Basis Sets, Electronic Properties, and Visualization

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Gwendoline Clarke
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Basis Sets, Electronic Properties, and Visualization Goals of the Exercise - Perform common quantum chemical calculations using the Gaussian package.

- Assess the impact of method and basis set size on the quality of the results. - Compute and visualize canonical and localized molecular orbitals and derived properties like multipoles.

1 Basis Sets, Electronic Properties, and Visualization Goals of the Exercise - Perform common quantum chemical calculations using the Gaussian package. - Practice preparation, monitoring, and analysis of the calculations using Molden and a text viewer or editor. - Estimate the relevance of the results. - Assess the impact of method and basis set size on the quality of the results. - Compute and visualize canonical and localized molecular orbitals and derived properties like multipoles. - Compute and visualize electron density and electrostatic potential. - Discuss the correlation of electrostatic potential maps and chemical function. Geometry Optimization of Glycine using Hartree-Fock Please see the previous exercise on how to use the Molden program. Molden already contains initial geometry templates for alpha-amino acids. Open the Z-matrix editor, click on Substitute atom by Fragment, and then on Amino acid. Click on Add, pick the one for glycine and use this as initial geometry for the subsequent calculations. Note that the initial structure is based on a zwitterionic configuration. Now perform a sequence of HF-calculations to compute the total energy (select Single Point as job type) for this geometry for the following sequence of basis sets: STO-3G, 4-31G, 6-31G, 6-31+G*, 6-311G, cc-pvdz, aug-cc-pvtz (Special note: for the cc-pv?z basis sets, also replace the 6D 10F keywords with 5D 7F. Those basis sets are not meant to be converted to a cartesian representation.). A few hints for the calculations: - After you log into your account, create a subdirectory for the project with "mkdir Exercise3" and change into that directory with "cd Exercise3". - Don't use file or directory names that contain special characters other than '.', '_' or '-'. They - especially blanks - will cause trouble sooner or later. - Make sure that each job input file has a descriptive file name, so you can easily find it and maintain a list for calculations and result summaries in a 00README.txt file. You can edit the file using programs GUI editors like "gedit" or "emacs", or text mode editors like "vi".

2 - Some of the basis sets that are not defined in the Molden Submit Job GUI, so you have to copy a.inp file for a different basis set, edit the basis set name in the file, save it and then submit the job manually via "g98sub job_name". - You can view the output of the calculations (the.lis file) using the aforementioned text editors, or "more", "less", or "view/gview". Using these so-called pager programs is usually more efficient, especially for large files. since they have no editing function. - The total number of basis functions is printed in the.log file, as is the total amount of time consumed. - You can also use Molden to extract some properties from the calculation by simply executing: "molden job_name.lis &". It will show you the geometry and when clicking on the SCF Conv. button, the change of the total energy during SCF convergence is shown. Now create an input file to perform a geometry optimization at HF level with an STO-3G basis set, but don't submit the job. After renaming the <jobname>.com file <jobname>.inp, load the <jobname>.inp file generated by Molden into a text editor and insert a new line: %Chk=myjobname.chk as the second line of the file (best you match the name of the.chk file and the.inp to have the same root). This will instruct Gaussian to create and maintain a so-called checkpoint file throughout the calculation, which contains all essential parameters of the calculation. Make sure that you never use the same name for two calculations running in the same directory, or else your results will be bogus. Submit the calculation using g98sub, and when it is done running, visualize the result of the calculation by loading the.lis file into Molden. What happens to the initial structure? As a next step, load the geometry optimization calculation into Molden and advance to the optimal configuration. Go to the ZMAT editor and prepare a new.inp file, but use a larger basis set (e.g. 6-31G) and re-optimize the geometry optimized with STO-3G. How much do geometry and total energy change? When you use checkpoint files, you can bypass the need for writing a new input file with Molden. Instead create an input that looks like this (note the empty lines, including the one at the end): %Chk=mycheckfile.chk #P HF/6-31G Opt Geom=(Check) Guess=(Read) # GFINPUT IOP(6/7=3) 6D 10F This is a job using a checkpoint file 0 1 And copy the checkpoint file of the previous calculation that matches the name in the.inp file. This will read the geometry and the wavefunction from the last calculation into the new job and use them as initial conditions. That should speed up the calculation massively compared to starting from scratch. Try a few more basis sets and discuss how much improvement for geometry and total energy you get, and how much additional computation effort this is costing you. Inclusion of Electron Correlation Perform a geometry optimization of a glycine molecule using Møller-Plesset second order perturbation theory (MP2) and a 6-31G** basis set. When starting from scratch, this

