Coupled Cluster Free Energies for Atmospheric Molecular Clusters: Benchmark and Matching Experimental Free Energies

The initial formation of secondary aerosols, a large cause of uncertainty in modern radiative forcing modeling, can be simulated using quantum chemical methods. When based on quantum chemistry, the simulations have an exponential dependence on the free energy, requiring a high-accuracy description. In this study, we have computed harmonic frequencies and quasi-harmonic free energies for a set of 10 monomers and 29 dimers relevant for atmospheric molecular clusters at the DF-CCSD(F12b)(T*)/cc-pVDZ-F12 level of theory. The set is used to benchmark the M06-2X, PW91, ωB97X-D3BJ functions with the Jensen, Karlsruhe, and Pople style basis sets. The composite methods B97-3c, r2SCAN-3c, and ωB97X- 3c are also tested. We find ωB97X-D3BJ/ma-def2-SVP to be an optimal choice as it has low errors (mean absolute error of 0.13 kcal/mol) and few outliers in the thermal contribution. For calculations on larger clusters, B97-3c stands out. Using the ωB97X-D3BJ/ma-def2-SVP and B97-3c level of theories, we compute anharmonic frequencies using the VPT2 method and determine an anharmonic scaling factor of 0.961 and 0.953 for ωB97X-D3BJ/ma-def2-SVP and B97-3c frequencies, re- spectively. The scaling factor together with incorporating multi-conformer entropy ef- fects and a high-level single-point correction at the Nnormal LNO-CCSD(T)/CBS(aug- 3,aug-4) are used to compare to experimental determined free energies of the 11 hydrogen-bonded systems. We find that we obtain sub 1 kcal/mol errors when incor- porating the scaling factor, the multi-conformer entropy effects, and the single point correction.