An exact solution to the self-consistent field screening problem is presented in terms of Bloch-state matrix elements of the bare perturbation. This solution is equivalent to one given by Sham and Ziman in terms of Fourier transforms of the bare perturbation, but unlike the latter it avoids the convergence problem in momentum space that arises in the screening of the electron–phonon interaction because of the 'deep' part of the ionic potential. The new form of the solution converts naturally into a pseudopotential formalism. At the same time it provides a framework in which to discuss and extend the two most common calculation schemes for the electron–phonon matrix element, the rigid Schrödinger potential model and the diffraction model. The inverse dielectric tensor is evaluated to first-order in the pseudopotential. Local field effects cause the Q → 0 limit of the electron–phonon interaction to deviate from its conventional value.
Electrons at a fixed density approach a strictly correlated limit as their Coulomb interaction is scaled to infinity. We find the exact energy for strictly correlated electrons in spherical two-electron densities, and a useful gradient expansion for general densities. We also propose a model for the coupling-constant dependence, which interpolates between the weak- and strong-interaction limits. This model defines a density functional which predicts accurate ground-state correlation energies for real atoms and the two-dimensional uniform electron gas.
Van der Waals interaction is an elusive many-body effect arising from instantaneous charge fluctuations. Fundamental understanding of this effect plays an important role in computational chemistry, physics and materials science. In this article, recent advances in the evaluation of van der Waals coefficients, in particular the higher-order ones, are reviewed.
Using a density-based local pseudopotential, we study the effect of local field or exchange–correlation corrections on lattice dynamics for several simple metals (the alkalis, aluminum, and lead). Turning on exchange and correlation in the dielectric function significantly reduces phonon frequencies for some metals. We consider three levels of description: the local density approximation (LDA), the generalized gradient approximation (GGA), and the nearly exact. Especially for the lower-density metals, the LDA linear response introduces negligible error into the phonon frequencies when exchange and correlation are treated together. This fact results from an almost complete cancellation between the nonlocalities of exchange and correlation. We find no static charge density wave in any of these metals at normal volume, even in the most favorable exchange-only case. For Na and Al at a volume about 50% bigger than normal, we find that a transverse phonon goes soft on the [110] zone boundary. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 359–369, 1998
Methylammonium lead iodide (CH3NH3PbI3 or MAPbI3) perovskite is a promising new photovoltaic material with high power conversion efficiency. However, its perovskite phase with corner-connected PbI6 octahedra shows poor environmental stability. More recently, MAPbI3 has been shown to be thermodynamically unstable with a positive formation enthalpy. Here, using first-principles density functional theory calculations, we predict a layered hexagonal phase of MAPbI3 consisting of infinite chains of face-shared PbI6 octahedra with P63mc space-group symmetry to be thermodynamically the most stable phase for a wide range of volume and temperature compared to any of the experimentally observed perovskite phases with a different tilt pattern of the corner-connected octahedra. The predicted hexagonal phase is also dynamically stable without any soft phonon modes. The change from corner to face-shared connectivity in the hexagonal phase leads to a predicted band gap of 2.6 eV and a band structure that favors highly anisotropic charge transport.
No abstract is provided for this article.
As the symbol of the partition clustering method, K-Means is well known and widely used in many fields for the easily implemented and high efficiency. However, the initial center problem may affect the final cluster result, sometimes the final cluster result might contain some empty clusters. In this paper, a new K-Mean initialization method is proposed which combines the statistical information and the distance computation. The statistical information contains the mean, median, and Gaussian kernel density estimation. At first, the high density points are selected for each dimension. Then the distance and the density are used to measure every possible initial centers. After this process works from high variance dimension to low variance ones, the final initial cluster centers are constructed with the K nearest neighbors. Experiments on public datasets show that this method can achieve comparable results compared with other conventional methods.
Because of an acquired obsession to understand as much as possible in a limited but important area of science and because of optimism, luck, and help from others, my life in science turned out to be much better than I or others could have expected or planned. This is the story of how that happened, and also the story of the groundstate density functional theory of electronic structure, told from a personal perspective.
