- An MP2(full)/6–31G* geometry optimization, wanted to get a high-quality
geometry for all the subsequent calculations (which are thus single-point jobs) - QCISD(T,E4T)/6–31G(d), single-point energy
- MP4/6–31þG(d), single-point energy
- MP4/6–31G(2df,p), single-point energy
- MP2¼Full/GTLarge, single-point energy
- Atomic spin-orbital corrections, sometimes empirical, and a “higher-level cor-
rection”, HLC, to (hopefully) take any remaining inadequacies into account
These eight basic steps are used to assemble a molecular energy as the sum of
various energy differences and a spin–orbit correction and a final empirical energy
increment (the “higher level correction”) based on the number of paired and
unpaired electrons. The G3 energy is essentially a kind of QCISD(T)/big basis
energy performed on an MP2(full)/6–31G geometry, with a HF/6–31G ZPE and
a spin–orbit and an empirical energy correction, but such a direct calculation would
be slower than breaking it into the steps used here. For the details see Curtiss et al.
[ 179 ]. A key improvement in G4 over G3 is the replacement of the quadratic CI
correlation method by the coupled cluster method (Section 5.4.3); this particular
change did not alter the accuracy for the test set of molecules, but it presumably
improves the reliability, as “...the QCISD(T) method has rather dramatic failures,
which does not occur with the CCSD(T) method” [ 180 ]. See too Hrusak et al. for a
comparison of quadratic CI and coupled-cluster [ 102 ]. In the G3(MP2) method, the
main change is that MP2 calculations replace MP4 ones [ 181 ]. Because of the
empirical energy corrections in the Gaussian multistep methods, they are not fully
ab initio, but rather somewhat semiempirical, except when these corrections cancel
out. This happens, for example, in calculating proton affinities as the energy
difference of the protonated and unprotonated species, where the spin–orbit correc-
tions and the number ofa- andb-spin electrons are the same on both sides of the
equation. Until the promising G4(MP2) method becomes readily available we shall
take G3(MP2) as being the choice Gaussian multistep method, a good compromise
between accuracy and speed. Gaussian methods are compared with CBS methods
below.
CBS Methods
The key to these methods is the extrapolation of the basis set to an infinite limit (to
completion). There are three basic CBS methods: CBS-4 (for fourth-order extrapo-
lation), CBS-Q (for quadratic CI) and CBS-APNO (for asymptotic pair natural
orbitals), in order of increasing accuracy (and increasing computer time) [ 113 ].
These methods are available with keywords in the Gaussian 94 and later Gaussian
programs, where the preferred versions of CBS-4 and CBS-Q are specified by the
keywords CBS-4M [ 185 ] and CBS-QB3 [ 186 ] (M for minimum population locali-
zation, B3 for use of the B3LYP density functional). CBS-4M can handle molecules
with up to about 20 heavy atoms and its has its “largest errors in the neutral
heats of formation ... for ClF3 (13.6 kcal/mol), O3 (12.6 kcal/mol), and C 2 Cl 4
5.5 Applications of the Ab initio Method 311