Machine learning techniques, specifically gradientenhanced Kriging (GEK), have been implemented for molecular geometry optimization. GEK-based optimization has many advantages compared to conventionalstep-restricted second-order truncated expansionmolecular optimization methods. In particular, the surrogate model given by GEK can have multiple stationary points, will smoothly converge to the exact model as the number of sample points increases, and contains an explicit expression for the expected error of the model function at an arbitrary point. Machine learning is, however, associated with abundance of data, contrary to the situation desired for efficient geometry optimizations. In this paper, we demonstrate how the GEK procedure can be utilized in a fashion such that in the presence of few data points, the surrogate surface will in a robust way guide the optimization to a minimum of a potential energy surface. In this respect, the GEK procedure will be used to mimic the behavior of a conventional second-order scheme but retaining the flexibility of the superior machine learning approach. Moreover, the expected error will be used in the optimizations to facilitate restricted-variance optimizations. A procedure which relates the eigenvalues of the approximate guessed Hessian with the individual characteristic lengths, used in the GEK model, reduces the number of empirical parameters to optimize to two: the value of the trend function and the maximum allowed variance. These parameters are determined using the extended Baker (e-Baker) and part of the Baker transition-state (Baker-TS) test suites as a training set. The so-created optimization procedure is tested using the e-Baker, full Baker-TS, and S22 test suites, at the density functional theory and second-order Møller−Plesset levels of approximation. The results show that the new method is generally of similar or better performance than a state-of-the-art conventional method, even for cases where no significant improvement was expected.

The developments of the open-source chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes can address, while showing that is an attractive platform for state-of-the-art atomistic computer simulations.

Gaussian process regression has recently been explored as an alternative to standard surrogate models in molecular equilibrium geometry optimization. In particular, the gradient-enhanced Kriging approach in association with internal coordinates, restricted-variance optimization, and an efficient and fast estimate of hyperparameters has demonstrated performance on par or better than standard methods. In this report, we extend the approach to constrained optimizations and transition states and benchmark it for a set of reactions. We compare the performance of the newly developed method with the standard techniques in the location of transition states and in constrained optimizations, both isolated and in the context of reaction path computation. The results show that the method outperforms the current standard in efficiency as well as in robustness.

A supersonic source of clusters has been used to prepare neutral complexes of ammonia in association with a metal atom. From these complexes the following metal-containing dications have been generated: [Mg(NH3)n](2+), [Ca(NH3)n](2+), and [Sr(NH3)n](2+), and for n in the range 4-20, kinetic energy release measurements following the evaporation of a single molecule have been undertaken using a high resolution mass spectrometer. Using finite heat bath theory, these data have been transformed into binding energies for individual ammonia molecules attached to each of the three cluster systems. In the larger complexes (n > 6) the results exhibit a consistent trend, whereby the experimental binding energy data for all three metal ions are very similar, suggesting that the magnitude of the charge rather than charge density influences the strength of the interaction. From a comparison with data recorded previously for (NH3)nH(+) it is found that the 2+ charge on a metal ion has an effect on the binding energy of molecules in complexes containing up to 20 solvent molecules. Although subject to comparatively large experimental errors, the results recorded for Ca(2+) and Sr(2+) when n ≤ 6 show evidence for the formation of an inner solvation shell containing up to 6 molecules. However, Mg(2+) exhibits relatively low binding energies when n = 5 and 6, which suggests that a second shell starts to form before there are 6 ammonia molecules bound to the metal ion. This conclusion is supported by DFT calculations and it is proposed that these complexes could take the form [Mg(NH3)4(NH3)](2+) when n = 5 and either [Mg(NH3)4(NH3)2](2+) or [Mg(NH3)5(NH3)](2+) when n = 6. In each case, additional molecules are hydrogen bonded to one or more molecules in the inner solvation shell.