Bauer's expression for the difference between the expectation values of an arbitrary quantum-mechanical operator with the physical interacting ground-state wave function and its corresponding noninteracting Kohn-Sham wave function is obtained here by a very simple and general derivation via the constrained-search formulation of density-functional theory. Our proof does not require v-representability or a coupling-constant integration. We show that the following expression of Bass for the kinetic part of the exact exchange-correlation energy ${\mathit{E}}_{\mathrm{xc}}$[n]: ${\mathit{T}}_{\mathrm{xc}}$[n]=${\mathit{a}}_{0}$ \ensuremath{\partial}${\mathit{E}}_{\mathrm{xc}}$[n]/\ensuremath{\partial}${\mathit{a}}_{0}$, where ${\mathit{a}}_{0}$=${\mathrm{\ensuremath{\Elzxh}}}^{2}$/${\mathit{me}}^{2}$ is the Bohr radius, can also be derived by a constrained-search proof and is equivalent to the following expression of Levy and Perdew: ${\mathit{T}}_{\mathrm{xc}}$[n]=(\ensuremath{\partial}${\mathit{E}}_{\mathrm{xc}}$[${\mathit{n}}_{\ensuremath{\lambda}}$]/\ensuremath{\partial}\ensuremath{\lambda})${\mathrm{\ensuremath{\Vert}}}_{\ensuremath{\lambda}=1}$-${\mathit{E}}_{\mathrm{xc}}$[n], where ${\mathit{n}}_{\ensuremath{\lambda}}$(x,y,z)=${\ensuremath{\lambda}}^{3}$n(\ensuremath{\lambda}x,\ensuremath{\lambda}y,\ensuremath{\lambda}z). When an approximate ${\mathit{E}}_{\mathrm{xc}}$ is employed, the two expressions will yield the same result for the corresponding ${\mathit{T}}_{\mathrm{xc}}$ if certain coordinate scaling relations, involving the electronic charge, are satisfied. Moreover, the Levy-Perdew relation has the advantage that it is applied at full electronic charge (e) and full electronic mass (m). Corresponding relations are also exhibited for the correlation hole. We discuss the high- and low-density limits of ${\mathit{T}}_{\mathrm{xc}}$, generalize our results to spin-density functional theory, and present numerical estimates of ${\mathit{T}}_{\mathrm{xc}}$ for atoms, evaluated within the local spin density, gradient expansion, and generalized gradient approximations.
Within a density-functional context, the random-phase approximation (RPA) for the correlation energy makes a short-range error that is well suited for correction by a local spin density or generalized-gradient approximation (GGA). Here we construct a GGA for the short-range correction, following the same reliable procedure used earlier to construct the GGA for the whole exchange-correlation energy: real-space cutoff of the spurious long-range contribution to the gradient expansion of the hole around an electron. The resulting density functional is nearly local and predicts a substantial correction to the RPA correlation energy of an atom but very small corrections to the RPA atomization energy of a molecule, which may by itself come close to ``chemical accuracy'' and to the RPA surface energy of a metal. A by-product of this work is a density functional for the system-averaged correlation hole within RPA.
The effectiveness of five temperature control algorithms for dual control volume grand canonical molecular dynamics is investigated in the study of hydrogen atom diffusion in a palladium bulk. The five algorithms, namely, Gaussian, generalized Gaussian moment thermostat (GGMT), velocity scaling, Nosé-Hoover (NH), and its enhanced version Nosé-Hoover chain (NHC) are examined in both equilibrium and nonequilibrium simulation studies. Our numerical results show that Gaussian yields the most inaccurate solutions for the hydrogen-palladium system due to the high friction coefficient generated from the large velocity fluctuation of hydrogen, while NHC, NH, and GGMT produce the most accurate temperature and density profiles in both equilibrium and nonequilibrium cases with their feedback control mechanisms. However, this feedback control also overestimates the self-diffusion coefficients in equilibrium systems and the diffusion coefficient in nonequilibrium systems. Velocity scaling thermostat produces slight inhomogeneities in the temperature and density profiles, but due to the dissipated heat accumulated in the control volumes it still yields accurate self-diffusion coefficients that are in good agreement with the experimental data at a wide range of temperatures while others tend to deviate.
We construct a generalized gradient approximation (GGA) for the density ${\mathit{n}}_{\mathrm{xc}}$(r,r+u) at position r+u of the exchange-correlation hole surrounding an electron at r, or more precisely for its system and spherical average 〈${\mathit{n}}_{\mathrm{xc}}$(u)〉=(4\ensuremath{\pi}${)}^{\mathrm{\ensuremath{-}}1}$\ensuremath{\int}d${\mathrm{\ensuremath{\Omega}}}_{\mathit{u}}$ ${\mathit{N}}^{\mathrm{\ensuremath{-}}1}$\ensuremath{\int}${\mathit{d}}^{3}$r n(r)${\mathit{n}}_{\mathrm{xc}}$(r,r+u). Starting from the second-order density gradient expansion, which involves the local spin densities ${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$(r),${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$(r) and their gradients \ensuremath{\nabla}${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$(r),\ensuremath{\nabla}${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$(r), we cut off the spurious large-u contributions to restore those exact conditions on the hole that the local spin density (LSD) approximation respects. Our GGA hole recovers the Perdew-Wang 1991 and Perdew-Burke-Ernzerhof GGA's for the exchange-correlation energy, which therefore respect the same powerful hole constraints as LSD. When applied to real systems, our hole model provides a more detailed test of these energy functionals, and also predicts the observable electron-electron structure factor. \textcopyright{} 1996 The American Physical Society.
A perturbation theory is derived for the study of molecular structure. For a large class of approximate formulations (including Hartree–Fock and higher-level schemes and exact exchange-only density-functional theory), it is proved that the change in the error of the energy, upon geometry change, is zero through the second-order perturbation term, thus helping to explain why approximate energy curves often closely parallel exact curves and give accurate geometries. In contrast, for each non-Coulomb potential considered, the error change is not zero through second order, suggesting that accurate geometries are due, in part, to a special quality of the Coulomb potential. Comparable results are obtained for atomic electron–nuclear attraction expectation values (isoelectronic energy changes), which are exact through second order in the Coulomb cases. The conclusions are supported by a nonperturbative argument and by a numerical example.
