MP2 ground state calculation - Tutorial

(UNDER CONSTRUCTION)

This tutorial introduces how to calculate the ground state energy using second order Møller-Plesset perturbation theory (MP2) with VASP. Currently there are three implementations available:

• MP2: this was the first implementation in VASP and is very efficient for small systems, i.e. systems with less than ~40 valence electrons per unit cell or unit cells smaller than ~200 ų. The system size scaling of this algorithm is N⁵.
• LTMP2: the Laplace transformed MP2 algorithm has a lower scaling (N⁴) than the previous MP2 algorithm and is therefore efficient for large systems with unit cells larger than ~200 ų and more than ~40 valence electrons.
• stochastic LTMP2: faster calculations at the price of statistical noise can be achieved with the stochastic MP2 algorithm. It is an optimal choice for very large systems where only relative errors per valence electron (say 1 meV per valence electron) are relevant. Keeping the absolute error fixed, the algorithm exhibits a cubic scaling with the system size, N³, whereas for a fixed relative error, a linear scaling, N¹, can be achieved. Note that there is no k-point sampling and no spin polarization implemented for this algorithm.

Both LTMP2 as well as stochastic LTMP2 are high performance algorithms that can parallelize the MP2 calculation over thousands of CPUs.

Furthermore, for very large systems, there is another technique to calcualte the MP2 ground state energy:

• high energy contributions using stochastic LTMP2: For very large systems it is also possible to calculate only the low energy MP2 contributions (very small cutoff parameters) with MP2 or LTMP2 and correct the missing high energy MP2 contributions with the stochastic LTMP2 algorithm. This allows for more accurate calculations for very large systems, since only a fraction of the MP2 energy is calulated stochastically.

At first, one should select the best algorithm according to the considered system size. In the following, a step by step instruction for each algorithm is presented.

1. Preparation: the HF ground state
2. Calculating the unoccupied HF orbitals
3. Using MP2
4. Using LTMP2
5. Using stochastic LTMP2
6. High energy contributions using stochastic LTMP2