Numerical Accuracy Matters: Applications of Machine Learned Potential Energy Surfaces.

The role of numerical accuracy in training and evaluating neural network-based potential energy surfaces is examined for different experimental observables. For observables that require third- and fourth-order derivatives of the potential energy with respect to Cartesian coordinates single-precision arithmetics as is typically used in ML-based approaches is insufficient and leads to roughness of the underlying PES as is explicitly demonstrated. Increasing the numerical accuracy to double-precision gives a smooth PES with higher-order derivatives that are numerically stable and yield meaningful anharmonic frequencies and tunneling splitting as is demonstrated for H2CO and malonaldehyde. For molecular dynamics simulations, which only require first-order derivatives, single-precision arithmetics appears to be sufficient, though.

The first HyDRA challenge for computational vibrational spectroscopy.

Vibrational spectroscopy in supersonic jet expansions is a powerful tool to assess molecular aggregates in close to ideal conditions for the benchmarking of quantum chemical approaches. The low temperatures achieved as well as the absence of environment effects allow for a direct comparison between computed and experimental spectra. This provides potential benchmarking data which can be revisited to hone different computational techniques, and it allows for the critical analysis of procedures under the setting of a blind challenge. In the latter case, the final result is unknown to modellers, providing an unbiased testing opportunity for quantum chemical models. In this work, we present the spectroscopic and computational results for the first HyDRA blind challenge. The latter deals with the prediction of water donor stretching vibrations in monohydrates of organic molecules. This edition features a test set of 10 systems. Experimental water donor OH vibrational wavenumbers for the vacuum-isolated monohydrates of formaldehyde, tetrahydrofuran, pyridine, tetrahydrothiophene, trifluoroethanol, methyl lactate, dimethylimidazolidinone, cyclooctanone, trifluoroacetophenone and 1-phenylcyclohexane-cis-1,2-diol are provided. The results of the challenge show promising predictive properties in both purely quantum mechanical approaches as well as regression and other machine learning strategies.

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 a 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 application programming interface. To illustrate the conception, validation, refining, and use of 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 CCl4. Moreover, relative intensities are largely consistent with experimental findings. The barrier for rotation of the -OH group increases from ∼3.5 kcal/mol in the gas phase to ∼4.1 kcal/mol from simulations in water due to favorable H-bonding interactions of the -OH group with surrounding water molecules.

Transfer-learned potential energy surfaces: Toward 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 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., density functional theory). 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). This work demonstrates that even with Hartree-Fock theory and a double-zeta basis set as the lower level model, transfer learning yields coupled-cluster single double triple [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-µs time scale in the gas phase are possible and the infrared spectra determined from the transfer-learned PESs are in good agreement with the experiment. It is concluded that routine, long-time atomistic simulations on PESs fulfilling CCSD(T)-standards become possible.

Conformational and state-specific effects in reactions of 2,3-dibromobutadiene with Coulomb-crystallized calcium ions.

Recent advances in experimental methodology enabled studies of the quantum-state- and conformational dependence of chemical reactions under precisely controlled conditions in the gas phase. Here, we generated samples of selected gauche and s-trans 2,3-dibromobutadiene (DBB) by electrostatic deflection in a molecular beam and studied their reaction with Coulomb crystals of laser-cooled Ca+ ions in an ion trap. The rate coefficients for the total reaction were found to strongly depend on both the conformation of DBB and the electronic state of Ca+. In the (4p)2P1/2 and (3d)2D3/2 excited states of Ca+, the reaction is capture-limited and faster for the gauche conformer due to long-range ion-dipole interactions. In the (4s)2S1/2 ground state of Ca+, the reaction rate for s-trans DBB still conforms with the capture limit, while that for gauche DBB is strongly suppressed. The experimental observations were analysed with the help of adiabatic capture theory, ab initio calculations and reactive molecular dynamics simulations on a machine-learned full-dimensional potential energy surface of the system. The theory yields near-quantitative agreement for s-trans-DBB, but overestimates the reactivity of the gauche-conformer compared to the experiment. The present study points to the important role of molecular geometry even in strongly reactive exothermic systems and illustrates striking differences in the reactivity of individual conformers in gas-phase ion-molecule reactions.

