Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session M1: Recent Advances in Density Functional Theory VI |
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Sponsoring Units: DCP DCOMP Chair: Jianwei Sun, Temple University Room: 103/105 |
Wednesday, March 5, 2014 11:15AM - 11:51AM |
M1.00001: The derivative discontinuity of the exchange-correlation functional Invited Speaker: Aron Cohen The derivative discontinuity is a fundamental feature of the exchange-correlation energy. It is the change in the derivative of the energy as the number of electrons goes through an integer, and it is often expressed as a potential that jumps by a constant on going from $N-\delta$ to $N+\delta$. In this talk we will show manifestations in the total energy of integer systems at fixed $N$. One manifestation is the complete failure of all functionals in the literature to give the energy of {\textbf{both}} infinitely stretched H$_2^+$ and infinitely stretched H$_2$. Another very clear example is the failure to correctly reproduce the density in a two electron H$_2$ like system when changing the charge of one of the protons to be non-integer. More examples in chemistry and physics will be shown, ranging from the behaviour of electrons in the simplest chemical reactions to the gap of the 1D-Hubbard model and electron transport in the Anderson model. To understand the derivative discontinuity in these systems it is important to consider three perspectives, (1) the true behaviour of electrons which can be found by an exact FCI calculation (2) the failures of most currently used approximate functionals, which are all missing the derivative discontinuity (3) investigating new functionals that may have some aspects of the derivative discontinuity. Overall this is a great challenge for $E_{xc}[\rho]$ that must be considered in the development of new functionals. [Preview Abstract] |
Wednesday, March 5, 2014 11:51AM - 12:03PM |
M1.00002: Hohenberg-Kohn Theorem Including Electron Spin in the Presence of a Magnetostatic Field Viraht Sahni, Xiao-Yin Pan We consider a system of $N$ electrons in the presence of an external electrostatic ${\mathbf{\cal{E}}}({\bf{r}}) = - {\mathbf{\nabla}} v({\bf{r}})$ and magnetostatic ${\bf{B}} ({\bf{r}}) = {\mathbf{\nabla}} \times {\bf{A}} ({\bf{r}})$ fields, and include the interaction of the latter with both the orbital and spin angular momentum. The relationship between the potentials $\{ v ({\bf{r}}), {\bf{A}} ({\bf{r}}) \}$ and the nondegenerate ground state $\Psi$ is many-to-one. Explicitly accounting for this, we prove as in the case\footnote{XYP and VS, IJQC 2013, DOI: 10.1002/qua.24532} when only the orbital interaction is considered, that for $\Psi$ real, there is the one-to-one relationship: $\{ v ({\bf{r}}), {\bf{A}} ({\bf{r}}) \} \leftrightarrow \{ \rho ({\bf{r}}), {\bf{j}} ({\bf{r}}) \}$, where $\rho ({\bf{r}})$ and ${\bf{j}} ({\bf{r}})$ are the corresponding density $\rho ({\bf{r}})$ and physical current density ${\bf{j}} ({\bf{r}})$. Thus, $\{ \rho ({\bf{r}}), {\bf{j}} ({\bf{r}}) \}$ are the basic variables of the system. At present, except for the one electron system, no proof of bijectivity exists for the case of $\Psi$ complex. [Preview Abstract] |
Wednesday, March 5, 2014 12:03PM - 12:15PM |
M1.00003: Wigner High Electron Correlation Regime of Nonuniform Electron Density Systems: A Quantal Density Functional Theory (QDFT) Study Doug Achan, Lou Massa, Viraht Sahni We investigate the Wigner regime of the nonuniform electron density system of the Hooke's atom characterized by the ``fat attractor'' profile via QDFT. We determine the quantal sources: the density; the nonlocal Fermi and Coulomb hole charges; and the single-particle and Dirac density matrices. From these sources we obtain, respectively, the Hartree, Pauli, Coulomb, and Correlation-Kinetic fields. The work done in these fields leads to the corresponding components of the local electron-interaction potential of the noninteracting fermions that reproduce the density. The corresponding components of the total energy are determined by the respective integral virial expressions in terms of the fields. We discover that Correlation-Kinetic effects are very significant. We propose that in addition to a high electron-interaction energy, the Wigner regime also be characterized by a high Correlation-Kinetic energy. [Preview Abstract] |
Wednesday, March 5, 2014 12:15PM - 12:27PM |
