MP2 scheme


This page describes technical aspects of the MP2 algorithm used in MP2 and double hybrid calculations. In order to use MP2 or double hybrids in your ADF calculation, you should request it in the XC input block.

The MP2 scheme directly builds on top of the Hartee-Fock RI scheme and some of the options specified in the RIHartreeFock input block will be used in the MP2 scheme as well (unless overwritten by the corresponding option in the MP2 input block). See the MP2 input options for more details.

Two variants for calculating the MP2 correlation energy are available in ADF: the RI-MP2, and the AO-PARI-MP2 algorithm (in the MP2 input block, these are refereed to as Formalism RI and Formalism LT respectively). By default, ADF will pick the most appropriate variant of the MP2 scheme. AO-PARI-MP2 is a very fast, potentially linear scaling algorithm. For DOD double-hybrids, the AO-PARI-MP2 algorithm leads to large computational savings compared to the RI-MP2 algorithm. In this implementation, the MP2 energy is evaluated in the AO basis. This reduced the asymptotic scaling for the evaluation of the MP2 energy to cubic for the same-spin component and to quadratic for the opposite-spin component of the MP2 energy. Due to a large prefactor, LT should not be specified if the same-spin component of the MP2 energy is required, unless, the system is large. If only the opposite-spin component is required (as for DOD double-hybrids), the algorithm is very fast already for small systems and is always recommended.

The amount of memory used in the MO-PARI-MP2 method grows as \(N^3\), which might give problems for larger systems. Typically an organic system with up to 50 atoms and a TZ2P basis set should not give problems on most machines. The amount of memory used in the AO-PARI-MP2 method only grows as \(N^2\) and this method can easily be used also for larger systems.

Technical aspects of the RI scheme can be tweaked in the MP2 input block

   Formalism [Auto | RI | LT | All]
   FitSetQuality [Auto | VeryBasic | Basic | Normal | Good | VeryGood]
   nLaplace integer
   ThresholdQuality [VeryBasic | Basic | Normal | Good | VeryGood]
   ThresholdQualityHalf float
   ThresholdQualityHalfTimesC float
   IntegrationQuality [VeryBasic | Basic | Normal | Good | VeryGood]
Description:Technical aspects of the MP2 algorithm.
Type:Multiple Choice
Default value:Auto
Options:[Auto, RI, LT, All]
Description:Specifies the formalism for the calculation of the MP2 correlation energy. ‘LT’ means Laplace Transformed MP2 (also referred to as AO-PARI-MP2), ‘RI’ means that a conventional RI-MP2 is carried out. If ‘Auto’, LT will be used in case of DOD double hybrids and SOS MP2, and RI will be used in all other cases. ‘All’ means that both RI and LT formalisms are used in the calculation.
Type:Multiple Choice
Default value:Auto
Options:[Auto, VeryBasic, Basic, Normal, Good, VeryGood]
Description:Speficies the fit set to be used in the MP2 calculation. ‘Normal’ quality is generally sufficient for basis sets up to and including TZ2P. For larger basis sets (or for benchmarking purposes) a ‘VeryGood’ fit set is recommended. Note that the FitSetQuality heavily influences the computational cost of the calculation. If not specified or ‘Auto’, the RIHartreeFock%FitSetQuality is used.
Default value:9
Description:Number of laplace points (only relevant in case the Laplace Transformed (LT) formalism is used). Transforming the MP2 equations to the AO basis requires the numerical evaluation of an integral (often referred to as a Laplace transform). 9 points is a rather safe choice, guaranteeing for practically all systems a good accuracy. Only for systems with a very small HOMO-LUMO gap more points might be necessary. For many systems, 6 points are sufficient for good accuracy. The computation time of a AO-PARI-MP2 calculation scales linearly with the number of quadrature points. If the HOMO-LUMO gap approaches zero, it is possible that the algorithm determining the weights for the quadrature points does not converge. In these cases, the double-hybrid calculation is not meaningful anyway, as a non-zero HOMO-LUMO gap is required for accurate MP2 energies.
Type:Multiple Choice
Options:[VeryBasic, Basic, Normal, Good, VeryGood]
Description:Controls the distances between atomic centers for which the product of two basis functions is not fitted any more. Especially for spatially extended, large systems, ‘VERYBASIC’ and ‘BASIC’ can lead to large computational savings, but the fit is also more approximate. This keyword is only meaningful when the LT formalism is used. If not specified, the RIHartreeFock%ThresholdQuality is used.
Default value:1e-08
Description:Speficies the treshold for neglecting half-transformed fit coefficients. (only relevant if the LT formalism is used). In the AO-PARI-MP2 algorithm, fit coefficients are contracted with so-called pseudo density matrices. If all elements of the resulting half-transformed fitfunction tensor are smaller than the values specified with ‘ThresholdQualityHalf’, all following tensor-contractions with this tensor are not carried out. This keyword is only relevant for very large and spatially extended systems. A low value, i.e. 1.0E-6, can lead to a linear-scaling evaluation of the opposite-spin MP2 energy, but also results in rather inaccurate results.
Default value:1e-10
Description:Speficies the treshold for neglecting products of halt-transformed fit-coefficients with fitfunctions.
Type:Multiple Choice
Options:[VeryBasic, Basic, Normal, Good, VeryGood]
Description:Speficies the integration quality to be used in the MP2 calculation. If not specified, the RIHartreeFock%IntegrationQuality is used.