# Extrapolating Local Coupled Cluster Calculations toward CCSD(T)/CBS Binding Energies of Atmospheric Molecular Clusters

## TL;DR

This paper improves the accuracy of simulating atmospheric particle formation by benchmarking and optimizing quantum chemical methods for calculating molecular cluster binding energies.

## Contribution

The study introduces a new benchmark set and demonstrates that LNO–CCSD(T) methods provide better accuracy-to-cost ratios for atmospheric clusters than DLPNO–CCSD(T0).

## Key findings

- LNO–CCSD(T) methods outperform DLPNO–CCSD(T0) in accuracy and cost for atmospheric molecular clusters.
- CBS extrapolation with aug-cc-pVTZ and aug-cc-pVQZ basis sets is feasible for LNO–CCSD(T) on clusters of 4–8 monomers.
- LAF extrapolation reduces basis set errors and improves simulated cluster formation rates.

## Abstract

Aerosols are the
largest source of uncertainty in modern global
radiative forcing modeling. Atmospheric molecular clusters are important
intermediates in atmospheric new particle formation (NPF). The evaporation
rate of clusters can be calculated using quantum chemical methods,
with an exponential dependence on the free energy. Hence, for simulating
accurate NPF rates, high-accuracy calculations are needed. We have
constructed a versatile benchmark set of 218 conformers of atmospheric
molecular dimer clusters consisting of sulfuric acid (SA), formic
acid (FA), nitric acid (NA), methanesulfonic acid (MSA), water (W),
ammonia (AM), methylamine (MA), dimethylamine (DMA), trimethylamine
(TMA), and ethylenediamine (EDA) molecules. Using this test set, we
benchmark the local coupled cluster methods, DLPNO–CCSD­(T0) and LNO–CCSD­(T), using different basis sets and locality
settings, and test extrapolation procedures to the complete basis
set (CBS), local approximation free (LAF), and complete PNO space
(CPS) limits. The extrapolations are tested against the binding energies
of high-level CCSD­(F12*)­(T+)/cc-pVTZ-F12 reference calculations. We
find that the LNO–CCSD­(T) methods offer a better accuracy-to-cost
ratio for atmospheric molecular clusters than the usually employed
DLPNO–CCSD­(T0) method. Furthermore, the CBS limit
extrapolation using the aug-cc-pVTZ and aug-cc-pVQZ basis sets should
be readily attainable for the LNO–CCSD­(T) method on the usually
studied cluster sizes (4–8 monomers). Simulating the new particle
formation rate of the (SA)1–4(AM)1–4 and (SA)1–4(DMA)1–4 systems
using the Atmospheric Cluster Dynamics Code, we find an increased
sensitivity to the locality settings for larger clusters, but the
basis set error is still the most dominant. Hence, simulated cluster
formation rates would also benefit from doing LAF extrapolation. Finally,
we illustrate the calculations of LNO–CCSD­(T)/CBS binding energies
of a large (SA)15(TMA)15 cluster (300 atoms).
Hence, the application of LNO–CCSD­(T) allows for significantly
more accurate binding energies of much larger clusters than previously
possible.