M1.00004: Magnetic Orders of LaTiO$3$ and YTiO$3$ Under Epitaxial Strain: a First-Principles study Yakui Weng, Xin Huang, Yankun Tang, Shuai Dong Perovskite $R$TiO$_3$ family is a typical Mott-insulator with localized $3$d electrons. In this work, the epitaxial strain effects on the ground magnetic orders of LaTiO$_3$ and YTiO$_3$ films have been studied using the first-principles density-functional theory. For the YTiO$_3$ films, A-type antiferromagnetic order emerges against the original ferromagnetic order under the in-plane compressive strain by LaAlO$_3$ ($001$) substrate, although the A-type antiferromagnetic order does not exist in any $R$TiO$_3$ bulks. Then, for the LaTiO$_3$ films under the compressive strain, e.g. LaTiO$_3$ films grown on LaAlO$_3$, LaGaO$_3$, and SrTiO$_3$ substrates, undergo a phase transition from the original G-type antiferromagnetism to A-type antiferromagnetism. While under the tensile strain, e.g. grown on the BaTiO$_3$ and LaScO$_3$ substrate, LaTiO$_3$ films show a tendency to transit to the C-type antiferromagnetism. Furthermore, our calculations find that the magnetic transitions under epitaxial strain do not change the insulating fact of LaTiO$_3$ and YTiO$_3$. [Preview Abstract] |
Wednesday, March 5, 2014 12:27PM - 12:39PM |
M1.00005: Testing the Standard Approach for Density-Functional Transport Calculations Justin Smith, Zhenfei Liu, Kieron Burke Conductance across a single molecular junction can be calculated via the Landauer formalism. This is the standard approach for density-functional theory calculations of transport, but it requires extremely accurate Kohn-Sham potentials that can only be achieved under certain conditions using accurate functionals. Recent work has shown an example where the standard approach works remarkably well for a site model [1, 2]. In this work, we test the standard approach for one dimension in real space where we can extract numerically exact potentials using density-matrix renormalization group [3]. \\[4pt] [1] J. P. Bergfield, Z.-F. Liu, K. Burke, and C. A. Stafford, ``Bethe ansatz approach to the kondo effect within density-functional theory,'' Phys. Rev. Lett., 108, 066801 (2012).\\[0pt] [2] Z.-F. Liu, J. P. Bergfield, K. Burke, and C. A. Stafford, ``Accuracy of density functionals for molecular electronics: the anderson junction,'' Phys. Rev. B (2012).\\[0pt] [3] E. M. Stoudenmire, L. O. Wagner, S. R. White, and K. Burke, ``One-dimensional continuum electronic structure with the density-matrix renormalization group and its implications for density-functional theory,'' Phys. Rev. Lett., 109, 056402 (2012). [Preview Abstract] |
Wednesday, March 5, 2014 12:39PM - 12:51PM |
M1.00006: Quantum oscillations in the kinetic energy density: Gradient corrections from the Airy gas Alexander Lindmaa, Ann E. Mattsson, Rickard Armiento We show how one can systematically derive exact quantum corrections to the kinetic energy density (KED) in the Thomas-Fermi (TF) limit of the Airy gas (AG). The resulting expression is of second order in the density variation and we demonstrate how it applies universally to a certain class of model systems in the slowly varying regime, for which the accuracy of the gradient corrections of the extended Thomas-Fermi (ETF) model is limited. In particular we study two kinds of related electronic edges, the Hermite gas (HG) and the Mathieu gas (MG), which are both relevant for discussing periodic systems. We also consider two systems with finite integer particle number, namely non-interacting electrons subject to harmonic confinement as well as the hydrogenic potential. Finally we discuss possible implications of our findings mainly related to the field of functional development of the local kinetic energy contribution. [Preview Abstract] |
Wednesday, March 5, 2014 12:51PM - 1:03PM |
M1.00007: Nuclear Quantum Effects in Liquid Water: A Highly Accurate \textit{ab initio} Path-Integral Molecular Dynamics Study Robert A. DiStasio Jr., Biswajit Santra, Hsin-Yu Ko, Roberto Car In this work, we report highly accurate \textit{ab initio} path-integral molecular dynamics (AI-PIMD) simulations on liquid water at ambient conditions utilizing the recently developed PBE0+vdW(SC) exchange-correlation functional, which accounts for exact exchange and a self-consistent pairwise treatment of van der Waals (vdW) or dispersion interactions, combined with nuclear quantum effects (\textit{via} the colored-noise generalized Langevin equation\footnote{M Ceriotti, DE Manolopoulus Phys. Rev. Lett., \textbf{109}, 100604 (2012).}). The importance of each of these effects in the theoretical prediction of the structure of liquid water will be demonstrated by a detailed comparative analysis of the predicted and experimental oxygen-oxygen (O-O), oxygen-hydrogen (O-H), and hydrogen-hydrogen (H-H) radial distribution functions as well as other structural properties. In addition, we will discuss the theoretically obtained proton momentum distribution, computed using the recently developed Feynman path formulation,\footnote{L Lin, JA Morrone, R Car, M Parrinello Phys. Rev. Lett., \textbf{105}, 110602 (2010).} in light of the experimental deep inelastic neutron scattering (DINS) measurements. [Preview Abstract] |
Wednesday, March 5, 2014 1:03PM - 1:15PM |
