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Numerous applications in computer vision, machine learning, electronic structure computation, system balancing and robot manipulation can be considered as solving optimization problems on manifolds (see [31 34]).
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Electron repulsion integral tensor has ubiquitous applications in electronic structure computations.
The convergence threshold for energy and electronic structure computations was considered to be 10−4 Hartree/bohr.
Symmetry-adapted molecular basis functions are widely applied for the electronic structure computations of molecules and clusters.
Hydrocarbon systems have been intensively studied via numerical methods, including electronic structure computations, molecular dynamics and Monte Carlo simulations.
Electronic structure computations are employed to assess the stability and surface activity of oxygen vacancies and lattice nitrogen at the (001) facet of nitrogen-doped perovskites.
Anderson acceleration was first proposed in 1965 and, for some years, has been used successfully to accelerate the convergence of self-consistent field iterations in electronic-structure computations.
The density functional theory (DFT) computation of electronic structure, total energy and other properties of materials, is a field in constant progress.
Modern theoretical studies involve the use of numerical computation of electronic structure and mathematical tools to understand phenomena such as high-temperature superconductivity, topological phases and gauge symmetries.
The most advanced methods for reliable and accurate computation of the electronic structure of molecular and nano systems are the coupled-cluster techniques.
Again, the obtained values are of the same order of magnitude, in agreement with the trend of electronic structure properties from the quantum chemical computations.
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