Interatomic Forces in Condensed Matter

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A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials (2017, methodology): “The method hinges on the underlying atomic potentials, which are used to approximate the atomic interactions [18].”
Approximation of the electron density of Aluminium clusters in tensor-product format (2012, unknown): “, [7, 23]) E(̺,R) = Ts(̺) + Exc(̺) + EH(̺) + Eext(̺,R) + Ezz(R), (1) where ̺ denotes the electron density such that”
Active learning of linearly parametrized interatomic potentials (2016, methodology): “cape the physical region and drive the system to a spurious minimum x !1. We next apply the AL approach to this problem by selecting two points (since there are two basis functions) from the interval [4;4] for the ﬁtting of E(x). The most optimal points are x 1 = 4 and x 2= 4, as they maximize det x”
Moment Tensor Potentials: A Class of Systematically Improvable Interatomic Potentials (2015, background): “The two major approaches to computing interatomic forces are (1) quantum mechanics (QM) calculations [10, 14] and (2) using empirical interatomic potentials.”
Molecular dynamics with on-the-fly machine learning of quantum-mechanical forces. (2015, methodology): “Much larger model systems and longer simulations are achievable using force fields (FFs), based on judiciously chosen para-metrized functional forms fitted on experimental or FP data [9 – 14].”