calculation will be more time consuming than the corresponding Hartree-Fock calculation (why?), so you have to employ a strategy to reduce the time until you get the desired result.

Now perform a single-point calculation (no optimization) based on the stored configuration using the Quadratic CI (Keyword: QCISD) method to include dynamic electron correlation.

3 calculation will be more time consuming than the corresponding Hartree-Fock calculation (why?), so you have to employ a strategy to reduce the time until you get the desired result. Make a copy of the resulting geometry (e.g. by writing and copying a checkpoint file) since we will be using it as a reference for future calculations. Now perform a single-point calculation (no optimization) based on the stored configuration using the Quadratic CI (Keyword: QCISD) method to include dynamic electron correlation. Take note of the energy, but make sure you pick the right value, as the calculation will contain multiple energies, one for each step of the calculation. Comparing two Conformers Create a new input for the zwitterionic glycine conformation from the internal template, but then modify the last entry in the Z-matrix (a hydrogen atom) to: H And optimize this geometry with HF/STO-3G, MP2/6-31G**. What is the difference to the previously found optimal geometries? We have found two (local) minima in the potential hypersurface. To decide which one is most likely the global minimum, perform a QCISD/6-31G** single point calculation using the MP2 optimized geometry in the same way as before. What are the differences in energy? Which unit is this energy difference in? Convert it to a more commonly used unit like kj or kcal. One more note about the calculations: the efficiency of SCF and particularly post-scf calculation can be influenced by the amount of memory allocated to the calculation. The default is very moderate but sufficient for most calculations. It can be increased by adding a line %Mem=500Mb, %Mem=1000Mb, or %Mem=2000Mb before or after the %Chk line. All calculations should complete without adding or changing %Mem. Calculation and Interpretation of Canonical and Localized Orbitals Perform a "good" geometry optimization for a single water molecule and use that geometry for the following calculations. Perform a single point calculation using Hartree-Fock and the STO-3G basis set and load the resulting.log file into Molden. Now click on the Dens. Mode button to change to the interface that allows inspection of the electron structure and related data in space. By default Molden picks the "HOMO" to display. Click on the Orbital button and select the orbital with the lowest energy instead. Why does it show a density for this orbital and not for the HOMO? Now click on the Space button and select a "Contour Value" of 0.2. This will render the same orbital in a more familiar, space-filling way rather than plotting the density along a given plane. Go back to the MO number 5 (the HOMO) and look at it in this representation. What can you derive from the shape of these molecular orbitals about which kind of (atomic) orbitals constitute the main contributions. Have a look at the.log file of the calculation and look for "Molecular Orbital Coefficients" and examine the following lines. This segment of the output file gives you the corresponding breakdown in numbers. This information is

