In this exercise we will explore the basis set dependence of geometries and vibrational frequencies for simple molecules.
1. Perform Hartree-Fock geometry optimizations and harmonic frequency calculations (use both opt and freq keywords) for the following molecules:
CH4, NH3, H2O, HF
with the following basis sets:
STO-3G, 6-31G, 6-31G(d), def2-SVP, cc-pVDZ, aug-cc-pVDZ, 6-311G, def2-TZVP, cc-pVTZ, aug-cc-pVTZ, def2-QZVP
1a. Compare how the bond length and vibrational frequencies change. Show the results either as tables or plots.
When comparing basis sets and discussing the results you should compare the different types of basis sets that you have used.
1b. Compare your data to experimental data.
Q1. Is the basis set convergence similar or different for bond lengths vs. vibrational frequencies ?
Q2. Do you get good convergence or do you think you should go to even larger basis sets ?
Q3. What seems to matter the most for good geometries/frequencies: a large zeta-level, polarization functions, diffuse functions ? A little bit of everything ?
Q4. Is size of the basis sets (compare contracted basis functions) the most important?
Q5. What basis set seems to give pretty good (close to basis set limit) results without being overly expensive (either in terms of number of basis functions or computational time)? I.e. a basis set that is a good balance between expense and accuracy.
Q6. Why should you compare the largest basis numbers to experiment and not the numbers that compare the best?
2. Using the basis set that you chose before (the one that is a balance between expense and accuracy), recalculate the molecules with the DFT method PBE0 (DFT calculations work almost exactly the same as HF calculations, only the equations are slightly different).
Q1. Does the agreement with experiment improve?