Chemistry Reference
In-Depth Information
degree of same-spin electron correlation due to the Pauli principle.
91
This led
him to introduce separate scale factors for the same-spin and opposite-spin
pair correlation energies, yielding the spin-component-scaled (SCS) MP2
method.
91
The scaling factors used by Grimme are
3
for same-spin and
5
for
opposite-spin components of the correlation energy. The introduction of these
two parameters does not increase the computational cost, but it leads to
improved properties such as bond lengths and vibrational frequencies.
92
A
related approach of Head-Gordon and co-workers
93
is the spin-opposite-
scaled MP2 (SOS-MP2) method, which neglects the same-spin term and scales
the opposite-spin term.
The SCS-MP2-type methods have generated significant interest from
scientists, particularly for applications to noncovalent interactions. One inves-
tigation of SCS-MP2 for the benzene dimer
94
by Hill, Platts, and Werner
demonstrated interaction energy errors of only 0.1-0.2 kcal mol
1
when com-
pared to benchmark
61
CCSD(T) results. Hill and Platts later reoptimized the
SCS-MP2 scaling parameters using nucleic acid base-pair interactions to
obtain better results for a wider array of
interactions.
95
These workers
dubbed the SCS-MP2 method with the new parameters (1.76 for same-spin
terms, and neglecting the opposite-spin terms) as SCSN-MP2, where the N
denotes the nucleic acids used in the parameterization. When applied to the
S22 test set
96
of intermolecular interaction energies, the (density-fitted, local)
MP2-based methods had mean absolute deviations of 0.81 (DF-LMP2), 0.27
(DF-SCSN-LMP2), 1.26 (DF-SCS-MP2), and 1.97 kcal mol
1
(DF-SOS-
LMP2).
95
Another study by Antony and Grimme
97
of 165 biologically rele-
vant, noncovalent complexes showed a clear improvement of SCS-MP2 over
MP2 when comparing to CCSD(T) results in the complete-basis-set limit.
Additionally, a good cancellation of errors was observed when using SCS-
MP2 with polarized triple-
p
basis sets (without diffuse functions or counter-
poise correction). However, in some saturated systems (e.g., methane dimer),
the original MP2 method is accurate, and spin-component scaling degrades the
quality of the results.
Apart from the first study of Hill et al.,
94
most of these studies consid-
ered only single-point energies. Our group investigated potential energy
curves for a variety of prototype noncovalent complexes, with and without
local correlation approximations.
88
In general, we found that both SCS-MP2
and SCSN-MP2 results are better than MP2 results for
interactions,
but both lead to larger errors for the methane dimer. Except for that test
case, the SCS-MP2 potential curves in the complete-basis-set limit tend
to lie slightly above, and SCSN-MP2 curves slightly below, the benchmark
CCSD(T) curves. SCSN-MP2 tends to overbind slightly at large intermole-
cular separations. On the other hand, more recent work
98
suggests that
the original SCS-MP2 method may be more reliable than SCSN-MP2
for the potential energy curves of parallel-displaced configurations of
p
p
-
p
interactions.
