The accuracy of MP2 calculations can be significantly improved by
semi-empirically scaling the opposite-spin (OS) and same-spin (SS) correlation
components with separate scaling factors, as shown by
Grimme.
434
J. Chem. Phys.
(2003),
118,
pp. 9095.
Link
Scaling with 1.2 and 0.33 (or OS and SS components)
defines the SCS-MP2 method, but other parameterizations are desirable for
systems involving intermolecular interactions, as in the SCS-MI-MP2 method,
which uses 0.40 and 1.29 (for OS and SS components).
296
Mol. Phys.
(2007),
105,
pp. 1073.
Link
Results of similar quality for thermochemistry can be obtained by only
retaining and scaling the opposite spin correlation (by 1.3), as was recently
demonstrated.
590
J. Chem. Phys.
(2004),
121,
pp. 9793.
Link
Furthermore, the SOS-MP2 energy can be
evaluated using the RI approximation together with a Laplace transform
technique, in effort that scales only with the 4th power of molecular size.
Efficient algorithms for the energy
590
J. Chem. Phys.
(2004),
121,
pp. 9793.
Link
and the analytical
gradient
774
J. Chem. Theory Comput.
(2007),
3,
pp. 988.
Link
of this method are available since Q-Chem v. 3.0, and
offer advantages in speed over MP2 for larger molecules, as well as
statistically significant improvements in accuracy.
However, we note that the SOS-MP2 method does systematically underestimate
long-range dispersion (for which the appropriate scaling factor is 2 rather
than 1.3) but this can be accounted for by making the scaling factor
distance-dependent, which is done in the modified opposite spin variant
(MOS-MP2) that has recently been proposed and tested.
772
J. Phys. Chem. A
(2005),
109,
pp. 7598.
Link
The
MOS-MP2 energy and analytical gradient are also available in Q-Chem 3.0 at a
cost that is essentially identical with SOS-MP2. Timings show that the
4th-order implementation of SOS-MP2 and MOS-MP2 yields substantial
speedups over RI-MP2 for molecules in the 40 heavy atom regime and larger. It is
also possible to customize the scale factors for particular applications, such
as weak interactions, if required.
A fourth order scaling SOS-MP2/MOS-MP2 energy calculation can be invoked
by setting the CORRELATION keyword to either SOSMP2 or
MOSMP2. MOS-MP2 further requires the specification of the $rem
variable OMEGA, which tunes the level of attenuation of the MOS
operator:
772
J. Phys. Chem. A
(2005),
109,
pp. 7598.
Link
| (6.22) |
The recommended OMEGA value is bohr.
772
J. Phys. Chem. A
(2005),
109,
pp. 7598.
Link
The fast algorithm makes use of auxiliary basis expansions and therefore, the
keyword AUX_BASIS should be set consistently with the user’s choice
of BASIS. Fourth-order scaling analytical gradient for both SOS-MP2
and MOS-MP2 are also available and is automatically invoked when
JOBTYPE is set to OPT or FORCE. The minimum memory
requirement is 3, where = the number of auxiliary basis functions,
for both energy and analytical gradient evaluations. Disk space requirement for
closed shell calculations is for energy evaluation and
for analytical gradient evaluation.
Summary of key $rem variables to be specified:
| CORRELATION | RIMP2 |
|---|---|
| SOSMP2 | |
| MOSMP2 | |
| JOBTYPE | sp (default) single point energy evaluation |
| opt geometry optimization with analytical gradient | |
| force evaluation with analytical gradient | |
| BASIS | user’s choice (standard or user-defined: GENERAL or MIXED) |
| AUX_BASIS | corresponding auxiliary basis (standard or user-defined: |
| AUX_GENERAL or AUX_MIXED | |
| OMEGA | no default ; use . The recommended value is |
| ( bohr) | |
| N_FROZEN_CORE | Optional |
| N_FROZEN_VIRTUAL | Optional |
| SCS | Turns on spin-component scaling with SCS-MP2(1), |
| SOS-MP2(2), and arbitrary SCS-MP2(3) |
Example 6.7 Example of SCS-MP2 geometry optimization
$molecule 0 1 C H 1 1.0986 H 1 1.0986 2 109.5 H 1 1.0986 2 109.5 3 120.0 0 H 1 1.0986 2 109.5 3 -120.0 0 $end $rem JOBTYPE opt CORRELATION rimp2 BASIS aug-cc-pvdz AUX_BASIS rimp2-aug-cc-pvdz BASIS2 racc-pvdz Optional Secondary basis SCS 1 Turn on spin-component scaling DUAL_BASIS_ENERGY true Optional dual-basis approximation integral_symmetry false point_group_symmetry False $end
Example 6.8 Example of SCS-MI-MP2 energy calculation
$molecule 0 1 C 0.000000 -0.000140 1.859161 H -0.888551 0.513060 1.494685 H 0.888551 0.513060 1.494685 H 0.000000 -1.026339 1.494868 H 0.000000 0.000089 2.948284 C 0.000000 0.000140 -1.859161 H 0.000000 -0.000089 -2.948284 H -0.888551 -0.513060 -1.494685 H 0.888551 -0.513060 -1.494685 H 0.000000 1.026339 -1.494868 $end $rem CORRELATION rimp2 BASIS aug-cc-pvtz AUX_BASIS rimp2-aug-cc-pvtz BASIS2 racc-pvtz Optional Secondary basis THRESH 12 SCF_CONVERGENCE 8 SCS 3 Spin-component scale arbitrarily SOS_FACTOR 0400000 Specify OS parameter SSS_FACTOR 1290000 Specify SS parameter DUAL_BASIS_ENERGY true Optional dual-basis approximation integral_symmetry false point_group_symmetry False $end
Example 6.9 Example of SOS-MP2 geometry optimization
$molecule 0 3 C1 H1 C1 1.07726 H2 C1 1.07726 H1 131.60824 $end $rem JOBTYPE opt METHOD sosmp2 BASIS cc-pvdz AUX_BASIS rimp2-cc-pvdz UNRESTRICTED true integral_symmetry false $end
Example 6.10 Example of MOS-MP2 energy evaluation with frozen core approximation
$molecule 0 1 Cl Cl 1 2.05 $end $rem METHOD mosmp2 BASIS cc-pVTZ AUX_BASIS rimp2-cc-pVTZ N_FROZEN_CORE fc OMEGA 600 THRESH 12 SCF_CONVERGENCE 8 $end