Four-component Dirac Hartree--Fock is an accurate mean-field method for treating molecular systems where relativistic effects are important. However, the computational cost and complexity of the two-electron interaction makes this method less common,
even though we can consider the Dirac Hartree--Fock Hamiltonian the ground truth of electronic structure, barring explicit quantum-electrodynamical effects. Being able to calculate these effects is then vital to the design of lower scaling methods for accurate predictions in computational spectroscopy and properties of heavy element complexes that must include relativistic effects for even qualitative accuracy. In this work, we present a Pauli quaternion formalism of maximal component- and spin-separation for computing the Dirac-Coulomb-Gaunt Hartree--Fock ground state, with a minimal floating-point-operation count algorithm. This approach also allows one to explicitly separate different spin physics from the two-body interactions, such as spin-free, spin-orbit, and the spin-spin contributions. Additionally, we use this formalism to examine relativistic trends in the periodic table, and analyze the basis set dependence of atomic gold and gold dimer systems.
We propose RIFE, a Real-time Intermediate Flow Estimation algorithm for Video Frame Interpolation (VFI). Many recent flow-based VFI methods first estimate the bi-directional optical flows, then scale and reverse them to approximate intermediate flows
, leading to artifacts on motion boundaries. RIFE uses a neural network named IFNet that can directly estimate the intermediate flows from coarse-to-fine with much better speed. We design a privileged distillation scheme for training intermediate flow model, which leads to a large performance improvement. Experiments demonstrate that RIFE is flexible and can achieve state-of-the-art performance on several public benchmarks. The code is available at url{https://github.com/hzwer/arXiv2020-RIFE}
