W1 (Weizmann1) theory is a compound method aiming at kJ/mol accuracy in thermochemical calculations.
The determination of W1 energies involves extrapolated values of SCF and correlation energies based on
a series of calculations with increasingly large basis sets. First and second row elements are treated
somewhat differently at various stages of the procedure:
(1) Geometry optimization is performed at the Becke3LYP/ccpVTZ+1 level of theory. The "ccpVTZ+1"
basis set is identical to the standard ccpVTZ basis set for first row elements and for hydrogen. For second row
elements a set of highexponent d functions is added, taken from the ccpV5Z basis set as the dfunctions
with highest exponent.
(2) Zeropoint vibrational energies and thermal corrections are obtained at the Becke3LYP/ccpVTZ+1 level
of theory using a scale factor of 0.986.
(3) The HartreeFock infinite basis set limit (E_{SCF,INF}) is derived from calculations with the aughccpVDZ+2d,
aughccpVTZ+2d1f and aughccpVQZ+2d1f basis sets. These basis sets have different meaning for different
elements: for hydrogen the corresponding ccpVnZ basis sets are used with n = D, T, Q. For first row elements
the augccpVnZ basis sets are used with n = D, T, Q. For second row elements the standard augccpVnZ basis
sets are augmented with high exponent d and ftype basis functions necccesary to describe innershell correlation
effects correctly.
Two different extrapolation schemes have been tested for extrapolating to the SCF infinite basis set limit:
(3a) Old style (threepoint) extrapolation:
E_{SCF,INF} = E_{SCF,AVQZ}  (E_{SCF,AVQZ}  E_{SCF,AVTZ})^{2}/ (E_{SCF,AVQZ}  2xE_{SCF,AVTZ} + E_{SCF,AVDZ})
(3a) New style (twopoint) extrapolation:
E_{SCF,INF} = E_{SCF,AVQZ} + (E_{SCF,AVQZ}  E_{SCF,AVTZ})/ ((4/3)^{5}  1)
(4) The infinite basis set limit of the CCSD valence correlation energy (E_{COR,CCSD,INF}) is obtained from
frozencore calculations with the aughccpVDZ+2d, aughccpVTZ+2d1f, and aughccpVQZ+2d1f basis sets
using the following extrapolation scheme:
E_{COR,CCSD,INF} = E_{COR,CCSD,AVQZ} + (E_{COR,CCSD,AVQZ}  E_{COR,CCSD,AVTZ})/ ((4/3)^{3.22}  1)
(5) The infinite basis set limit of the contributions of triple excitations to the CCSD(T) valence correlation
energy (E_{COR,T,INF}) is obtained from frozencore calculations with the aughccpVDZ+2d and aughccpVTZ+2d1f
basis sets using the following extrapolation scheme:
E_{COR,T,INF} = E_{COR,T,AVTZ} + (E_{COR,T,AVTZ}  E_{COR,T,AVDZ})/ ((3/2)^{3.22}  1)
(6) Relativistic effects and the effects of corevalence correlation are covered as the energy difference between
a frozen core CCSD(T) calculation and a scalarrelativistic calculation with the DouglasKrollHess model using
all electrons. In both cases the MTsmall basis set is used:
E_{CV,DKH} = E_{tot}(CCSD(T,Full)/MTsmall/dkh)  E_{tot}(CCSD(T,FC)/MTsmall)
The final total energy of the system is then simply the sum of the components:
E_{tot}(W1) = E_{SCF,INF} + E_{COR,CCSD,INF} + E_{COR,T,INF} + E_{CV,DKH}
Using ammonia (NH_{3}) as an example, the following results are obtained:

Collecting the data from the above table the W1 total energy amounts to:
E_{tot}(W1) = 56.224998 + 0.270188 + 0.009389 + 0.081843 = 56.586418 au (oldstyle extrapolation)
E_{tot}(W1) = 56.224938 + 0.270188 + 0.009389 + 0.081843 = 56.586358 au (newstyle extrapolation)
For this particular example the oldstyle and newstyle extrapolation procedures yield very similar results differing by
only 0.000060 au (= 0.16 kJ/mol). Combination of the latter W1 total energy with zero point vibrational energies and
thermal corrections yield the energies at a given temperature:
E_{0} = 56.552637 au
H_{298} = 56.548825 au
G_{298} = 56.570666 au
The necessary energies can be calculated most efficiently in the following sequence:
The "aughccpVnZ+2df" acronym can be used in Gaussian 03 to conveniently load the correct basis functions
for a given job step for first and second row elements. The W1 method currently invoked in Gaussian 03
with the W1 keyword uses the "newstyle" twopoint extrapolation scheme for the SCF component.
Literature:
last changes: 09.03.2017, HZ questions & comments to: zipse@cup.unimuenchen.de