G3 theory

G3 Theory

G3 is an improvement over G2 theory in several ways and tries to reproduce effectively QCISD(T)/G3large
energies through a series of calculations at lower level. The G3large basis set is a slightly modified
version of the 6-311+G(3df,2p) basis set used in the G2 procedure. The G3 energy at 0 degrees Kelvin
E₀(G3) is defined as:

The definition of the components being:

The necessary energies can be calculated most efficiently in the following sequence:

Optimization and frequency calculation at the HF/6-31G(d) level of theory
Optimization at the MP2(FULL)/6-31G(d) level of theory
QCISD(T,FC)/6-31G(d)//MP2(FULL)/6-31G(d) single point
MP4(FC)/6-31+G(d)//MP2(FULL)/6-31G(d) single point
MP4(FC)/6-31G(2df,p)//MP2(FULL)/6-31G(d) single point
MP2(Full)/G3large//MP2(FULL)/6-31G(d) single point

Comments:

While a 6-311+G(3df) basis set has been used in G2 theory for all first and second row
elements, a different strategy has been pursued in G3 theory. First, a slightly smaller
6-311+G(2df) basis has been chosen for the first row elements, while a larger 6-311+G(3d2f)
basis has been chosen for the second row elements. In both cases core polarization functions
(e.g. p- and d-type for carbon) have also been added. Hydrogen is still treated with a 311+G(2p)
basis. The G3large basis sets can be found on the G3 theory web site set up by Larry Curtiss.
A local copy can be found here.
Open shell systems are treated using unrestricted wavefunctions (UHF, UMP2 . . )
The higher level correction (HLC) is supposed to compensate for the remaining deficiencies
of the method. In contrast to G2 theory, different parameters A and B are used for
atoms and molecules to give the smallest average absolute deviation from experiment.
Spin orbit correction terms E(SO) (mainly of experimental origin) are added only for atoms
The mean absolute deviation for the original G2 neutral set (125 reaction energies) is
1.00 kcal/mol. The mean absolute deviation for the extended G2 neutral set (148 reaction
energies) is 0.9 kcal/mol.

Literature:

L. A. Curtiss, K. Raghavachari, P. C. Redfern, V. Rassolov, J. A. Pople,
"Gaussian-3 (G3) theory for molecules containing first and second-row atoms"
J. Chem. Phys. 1998, 109, 7764 - 7776.
L. A. Curtiss, K. Raghavachari,
"G2 Theory"
The Encyclopedia of Computational Chemistry, P. v. R. Schleyer (editor-in-chief),
John Wiley & Sons Ltd, Athens, USA, 1998, 2, 1104 - 1114.
L. A. Curtiss, P. C. Redfern, K. Raghavachari, V. Rassolov, J. A. Pople,
"Gaussian-3 theory using reduced Møller-Plesset order"
J. Chem. Phys. 1999, 110, 4703 - 4709.
A. G. Baboul, L. A. Curtiss, P. C. Redfern, K. Raghavachari,
"Gaussian-3 theory using density functional geometries and zero-point energies"
J. Chem. Phys. 1999, 110, 7650 - 7657.

last changes: 01.04.2008, AS
questions & comments to: axel.schulz@uni-rostock.de