Related papers: Completeness of Atomic Structure Representations

Recent advances in scanning transmission electron and scanning probe microscopies have opened exciting opportunities in probing the materials structural parameters and various functional properties in real space with angstrom-level…

When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…

Predicting the physico-chemical properties of pure substances and mixtures is a central task in thermodynamics. Established prediction methods range from fully physics-based ab-initio calculations, which are only feasible for very simple…

We review pedagogically non-Abelian discrete groups, which play an important role in the particle physics. We show group-theoretical aspects for many concrete groups, such as representations, their tensor products. We explain how to derive,…

While investigating quantum correlations in atomic systems, we note that single measurements contain information about these correlations. Using a simple model of measurement -- analogous to the one used in quantum optics -- we show how to…

Many molecular "quantum" theories, like "quantum chemistry", conceal that they are actually quantum-classical approaches---they treat one set of molecular degrees of freedom classically while the remaining degrees of freedom follow the laws…

A cluster consisting of many atoms or molecules may be considered, in some circustances, to be a single large molecule with a well defined polarizability. Once the polarizability of such a cluster is known, one can evaluate certain…

Analysis of three-particle correlations is performed on the basis of simulation data of atomic dynamics in liquid and amorphous aluminium. A three-particle correlation function is introduced to characterize the relative positions of various…

Atomic nuclei can exhibit shape coexistence and multi-reference physics that enters in their ground states, and to accurately capture the ensuing correlations and entanglement is challenging. We address this problem by applying…

In many cases, the predictions of machine learning interatomic potentials (MLIPs) can be interpreted as a sum of body-ordered contributions, which is explicit when the model is directly built on neighbor density correlation descriptors, and…

Electronic structure methods for accurate calculation of molecular properties have a high cost that grows steeply with the problem size, therefore, it is helpful to have the underlying atomic basis functions that are less in number but of…

In a world made of atoms, the computer simulation of molecular systems, such as proteins in water, plays an enormous role in science. Software packages that perform these computations have been developed for decades. In molecular…

Accurate prediction of the physicochemical properties of molecular mixtures using graph neural networks remains a significant challenge, as it requires simultaneous embedding of intramolecular interactions while accounting for mixture…

Structural quantities such as order parameters and correlation functions are often employed to gain insight into the physical behavior and properties of condensed matter systems. While standard quantities for characterizing structure exist,…

We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…

Structural defects within amorphous packings of symmetric particles can be characterized using a machine learning approach that incorporates structure functions of radial distances and angular arrangement. This yields a scalar field,…

Anisotropic decompositions using representation systems based on parabolic scaling such as curvelets or shearlets have recently attracted significantly increased attention due to the fact that they were shown to provide optimally sparse…

Accurate measurement of relative distance and orientation of two nearby quantum particles is discussed. We are in particular interested in a realistic description requiring as little prior knowledge about the system as possible. Thus,…

Atomic level qubits in silicon are attractive candidates for large-scale quantum computing, however, their quantum properties and controllability are sensitive to details such as the number of donor atoms comprising a qubit and their…

Scanning probe experiments such as scanning tunneling microscopy (STM) and atomic force microscopy (AFM) on strongly correlated electronic systems often reveal complex pattern formation on multiple length scales. By studying the universal…