A review of the basic ideas and techniques of the spectral density-functional theory is presented. This method is currently used for electronic structure calculations of strongly correlated materials where the one-electron description breaks down. The method is illustrated with several examples where interactions play a dominant role: systems near metal-insulator transitions, systems near volume collapse transitions, and systems with local moments.
First-principles calculations within the Local Density Approximation (LDA) or Generalized Gradient Approximation (GGA), though very successful, are known to underestimate redox potentials, such as those at which lithium intercalates in transition metal compounds. We argue that this inaccuracy is related to the lack of cancellation of electron self-interaction errors in LDA/GGA and can be improved by using the DFT+U method with a self-consistent evaluation of the U parameter.We show that, using this approach, the experimental lithium intercalation voltages of a number of transition metal compounds, including the olivine Li x MPO 4 (M=Mn, Fe Co, Ni), layered Li x MO 2 (x =Co, Ni) and spinel-like Li x M 2 O 4 (M=Mn, Co), can be reproduced accurately.
We report on a significant failure of the local density approximation (LDA) and the generalized gradient approximation (GGA) to reproduce the phase stability and thermodynamics of mixed-
The nonlinear in-plane elastic properties of graphene are calculated using density-functional theory. A thermodynamically rigorous continuum description of the elastic response is formulated by expanding the elastic strain energy density in a Taylor series in strain truncated after the fifth-order term. Upon accounting for the symmetries of graphene, a total of fourteen nonzero independent elastic constants are determined by least-squares fit to the ab initio calculations. The nonlinear continuum description is valid for infinitesimal and finite strains under arbitrary in-plane tensile loading in circumstance for which the bending stiffness can be neglected. The continuum formulation is suitable for incorporation into the finite element method.
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