Hartree-Fock Method

The Hartree-Fock method is the most common ab initio method that is implemented in nearly every computational chemistry program. For example, the program Jaguar that is interfaced to the Maestro graphical interface can carry out energy evaluations and structure optimizations at the Hartree-Fock level. Furthermore, scans of torsional coordinates or reaction paths are supported and facilitate localization of saddle points (transition states). Similarly, the program Gaussian allows calculation of energies, structures, and many properties at the HF level. For Windows PC's, the program PC GAMESS is recommended due to its excellent speed.

Molecular Symmetry in QM calculations

Many small molecules are symmetric. For example, methane, ethane, water, methanol, and benzene have certain symmetry elements that chemists are able to intuitively recognize. Modern computational chemistry programs are also able to recognize molecular symmetry and take advantage of the symmetry during calculations. The calculation on a symmetric molecule is much faster that a similar calculation on asymmetric molecule. The main reason for this is that the number of unique integrals that must be evaluated is smaller than for non symmetric molecules.

It is important that you construct the input structures for symmetric molecules taking into account all the symmetry elements present in the molecule. Many molecular editors help you out in this task. For example, Maestro provides the Geometry Symmetrizer tool in the builder (Diamond icon) and the minimization with the Clean-Up tool often produces symmetric structures. The program MOLDEN utilizes pre-symmetrized fragments and building a molecule from fragments usually gives the structure with a correct symmetry.

Hartree-Fock Quantum Mechanics with Jaguar

The first part of the tutorial illustrates how to perform ab initio single point energy evaluations with the program Jaguar, which is integrated with the Maestro graphical interface. First, build neopentane (2,2-dimethylpropane) molecule using the Maestro Builder but do not clean up your geometry. Inspect the structure by rotating it in the Builder window. The structure you built has a correct chemical connectivity but incorrect valence angles and symmetry. Create an entry from your workspace.

  1. In the Applications menu, select Jaguar -> Single Point Energy.
  2. Inspect possible options in the Molecule Folder. Make sure that Symmetry: Use if present is selected. Pick a small basis set, such as 6-31G and with one polarization function but no diffuse functions. Notice that this basis set employs 6 Cartesian D functions.
  3. Inspect possible options in the Theory Folder. We will be using HF level of theory for now and because this is a closed-shell ground state molecule, we do not need to use spin-unrestricted methods or configuration interaction singles (CIS) theory.
  4. Inspect possible options in the SCF Folder. Select Fully Analytic for accuracy level. We choose the Fully Analytic option simply because this way the calculation follows the description outlined in the lecture and your textbook; the Quick and Accurate options lead to use of pseudospectral algorithms that are faster but unfamiliar to you. Notice that you can also change the convergence criteria for the iterative SCF solution.
  5. To perform single point calculation at this geometry hit Start .... Another window pops up, asking what shall be done with the results. You may keep the defaults. Hit Start to launch the calculation.
  6. Examine the output in the Job Monitor window. Notice the Point Group used, Cs indicates plane of symmetry. Calculate the total time it took to perform the calculation by subtracting the starting time from the finish time. Record the last value for total energy.
  7. Hit Close to close the Monitor window
  8. Hit Close to close the Minimization window
  9. Return to the Maestro Builder and perform Geometry Clean-up (Sponge Icon). Click on Geometry Symmetrizer (Diamond Icon); it should report Td as the symmetry group. Inspect the molecule by rotating it in the builder window and notice how it is more symmetric than previously.
  10. Repeat the Hartree-Fock Calculation and record the point group, time required to minimize the structure, and the final energy. Why was this calculation faster? Why was the energy lower?

Hartree-Fock Quantum Mechanics with Gaussian

Repeat this analysis using MOLDEN to build the neopentane molecule and use Gaussian to perform calculations. MOLDEN will automatically produce correct symmetry if you build a five-carbon tetrahedral core and then substitute four terminal carbons with methyl group. Save this file as Gaussian Z-matrix, add required header lines (request 16 MW of memory, and use #P HF/6-31G(d) for the command line. The charge is zero and multiplicity 1 in this case). Submit your calculation to the queue. The run time is less than a minute. Inspect the text of the output using the command more (more filename.log. Verify that the Full point group is TD and record the final energy (SCF Done: E(RHF) line). Look at the end of your output file and record the CPU time. Alternatively, you may use the UNIX command tail filename.log to see the last ten lines of a text file.

Inspect the output with MOLDEN. Click on the SCF conv button to inspect the convergence of the iterative SCF solution (this is single point calculation, the geometry is fixed). Verify that the final energy matches what you wrote down. Now change the structure in the Z-matrix editor such that each carbon-carbon bond has an unique length in the range of 1.45-1.6 Angstroms. Press Enter to let changes take effect and write out this Gaussian Z-matrix and perform calculation on this slightly non-symmetric structure.

Inspect the log file as before. Notice that the Full point group for asymmetric molecules is C1. Record the final energy and computational time. Why is the computational time longer for the asymmetric structure?

Related Publications and Further Reading


Tutorial by Dr. Kalju Kahn, Department of Chemistry and Biochemistry, UC Santa Barbara. ©2006