# A Linear-Scaling Integral-Direct Explicitly Correlated Second-Order Møller–Plesset Approach

## TL;DR

This paper introduces a new method for calculating electron correlations in large molecules efficiently, enabling accurate results for systems with hundreds of atoms.

## Contribution

A linear-scaling, integral-direct, local MP2-F12 approach that enables explicitly correlated calculations for large systems.

## Key findings

- The method recovers at least 99.9% of the canonical MP2-F12 correlation energy.
- Reaction energies have a mean error of less than 1 kJ/mol.
- The approach successfully computed a system with 644 atoms, the largest for explicitly correlated calculations.

## Abstract

We present an integral-direct, iteration-free, linear-scaling,
local explicitly correlated second-order Møller–Plesset
(MP2-F12) approach, extending our previous local MP2 method [J. Chem. Theory Comput.
2016, 12, 4897]. The
correlation contributions for individual electron pairs are computed
within domains defined by the corresponding localized orbitals, while
the correlation energies of spatially distant electron pairs are determined
via multipole expansions. All the various types of integrals are computed
and transformed directly, thereby precluding the need for integral
storage and yielding asymptotically constant memory as well as negligible
disk I/O demand. Another competitive advantage is the implementation
of the 2B MP2-F12 ansatz, the most complete one so far with local
approximations, enabling excellent basis set convergence even with
double-ζ basis sets. Our validation studies indicate that the
approach recovers at least 99.9% of the canonical MP2-F12 correlation
energy and yields reaction energies with a mean error of less than
1 kJ/mol. With respect to the complete basis set limit of MP2, the
error of our local approach is just slightly larger than that of canonical
MP2-F12. With the new local MP2-F12 approach, we were able to compute
the correlation energy for a small protein containing 644 atoms, which
is the largest system ever considered in an explicitly correlated
calculation.