M1.00008: Gutzwiller density functional theory for solid hydrogen calculations Jun Liu, Yongxin Yao, Chen Liu, Wencai Lu, Cai-zhuang Wang, Kai-Ming Ho We have recently proposed a Gutzwiller density functional theory (G-DFT) by innovatively replacing the noninteracting trial wavefunction in Kohn-Sham DFT with the Gutzwiller projected trial wavefunction to explicitly account for correlation effects, which renders a renormalized correlation matrix in the calculation as the key ingredient in our theory. Our approach does not require adjustable Coulomb interaction parameters, nor need of double counting terms present in LDA$+$U and LDA$+$DMFT. Our method has been demonstrated to work well in hydrogen and nitrogen molecule systems. In the presentation we will show its performance on the Hydrogen solid by specifically work out the total energy curves for different phases discussed in the literature, and compare them against the benchmark Quantum Monte Carlo (QMC) calculations. [Preview Abstract] |
Wednesday, March 5, 2014 1:15PM - 1:27PM |
M1.00009: Understanding Machine-learned Density Functionals Li Li, John Snyder, Matthias Rupp, Klaus-Robert M{\"u}ller, Kieron Burke Recently, some of us applied machine learning (ML) in a completely new approach to approximating density functionals [1,2]. In a proof of principal, kernel ridge regression was used to approximate the kinetic energy of non-interacting fermions confined to a 1d box as a functional of the electron density [1]. In that work, a modified orbital-free DFT scheme was able to produce highly accurate self-consistent densities and energies, which were systemically improvable with additional training data. In this work, we explore the properties of the ML approximated functional derived in [1]. In particular, we investigate the use of various kernels and their properties and compare various cross validation methods. We discuss the issue of functional derivatives in greater detail, explain how a modified constraint to the standard Euler equation enables highly accurate self-consistent densities, and derive a projected gradient descent algorithm using local principal component analysis. Finally, we explore the use of a sparse grid representation of the electron density and its effects on the method.\\[4pt] [1] J. C. Snyder, et al. Phys. Rev. Lett., 108, 253002 (2012).\\[0pt] [2] J. C. Snyder, et al. accepted to J. Chem. Phys. (2013). [Preview Abstract] |
Wednesday, March 5, 2014 1:27PM - 1:39PM |
M1.00010: ABSTRACT WITHDRAWN |
Wednesday, March 5, 2014 1:39PM - 1:51PM |
M1.00011: Exorcising Ghost Transmission from Electron Transport Calculations: Refighting Old Battles in New Contexts Matthew Reuter, Robert Harrison First-principles calculations of electron transport aim to understand the dynamics of electrons as they traverse quantum mechanical systems. For instance, how does electric current travel through a molecule? Despite their successes over the years, these calculations are known to be haunted by several numerical artifacts. Ghost transmission is among the most serious of these unphysical results, causing transmission coefficients to show an extreme dependence on the basis set and to be many orders of magnitude too large. In this talk, we discuss electron transport formalisms, uncover the cause of ghost transmission, develop exorcism strategies, and present several numerical examples. In the end, ghost transmission is a ramification of poorly chosen spatial partitions. Instead of choosing partitions with the basis set (in a manner reminiscent of Mulliken or L\"owdin population analyses), the relevant projection operators must be selected without referencing the basis set. [Preview Abstract] |
Wednesday, March 5, 2014 1:51PM - 2:03PM |
M1.00012: Green's functions in equilibrium and nonequilibrium from real-time bold-line Monte Carlo Guy Cohen, Emanuel Gull, David R. Reichman, Andrew J. Millis Green's functions for the Anderson impurity model are obtained within a numerically exact formalism. We investigate the limits of analytical continuation for equilibrium systems, and show that with real time methods even sharp high-energy features can be reliably resolved. Continuing to an Anderson impurity in a junction, we evaluate two-time correlation functions, spectral properties, and transport properties, showing how the correspondence between the spectral function and the differential conductance breaks down when nonequilibrium effects are taken into account. Finally, a long-standing dispute regarding this model has involved the voltage splitting of the Kondo peak, an effect which was predicted over a decade ago by approximate analytical methods but never successfully confirmed by numerics. We settle the issue by demonstrating in an unbiased manner that this splitting indeed occurs. [Preview Abstract] |
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