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An overview of computational methods to describe high-dimensional potential energy surfaces suitable for atomistic simulations is given. Particular emphasis is put on accuracy, computability, transferability and extensibility of the methods discussed. They include empirical force fields, representations based on reproducing kernels, using permutationally invariant polynomials, and neural network-learned representations and combinations thereof. Future directions and potential improvements are discussed primarily from a practical, application-oriented perspective.
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The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with a partition of unity approach. The adaptive node refinement allows to greatly reduce the number of sample points by employing a local error estimate. The algorithm and its scaling behavior is evaluated for a model function in 2, 3 and 4 dimensions. The developed algorithm allows for a more rapid and reliable interpolation of a potential energy surface within a given accuracy compared to the non-adaptive version.
We refine the OrbNet model to accurately predict energy, forces, and other response properties for molecules using a graph neural-network architecture based on features from low-cost approximated quantum operators in the symmetry-adapted atomic orbital basis. The model is end-to-end differentiable due to the derivation of analytic gradients for all electronic structure terms, and is shown to be transferable across chemical space due to the use of domain-specific features. The learning efficiency is improved by incorporating physically motivated constraints on the electronic structure through multi-task learning. The model outperforms existing methods on energy prediction tasks for the QM9 dataset and for molecular geometry optimizations on conformer datasets, at a computational cost that is thousand-fold or more reduced compared to conventional quantum-chemistry calculations (such as density functional theory) that offer similar accuracy.
Machine Learning techniques can be used to represent high-dimensional potential energy surfaces for reactive chemical systems. Two such methods are based on a reproducing kernel Hilbert space representation or on deep neural networks. They can achieve a sub-1 kcal/mol accuracy with respect to reference data and can be used in studies of chemical dynamics. Their construction and a few typical examples are briefly summarized in the present contribution.
Molecular Dynamics studies of chemical processes in solution are of great value in a wide spectrum of applications, which range from nano-technology to pharmaceutical chemistry. However, these calculations are affected by severe finite-size effects, such as the solution being depleted as the chemical process proceeds, which influence the outcome of the simulations. To overcome these limitations, one must allow the system to exchange molecules with a macroscopic reservoir, thus sampling a Grand-Canonical ensemble. Despite the fact that different remedies have been proposed, this still represents a key challenge in molecular simulations. In the present work we propose the Constant Chemical Potential Molecular Dynamics (C$mu$MD) method, which introduces an external force that controls the environment of the chemical process of interest. This external force, drawing molecules from a finite reservoir, maintains the chemical potential constant in the region where the process takes place. We have applied the C$mu$MD method to the paradigmatic case of urea crystallization in aqueous solution. As a result, we have been able to study crystal growth dynamics under constant supersaturation conditions, and to extract growth rates and free-energy barriers.
We present four-dimensional ab initio potential energy surfaces for the three spin states of the NH-NH complex. The potentials are partially based on the work of Dhont et al. [J. Chem. Phys. 123, 184302 (2005)]. The surface for the quintet state is obtained at the RCCSD(T)/aug-cc-pVTZ level of theory and the energy diferences with the singlet and triplet states are calculated at the CASPTn/aug-cc-pVTZ (n = 2; 3) level of theory. The ab initio potentials are fitted to coupled spherical harmonics in the angular coordinates, and the long range is further expanded as a power series in 1/R. The RCCSD(T) potential is corrected for a size-consistency error prior to fitting. The long-range coeficients obtained from the fit are found to be in good agreement with perturbation theory calculations.
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