A machine-learning-based exchange-correlation functional is proposed for general-purpose density functional theory calculations. It is built upon the long-range-corrected Becke-Lee-Yang-Parr (LC-BLYP) functional, along with an embedded neural network which determines the value of the range-separation parameter μ for every individual system. The structure and the weights of the neural network are optimized with a reference data set containing 368 highly accurate thermochemical and kinetic energies. The newly developed functional (LC-BLYP-NN) achieves a balanced performance for a variety of energetic properties investigated. It largely improves the accuracy of atomization energies and heats of formation on which the original LC-BLYP with a fixed μ performs rather poorly. Meanwhile, it yields a similar or slightly compromised accuracy for ionization potentials, electron affinities, and reaction barriers, for which the original LC-BLYP works reasonably well. This work clearly highlights the potential usefulness of machine-learning techniques for improving density functional calculations.

In this work, we establish a so-called "system-bath entanglement theorem", for arbitrary systems coupled with Gaussian environments. This theorem connects the entangled system-bath response functions in the total composite space to those of local systems, as long as the interacting bath spectral densities are given. We validate the theorem with the direct evaluation via the exact dissipaton-equation-of-motion approach. Therefore, this work enables various quantum dissipation theories, which originally describe only the reduced system dynamics, for their evaluations on the system-bath entanglement properties. Numerical demonstrations are carried out on the Fano interference spectroscopies of spin-boson systems.

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