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.^{328} 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).^{226}

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.^{442} 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^{442} and the analytical
gradient^{589} 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.^{587} 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:^{587}

$${g}_{\omega}({r}_{12})=\frac{1}{{r}_{12}}+{c}_{\mathrm{MOS}}\frac{\mathrm{erf}\left(\omega {r}_{12}\right)}{{r}_{12}}$$ | (6.22) |

The recommended OMEGA value is $\omega =0.6$ bohr${}^{-1}$.^{587}
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${X}^{2}$, where $X$ = the
number of auxiliary basis functions, for both energy and analytical gradient
evaluations. Disk space requirement for closed shell calculations is $\sim 2OVX$ for energy evaluation and $\sim 4OVX$ 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 $n$; use $\omega =n/1000$. The recommended value is |

$n=600$ ($\omega =0.6$ bohr${}^{-1}$) | |

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) |

$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 EXCHANGE hf CORRELATION rimp2 BASIS aug-cc-pvdz AUX_BASIS rimp2-aug-cc-pvdz BASIS2 racc-pvdz Optional Secondary basis THRESH 12 SCF_CONVERGENCE 8 MAX_SUB_FILE_NUM 128 SCS 1 Turn on spin-component scaling DUAL_BASIS_ENERGY true Optional dual-basis approximation N_FROZEN_CORE fc SYMMETRY false SYM_IGNORE true $end

$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 EXCHANGE hf CORRELATION rimp2 BASIS aug-cc-pvtz AUX_BASIS rimp2-aug-cc-pvtz BASIS2 racc-pvtz Optional Secondary basis THRESH 12 SCF_CONVERGENCE 8 MAX_SUB_FILE_NUM 128 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 N_FROZEN_CORE fc SYMMETRY false SYM_IGNORE true $end

$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 SYMMETRY false $end

$molecule 0 1 Cl Cl 1 2.05 $end $rem JOBTYPE sp METHOD mosmp2 OMEGA 600 BASIS cc-pVTZ AUX_BASIS rimp2-cc-pVTZ N_FROZEN_CORE fc THRESH 12 SCF_CONVERGENCE 8 $end