G2 theory aims to reproduce effectively QCISD(T)/6-311+G(3df,2p) energies
through a series of calculations at lower level. The G2 energy at 0 degree Kelvin
E_{0}(G2) is defined as:
E_{0}(G2) = E[QCISD(T,FC)/6-311G(d,p)//MP2(FULL)/6-31G(d)]
+ DE(+)
+ DE(2df)
+ DE(+3df,2p)
+ DE(HLC)
+ ZPE
The definition of the components being:
DE(+) = E[MP4(FC)/6-311+G(d,p)//MP2(FULL)/6-31G(d)] - E[MP4(FC)/6-311G(d,p)//MP2(FULL)/6-31G(d)]
DE(2df) = E[MP4(FC)/6-311G(2df,p)//MP2(FULL)(6-31G(d)] - E[MP4(FC)/6-311G(d,p)//MP2(FULL)/6-31G(d)]
DE(+3df,2p) = E[MP2(FC)/6-311+G(3df,2p)//MP2(FULL)/6-31G(d)] - E[MP2(FC)/6-311G(2df,p)//MP2(FULL)/6-31G(d)]
- E[MP2(FC)/6-311+G(d,p)//MP2(FULL)/6-31G(d)] + E[MP2(FC)/6-311G(d,p)//MP2(FULL)/6-31G(d)]
DE(HLC) = -An(beta) - Bn(alpha)
A = 4.81 mHartrees; B = 0.19 mHartrees
n(alpha) = No. of alpha valence electrons
n(beta) = No. of beta valence electrons
ZPE = 0.8929 * ZPE[HF/6-31G(d)]
Comments:
The necessary energies can be calculated most efficiently in the following sequence:
All of these energies can be calculated step by step or in an automated manner using the G2 keyword
in Gaussian (here using water as an example):
#P G2
test154 G2 theory for water
0 1
O1
H2 1 r2
H3 1 r2 2 a3
r2=0.947323
a3=105.4974
The energy components will then be calculated in a sequence of different consecutive jobs.
The results will be listed at the very end of the output file in the following manner:
Temperature= 298.150000 Pressure= 1.000000
E(ZPE)= 0.020515 E(Thermal)= 0.023350
E(QCISD(T))= -76.276068 E(Empiric)= -0.024560
DE(Plus)= -0.010833 DE(2DF)= -0.037392
G1(0 K)= -76.328338 G1 Energy= -76.325502
G1 Enthalpy= -76.324558 G1 Free Energy= -76.345935
E(Delta-G2)= -0.008273 E(G2-Empiric)= 0.004560
G2(0 K)= -76.332051 G2 Energy= -76.329216
G2 Enthalpy= -76.328271 G2 Free Energy= -76.349648
DE(MP2)= -0.054454
G2MP2(0 K)= -76.330008 G2MP2 Energy= -76.327172
G2MP2 Enthalpy= -76.326228 G2MP2 Free Energy= -76.347605
The values given for the G2 Energy, the G2 Enthalpy and the G2 Free Energy all refer to a temperature
of 298.15K. Values for different temperatures can be computed using the G2(Restart,ReadIso) keyword.
What is listed here as E(Empiric) corresponds to the HLC correction as defined for the G1 procedure.
The G2-type HLC energy is obtained by addition of what is listed as E(G2-Empiric) (corresponding to
1.14 mHartrees per valence electron pair).
Literature: