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Second-order geometry
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Classroom Contents
Error Bounds for Properties in Planewave Electronic Structure Calculations
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- 1 Intro
- 2 Computing properties of materials systems
- 3 Outline
- 4 Density Functional Theory
- 5 Modelling crystalline systems
- 6 Errors arising in the course of the calculation
- 7 The perfect error bound
- 8 Abstract formulation
- 9 Guaranteed bounds
- 10 Main difficulties for applications to DFT
- 11 Formulation of the DFT ground state problem
- 12 Discretization with planewaves
- 13 First-order optimality conditions
- 14 Orthogonal projectors vs orbitals
- 15 Second-order geometry
- 16 Linearization in the asymptotic regime
- 17 Linearization : Numerical results
- 18 Choosing an adequate norm
- 19 Results: Force estimation for Silicon
- 20 Frequency splitting
- 21 Improved error bound
- 22 New estimation on the forces
- 23 Conclusion
