Accelerating Fourth-Generation Machine Learning Potentials Using Quasi-Linear Scaling Particle Mesh Charge Equilibration.

Machine learning potentials (MLPs) have revolutionized the field of atomistic simulations by describing atomic interactions with the accuracy of electronic structure methods at a small fraction of the cost. Most current MLPs construct the energy of a system as a sum of atomic energies, which depend on information about the atomic environments provided in the form of predefined or learnable feature vectors. If, in addition, nonlocal phenomena like long-range charge transfer are important, fourth-generation MLPs need to be used, which include a charge equilibration (Qeq) step to take the global structure of the system into account. This Qeq can significantly increase the computational cost and thus can become a computational bottleneck for large systems. In this Article, we present a highly efficient formulation of Qeq that does not require the explicit computation of the Coulomb matrix elements, resulting in a quasi-linear scaling method. Moreover, our approach also allows for the efficient calculation of energy derivatives, which explicitly consider the global structure-dependence of the atomic charges as obtained from Qeq. Due to its generality, the method is not restricted to MLPs and can also be applied within a variety of other force fields.

COMPASS: Double-ended saddle point search as a constrained optimization problem.

We present an algorithm to find first order saddle points on the potential energy surface (PES). The algorithm is formulated as a constrained optimization problem that involves two sets of atomic coordinates (images), a time-varying distance constraint and a constraint on the energy difference. Both images start in different valleys of the PES and are pulled toward each other by gradually reducing the distance. The search space is restricted to the pairs of configurations that share the same potential energy. By minimizing the energy while the distance shrinks, a minimum of the constrained search space is tracked. In simple cases, the two images are confined to their respective sides of the barrier until they finally converge near the saddle point. If one image accidentally crosses the barrier, the path is split at suitable locations and the algorithm is repeated recursively. The optimization is implemented as a combination of a quasi-Newton optimization and a linear constraint. The method was tested on a set of Lennard-Jones-38 cluster transitions and a set of 121 molecular reactions using density functional theory calculations. The efficiency in terms of energy and force evaluation is better than with competing methods as long as they do not switch to single-ended methods. The construction of a continuous search path with small steps and the ability to focus on arbitrary subsegments of the path provide an additional value in terms of robustness and flexibility.