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Register a new userComparison of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water interactions through many-body expansions
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The accurate representation of multidimensional potential energy surfaces is a necessary requirement for realistic computer simulations of molecular systems. The continued increase in computer power accompanied by advances in correlated electronic structure methods nowadays enable routine calculations of accurate interaction energies for small systems, which can then be used as references for the development of analytical potential energy functions (PEFs) rigorously derived from many-body expansions. Building on the accuracy of the MB-pol many-body PEF, we investigate here the performance of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water two-body and three-body interaction energies, denoting the resulting potentials PIP-MB-pol, BPNN-MB-pol, and GAP-MB-pol, respectively. Our analysis shows that all three analytical representations exhibit similar levels of accuracy in reproducing both two-body and three-body reference data as well as interaction energies of small water clusters obtained from calculations carried out at the coupled cluster level of theory, the current gold standard for chemical accuracy. These results demonstrate the synergy between interatomic potentials formulated in terms of a many-body expansion, such as MB-pol, that are physically sound and transferable, and machine-learning techniques that provide a flexible framework to approximate the short-range interaction energy terms.
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We investigate genuine multipartite nonlocality of pure permutationally invariant multimode Gaussian states of continuous variable systems, as detected by the violation of Svetlichny inequality. We identify the phase space settings leading to the largest violation of the inequality when using displaced parity measurements, distinguishing our results between the cases of even and odd total number of modes. We further consider pseudospin measurements and show that, for three-mode states with asymptotically large squeezing degree, particular settings of these measurements allow one to approach the maximum violation of Svetlichny inequality allowed by quantum mechanics. This indicates that the strongest manifestation of genuine multipartite quantum nonlocality is in principle verifiable on Gaussian states.
We report the results of molecular dynamics simulations of the properties of a pseudo-atom model of dodecane thiol ligated 5-nm diameter gold nanoparticles (AuNP) in vacuum as a function of ligand coverage and particle separation in three state of aggregation: the isolated AuNP, an isolated pair of AuNPs and a square assembly of AuNPs. Our calculations show that for all values of the coverage the ligand density along a radius emanating from the core of an isolated AuNP oscillates along the chain up to the fourth pseudo-atom, then smoothly decays to zero. We examine the ligand envelope as a function of the coverage and demonstrate that the deformation of that envelope generated by interaction between the NPs is coverage-dependent, so that the shape, depth and position of the minimum of the potential of mean force displays a systematic dependence on the coverage. We propose an accurate analytical description of the calculated potential of mean force with parameters that scale linearly with the ligand coverage. We define and calculate an effective pair potential of mean force for a square configuration of particles; our definition contains, implicitly, both the three- and four-particle contributions to deviation from additivity. We find that the effective pair potential of mean force in this configuration has a different minimum and a different well depth than the isolated pair potential of mean force. Previous work has found that the three-particle contribution to deviation from additivity is monotone repulsive, whereas we find that the combined three- and four-particle contributions have an attractive well, implying that the three- and four-particle contributions are of comparable magnitude but opposite sign, thereby suggesting that even higher order correction terms likely play a significant role in the behavior of assemblies of many nanoparticles.
We investigate the use of invariant polynomials in the construction of data-driven interatomic potentials for material systems. The atomic body-ordered permutation-invariant polynomials (aPIPs) comprise a systematic basis and are constructed to preserve the symmetry of the potential energy function with respect to rotations and permutations. In contrast to kernel based and artificial neural network models, the explicit decomposition of the total energy as a sum of atomic body-ordered terms allows to keep the dimensionality of the fit reasonably low, up to just 10 for the 5-body terms. The explainability of the potential is aided by this decomposition, as the low body-order components can be studied and interpreted independently. Moreover, although polynomial basis functions are thought to extrapolate poorly, we show that the low dimensionality combined with careful regularisation actually leads to better transferability than the high dimensional, kernel based Gaussian Approximation Potential.
Basis set incompleteness error and finite size error can manifest concurrently in systems for which the two effects are phenomenologically well-separated in length scale. When this is true, we need not necessarily remove the two sources of error simultaneously. Instead, the errors can be found and remedied in different parts of the basis set. This would be of great benefit to a method such as coupled cluster theory since the combined cost of $n_{occ}^6 n_{virt}^4$ could be separated into $n_{occ}^6$ and $n_{virt}^4$ costs with smaller prefactors. In this Communication, we present analysis on a data set due to Baardsen and coworkers, containing coupled cluster doubles energies for the 2DEG for $r_s=$ 0.5, 1.0 and 2.0 a.u.~at a wide range of basis set sizes and particle numbers. In obtaining complete basis set limit thermodynamic limit results, we find that within a small and removable error the above assertion is correct for this simple system. This approach allows for the combination of methods which separately address finite size effects and basis set incompleteness error.
Kernel ridge regression (KRR) that satisfies energy conservation is a popular approach for predicting forcefield and molecular potential, to overcome the computational bottleneck of molecular dynamics simulation. However, the computational complexity of KRR increases cubically as the product of the number of atoms and simulated configurations in the training sample, due to the inversion of a large covariance matrix, which limits its applications to the simulation of small molecules. Here, we introduce the atomized force field (AFF) model that requires much less computational costs to achieve the quantum-chemical level of accuracy for predicting atomic forces and potential energies. Through a data-driven partition on the covariance kernel matrix of the force field and an induced input estimation approach on potential energies, we dramatically reduce the computational complexity of the machine learning algorithm and maintain high accuracy in predictions. The efficient machine learning algorithm extends the limits of its applications on larger molecules under the same computational budget. Using the MD17 dataset and another simulated dataset on larger molecules, we demonstrate that the accuracy of the AFF emulator ranges from 0.01-0.1 kcal mol$^{-1}$ or energies and 0.001-0.2 kcal mol$^{-1}$ $require{mediawiki-texvc}$$AA^{-1}$ for atomic forces. Most importantly, the accuracy was achieved by less than 5 minutes of computational time for training the AFF emulator and for making predictions on held-out molecular configurations. Furthermore, our approach contains uncertainty assessment of predictions of atomic forces and potentials, useful for developing a sequential design over the chemical input space, with nearly no increase of computational costs.
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