Chemistry Reference
In-Depth Information
To illustrate the point, consider two noninteracting (i.e., well-separated)
HF molecules. (This can effectively be achieved in a computation by placing
the HF molecules on the
z
axis and separating them by
1000
˚
so that the
F atoms are at 0 and 1000
˚
while the H atoms are at 0.900 and 1000.900
˚
.) Using the data in Table 1, we know the electronic energy of a single HF
molecule is
033816 E
h
when computed with the SCF method and the
aug-cc-pVDZ basis set. As you would expect, the corresponding energy
of two noninteracting HF molecules (i.e., separated by 1000
˚
) is exactly
2
100
:
067632 E
h
but only because the SCF method is
size consistent. Truncated configuration interaction (CI) methods such as the
one including only single and double configurations (CISD) are not. The
CISD/aug-cc-pVDZ energy is
100
:
033816
¼
200
:
253275 E
h
if all electrons are correlated
while that of two monomers separated by 1000
˚
100
:
is
200
:
488703 E
h
, which
is significantly different than 2
506551 E
h
.Asmen-
tioned in the Introduction, this review only focuses on size-consistent electronic
structure techniques. In the final step (step 7) of this tutorial, you should com-
pute the SCF and CISD (all electrons correlated) energies of two HF monomers
separated by 1000
˚
. Compare these energies to those of a single monomer.
100
:
253275
¼
200
:
Summary of Steps in Tutorial
1. Reproduce electronic energies in Table 1.
2. Calculate
E
int
values on the left side of Table 2 (Eq. [2]).
3. Reproduce electronic energies in Table 2.
4. Calculate
E
CP
int
values on the right side of Table 2 (Eq. [8]).
5. Reproduce electronic energies in Table 3.
6. Calculate components of
E
int
in Table 4 (Eqs. [12], [16], [17], [25]-[27]).
7. Reproduce the electronic energies discussed in the proceedings section and
check the size consistency of the results obtained with the SCF and CISD
methods.
Sample input files for various software packages are available online.
92
If the elec-
tronic energies that you compute do not agree with those presented here, make
sure that the energy is converged to at least eight decimal places in the SCF pro-
cedure and that tolerances for integral screening are no larger than 10
10
.Addi-
tionally, discrepancies on the order of 1
10
6
E
h
have been observed in some
cases that can be attributed to differences in the conversion factor used to change
angstroms to bohrs. Finally, rounding errors may lead to discrepancies on the
order of 0
01 kJ mol
1
for the other data presented in Tables 2 and 4.
:
HIGH-ACCURACY COMPUTATIONAL STRATEGIES
Although quantum mechanical studies of weak interactions can be
traced back to Slater's 1929 work on He,
109
the first supermolecule ab initio
