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Register a new userAn adaptive interpolation scheme for molecular potential energy surfaces
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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.
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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.
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.
We present a model intended for rapid sampling of ground and excited state potential energy surfaces for first-row transition metal active sites. The method is computationally inexpensive and is suited for dynamics simulations where (1) adiabatic states are required on-the-fly and (2) the primary source of the electronic coupling between the diabatic states is the perturbative spin-orbit interaction among the 3d electrons. The model Hamiltonian we develop is a variant of the Anderson impurity model and achieves efficiency through a physically motivated basis set reduction based on the large value of the d-d Coulomb interaction U_{d} and a Lanczos matrix diagonalization routine to solve for eigenvalues. The model parameters are constrained by fits to the partial density of states (PDOS) obtained from ab initio density functional theory calculations. For a particular application of our model we focus on electron-transfer occuring between cobalt ions solvated by ammonium, incorporating configuration interaction between multiplet states for both metal ions. We demonstrate the capability of the method to efficiently calculate adiabatic potential energy surfaces and the electronic coupling factor we have calculated compares well to previous calculations and experiment.
The concept of machine learning configuration interaction (MLCI) [J. Chem. Theory Comput. 2018, 14, 5739], where an artificial neural network (ANN) learns on the fly to select important configurations, is further developed so that accurate ab initio potential energy curves can be efficiently calculated. This development includes employing the artificial neural network also as a hash function for the efficient deletion of duplicates on the fly so that the singles and doubles space does not need to be stored and this barrier to scalability is removed. In addition configuration state functions are introduced into the approach so that pure spin states are guaranteed, and the transferability of data between geometries is exploited. This improved approach is demonstrated on potential energy curves for the nitrogen molecule, water, and carbon monoxide. The results are compared with full configuration interaction values, when available, and different transfer protocols are investigated. It is shown that, for all of the considered systems, accurate potential energy curves can now be efficiently computed with MLCI. For the potential curves of N$_{2}$ and CO, MLCI can achieve lower errors than stochastically selecting configurations while also using substantially less processor hours.
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