Molecular modeling is a powerful tool which allows property calculation once the true wavefunction is known. Unfortunately, for multi-electron atoms and molecules, Schrodinger's equation cannot be solved and only an approximate wavefunction can be found.  The variational principle states that calculated energies from approximate wavefunctions are greater than true energies.  Wavefunctions that predict energies closest to experimental energies serve as the best approximations to true wavefunctions.

In approximate wavefunctions, molecular orbitals are represented as sums of "basis functions" which are atomic orbitals centered on the various atoms (most modern ab initio methods express each basis function as a sum of Gaussian type orbitals to increase the speed of the calculation).  Larger sets of basis functions generally do better at predicting properties, but come with greater computational costs.  For large molecules (such as proteins), ab initio calculations are not practical and semi-empirical or molecular mechanics methods have to be used.  For small molecules, ab initio methods are quite practical.

In this lab, calculations for water will use basis sets of increasing sophistication to determine the effect of basis set selection on property prediction and computational requirements.

Larger basis sets involve 1) more Gaussian functions for core or valence shells, 2) multiple sets (e.g. double zeta) of valence basis functions to account for anisotropic (nonspherical) electron distributions, and 3) polarization functions (p-type for H atoms, d-type for other atoms (**notation indicates both types of polarization functions are used, * indicates polarization functions for H atoms).  Polarization basis functions allow the electronic charge to be off-center from a nucleus.

1. Using geometry optimization, predict the properties of water listed below with each of these five basis sets: STO-3G, STO3-21G*, STO6-31G*, STO6-311G**, and STO6-311G** with MP2 (Note: MP2 is an ab initio procedure to correct for the correlation energy which the HF method does not account for).  In each case, compare your results with experimental values and with computational requirements (CPU time found under display, output at end of file).

a.  Total Energy (found under the properties menu)
(Note:  The total energy includes all electron-electron repulsions, electron-nucleus attractions, nucleus-nucleus repulsions, and electron kinetic energies.  It does not include molecular translational energy, rotational energy, or vibration energy.  The experimental total electronic energy of water is -76.481 hartrees. (Levine, Quantum Chemistry, p.395).
b.  Bond angle (found under the geometry menu)
c.  Bond distance (found under the geometry menu)
d.  Dipole moment (found under the properties menu)
e.  Vibrational frequencies (there are three of these for water) (found under the properties menu, must select Frequency box in ab initio setup as option)
f.  Ionization energy (use Koopman's theorem) (remember to include PRINTMO as an option)