"Gold-Standard" $\Delta$-Machine Learned and Transferable Potential for Linear Alkanes

The conformational properties of linear alkanes, C$_n$H$_{2n+2}$, have been of intense interest for many years. Experiments and corresponding electronic structure calculations were first reported in the mid-2000s and continue to the present time. These focus on the minimum chain length where the transition from the linear minimum to the hairpin minimum occurs. We recently reported a transferable many-body permutationally invariant polynomial (MB-PIP) for linear alkanes using B3LYP electronic energies, which do not account for dispersion. Here we report a $\Delta$-ML approach to elevate this B3LYP-based and new PBE0+MBD MB-PIP potentials using PNO-LCCSD(T)-F12 energies. The new $\Delta$-corrected potentials predict the difference in these minima accurately, compared to benchmark CCSD(T) results, over the range C$_{12}$H$_{28}$ to C$_{28}$H$_{58}$. Vibrational power spectra are also reported for C$_{14}$H$_{30}$ and C$_{30}$H$_{62}$ using the uncorrected and $\Delta$-ML B3LYP. These new PIP-MB potentials for linear alkanes are the most accurate ones currently available and can be used in studies of properties of linear alkanes.