Accurate Thermodynamic Properties; the Gn Models - Molecular Modelling - page 352

with triplet state molecules and with hypervalent molecules. Gaussian 2 (G2) theory was
introduced by Curtiss et al. (1991), and it eliminates some of the difficulties by making
three improvements to G1.
1. G2 theory eliminates the assumption of additivity of the diffuse sp and the 2df basis
functions used in G1 theory. This change gives a significant improvement for ionic
species and some anions.
2. It adds a third d function to the nonhydrogen atoms and a second p function to the hydro-
gen atoms. The third d function is especially important for some hypervalent molecules
such as SO 2 , whilst the second p function significantly improves the atomization energy
of some hydrogen-containing molecules.
3. The higher level correction is determined by a least squares fit for 55 molecules rather
than just the hydrogen atom and dihydrogen. This also contributes to an improvement
in calculated energies.
In fact, G2 only requires one extra calculation above G1, namely MP2/6-311+G(3df,2p).
A comparison was made for 79 well-established molecules, including 43 that were
not included in the original G1 papers. The final total energies are essentially at the
QCISD(T)/6-311+G(3df,2p) level of theory.
21.2.1 G2(MP2)
It was subsequently found that significant savings in computer resource could be obtained
at little cost in accuracy by reducing the order of the MP4 calculation to MP2 (giving the
G2 (MP2) variant).
21.3 G3 Theory
A recent reassessment by Curtiss et al. (1998) of G2 theory used 302 energies which
included 148 enthalpies of formation, 88 ionization energies, 58 electron affinities and 8
proton affinities for larger and more diverse molecules. This revealed some interesting dis-
crepancies. For example, the enthalpy of formation of CF 4 is too positive by 7.1 kcal mol − 1
whilst that of SiF 4 is too negative by 5.5 kcal mol − 1 . The deviations were also much lar-
ger for unsaturated systems than for saturated ones. These considerations led Curtiss et al.
(1999) to propose Gaussian-3 (G3) theory , which follows along the same lines as the earlier
G1 and G2 theories in that it is a well-defined sequence of ab Initio steps to arrive at the
total energy of a given molecule. As will be seen from the discussion below, G3 differs
from G2 theory in several major ways.
1. An initial HF/6-31G(d) equilibrium structure is obtained using the RHF or UHF
treatment (as in G2 theory).
2. HF/6-31G(d) structure is used to find vibration frequencies that are then scaled by
0.8929. The zero-point energy is calculated (as in G2 theory).
3. Equilibrium geometry is refined at MP2/6-31G(d) level, including all electrons. This
geometry is then used in single point calculations (as in G2 theory).