Data for: Thermodynamics of the gas-phase dimerization of formic acid: fully anharmonic finite temperature calculations at the CCSD(T) and many DFT levels

We provide data files needed to reproduce the MLPT calculations presented in work of Dávid Vrška, Michal Pitoňák and Tomáš Bučko: "Thermodynamics of the gas-phase dimerization of formic acid: Fully anharmonic finite temperature calculations at the CCSD(T) and many DFT levels" or to perform such calculation for any other electronic structure method not considered in mentioned work. In particular, the structural data are available in the standard xyz file format containing the atomic labels and atomic coordinates in Angstroms (Å), and the energies are provided as data files in a two-column format, where the items in the first column represent the identification numbers of each configuration and those in the second column are the corresponding energies in electronvolts (eV).

Methods
Ab initio density functional theory (DFT) simulations were employed using the periodic DFT software package VASP [1-3]. Coupled Clusters (CCSD(T)) [4] calculations were performed using the program ORCA (version 5.0.4) [5,6]. 

Ab initio molecular dynamics (AIMD) calculations with a time step of 0.5 fs were performed at the PBE+D2 level. The simulation temperature of 300 K was maintained by employing Andersen thermostat [7], whereby the mass of hydrogen atoms was increased to 3 amu. The total length of all AIMD trajectories was 100 ps out of which the equilibration period identified via Mann Kendall test [8] (up to 15 ps) was discarded. 

For determining energy at the target level of theory (CCSD(T) and various DFAs) we employed Machine Learning Perturbation Theory (MLPT) aproach using the data obtained at computationally less expensive method (PBE+D2). We used the training set with 100 training points obtained as 100 single point calculations at the target level. Within MLPT, the kernel ridge regression [9] as implemented in scikit-learn library [10,11] with the REMatch kernel [12] and the SOAP (smooth overlap of atomic positions) descriptors [13] as implemented in DScribe library [14] are used.

In the cases of a poor overlap, corresponding to cases with index Iw < 0.05, see Herzog et al. [15] proposed to perform machine learning Monte Carlo (MLMC) resampling.

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