# Tutorial - Quantum Chemistry - Intro to Gaussian Part II

This is part two of the Introduction to Gaussian tutorial series. Topics that are covered include: Single point energy calculations, Geometry optimization, Frequencies and normal mode calculations. Update: to submit Gaussian jobs on the SCS cluster lop please use new script submit-g16.

QUANTUM CHEMISTRY WITH GAUSSIAN: A VERY BRIEF INTRODUCTION (PART 2)

TARAS V. POGORELOV AND MIKE HALLOCK SCHOOL OF CHEMICAL SCIENCES, UIUC
Created 2011. Updated/reviewed August 25, 2021.
This tutorial continues introduction to Gaussian [2]. Here we concentrate on single point energy calculations on a molecules of water and formaldehyde, geometry optimization, frequencies and normal modes. For more detailed discussion, please see [2, 1]. Basic knowledge of Unix/Linux and Gaussian is assumed. See for example previous tutorials [4, 5]. Estimated time to complete this tutorial is 1.5 hrs.

### 1. SOFTWARE

One will need: text editor, ssh client, molecule builder and viewer.
Suggestions:
• Molecule viewer: Molden (https://www3.cmbi.umcn.nl/molden/)
Mac:
• Text editors: TextEdit, Vim,
• SSH client: built in Terminal , scp or Fugu for file transfers
PC:
• SSH client: putty, WinSCP for file transfer

### 2. FORMALDEHYDE SINGLE POINT ENERGY AND MOLECULAR ORBITALS WITH MP2

Open Avogadro and Select Element: Carbon(6)
Click once anywhere is the main window and watch an atom of carbon to appear and four hydrogens being added.
Select Element: Oxygen(8) and click on one of the hydrogens. It will be converted into an oxygen atom with a hydrogen atom.
Select Bond: double and pull from the oxygen towards carbon. Double bond will be formed and hydrogen removed.
Prepare Gaussian input file: Open Extensions, Gaussian.
Note: the coordinates are already listed in the Gaussian Input plugin.
Enter title: CH20 SP MP2
Select: Calculation: Single Point Energy, Theory level: MP2, Basis: 6-31G(d), Charge: 0, Multiplicity: 1.
To use the Z matrix form select Format Z-matrix. Please make sure to understand the way Z-matrix is generated from Cartesian coordinates. Briefly, it is a way to describe molecular structure using internal coordinates. First line introduces the starting atom. Second line contains the second atom and the bond distance to the first. Third line gives the bond length to the first and the angle formed by this bond and the bond between two previous atoms. Fourth line adds the value of the dihedral angle between two planes: formed by atoms one through three and the current atom and atoms one and two.
Click: Generate button.
Save as: GH20-SPE-MP2.com
Open the newly created CH2O-SPE-MP2.com file in a text editor of your choice.
Add in the end of the first line "Pop=Reg formcheck" to request information about molecular orbitals to be printed.
Copy Gaussian input file to cluster using scp command.
`> ssh netid@lop.scs.illinois.edu`
Make a directory ch2oSP in your home directory.
`> mkdir ch2osp`
Copy Gaussian input file to cluster using scp command. (example is if you are on your computer in the directory containing the file)
`> scp GH20-SPE-MP2.com netid@lop.scs.illinois.edu:~/ch2oSP/`
Note: please see the Unix/Linux Primer if you need to refresh your knowledge of the OS.
`> module load gaussian/g16`
Start Gaussian job with prepared files:
`> g16 < CH20-SPE-MP2.com > CH20-SPE-MP2.log`
Note: < is the ”pipe” flag to direct the input file to Gaussian and the output into .log file.

### 3. Gaussian OUTPUT: BASIC ANALYSIS

Open CH20-SPE-MP2.log in a text editor and locate the following: Input data, Standard orientation, Number of basis functions used, Single point energy, Symmetry, Mulliken charges.
Note: energy values are reported for MP2 and for lower-level HF.
Note: energy is reported in A.U. Recall 1 hartree is 627.51 kcal/mol.

3.1. Find data in the output without opening. Close the output file and use grep to find the energy value, without opening the file. This can become important for larger systems, as the size of the output file will grow very fast.
Note: the checkpoint Test.FChk was produced. This is an ASCII file which has MO information. Please see the previous tutorial Gaussian: Intro for a reminder of how to display MOs with Avogadro.

### 4. GEOMETRY OPTIMIZATION

Here we consider geometry optimization as a search for mimina on the potential energy surface. Optimization methods calculate the second derivative of the energy with respect to the coordinates. Matrix of forces (Hessian) is updated for each new conformation.
Convergence criteria in Gaussian:
• The force components are less than 0.00045;
• The root-mean-square of the forces are less than 0.0003;
• Displacement for the next step is less that 0.0018;
• The root-mean-square of the displacement for the next step is less than 0.0012.
Note: please comment on why convergence criteria contain conditions on force and coordinate. Think of examples of potential energy surface where one criterium alone would not suffice.

