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The positions of grid points for representing a multidimensional potential energy surface (PES) have a non-negligible impact on its accuracy and the associated computational effort for its generation. Six different positioning schemes were studied for PESs represented by n-mode expansions as needed for the accurate calculation of anharmonic vibrational frequencies by means of vibrational configuration interaction theory. A static approach, which has successfully been used in many applications, and five adaptive schemes based on Gaussian process regression have been investigated with respect to the number of necessary grid points and the accuracy of the fundamental modes for a small set of test molecules. A comparison with a related, more sophisticated, and consistent approach by Christiansen et al. is provided. The impact of the positions of the ab initio grid points is discussed for multilevel PESs, for which the computational effort of the individual electronic structure calculations decreases for increasing orders of the n-mode expansion. As a result of that, the ultimate goal is not the maximal reduction of grid points but rather the computational cost, which is not directly related. [ABSTRACT FROM AUTHOR]

The vibrational spectra of simple C H 3 + —Rg (Rg = He, Ne, Ar, Kr) complexes have been studied by vibrational configuration interaction theory relying on multidimensional potential energy surfaces (PESs) obtained from explicitly correlated coupled cluster calculations, CCSD(T)-F12a. In agreement with experimental results, the series of rare gas atoms leads to rather unsystematic results and indicates huge zero point vibrational energy effects for the helium complex. In order to study these sensitive complexes more consistently, we also introduce configuration averaged vibrational self-consistent field theory, which is a generalization of standard vibrational self-consistent field theory to several configurations. The vibrational spectra of the complexes are compared to that of the methyl cation, for which corrections due to scalar-relativistic effects, high-order coupled-cluster terms, e.g., quadruple excitations, and core-valence correlation have explicitly been accounted for. The occurrence of tunneling splittings for the vibrational ground-state of C H 3 + —He has been investigated on the basis of semiclassical instanton theory. These calculations and a direct comparison of the energy profiles along the intrinsic reaction coordinates with that of the hydronium cation, H3O+, suggest that tunneling effects for vibrationally excited states should be very small. [ABSTRACT FROM AUTHOR]

Microcanonical instanton theory offers the promise of providing rate constants for chemical reactions including quantum tunneling of atoms over the whole temperature range. We discuss different rate expressions, which require the calculation of stability parameters of the instantons. The traditional way of obtaining these stability parameters is shown to be numerically unstable in practical applications. We provide three alternative algorithms to obtain such stability parameters for non-separable systems, i.e., systems in which the vibrational modes perpendicular to the instanton path couple to movement along the path. We show the applicability of our algorithms on two molecular systems: H2 + OH → H2O + H using a fitted potential energy surface and HNCO + H → NH2CO using a potential obtained on-the-fly from density functional calculations. [ABSTRACT FROM AUTHOR]

The diffusion of atoms and radicals on interstellar dust grains is a fundamental ingredient for predicting accurate molecular abundances in astronomical environments. Quantitative values of diffusivity and diffusion barriers usually rely heavily on empirical rules. In this paper, we compute the diffusion coefficients of adsorbed nitrogen atoms by combining machine learned interatomic potentials, metadynamics, and kinetic Monte Carlo simulations. With this approach, we obtain a diffusion coefficient of nitrogen atoms on the surface of amorphous solid water of merely |$(3.5 \pm 1.1)\, \times 10^{-34}$|  cm2 s−1 at 10 K for a bare ice surface. Thus, we find that nitrogen, as a paradigmatic case for light and weakly bound adsorbates, is unable to diffuse on bare amorphous solid water at 10 K. Surface coverage has a strong effect on the diffusion coefficient by modulating its value over 9–12 orders of magnitude at 10 K and enables diffusion for specific conditions. In addition, we have found that atom tunnelling has a negligible effect. Average diffusion barriers of the potential energy surface (2.56 kJ mol−1) differ strongly from the effective diffusion barrier obtained from the diffusion coefficient for a bare surface (6.06 kJ mol−1) and are, thus, inappropriate for diffusion modelling. Our findings suggest that the thermal diffusion of N on water ice is a process that is highly dependent on the physical conditions of the ice. [ABSTRACT FROM AUTHOR]

