Chris A. Marianetti

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 $\mathrm{DFT}+U$ 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 ${\mathrm{Li}}_{x}{\mathrm{MPO}}_{4}$ ($\mathrm{M}=\mathrm{Mn}$, Fe Co, Ni), layered ${\mathrm{Li}}_{x}{\mathrm{MO}}_{2}$ ($x=\mathrm{Co}$, Ni) and spinel-like ${\mathrm{Li}}_{x}{\mathrm{M}}_{2}{\mathrm{O}}_{4}$ ($\mathrm{M}=\mathrm{Mn}$, Co), can be reproduced accurately.

This research explores the nonlinear elastic properties of two-dimensional molybdenum disulfide. We derive a thermodynamically rigorous nonlinear elastic constitutive equation and then calculate the nonlinear elastic response of two-dimensional MoS${}_{2}$ with first-principles density functional theory (DFT) calculations. The nonlinear elastic properties are used to predict the behavior of suspended monolayer MoS${}_{2}$ subjected to a spherical indenter load at finite strains in a multiple-length-scale finite element analysis model. The model is validated experimentally by indenting suspended circular MoS${}_{2}$ membranes with an atomic force microscope. We find that the two-dimensional Young's modulus and intrinsic strength of monolayer MoS${}_{2}$ are 130 and 16.5 N/m, respectively. The results approach Griffith's predicted intrinsic strength limit of ${\ensuremath{\sigma}}_{\mathrm{int}}\ensuremath{\sim}\frac{E}{9}$, where $E$ is the Young's modulus. This study reveals the predictive power of first-principles density functional theory in the derivation of nonlinear elastic properties of two-dimensional MoS${}_{2}$. Furthermore, the study bridges three main gaps that hinder understanding of material properties: DFT to finite element analysis, experimental results to DFT, and the nanoscale to the microscale. In bridging these three gaps, the experimental results validate the DFT calculations and the multiscale constitutive model.

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.

A combination of density functional and dynamical mean field theory calculations are used to show that the remarkable metal-insulator transition in the rare-earth-element nickelate perovskites arises from a site-selective Mott phase, in which the d electrons on half of the Ni ions are localized to form a fluctuating moment while the d electrons on other Ni ions form a singlet with holes on the surrounding oxygen ions. The calculation reproduces key features observed in the nickelate materials, including an insulating gap in the paramagnetic state, a strong variation of static magnetic moments among Ni sites and an absence of charge order. A connection between structure and insulating behavior is documented. The site-selective Mott transition may be a more broadly applicable concept in the description of correlated materials.