Transfer-Learned Potential Energy Surfaces: Towards Microsecond-Scale Molecular Dynamics Simulations in the Gas Phase at CCSD(T) Quality

The rise of machine learning has greatly influenced the field of computational chemistry, and that of atomistic molecular dynamics simulations in particular. One of its most exciting prospects is the development of accurate, full-dimensional potential energy surfaces (PESs) for molecules and clusters, which, however, often require thousands to tens of thousands of ab initio data points restricting the community to medium sized molecules and/or lower levels of theory (e.g. DFT). Transfer learning, which improves a global PES from a lower to a higher level of theory, offers a data efficient alternative requiring only a fraction of the high level data (on the order of 100 are found to be sufficient for malonaldehyde). The present work demonstrates that even with Hartree-Fock theory and a double-zeta basis set as the lower level model, transfer learning yields CCSD(T)-level quality for H-transfer barrier energies, harmonic frequencies and H-transfer tunneling splittings. Most importantly, finite-temperature molecular dynamics simulations on the sub-microsecond time scale in the gas phase are possible and the infrared spectra determined from the transfer learned PESs are in good agreement with experiment. It is concluded that routine, long-time atomistic simulations on PESs fulfilling CCSD(T)-standards become possible

Isomerization and Decomposition Reactions of Acetaldehyde Relevant to Atmospheric Processes from Dynamics Simulations on Neural Network-Based Potential Energy Surfaces

Acetaldehyde (AA) isomerization (to vinylalcohol, VA) and decomposition (into either CO+CH$_4$ and H$_2$+H$_2$CCO) is studied using a fully dimensional, reactive potential energy surface represented as a neural network (NN). The NN, trained on 432'399 reference structures from MP2/aug-cc-pVTZ calculations has a MAE of 0.0453 kcal/mol and an RMSE of 1.186 kcal/mol for a test set of 27'399 structures. For the isomerization process AA $\rightarrow$ VA the minimum dynamical path implies that the C-H vibration, and the C-C-H (with H being the transferring H-atom) and the C-C-O angles are involved to surmount the 68.2 kcal/mol barrier. Using an excess energy of 93.6 kcal/mol - the energy available in the solar spectrum and sufficient to excite to the first electronically excited state - to initialize the molecular dynamics, no isomerization to VA is observed on the 500 ns time scale. Only with excess energies of $\sim$ 127.6 kcal/mol (including the zero point energy of the AA molecule), isomerization occurs on the nanosecond time scale. Given that collisional de-excitation at atmospheric conditions in the stratosphere occurs on the 100 ns time scale, it is concluded that formation of VA following photoexcitation of AA from actinic photons is unlikely. This also limits the relevance of this reaction pathway to be a source for formic acid

Reactive Dynamics and Spectroscopy of Hydrogen Transfer from Neural Network-Based Reactive Potential Energy Surfaces

The in silico exploration of chemical, physical and biological systems requires accurate and efficient energy functions to follow their nuclear dynamics at a molecular and atomistic level. Recently, machine learning tools gained a lot of attention in the field of molecular sciences and simulations and are increasingly used to investigate the dynamics of such systems. Among the various approaches, artificial neural networks (NNs) are one promising tool to learn a representation of potential energy surfaces. This is done by formulating the problem as a mapping from a set of atomic positions $\mathbf{x}$ and nuclear charges $Z_i$ to a potential energy $V(\mathbf{x})$. Here, a fully-dimensional, reactive neural network representation for malonaldehyde (MA), acetoacetaldehyde (AAA) and acetylacetone (AcAc) is learned. It is used to run finite-temperature molecular dynamics simulations, and to determine the infrared spectra and the hydrogen transfer rates for the three molecules. The finite-temperature infrared spectrum for MA based on the NN learned on MP2 reference data provides a realistic representation of the low-frequency modes and the H-transfer band whereas the CH vibrations are somewhat too high in frequency. For AAA it is demonstrated that the IR spectroscopy is sensitive to the position of the transferring hydrogen at either the OCH- or OCCH$_3$ end of the molecule. For the hydrogen transfer rates it is demonstrated that the O-O vibration is a gating mode and largely determines the rate at which the hydrogen is transferred between the donor and acceptor. Finally, possibilities to further improve such NN-based potential energy surfaces are explored. They include the transferability of an NN-learned energy function across chemical species (here methylation) and transfer learning from a lower level of reference data (MP2) to a higher level of theory (pair natural orbital-LCCSD(T))

Transfer learning for affordable and high quality tunneling splittings from instanton calculations

The combination of transfer learning (TL) a low level potential energy surface (PES) to a higher level of electronic structure theory together with ring-polymer instanton (RPI) theory is explored and applied to malonaldehyde. The RPI approach provides a semiclassical approximation of the tunneling splitting and depends sensitively on the accuracy of the PES. With second order M{\o}ller-Plesset perturbation theory (MP2) as the low-level (LL) model and energies and forces from coupled cluster singles, doubles and perturbative triples (CCSD(T)) as the high-level (HL) model, it is demonstrated that CCSD(T) information from only 25 to 50 judiciously selected structures along and around the instanton path suffice to reach HL-accuracy for the tunneling splitting. In addition, the global quality of the HL-PES is demonstrated through a mean average error of 0.3 kcal/mol for energies up to 40 kcal/mol above the minimum energy structure (a factor of 2 higher than the energies employed during TL) and $< 2$ cm$^{-1}$ for harmonic frequencies compared with computationally challenging normal mode calculations at the CCSD(T) level