4 subsequently used for the "Mulliken Population Analysis" to estimate partial atomic charges. The SCF calculation produces the so-called "canonical" orbitals, but they do not correlate very well to the chemical picture of bonding through electron pairs and the existence of lone pairs. This can, however, be approximated by a unitary transformation between the occupied orbitals. This will change how the molecular orbitals are decomposed into the atomic orbitals of the basis set, but not change the total electron density distribution or many electron wavefunction. As a consequence the localized orbitals no longer diagonalize the Fock matrix and the energy eigenvalues that are (still) displayed along them, have no meaning. To compute the localized orbitals, we first need to generate a checkpoint file with the full matrix of all orbitals. For that purpose take the input for the previous calculation and insert a %Chk line and add the keyword NOSYMM to the "Route" section of the input, the part that determines which calculation to do. After the calculation has completed copy the input file to a new name and replace the "Route" section with #P GUESS=(READ,LOCAL,ONLY) NOSYMM POP=FULL CHECKBASIS GFINPUT IOP(6/7=3) 6D 10F. Run this calculation and visualize the resulting.log file in Molden. How do the orbitals that you can see now correspond to your understanding of the chemical bonds in a water molecule? Calculation and Visualization of the Electrostatic Potential For the interpretation of the physical and chemical properties of a molecule, it can be useful to compute and visualize the electrostatic potential on the "outside" of a molecule. The surface of a molecule can be derived from the electron density: one computes an isosurface, a surface that connects point with the same density at a low reference value. Secondly one computes the local electrostatic potential at this isosurface and color codes the surface with this value. This is most easily done by computing all values on a regular (cubic) grid and then using a visualization software that computes isosurface and color mapping on the fly based on so-called "cube" files containing those gridded data sets. To generate the cube files with Gaussian, you need a checkpoint file from you calculation. This needs to be converted into a "formatted" variant using 'formchk name.chk'. The resulting 'name.fchk' file is used as input to the 'cubegen' utility that will generate the cubefile. To generate a density cube file do: cubegen 0 density=scf name.fchk name-dens.cube and to generate a matching electrostatic potential cube file do: cubegen 0 potential=scf name.fchk name-pot.cube The resulting two cube files can be loaded into VMD ( vmd name-pot.cube name-dens.cube ) and then visualized by: - adding an Isosurface representation (Graphics->Representations, Create Rep and switch "Drawing Method" from Lines to Isosurface - use the following settings in "Draw Style": Vol: name-dens.cube, Draw: Solid Surface, Isovalue: 0.02, Coloring Method: Volume / 0: name-pot.cube - and the following settings in the "Trajectory" tab: Color Scale Data Rang: , followed by clicking on Set. - images can be saved using File->Render->Snapshot and then saving the file in the ImageMagick viewer in the desired format under the desired name, higher quality images can be produced using the TachyonInternal setting, which will regenerate the image using the integrated raytracing library. Warning: This setting should only be used for final images, as it can be quite time consuming to render complex scenes.

5 Homework Questions: 1) Prepare a table and graph that illustrates the correlation between the size of the basis set and the duration of the glycine HF calculations. Prepare a similar graph of the final value of the total energy as a function of the basis set. Explain the patterns you see based on what you know about basis sets. 2) Describe what happened to the zwitterionic structure of glycine when it was optimized. Why do you think this happened? 3) Make a table comparing the energies of the two conformers of glycine. Based on the calculations that you did, what is your best estimate of the difference in energy between these two conformers (use chemically relevant units, not Hartree)? Compare your results to the experimental findings from: S. J. McGlone, P. S. Elmes, R. D. Brown, P. D. Godfrey, J. Mol. Struc , (1999). 4) Which atomic orbital(s) make up the HOMO of water, according to your Hartree-Fock calculation? Which atomic orbital(s) make up the lowest energy orbital of water, according to your Hartree-Fock calculation? 5) Describe the 5 occupied localized orbitals for water. (Note that these are a unitary transformation of the canonical orbitals.) 6) Describe the electronstatic potential map of water. Based on this calculation, how would you expect two water molecules to interact with one another?

Viewing Gaussian Structures with GaussView (GaussView Version: 3.09)

Viewing Gaussian Structures with GaussView (GaussView Version: 3.09) In GaussView, there are several ways to visualize structures from a Gaussian output file. The log file, checkpoint file, and formatted