.
Therefore, at the UHF level, we investigate the influence of the
basis set to check if the problem could
be related to a basis set effect .
It is difficult to know when the quality of a basis set is approaching
the Hartree-Fock limit. It is a rather elusive notion.
Most basis sets thought earlier of Hartree-Fock
limit quality, even
in the case of
a simple triatomic molecule as
H2O
, are in reality far from said limit.
Bawagan and Feller
[Bawagan 87]
in order to
compare
electron momentum spectroscopy (EMS) results with
ab initio predictions,
were obliged to employ basis sets comprising up to 99 gaussians
functions.
Since the discrepancy found between EMS experimental results and
earlier
computationnal results was mainly found in a inaccurate description
of the low-momentum outer valence electrons .
There is little doubt
that for a still slower Rydberg electron, an accurate description
would be even more difficult to achieve.
The total electronic energy is not a very sensible
indicator of the accuracy of the description
of a diffuse orbital.
In order to describe as well as possible the
outer "Rydberg" orbital, we employ the following procedure :
we inspect the MO coefficients produced by the variational procedure.
When the variational procedure gives a large value ( "e.g" 0.5 ) for
the smaller exponent, we know that the diffuse space has not been
sufficiently described. Then we add yet another more diffuse
exponent, until the value of the corresponding MO
coefficient goes down under the
0.01 threshold value.
So our constructed basis sets should be large enough to
describe correctly the diffuse character of the HOMO.
In the heroic days of quantum chemistry, it was
customary of discussing MO coefficients.
The not so tedious but worthwhile inspection of MO coefficients
is very seldom reported nowadays, probably because of the
predominance of a "black box" approach.
A first series of UHF
computations were done using four different relatively small basis sets.
A small basis set, denoted
, 4-31G/R1 , was constructed as follows :
a Gaussian 86
built-in 4-31G split-valence basis set [Poirier 85] is supplemented
with diffuse orbitals. On the oxygen atom,
we add three sets of s-type gaussian functions with respective exponents
0.10 , 0.050 and 0.025, and one set of p-type functions with exponent 0.025.
On each of the three hydrogen atoms, we add
one set of s functions with exponent 0.025.
The exponent 0.10 is used to represent the overlap of the Rydberg orbital with
the valence region, and the exponents 0.050 and 0.025
of the s-type gaussian describe the
diffuse 3 s character of the Rydberg
electron around the oxygen atom.
In order to account for the perturbation to the 3s symmetry of the
Rydberg orbital, due to the hydrogen atoms, we add one p-type on the
oxygen and one s-type gaussians on the hydrogens.
A second basis used, denoted 4-31G/R2 , was derived from the first
basis set, by replacing the exponents 0.050 and 0.025 by
0.061 and 0.024 respectively.
The third basis set used, denoted D95**/R3 is constructed as follow :
we take
the Gaussian 86 built-in Dunning-Huzinaga
full double-zeta basis set
[Poirier 85]
supplemented by the built-in Gaussian 86
polarization functions
[Frisch 86]
;
we then add on the oxygen atom
two sets of s-type gaussian functions with exponents 0.061 and 0.024 ,
two sets of p-functions with exponents 0.059 and 0.028 , and one set of
d-functions with exponent 0.015. On the hydrogen atoms, we add
one set of s functions with exponent 0.08 as well as a set of p
functions with exponent 0.08.
The exponents 0.061 and 0.024
are derived from the Dunning exponents
[Dunning 77]
describing the 3s Rydberg orbital
on the oxygen, with the recommended splitting factors 0.75 and 1.9.
The exponent 0.028 is the 3p Rydberg oxygen exponent of Dunning, and
0.059 is a Dunning intermediate exponent describing a possible ionic character
A fourth more extended basis set is denoted D95**++/R4 .
In order to construct the D95**++/R3 basis set, we add to the D95**/R3
basis set,
the built-in Gaussian 86
[Frisch 86]
diffuse fonctions :
one sp gaussian function
of exponent 0.0845 on the oxygen, and s gaussian function of
exponent 0.036 on the hydrogen atoms .
We then add
two sets of s-type gaussian functions with exponents 0.10 and 0.0066 on the
oxygen atom, and one set of s-type functions with exponent 0.025 on each of
the hydrogen atoms.
The s-type orbital with exponent 0.10 describes the penetration of the
Rydberg electron into the valence region and the very diffuse orbital
with exponent 0.0066 is used to check if the Rydberg electron has a further
diffuse character. The latter exponent is the Dunning exponent
[Dunning 77]
for the 4 s orbital around the oxygen atom.
In a second series of UHF computations, we employed four
different large basis set obtained by completing
valence bases with an even-tempered expansion of diffuse functions.
We completed
a large Van Duijneveldt
[Van Duijneveldt 71] ,
[Poirier 85]
valence basis set in three
different ways (VD/R5, VD/R6, VD/R7 )
We also
used the smaller
GAMESS built-in Dunning-Hay valence basis set
[Poirier 85]
and completed it by an even-tempered expansion (
DH/R8 ).
