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A subspace formulation of time-dependent density functional theory (TDDFT) is proposed for large-scale calculations based on density functional perturbation theory. The formulation is implemented in conjunction with projector augmented-wave method and plane-wave basis set. A key bottleneck of conventional TDDFT method is circumvented by projecting the time-dependent Kohn-Sham eigenvalue equations from a full Hilbert space to a substantially reduced sub-Hilbert space. As a result, both excitation energies and ionic forces can be calculated accurately within the reduced subspace. The method is validated for several model systems and exhibits the similar accuracy as the conventional TDDFT method but at a computational cost of the ground state calculation. The Born-Oppenheimer molecular dynamics can be successfully performed for excited states in C60 and T12 molecules, opening doors for many applications involving excited state dynamics.

Autophagy, or self-eating, is an evolutionarily conserved process in which cytosol and organelles are sequestered within double-membrane vesicles that deliver the contents to the lysosome/vacuole for the degradation and recycling of cytoplasmic components in eukaryotes. It is well recognized that autophagy plays an important role in maintaining cellular homeostasis under physiological and pathophysiological con­ditions and the upregulation of autophagy may serve as an adaptive process to provide nutrients and energy when under stresses. Recently, studies have illustrated that autophagy is intricately related to skin diseases. This review provides a brief synopsis of the process of autophagy and aims to elucidate the roles of autophagy in different skin diseases and to highlight the need for increased research in the field.

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