4.1. Prepare input file for geometry optimization of a formaldehyde molecule. Using Avogardo follow the steps above for single point energy calculation with the exception of selecting Calculation: Geometry Optimization.
Note: Opt was added to the input file.
Transfer .com file to lop and run the calculation.

4.2. Analysis of the output file. Open the .log file and locate the following information:
• Did optimization converged? Hint: search for YES
• If yes, how many steps were required to converge?
• Predicted energy for the optimized structure?
• Locate final optimized structure. Hint: look for the statement: Stationary point found.
• Reflect on which bonds, angles, dihedrals changed.
4.3. Visualizing geometries using Molden. Note: Use ssh -C to connect to X to speed this up. NOTE (6-11-2021): MOLDEN is not installed on the cluster LOP. It can be if needed, though Gaussview should suffice for now
Type gmolden in your terminal on X to start the program.
Note: molden will start the Xwindows version and whereas gmolden will start the OpenGL one.
Click Read button and select your .log output file. Choose Draw Mode: Solid -¿ Ball and Stick.
To see how conformations changes during minimization, click  Select Point: Next. Click through to the final structure. Click Forces and go through frames once again to see how forces changed during this process.

### 5. FREQUENCY AND NORMAL MODE CALCULATION

Frequencies are functions of second derivative of the energy with respect to the nuclear positions. Second derivatives can be computed analytically: Hartree-Fock (HF), density functional theory (e.g. B3LYP), second-order Moller-Plesset (MP2), and CASSCF (CASSCF) or numerically.
Gaussian is capable of computing the vibrational spectra of molecule on ground and excited states.
5.1. Frequency calculation for a water molecule. Prepare input file using Avogardo and select Calculation: Frequencies. Chose RHF for Theory.
Submit job to lop and study resulting output file.

5.2. Results of the frequency calculation. Locate frequencies and intensities. Compare to the experimental results.
Note: output frequencies are in cm−1 .
Note: due to a systematic error in this calculation use empirical scale factor to multiply the resulting frequencies: 0.8929 for HF/6-31(d) and 0.9427 for MP2/6-31(d), see [3].
Comment on why the accuracy of MP2/6-31(d) is higher.
Locate normal mode displacements. Hint: they are listed after the IR Inten.
Note: one needs the Standard orientation printed in the beginning of the output file to visualize the displacements.
Note: if the molecule is planar one coordinate, usually X, initially will be set to zero for all atoms. Complete the following if you have time, otherwise see next section on how to use Molden on how to visualize normal modes. Sketch normal modes on a sheet of paper. Use the displacements with the largest magnitudes as a guide to which atoms move the most. Additionally see which atoms move closer together.

5.3. Visualizing normal modes and spectrum using Molden. Note: Use ssh -C to connect to X to speed this up. NOTE (6-11-2021): MOLDEN is not installed on the cluster LOP. It can be if needed, though Gaussview should suffice for now
Type gmolden in your terminal on X to start the program.
Note: molden will start the Xwindows version and whereas gmolden will start the OpenGL one.
Click Read button and select your .log output file. Choose Draw Mode: Solid -¿ Ball and Stick.
To see normal modes, click Frequencies: Norm. Modes. New window Molden Frequency Select will allow you to choose which mode to see. Try them all one by one.
Note: there is a window with the calculated spectrum. You can use it to print and save the frequencies.

5.4. Frequencies and normal modes for a formaldehyde molecule. Repeat previous calculation for formaldehyde. Display the normal modes using Molden. Look at the representation of normal modes in the output file and see whether you can describe the motions by just studying the matrices.

5.5. Frequencies and normal modes using MP2. Repeat frequency and normal modes calculations for a formaldehyde molecule using MP2 for Theory. Comment on the differences of results, if any.

### 6. SUMMARY

This tutorial covered material using Gaussian for single point energy, geometry optimization, frequency and normal modes.

### 8. APPENDIX: RUNNING Gaussian IN QUEUE ON SCS LINUX CLUSTER

Please make sure to understand each line of the shell script below. Edit it to match your file names.
Submit the queue script to the queue:
> submit-g16 inputfile.com
Note: The following is probably not needed for the fast test job.
Check the status of your job:
`> qstat`
Delete the job if need:
`> qdel`

### REFERENCES

[1] Christopher J. Cramer. Essentials of computational chemistry: theories and models. Wiley, Hoboken, NJ, second edition, 2004.
[2] James B. Foresman and Aellen Frisch. Exploring chemistry with electronic structure methods. Gaussian, Inc, Pittsburg, PA, second edition, 1996.
[3] Jeffey P. Merrick, Damian Moran, and Leo Radom. An evaluation of harmonic vibrational frequency scale factors. J. Phys. Chem., 111:11683–11700, 2007.
[5] Taras V. Pogorelov and Mike Hallock. Unix/linux primer. https://netfiles.uiuc.edu/pogorelo/www/Tutorials, February 2010. Tutorial.