You have already learned, in your Mathcad work, how to expand a function in a complete set (or basis set). In that work you learned that using more functions gives results that are more correct but also takes more computing time. You also learned that each function of the basis has a coefficient or weight assigned to it when it is used to approximate a function. In this exercise, you will observe how basis functions are used in computational chemistry and how different basis function produce different properties of the atom or molecule. There are two parts to the experiment, one part for atoms and the second part for molecules.
You will perform ab-initio Hartree-Fock calculations. You will use these basis sets:
STO-3G, 3-21G*, 6-31G*, 6-31G**, 6-31G+
You will be using the PC Spartan for these calculations:
Perform the calculation on your atom for all basis sets in Spartan. Start with STO-3G and work your way through the list. You will have five calculations. Copy the total energy for each case. Make sure you do the calculation on the correct ground state multiplicity for your atom. You can look this up in the NIST database.
Amber, Kat, Jeff: carbon Bill & Emir: nitrogen
Lou & Jim: fluorine Andrea & Jay: boron Vanessa & Natalie: oxygen
For the molecular calculations, we will observe both the energy and the atomic charges as the basis set changes. We will use the water molecule for our prototype. First, build the water molecule, and optimize the geometry with an STO-3G calculation; save the results. For your other basis sets, start with this optimized geometry and do single point calculations. As in the previous part, we need to know the basis set, the energy, and the charge on hydrogen and oxygen. Be sure to check the box in the calculation menu to print the atomic charges.
Questions:
Explain the details of each basis set. In other words, what information is conveyed by the acronym STO-3G? In the water molecule, how many primitive and contracted functions are used for each basis set that was used? The number of integral calculations for a basis set of N functions is roughly N4. How many integrals are calculated for your atom with each basis set you used?
What effect does the basis set have on atomic energies? Is this effect what you would expect? Explain.
Is there a specific correlation between basis set and energy? In other words, if you plot the data, is there a definite relationship such as a straight line, curve, or some other form, or are the data random?
Graph the hydrogen charge and the oxygen charge as a function of basis set. What trend is evident in your graph?
What is the relationship between basis set and molecular charge?
Are there significant differences between the Mulliken and Natural charges?
Do we need a large basis to compute reasonable charges in molecules? Explain your reasoning.