5.6 Short-Range Correlation Methods

5.6.1 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[221, 220], 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 noncovalent interactions. Attenuated MP2 improves upon MP2 for inter- and intramolecular interactions, with significantly better performance for relative and binding energies of noncovalent complexes, frequently outperforming complete basis set estimates of MP2[255, 256].

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

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

(5.23)

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[255] and aug-cc-pVTZ[256]. 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.

5.6.2 Examples

Example 5.90 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 5.91 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