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1. Molecular Orbitals

Understanding Organic Reactivity

What are some of the fundamental principles that govern the reactivity of molecules? What makes a molecule a good nucleophile or a strong electrophile? How can we predict which position of an aromatic ring undergoes electrophilic or nucleophilic substitutions? The simple understanding that a nucleophile is electron-rich molecule that attacks sites with low electron density, and that electrophile is electron-poor molecule that will attack a position of large electron density allows to understand many organic reaction.

For example, consider a diazo coupling reaction in which benzenediazonium chloride reacts with aniline. One can deduce from the positive charge that the diazonium group is very electron-poor, and thus acts as a good electrophile. Aniline acts as a nucleophile but what is the nucleophilic site? Recall that in aniline, the lone pair of the amino group is delocalized. Consideration of possible resonance contributors to the conclusion that the ortho and para-positions in aniline are nucleophilic. The ortho position is sterically hindered, and one could correctly predict that the azo compound forms when the electrophile attacks the para position of aniline.

Diazo coupling with aniline

In other situations, this simple understanding is insufficient. For example, how can we rationalize the observed preference of nitration of the 1-position in naphthalene by nitric acid if the total π electron densities in the 1 and 2 position are expected to be the same? Recall that in the nitration reaction, nitronium ion (NO2+) acts as an electrophile, and naphthalene behaves as a nucleophile. But which position in naphthalene is more nucleophilic? In principle, the answer can be reached by considering the structures and energies of the two transition states leading to the two products but this approach is often impractical.

Electrophilic nitration of naphthalene

Frontier Orbital Theory

Naphthalene HOMO at 0.06 A powerful practical model for describing chemical reactivity is the frontier molecular orbital (FMO) theory, developed by Kenichi Fukui in 1950's. The important aspect of the frontier electron theory is the focus on the highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO). For example, instead of thinking about the total electron density in a nucleophile, we should think about the localization of the HOMO orbital because electrons from this orbital are most free to participate in the reaction. The image on the right shows the distribution of HOMO in naphthalene; we can see that the frontier electron density is highest at the position 1. Thus, the electrophile reacts with position 1 of naphthalene.

Similarly, the frontier orbital theory predicts that a site where the lowest unoccupied orbital is localized, is a good electrophilic site. The FMO theory was initially used for explaining the electrophilic substitution in naphthalene but it became gradually clear that the scope of this theory is much broader. For example, the concept of frontier orbital symmetries was successfully used to rationalize the outcomes of cycloaddition reactions and other pericyclic reactions. Frontier molecular orbital models for some organic compounds are available here.

You can read more about the frontier orbital theory from Kenichi Fukui Nobel Prize lecture.

Calculating and Visualizing Molecular Orbitals

Standard quantum chemistry calculations yield delocalized molecular orbital. In Gaussian, keyword Pop requests printout of molecular orbitals. Alternatively, keywords GFINPUT, IOP(6/7)=3 can be used to ccreate output that can be visualized with MOLDEN. Your directory on the workstation contains a file naphthalene_TZ_MPD.out that contains MO information on naphthalene. You do not need to repeat this calculation because it will be time consuming. Also notice that this calculation included some treatment of electron correlation by invoking the MP2 keyword; the result of this is that many MO orbitals will have fractional populations.

You can read more about the frontier orbital theory from Kenichi Fukui Nobel Prize lecture.

2. Molecular Surfaces

Molecular Shape Surfaces

The shape of a molecule is determined by the electron density of the molecule and this electron density depends on the atomic composition of the molecule. One way to determine molecular shape is to calculate electron density and display the region where electron density is larger than some cut-off value as a three-dimensional surface. Such calculations necessitate quantum chemical approach and are possible with not too large molecules. For larger molecules, Connolly surfaces and solvent-accessible surfaces can be calculated rapidly based on empirical van der Waals radii of atoms.

Electrostatic Potential Surfaces

TETRAKETIDE

Electrostatic potential surfaces are valuable in computer-aided drug design because they help in optimization of electrostatic interactions between the protein and the ligand. These surfaces can be used to compare different inhibitors with substrates or transition states of the reaction. Electrostatic potential surfaces can be either displayed as isocontour surfaces or mapped onto the molecular electron density. The latter are more widely used because they retain the sense of underlying chemical structure better than isocontour plots.