Neural network potentials for chemistry: concepts, applications and prospects.

Artificial Neural Networks (NN) are already heavily involved in methods and applications for frequent tasks in the field of computational chemistry such as representation of potential energy surfaces (PES) and spectroscopic predictions. This perspective provides an overview of the foundations of neural network-based full-dimensional potential energy surfaces, their architectures, underlying concepts, their representation and applications to chemical systems. Methods for data generation and training procedures for PES construction are discussed and means for error assessment and refinement through transfer learning are presented. A selection of recent results illustrates the latest improvements regarding accuracy of PES representations and system size limitations in dynamics simulations, but also NN application enabling direct prediction of physical results without dynamics simulations. The aim is to provide an overview for the current state-of-the-art NN approaches in computational chemistry and also to point out the current challenges in enhancing reliability and applicability of NN methods on a larger scale.

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.

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 Møller-Plesset perturbation theory (MP2) as the low-level 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 25-50 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.

Correction: Transfer learned potential energy surfaces: accurate anharmonic vibrational dynamics and dissociation energies for the formic acid monomer and dimer.

Correction for 'Transfer learned potential energy surfaces: accurate anharmonic vibrational dynamics and dissociation energies for the formic acid monomer and dimer' by Silvan Käser et al., Phys. Chem. Chem. Phys., 2022, 24, 5269-5281, https://doi.org/10.1039/D1CP04393E.

Double proton transfer in hydrated formic acid dimer: Interplay of spatial symmetry and solvent-generated force on reactivity.

The double proton transfer (DPT) reaction in the hydrated formic acid dimer (FAD) is investigated at molecular-level detail. For this, a global and reactive machine learned (ML) potential energy surface (PES) is developed to run extensive (more than 100 ns) mixed ML/MM molecular dynamics (MD) simulations in explicit molecular mechanics (MM) solvent at MP2-quality for the solute. Simulations with fixed - as in a conventional empirical force field - and conformationally fluctuating - as available from the ML-based PES - charge models for FAD show a significant impact on the competition between DPT and dissociation of FAD into two formic acid monomers. With increasing temperature the barrier height for DPT in solution changes by about 10% (∼1 kcal mol-1) between 300 K and 600 K. The rate for DPT is largest, ∼1 ns-1, at 350 K and decreases for higher temperatures due to destabilisation and increased probability for dissociation of FAD. The water solvent is found to promote the first proton transfer by exerting a favourable solvent-induced Coulomb force along the O-H⋯O hydrogen bond whereas the second proton transfer is significantly controlled by the O-O separation and other conformational degrees of freedom. Double proton transfer in hydrated FAD is found to involve a subtle interplay and balance between structural and electrostatic factors.

Transfer learned potential energy surfaces: accurate anharmonic vibrational dynamics and dissociation energies for the formic acid monomer and dimer.

The vibrational dynamics of the formic acid monomer (FAM) and dimer (FAD) is investigated from machine-learned potential energy surfaces at the MP2 (PESMP2) and transfer-learned (PESTL) to the CCSD(T) levels of theory. The normal mode (MAEs of 17.6 and 25.1 cm-1) and second order vibrational perturbation theory (VPT2, MAEs of 6.7 and 17.1 cm-1) frequencies from PESTL for all modes below 2000 cm-1 for FAM and FAD agree favourably with experiment. For the OH stretch mode the experimental frequencies are overestimated by more than 150 cm-1 for both FAM and FAD from normal mode calculations. Conversely, VPT2 calculations on PESTL for FAM reproduce the experimental OH frequency to within 22 cm-1. For FAD the VPT2 calculations find the high-frequency OH stretch at 3011 cm-1, compared with an experimentally reported, broad (∼100 cm-1) absorption band with center frequency estimated at ∼3050 cm-1. In agreement with earlier reports, MD simulations at higher temperature shift the position of the OH-stretch in FAM to the red, consistent with improved sampling of the anharmonic regions of the PES. However, for FAD the OH-stretch shifts to the blue and for temperatures higher than 1000 K the dimer partly or fully dissociates using PESTL. Including zero-point energy corrections from diffusion Monte Carlo simulations for FAM and FAD and corrections due to basis set superposition and completeness errors yields a dissociation energy of D0 = -14.23 ± 0.08 kcal mol-1 compared with an experimentally determined value of -14.22 ± 0.12 kcal mol-1.

