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Register a new userPulay forces in density-functional theory with extended Hubbard functionals: From nonorthogonalized to orthogonalized manifolds
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We present a derivation of the exact expression for Pulay forces in density-functional theory calculations augmented with extended Hubbard functionals, and arising from the use of orthogonalized atomic orbitals as projectors for the Hubbard manifold. The derivative of the inverse square root of the orbital overlap matrix is obtained as a closed-form solution of the associated Lyapunov (Sylvester) equation. The expression for the resulting contribution to the forces is presented in the framework of ultrasoft pseudopotentials and the projector-augmented-wave method, and using a plane wave basis set. We have benchmarked the present implementation with respect to finite differences of total energies for the case of NiO, finding excellent agreement. Owing to the accuracy of Hubbard-corrected density-functional theory calculations - provided the Hubbard parameters are computed for the manifold under consideration - the present work paves the way for systematic studies of solid-state and molecular transition-metal and rare-earth compounds.
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I summarize Density Functional Theory (DFT) in a language familiar to quantum field theorists, and introduce several apparently novel ideas for constructing {it systematic} approximations for the density functional. I also note that, at least within the large $K$ approximation ($K$ is the number of electron spin components), it is easier to compute the quantum effective action of the Coulomb photon field, which is related to the density functional by algebraic manipulations in momentum space.
In spin-density-functional theory for noncollinear magnetic materials, the Kohn-Sham system features exchange-correlation (xc) scalar potentials and magnetic fields. The significance of the xc magnetic fields is not very well explored; in particular, they can give rise to local torques on the magnetization, which are absent in standard local and semilocal approximations. We obtain exact benchmark solutions for two electrons on four-site extended Hubbard lattices over a wide range of interaction strengths, and compare exact xc potentials and magnetic fields with approximations obtained from orbital-dependent xc functionals. The xc magnetic fields turn out to play an increasingly important role as systems becomes more and more correlated and the electrons begin to localize; the effects of the xc torques, however, remain relatively minor. The approximate xc functionals perform overall quite well, but tend to favor symmetry-broken solutions for strong interactions.
Linear scaling methods for density-functional theory (DFT) simulations are formulated in terms of localised orbitals in real-space, rather than the delocalised eigenstates of conventional approaches. In local-orbital methods, relative to conventional DFT, desirable properties can be lost to some extent, such as the translational invariance of the total energy of a system with respect to small displacements and the smoothness of the potential energy surface. This has repercussions for calculating accurate ionic forces and geometries. In this work we present results from textsc{onetep}, our linear scaling method based on localised orbitals in real-space. The use of psinc functions for the underlying basis set and on-the-fly optimisation of the localised orbitals results in smooth potential energy surfaces that are consistent with ionic forces calculated using the Hellmann-Feynman theorem. This enables accurate geometry optimisation to be performed. Results for surface reconstructions in silicon are presented, along with three example systems demonstrating the performance of a quasi-Newton geometry optimisation algorithm: an organic zwitterion, a point defect in an ionic crystal, and a semiconductor nanostructure.
The ferroelectricity of the spiral magnets LiCu2O2 and LiCuVO4 was examined by calculating the electric polarizations of their spin spiral states on the basis of density functional theory with spin-orbit coupling. Our work unambiguously reveals that spin-orbit coupling is responsible for the ferroelectricity with the primary contribution from the spin-orbit coupling on the Cu sites, but the asymmetric density distribution responsible for the electric polarization occurs mainly around the O atoms. The electric polarization is calculated to be much greater for the ab- than for the bc-plane spin spiral. The observed spin-spiral plane is found to be consistent with the observed direction of the electric polarization for LiCuVO4, but inconsistent for LiCu2O2.
Density functional theory is generalized to incorporate electron-phonon coupling. A Kohn-Sham equation yielding the electronic density $n_U(mathbf{r})$, a conditional probability density depending parametrically on the phonon normal mode amplitudes $U={U_{mathbf{q}lambda}}$, is coupled to the nuclear Schrodinger equation of the exact factorization method. The phonon modes are defined from the harmonic expansion of the nuclear Schrodinger equation. A nonzero Berry curvature on nuclear configuration space affects the phonon modes, showing that the potential energy surface alone is generally not sufficient to define the phonons. An orbital-dependent functional approximation for the non-adiabatic exchange-correlation energy reproduces the leading-order nonadiabatic electron-phonon-induced band structure renormalization in the Frohlich model.
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