Example: Oxamic Acid

This tutorial illustrates how to use quantum chemistry calculations to generate and display molecular electron density surfaces and map electrostatic potential values to the surface. You will compare two conformers of oxamic acid. Oxamate, anion of oxamic acid is a powerful inhibitor for Plasmodium falciparum lactate dehydrogenase and thus may serve as a fragment or lead in developing novel anti-malaria drugs. The molecule has two low energy conformers that differ in the dihedral angle about the central C-C bond. These conformers are shown in the image on the right.

Your task is to calculate and display electrostatic potential of cis and trans oxamic acid. Molecular surfaces should be calculated based on optimized molecular geometries. While molecular mechanics force fields can be used to generate reasonable initial geometries, it is considered a good practice to optimize molecular geometries with quantum mechanical methods prior generation of electron molecular electrostatic potential surfaces. In this tutorial you start with previously optimized structures of cis and trans oxamic acid because optimization jobs can be time-consuming. The quantum chemistry program Gaussian was used to perform geometry optimization for the two conformers. The calculation was performed at the Moller-Plesset second order perturbation theory level with a moderate-sized basis set to describe molecular orbitals. Specifically, a 6-311+G(d,p) basis set was used which allows for some polarization of electron density on both heavy atoms and hydrogens. In computational jargon, the molecule was optimized at the MP2/6-311+G** level. The comparison of relative energies of the two conformers suggests that s-trans conformer is more stable by 1.68 kcal/mol. You can use MOLDEN to launch quantum mechanical geometry optimizations but keep in mind that optimizing a larger molecule using accurate QM methods can be very time-consuming.

You will be performing these calculations on a remote workstation. The files that you need to start the calculation are on your SGI directory, though. You can transfer files between computers using File Transfer Protocol, or FTP. You can access your files from the workstation by opening an ftp connection to the SGI file server (the address will be given in the class). After opening the FTP connection, navigate to your directory on the SGI file server by typing cd PERM where PERM is your perm number and hit enter. Then transfer the two input files to the workstation by typing get oxamic_ac_trs.mol2 and get oxamic_ac_cis.mol2. Exit the ftp program by typing bye. Verify that the input files are in your directory on the workstation.

