Regularized Second-Order Møller–Plesset Theory: Linear Scaling Implementation and Assessment on Large-Molecule Problems

Formally fifth-order scaling with molecular size, second-order
Møller–Plesset (MP2) theory is widely used in its own
right, and as a component of double hybrid density functional theory.
Nevertheless, MP2 is well-known to have limited accuracy for large
intermolecular interactions, and the MP2 energy is not bounded from
below. Regularized MP2 methods aim to address these issues without
changing the formal fifth-order scaling and are therefore of interest
as more accurate and robust alternatives. In this work, we report
a linear scaling algorithm with shared and distributed memory parallel
implementations, for the evaluation of two regularized MP2 methods:
κ-MP2 and the size-consistent second-order Brillouin–Wigner
perturbation theory (BW-s2). The algorithm uses a single numerical
threshold to control accuracy, which is demonstrated to yield a roughly
10-fold reduction in numerical error for each factor of 10 reduction
in the threshold. The scaling of time-to-solution is assessed as a
function of molecule size (up to 1800 atoms and 25000 atomic orbitals),
the choice of threshold, and the number of processors (up to 2000
cores), for a range of systems including linear alkanes and three-dimensional
complexes. The results show an earlier crossover against the canonical
implementation for BW-s2 than for either MP2 or κ-MP2. The new
implementation is used to evaluate the accuracy of the κ-MP2
and BW-s2 methods for some of the largest test sets of intermolecular
interactions for which coupled cluster benchmark data are available,
including IONPI19, L7, S12L, and C60ISO. The results show that κ-MP2
and BW-s2 perform far better than MP2. Additional tests of κ-MP2
and BW-s2 are reported for the case of short-range amino acid interactions,
where MP2 performs exceptionally well.