Transfer Learning to CCSD(T): Accurate Anharmonic Frequencies from Machine Learning Models.

The calculation of the anharmonic modes of small- to medium-sized molecules for assigning experimentally measured frequencies to the corresponding type of molecular motions is computationally challenging at sufficiently high levels of quantum chemical theory. Here, a practical and affordable way to calculate coupled-cluster quality anharmonic frequencies using second-order vibrational perturbation theory (VPT2) from machine-learned models is presented. The approach, referenced as "NN + VPT2", uses a high-dimensional neural network (PhysNet) to learn potential energy surfaces (PESs) at different levels of theory from which harmonic and VPT2 frequencies can be efficiently determined. The NN + VPT2 approach is applied to eight small- to medium-sized molecules (H2CO, trans-HONO, HCOOH, CH3OH, CH3CHO, CH3NO2, CH3COOH, and CH3CONH2) and frequencies are reported from NN-learned models at the MP2/aug-cc-pVTZ, CCSD(T)/aug-cc-pVTZ, and CCSD(T)-F12/aug-cc-pVTZ-F12 levels of theory. For the largest molecules and at the highest levels of theory, transfer learning (TL) is used to determine the necessary full-dimensional, near-equilibrium PESs. Overall, NN + VPT2 yields anharmonic frequencies to within 20 cm-1 of experimentally determined frequencies for close to 90% of the modes for the highest quality PES available and to within 10 cm-1 for more than 60% of the modes. For the MP2 PESs only ∼60% of the NN + VPT2 frequencies were within 20 cm-1 of the experiment, with outliers up to ∼150 cm-1, compared to the experiment. It is also demonstrated that the approach allows to provide correct assignments for strongly interacting modes such as the OH bending and the OH torsional modes in formic acid monomer and the CO-stretch and OH-bend mode in acetic acid.

Machine Learning Models of Vibrating H2CO: 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 (NNs), reproducing kernel Hilbert space (RKHS+F), and kernel ridge regression (KRR) is presented. Learning curves for energies and atomic forces indicate rapid convergence toward excellent predictions for B3LYP, MP2, and CCSD(T)-F12 reference results for modestly sized (in the hundreds) training sets. Typically, learning curve offsets decay as one goes from NN (PhysNet) to RKHS+F to KRR (FCHL). Conversely, the predictive power for extrapolation of energies toward 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 accuracies of ∼1 and ∼0.2 cm-1, respectively, 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 using the PESs from the three ML methods with identical 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.

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. All three methods predict final state distributions from explicit quasi-classical trajectory simulations with R2 > 0.998. Although a function-based approach is found to be more than two times better in computational performance, the grid-based approach is preferred in terms of prediction accuracy, practicability, and generality. For the function-based approach, the choice of parametrized functions is crucial and this aspect is explicitly probed for final vibrational state distributions. Applications of the grid-based approach to nonequilibrium, multitemperature initial state distributions are presented, a situation common to energy and state distributions in hypersonic flows. The role of such models in direct simulation Monte Carlo and computational fluid dynamics simulations is also discussed.

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 + CH4 or H2 + C2H2O) are 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 mean absolute error of 0.0453 kcal/mol and a root mean squared error of 1.186 kcal mol-1 for a test set of 27 399 structures. For the isomerization process AA → 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 typical 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 ∼127.6 kcal/mol (including the zero point energy of the AA molecule), isomerization occurs on the nanosecond time scale. Given that collisional quenching times under tropospheric conditions are ∼1 ns, 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.