  1. The optimized structures have been saved in the MOL2 format. Read the structure of the trans conformer into MOLDEN by typing molden oxamic_ac_trs.mol2. The structure should show up in the graphical window.
  2. Open the Z-matrix editor but do not change the structure this time. Select Gaussian from the Format menu and hit Submit Job.
  3. A new window, titled Submit Gaussian Job, opens. Change the Task to Single Point, keep the Method HF, and change the basis to 6-31G**. This basis is somewhat inferior to the basis used for optimization but it allows for speedy calculation.
  4. Examine the molecule on the screen to verify that all formal valences are satisfied. Molecules like these are net neutral with all the electrons paired, hence keep 0 for charge and Singlet for Spin.
  5. Notice that the Gaussian program uses keywords to decide what kind of calculation to perform and what kind of results to produce. The extra keywords, like GFINPUT, IOP(6/7)=3, and 6D are required by MOLDEN to visualize results from Gaussian. You can modify the Keyword lines to add advanced options. For example, to request a rather expensive CCSD/cc-pVTZ calculation, you could change HF/6-31G** to CCSD/cc-pVTZ. Gaussian options are discussed in detail at http://www.gaussian.com/g_ur/keywords.htm
  6. Give an unique and easy-to-identify name to the job. For example, you may name it oxamic_ac_trs_esp.
  7. The title line is for optional comments. People typically add some description as of the purpose of this calculation. You may want to give your name here as it will help when your files are misplaced.
  8. Hit Submit, then OK. A confirmation window opens reporting that the job started. Hit OK to close this window.
  9. Unlike force field calculations, the results are not automatically returned to MOLDEN when the calculation completes. In fact, when running longer jobs, you may want to close MOLDEN, or even log out as the Gaussian calculation is now independent of MOLDEN. For oxamic acid, the calculation should take about 20-30 seconds to complete. Load the results by reading the log file that was created (e.g. oxamic_ac_trs_esp.log)
  10. Notice that some information about coordinates, charges, and dipole moments will be printed into the Unix shell from which you started MOLDEN.
  11. Click on Dens. Mode to enter Density Mode. This mode allows you to visualize variety of quantum-mechanical features, such as total electron density, molecular orbitals, and electrostatic potential. These features can be either mapped to two-dimensional grid, or shown as isocontour surfaces around the molecule. The latter are most intuitive to grasp.
  12. By default, HOMO is mapped on 2D grid. Click on Density to display the electron density distribution of the molecule. As expected, the total electron density is highest at the location of heavy atoms.
  13. Click on PlotPlane icon and type align to center the molecule and calculate optimal extent of the grid. If the molecular surface that you will generate later shows unexpected holes, then increase the edge value to be little larger than the radius reported in the Unix shell window. Close Molden Query Box window.
  14. Click on Space and give a contour value. Values in the range of 0.01 to 0.03 give reasonable-looking surfaces; regions with electron density larger than the countour value will be enclosed in the contour. Calculating the contour will take some time.
  15. Click on Write Grid. This generates a file called 3dgridfile in your directory.
  16. We need to generate two 3D grids, one for total electron density, another for electrostatic potential. Molden currently expects that the 3D grid file is in the current directory and has file name 3dgridfile. To get around this limitation, we need to temporarily rename the density grid file. Open another connection to the workstation and rename this file: mv 3dgridfile 3dgridfile_dens.
  17. Click on Elec. Pot. and choose Multipole Derived to display the electrostatic potential isocontour. The result is difficult to interpret with untrained eye but the map shows regions on negative and positive potentials around the molecule.
  18. Click on Write Grid. This generates a file called 3dgridfile in your directory. Use the other connection to the workstation and rename this file: mv 3dgridfile 3dgridfile_elps; then copy the density contour back into a file 3dgridfile by typing cp 3dgridfile_dens 3dgridfile in the same shell.
  19. Reload the grid file with density by clicking on Read Grid and select Replace Grid.
  20. Click on \R/ icon that allows export of 3D data in formats such as VRML and OpenGL. Choose Color Mapped. A new window, titled Mapped Surface, opens.
  21. On the Map file: line, enter 3dgridfile_elps, which contained the electrostatic density map.
  22. On the VRML/OpenGL file: line, select type OpenGL and rename the output file to something more specific, like oxamic_ac_trs.ogl. Enter the same contour value that you used for the density surface before and hit Apply.
  23. Visual examination of the potential-mapped density file in the OpenGL format over the network is too slow, so you should use FTP to transfer this large file to SGI file server. To transfer the file, open the connection to the SGI file server, change directory to your PERM directory, and type put oxamic_ac_trs.ogl to transfer the OpenGL file from the workstation to the SGI server. Close the ftp program. After successful transfer, type ../moldenogl oxamic_ac_trs.ogl into Unix shell on the SGI workstation to open the 3D dataset in OpenGL visualizer. You can rotate the 3D volumetric model with mouse or click the right mouse button for additional options. Manipulation is little slow on SGI computers and you are welcome to try it out on the Linux workstation screen. Rotate the molecule into a pleasing orientation and save a picture in BMP format via the Screen Capture menu.
  24. You can convert pictures into more common formats using the convert tool. On SGI, you can convert to the GIF format but on Linux workstations you can convert files also into the JPEG or PNG formats.
  25. You can also capture screen images into image files. On SGI computers, snapshot allows writing images in SGI-specific RGB format; on Linux workstation programs display, gimp allow capture screens into image editors. The Unix command xwd -out dumps images from X-windows into xwd files.


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Tutorial by Dr. Kalju Kahn, Department of Chemistry and Biochemistry, UC Santa Barbara. ©2005-2007.
Portions of MOLDEN instructions are adopted from http://www.cmbi.ru.nl/molden/mapped.html, which were written by Dr. Gijs Schaftenaar, University of Nijmegen.