Machine Learning for Observables: Reactant to Product State Distributions for Atom-Diatom Collisions

Machine learning-based models to predict product state distributions from a distribution of reactant conditions for atom-diatom collisions are presented and quantitatively tested. The models are based on function-, kernel- and grid-based representations of the reactant and product state distributions. While all three methods predict final state distributions from explicit quasi-classical trajectory simulations with R$^2$ > 0.998, the grid-based approach performs best. Although a function-based approach is found to be more than two times better in computational performance, the kernel- and grid-based approaches are preferred in terms of prediction accuracy, practicability and generality. The function-based approach also suffers from lacking a general set of model functions. Applications of the grid-based approach to nonequilibrium, multi-temperature initial state distributions are presented, a situation common to energy distributions in hypersonic flows. The role of such models in Direct Simulation Monte Carlo and computational fluid dynamics simulations is also discussed

PhysNet Meets CHARMM: A Framework for Routine Machine Learning / Molecular Mechanics Simulations

Full dimensional potential energy surfaces (PESs) based on machine learning (ML) techniques provide means for accurate and efficient molecular simulations in the gas- and condensed-phase for various experimental observables ranging from spectroscopy to reaction dynamics. Here, the MLpot extension with PhysNet as the ML-based model for a PES is introduced into the newly developed pyCHARMM API. To illustrate conceiving, validating, refining and using a typical workflow, para-chloro-phenol is considered as an example. The main focus is on how to approach a concrete problem from a practical perspective and applications to spectroscopic observables and the free energy for the -OH torsion in solution are discussed in detail. For the computed IR spectra in the fingerprint region the computations for para-chloro-phenol in water are in good qualitative agreement with experiment carried out in CCl$_4$. Also, relative intensities are largely consistent with experimental findings. The barrier for rotation of the -OH group increases from $\sim 3.5$ kcal/mol in the gas phase to $\sim 4.1$ kcal/mol from simulations in water due to favourable H-bonding interactions of the -OH group with surrounding water molecules.Comment: 38 pages, 11 figure

ML Models of Vibrating H2_2CO: Comparing Reproducing Kernels, FCHL and PhysNet

Machine Learning (ML) has become a promising tool for improving the quality of atomistic simulations. Using formaldehyde as a benchmark system for intramolecular interactions, a comparative assessment of ML models based on state-of-the-art variants of deep neural networks (NN), reproducing kernel Hilbert space (RKHS+F), and kernel ridge regression (KRR) is presented. Learning curves for energies and atomic forces indicate rapid convergence towards excellent predictions for B3LYP, MP2, and CCSD(T)-F12 reference results for modestly sized (in the hundreds) training sets. Typically, learning curve off-sets decay as one goes from NN (PhysNet) to RKHS+F to KRR (FCHL). Conversely, the predictive power for extrapolation of energies towards new geometries increases in the same order with RKHS+F and FCHL performing almost equally. For harmonic vibrational frequencies, the picture is less clear, with PhysNet and FCHL yielding respectively flat learning at $\sim$ 1 and $\sim$ 0.2 cm$^{-1}$ no matter which reference method, while RKHS+F models level off for B3LYP, and exhibit continued improvements for MP2 and CCSD(T)-F12. Finite-temperature molecular dynamics (MD) simulations with the same initial conditions yield indistinguishable infrared spectra with good performance compared with experiment except for the high-frequency modes involving hydrogen stretch motion which is a known limitation of MD for vibrational spectroscopy. For sufficiently large training set sizes all three models can detect insufficient convergence (``noise'') of the reference electronic structure calculations in that the learning curves level off. Transfer learning (TL) from B3LYP to CCSD(T)-F12 with PhysNet indicates that additional improvements in data efficiency can be achieved

Hydration dynamics and IR spectroscopy of 4-fluorophenol

Halogenated groups are relevant in pharmaceutical applications and potentially useful spectroscopic probes for infrared spectroscopy. In this work, the structural dynamics and infrared spectroscopy of para-fluorophenol (F-PhOH) and phenol (PhOH) is investigated in the gas phase and in water using a combination of experiment and molecular dynamics (MD) simulations. The gas phase and solvent dynamics around F-PhOH and PhOH is characterized from atomistic simulations using empirical energy functions with point charges or multipoles for the electrostatics, Machine Learning (ML) based parametrizations and with full ab initio (QM) and mixed Quantum Mechanical/Molecular Mechanics (QM/MM) simulations with a particular focus on the CF- and OH-stretch region. The CF-stretch band is heavily mixed with other modes whereas the OH-stretch in solution displays a characteristic high-frequency peak around 3600 cm−1 most likely associated with the –OH group of PhOH and F-PhOH together with a characteristic progression below 3000 cm−1 due to coupling with water modes which is also reproduced by several of the simulations. Solvent and radial distribution functions indicate that the CF-site is largely hydrophobic except for simulations using point charges which renders them unsuited for correctly describing hydration and dynamics around fluorinated sites. The hydrophobic character of the CF-group is particularly relevant for applications in pharmaceutical chemistry with a focus on local hydration and interaction with the surrounding protein