Chemistry Reference
In-Depth Information
whose number is given by the binomial coefficient
¼
1
2
ð
L
þ
1
Þð
L
þ
2
Þ
L
þ
2
L
if L
¼
u
þ
v
þ
w.
To reduce the large number of primitives usually needed in GTO
calculations it is customary to resort to contracted GTOs, where each
function is the sum of a certain number of primitives, each contraction
scheme being specified by fixed numerical coefficients. The best basis is, of
course, uncontracted.
As an example, a contraction scheme used for LiHby Tunega andNoga
(1998) is based on the following spherical GTOs for Li and H:
ð
14s 8p 6d 5f
j
12s 8p 6d 5f
Þ)½
11s 8p 6d 5f
j
9s 8p 6d 5f
ð
7
:
45
Þ
The 204 primitives (103 GTOs on Li, 101 on H) are contracted to 198
functions (100 GTOs on Li, 98 GTOs on H), with the polarization
functions left uncontracted. This gives a rather moderate contraction.
Another example of a more sensible contraction can be taken from
Lazzeretti and Zanasi (1981) in their roughly HF Cartesian GTO calcula-
tion on H
2
O, which includes polarization functions on O and H:
ð
14s 8p 3d 1f
j
10s 2p 1d
Þ)½
9s 6p 3d 1f
j
6s 2p 1d
ð
7
:
46
Þ
The 110 GTO primitives are here reduced to 91 contracted GTOs,
giving an SCF molecular energy of
76
066 390E
h
. A more extended
basis for H
2
Owas the
½
13s 10p 5d 2f
j
8s 4p 1d
contracted CartesianGTO
basis set recently used by Lazzeretti (personal communication, 2004) in an
SCF calculation on H
2
O, giving a molecular energy of
76
:
:
066 87E
h
,
63
10
3
E
h
above the HF limit of
76
only 0
:
:
067 50E
h
estimated by
Rosenberg and Shavitt (1975) for H
2
O.
Use is sometimes made of even-tempered (or geometrical) sequences of
primitives, where the orbital exponents c
i
are restricted by
c
i
¼
ab
i
ð
7
:
47
Þ
i
¼
1
;
2
; ...;
m
with a and b fixed and different for functions of s, p, d, f,
symmetry.
Thus, the number of nonlinear parameters (orbital exponents) to be
optimized in a variational calculation is drastically reduced.
...
