eclipsed Conformer:

Here is the result of typing the above command on the output file of the eclipsed conformer:

 SCF Done:  E(RB3LYP) =  -79.8193127879     A.U. after   10 cycles
SCF Done:  E(RB3LYP) =  -79.8244075937     A.U. after    9 cycles
SCF Done:  E(RB3LYP) =  -79.8245992450     A.U. after    6 cycles
SCF Done:  E(RB3LYP) =  -79.8246214099     A.U. after    6 cycles
SCF Done:  E(RB3LYP) =  -79.8246214099     A.U. after    1 cycles

The last energy is what we want. Another command to type to simply get the last energy is

% grep "SCF Done:" 1.out | tail -1
SCF Done:  E(RB3LYP) =  -79.8246214099     A.U. after    1 cycles

## Relative Energies

Absolute energies are, on their own, not very useful. We will convert our two absolute energies into relative energies. Here, I will subtract both absolute energies from the absolute energy of the staggered conformation. I will then convert this energy to kcal mol–1 by multiplying by 627.51. This can be done in an Excel spreadsheet for convenience.

Conformer Absolute Energy (H) Relative Energy (H) $$\Delta E$$ (kcal mol–1)
Staggered -79.8292865564 0.00 0.00
Eclipsed -79.8246214099 0.004665147 2.93

General chemistry knowledge tells us that the staggered conformer for ethane should be lower in energy than the eclipsed conformer. The B3LYP/cc-pVDZ level of theory indicates that the eclipsed conformer is 2.73 kcal mol–1 higher in energy than the staggered conformer.

## Nature of Stationary Points

An optimization does not always lead to a minimum on the potential energy surface. A frequency computation (via freq in a Gaussian input file) must be done following an optimization to determine the nature of the stationary point.

Staggered Conformer:

Type the following command to print the vibrational modes to the screen. The output is immediately shown.

% grep "Frequencies" 1.out
Frequencies --    318.1062               821.1006               821.1006
Frequencies --   1008.8704              1204.3804              1204.3834
Frequencies --   1385.7120              1408.8932              1474.0491
Frequencies --   1474.0497              1476.6993              1476.7007
Frequencies --   3026.6556              3029.0296              3083.7664
Frequencies --   3083.7670              3107.9862              3107.9875

Notice that all the values printed are listed as positive values. This means that all the modes are real and, therefore, the geometry from the optimization is indeed a minimum on the B3LYP/cc-pVDZ potential energy surface.

WATCH: Pull the frequencies from the output file.

Commands:

• grep "Frequencies" 1.out will print to the screen every line in 1.out that contains the string “Frequencies”.

Eclipsed Conformer:

Doing the same for the eclipsed conformer output file, the following is seen:

% grep "Frequencies" 1.out
Frequencies --   -307.6615               884.6129               884.6136
Frequencies --   1005.7447              1156.6530              1156.6551
Frequencies --   1382.2238              1420.4588              1472.5773
Frequencies --   1472.5778              1478.5955              1478.5957
Frequencies --   3032.8235              3041.8071              3090.9041
Frequencies --   3090.9054              3111.9915              3111.9916

Here, one of the modes is listed with a negative sign. The negative sign is used to denote that the vibrational mode is imaginary. If one vibrational mode is imaginary, the geometry is a transition state. According to the B3LYP/cc-pVDZ level of theory, the eclipsed conformer of ethane is a transition state, as expected.

##### Eric Van Dornshuld
###### Assistant Clinical Professor

My research interests include ab initio and DFT approaches to characterizing the properties of small, chemical systems.