Geometric optimizations of Hydrogen Peroxide (H₂O₂) molecule

In this section the results obtained from geometric optimization calculations done by the software GAMESS is displayed for H₂O₂.  Four different basis sets were used in the calculations, the illustrations go from the basis set containing the most sets, double zeta valence (DZV), to the one containing the least (AM1).  A basis set is essentially "all the atomic orbitals that are used in the calculation."¹  The larger the basis set, the more atomic orbitals that will be used to make the molecular orbitals for each electron.  It would appear that the 6-21G basis set provides the best answer out of the three ab initio basis sets. The basis sets 6-21G, 6-31G, and DZV belong to a level of theory known as ab initio.  This theory calculates all of the integrals in the schrodinger equations; this results in a greater accuracy of the calculation.  The AM1 basis sets belongs to a level of theory called the semi-emperical method.  This method uses some experimental data to estimate the values of some of the integrals in the Hamiltonian.  The bond lengths and angles are tabulated and compared to literature values in the table below.  As one can see the values produced by the 6-21G basis set gives the closest results to those from the literature.  But even this basis set does not do a great job of estimating the dihedral angle.  This is because the values obtained from the literature were gotten using more sophisticated basis sets and extra algorithms.  It was not possible for us to do this because of time restraints and limited computing power.  The dipole moments of each of these geometries was also calculated from each basis set and compared to literature values.  The dipole moment is very inaccurate because the optimal geometry was not obtained from our calculations.  The calculated dipole moment can be improved by including polarization functions in the calculations, but this inclusion is insignificant when the incorrect geometry is being used to calculate the dipole.

Table 1: List of bond angles, lengths, and dipole moments, from the basis sets compared to experimentally determined bond lengths and angles.

	Atoms linked	AM1	6-21G	6-31G	DZV	Experimentally determined
Bond length (nm)	O-O	0.145	0.145	0.148	0.146	0.1452
	O-H	0.098	0.098	0.097	0.095	.097
Bond angle	O-O-H	96.8	96.8	99.3	101.2	95
Dihedral angle	H-O-O-H	129.4	129.4	179.8	179.7	119.8
Dipole moments		1.371946	0.009117	0.009882	0.010116	1.77

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