6.7 Attenuated MP2

MP2(attenuator, basis) approximates MP2 by splitting the Coulomb operator in two pieces and preserving only short-range two-electron interactions, akin to the CASE approximation,[Dombroski et al.(1996)Dombroski, Taylor, and Gill, Adamson et al.(1996)Adamson, Dombroski, and Gill] but without modification of the underlying SCF calculation. While MP2 is a comparatively efficient method for estimating the correlation energy, it converges slowly with basis set size — and, even in the complete basis limit, contains fundamentally inaccurate physics for long-range interactions. Basis set superposition error and the MP2-level treatment of long-range interactions both typically artificially increase correlation energies for non-covalent interactions. Attenuated MP2 improves upon MP2 for inter- and intramolecular interactions, with significantly better performance for relative and binding energies of non-covalent complexes, frequently outperforming complete basis set estimates of MP2.[Goldey and Head-Gordon(2012), Goldey et al.(2013)Goldey, Dutoi, and Head-Gordon]

Attenuated MP2, denoted MP2(attenuator, basis) is implemented in Q-Chem based on the complementary terf function, below:

$\begin{equation} \rm {s}(r)=\rm {terfc}(r,r_0)=\frac{1}{2} \left\{ \rm {erfc} \left[ \omega (r-r_0) \right] + \rm {erfc} \left[ \omega (r+r_0) \right] \right\} \end{equation}$

(6.23)

By choosing the terfc short-range operator, we optimally preserve the short-range behavior of the Coulomb operator while smoothly and rapidly switching off around the distance $r_0$ . Since this directly addresses basis set superposition error, parameterization must be done for specific basis sets. This has been performed for the basis sets, aug-cc-pVDZ[Goldey and Head-Gordon(2012)] and aug-cc-pVTZ.[Goldey et al.(2013)Goldey, Dutoi, and Head-Gordon] Other basis sets are not recommended for general use until further testing has been done.

Energies and gradients are functional with and without the resolution of the identity approximation using correlation keywords ATTMP2 and ATTRIMP2.

Example 6.82 Example of RI-MP2(terfc, aug-cc-pVDZ) energy evaluation

$molecule
   0 1
   O    -1.551007   -0.114520    0.000000
   H    -1.934259    0.762503    0.000000
   H    -0.599677    0.040712    0.000000
$end

$rem
   JOBTYPE         sp
   METHOD          attrimp2
   BASIS           aug-cc-pvdz
   AUX_BASIS       rimp2-aug-cc-pvdz
   N_FROZEN_CORE   fc
$end

Example 6.83 Example of MP2(terfc, aug-cc-pVTZ) geometry optimization

$molecule
   0 1
   H    0.0   0.0   0.0
   H    0.0   0.0   0.9
$end

$rem
   JOBTYPE         opt
   METHOD          attmp2
   BASIS           aug-cc-pvtz
   N_FROZEN_CORE   fc
$end