We present a differentiation framework for plane-wave density-functional theory(DFT)that combines the strengths of forward-mode algorithmic differentiation(AD)and density-functional perturbation theory(DFPT).In the re...We present a differentiation framework for plane-wave density-functional theory(DFT)that combines the strengths of forward-mode algorithmic differentiation(AD)and density-functional perturbation theory(DFPT).In the resulting AD-DFPT framework derivatives of any DFT output quantity with respect to any input parameter(e.g.,geometry,density functional or pseudopotential)can be computed accurately without deriving gradient expressions by hand.We implement AD-DFPT into the Density-Functional ToolKit(DFTK)and show its broad applicability.Amongst others we consider the inverse design of a semiconductor band gap,the learning of exchange-correlation functional parameters,or the propagation of DFT parameter uncertainties to relaxed structures.These examples demonstrate a number of promising research avenues opened by gradient-driven workflows in first-principles materials modeling.展开更多
基金supported by the Swiss National Science Foundation (SNSF, Grant No. 221186)the NCCR MARVEL, a National Centre of Competence in Research, funded by the SNSF (Grant No. 205602). The funder played no role in study design, data collection, analysis and interpretation of data, or the writing of this manuscript. Fruitful discussions with Andrea Azzali, Gaspard Kemlin, Antoine Levitt, Uwe Naumann, Étienne Polack, and Markus Towara on the technical aspects of our AD-DFPT implementation and with Giovanni Pizzi regarding the pseudopotential training example are gratefully acknowledged.
文摘We present a differentiation framework for plane-wave density-functional theory(DFT)that combines the strengths of forward-mode algorithmic differentiation(AD)and density-functional perturbation theory(DFPT).In the resulting AD-DFPT framework derivatives of any DFT output quantity with respect to any input parameter(e.g.,geometry,density functional or pseudopotential)can be computed accurately without deriving gradient expressions by hand.We implement AD-DFPT into the Density-Functional ToolKit(DFTK)and show its broad applicability.Amongst others we consider the inverse design of a semiconductor band gap,the learning of exchange-correlation functional parameters,or the propagation of DFT parameter uncertainties to relaxed structures.These examples demonstrate a number of promising research avenues opened by gradient-driven workflows in first-principles materials modeling.
