6.6 Auxiliary Basis (Resolution of the Identity) MP2 Methods

6.6.4 Spin-Biased MP2 Methods (SCS-MP2, SOS-MP2, and MOS-MP2)

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 energy442 and the analytical gradient589 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

gω(r12)=1r12+cMOSerf(ωr12)r12 (6.22)

The recommended OMEGA value is ω=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 3X2, where X = the number of auxiliary basis functions, for both energy and analytical gradient evaluations. Disk space requirement for closed shell calculations is 2OVX for energy evaluation and 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 ω=n/1000. The recommended value is
n=600 (ω=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)

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
   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

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
   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

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
   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
   JOBTYPE           sp
   METHOD            mosmp2
   OMEGA             600
   BASIS             cc-pVTZ
   AUX_BASIS         rimp2-cc-pVTZ
   N_FROZEN_CORE     fc
   THRESH            12
   SCF_CONVERGENCE   8
$end