Dynamics of adsorption and desorption of (4S)-N on amorphous solid water are analysed using molecular dynamic simulations. The underlying potential energy surface was provided by machine-learned interatomic potentials. Binding energies confirm the latest available theoretical and experimental results. The nitrogen sticking coefficient is close to unity at dust temperatures of 10 K but decreases at higher temperatures. We estimate a desorption time-scale of 1 μ s at 28 K. The estimated time-scale allows chemical processes mediated by diffusion to happen before desorption, even at higher temperatures. We found that the energy dissipation process after a sticking event happens on the picosecond time-scale at dust temperatures of 10 K, even for high energies of the incoming adsorbate. Our approach allows the simulation of large systems for reasonable time-scales at an affordable computational cost and ab initio accuracy. Moreover, it is generally applicable for the study of adsorption dynamics of interstellar radicals on dust surfaces. [ABSTRACT FROM AUTHOR]

A trivial flaw in the utilization of artificial neural networks in interpolating chemical potential energy surfaces (PES) whose descriptors are Cartesian coordinates is their dependence on simple translations and rotations of the molecule under consideration. A different set of descriptors can be chosen to circumvent this problem, internuclear distances, inverse internuclear distances or z‐matrix coordinates are three such descriptors. The objective is to use an interpolated PES in instanton rate constant calculations, hence information on the energy, gradient, and Hessian is required at coordinates in the vicinity of the tunneling path. Instanton theory relies on smoothly fitted Hessians, therefore we use energy, gradients, and Hessians in the training procedure. A major challenge is presented in the proper back‐transformation of the output gradients and Hessians from internal coordinates to Cartesian coordinates. We perform comparisons between our method, a previous approach and on‐the‐fly rate constant calcuations on the hydrogen abstraction from methanol and on the hydrogen addition to isocyanic acid. © 2018Wiley Periodicals, Inc. The challenge of utilizing instanton theory on interpolated potential energy surfaces, trained using a deep neural network, where energies, gradients and Hessians are required, in coordinates invariant to rotational and translational degrees of freedom, has been examined in this contribution. One of the studied reactions, shows good agreement both with existing neural network based approaches and with on‐the‐fly rate calculations based on a UCCSD(T)‐pVTZ‐F12 potential energy surface. [ABSTRACT FROM AUTHOR]

We implemented a geometry optimizer based on Gaussian process regression (GPR) to find minimum structures on potential energy surfaces. We tested both a two times differentiable form of the Matérn kernel and the squared exponential kernel. The Matérn kernel performs much better. We give a detailed description of the optimization procedures. These include overshooting the step resulting from GPR in order to obtain a higher degree of interpolation vs. extrapolation. In a benchmark against the Limited-memory Broyden–Fletcher–Goldfarb–Shanno optimizer of the DL-FIND library on 26 test systems, we found the new optimizer to generally reduce the number of required optimization steps. [ABSTRACT FROM AUTHOR]

Artificial neural networks are used to fit a potential energy surface (PES). We demonstrate the benefits of using not only energies but also their first and second derivatives as training data for the neural network. This ensures smooth and accurate Hessian surfaces, which are required for rate constant calculations using instanton theory. Our aim was a local, accurate fit rather than a global PES because instanton theory requires information on the potential only in the close vicinity of the main tunneling path. Elongations along vibrational normal modes at the transition state are used as coordinates for the neural network. The method is applied to the hydrogen abstraction reaction from methanol, calculated on a coupled-cluster level of theory. The reaction is essential in astrochemistry to explain the deuteration of methanol in the interstellar medium. [ABSTRACT FROM AUTHOR]

The calculation of free-energy barriers by umbrella sampling and many other methods is hampered by the necessity for an a priori choice of the reaction coordinate along which to sample. We avoid this problem by providing a method to search for saddle points on the free-energy surface in many coordinates. The necessary gradients and Hessians of the free energy are obtained by multidimensional umbrella integration. We construct the minimum free-energy path by following the gradient down to minima on the free-energy surface. The change of free energy along the path is obtained by integrating out all coordinates orthogonal to the path. While we expect the method to be applicable to large systems, we test it on the alanine dipeptide in vacuum. The minima, transition states, and free-energy barriers agree well with those obtained previously with other methods. [ABSTRACT FROM AUTHOR]

Quantum mechanical tunneling of atomsplays a significant rolein many chemical reactions. The crossover temperature between classicaland quantum movement is a convenient preliminary indication of theimportance of tunneling for a particular reaction. Here we show, usinginstanton theory, that quantum tunneling is possible significantlyabove this crossover temperature for specific forms of the potentialenergy surface. We demonstrate the effect on an analytic potentialas well as a chemical system. While protons move asynchronously alonga Grotthuss chain in the classical high-temperature range, the onsetof tunneling results in a synchronization of their movement. [ABSTRACT FROM AUTHOR]