Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session B31: Advances in Density Functional Theory IIFocus

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Sponsoring Units: DCP Chair: John Perdew, Temple University Room: 331 
Monday, March 14, 2016 11:15AM  11:51AM 
B31.00001: SelfInteraction Corrected Density Functional Approximations with Unitary Invariance: Applications to Molecules Invited Speaker: Mark Pederson For a system of 2N electrons, the Fermihole may be interpreted as the square of a normalized "Fermi orbital", $F({\bf a}) \equiv \rho_\sigma({\bf a},{\bf r})/\sqrt{\rho_\sigma({\bf a})}$. This normalized orbital captures all of the spin density at its position of definition, or descriptor, $({\bf a})$. Given a set of N quasiclassical electronic positions $({\bf a_i})$ and a spin densitymatrix composed of N KohnSham orbitals, the resulting set of Fermi orbitals may then be used to construct a set of localized Loewdinorthonormalized orbitals[1]. These orbitals are explicitly a functional of the spin density and are related to the KohnSham orbitals by a unitary transformation that is parametrically dependent on the set quasiclassical electronic descriptors. The construction of such localized orbitals allows for the restoration of unitary invariance into the original PerdewZunger selfinteraction correction[2,3] and provides a possible simplification compared to the localizationequation based solution of selfinteraction corrected functionals[4]. This talk will discuss the construction of this Fermiorbitalbased selfinteraction corrected method and the minimization algorithm that relies upon analytical derivatives[3] of the selfinteraction energy with respect to the Fermiorbital descriptors. Recent applications to a large set of molecules including aromatic molecules, molecules with open transitionmetal centers, and molecules with frustrated Kekule' structures will be discussed. Initial applications indicate improvements in atomization energies of pibonded systems and demonstrate the desired downward shift of orbital energies relative to their KohnSham counterparts. [1]W.L.Luken and D.N. Beratan, Theo. Chim. Acta {\bf 61}, 265281 (1982). [2]M.R. Pederson, A. Ruzsinszky and J. P. Perdew, J. Chem. Phys. ${\bf 140}$, 121103 (2014). [3]M.R. Pederson and T. Baruah, Advance in Atomic, Molecular and Optical Physics ${\bf 64}$, 153180 (2015). [4]M. R. Pederson, R. A. Heaton, and C. C. Lin, J. Chem. Phys. ${\bf 80}$, 1972 (1984). [Preview Abstract] 
Monday, March 14, 2016 11:51AM  12:03PM 
B31.00002: Fermiorbitals for improved electronic structure calculations on coordination complexes. Deryou Kao, Mark R. Pederson, James D. Lee An improved densityfunctional formalism[1,2] proceeds by adopting the PerdewZunger expression for a selfinteractioncorrected (SIC) densityfunctional energy but evaluates the total energy based on Fermi Orbitals (FOs). Each localized electron is represented by an FO, determined from the occupied KohnSham orbitals and a semiclassical FO descriptor. The SIC energy is then minimized through the gradients of the energy with respect to these descriptors. In addition to providing a review of the methodology, work here identifies the need for an algorithm which thoroughly searches over initial configurations. The strategy for sampling and prioritizing initial configurations is described. Applications on coordination complexes are presented. The FO descriptors and FOs for semiclassical and quantummechanical understanding of bondingis discussed. Cohesive energies are improved andthe eigenvalues are shifted downward relative to the standard DFT results.Spindependent vibrational spectra, as a possible means for spectroscopic determination of the transitionmetal moment, are also presented. [1]Pederson et al, JCP,140, 121103 (2014). [2]Baruah {\&} Pederson, AAMOPS, 64, 153180 (2015). [Preview Abstract] 
Monday, March 14, 2016 12:03PM  12:15PM 
B31.00003: Fermi orbital selfinteraction corrected electronic structure of molecules beyond local density approximation Torsten Hahn, Simon Liebing, Jens Kortus, Mark Pederson The correction of the selfinteraction error that is inherent to all standard density functional theory (DFT) calculations is an object of increasing interest. We present our results on the application of the recently developed Fermiorbital based approach for the selfinteraction correction (FOSIC) to a set of different molecular systems [1,2]. Our study covers systems ranging from simple diatomic to large organic molecules. Our focus lies on the direct estimation of the ionization potential from orbital eigenvalues and on the ordering of electronic levels in metalorganic molecules. Further, we show that the Fermi orbital positions in structurally similar molecules appear to be transferable. [1] M. R. Pederson, A. Ruzsinszky, and J. P. Perdew, J. Chem. Phys. 140, 121103 (2014). [2] M. R. Pederson, J. Chem. Phys. 142, 064112 (2015). [Preview Abstract] 
Monday, March 14, 2016 12:15PM  12:27PM 
B31.00004: Magnetic Exchange Couplings in Transition Metal Complexes from DFT Juan Peralta In this talk I will review our current efforts for the evaluation of magnetic exchange couplings in transition metal complexes from density functional theory. I will focus on the performance of different DFT approximations, including a variety of hybrid density functionals, and show that hybrid density functionals containing approximately 30{\%} HartreeFock type exchange are in general among the best choice in terms of accuracy. I will also describe a novel computational method to evaluate exchange coupling parameters using analytic selfconsistent linear response theory. This method avoids the explicit evaluation of energy differences, which can become impractical for large systems. Our approach is based on the evaluation of the transversal magnetic torque between two magnetic centers for a given spin configuration using explicit constraints of the local magnetization direction \textit{via} Lagrange multipliers. This method is applicable in combination with any modern density functional with a noncollinear spin generalization and can be utilized as a ``blackbox''. I will show proofofconcept calculations in frustrated Fe$^{\mathrm{III}}_{\mathrm{7}}$ diskshaped clusters, and dinuclear Cu$^{\mathrm{II}}$, Fe$^{\mathrm{III}}$, and heteronuclear complexes. [Preview Abstract] 
Monday, March 14, 2016 12:27PM  12:39PM 
B31.00005: Local spin analyses using density functional theory Bayileyegn Abate, Juan Peralta Local spin analysis is a valuable technique in computational investigations magnetic interactions on mono and polynuclear transition metal complexes, which play vital roles in catalysis, molecular magnetism, artificial photosynthesis, and several other commercially important materials. The relative size and complex electronic structure of transition metal complexes often prohibits the use of multideterminant approaches, and hence, practical calculations are often limited to singledeterminant methods. Density functional theory (DFT) has become one of the most successful and widely used computational tools for the electronic structure study of complex chemical systems; transition metal complexes in particular. Within the DFT formalism, a more flexible and complete theoretical modeling of transition metal complexes can be achieved by considering noncollinear spins, in which the spin density is 'allowed to' adopt noncollinear structures in stead of being constrained to align parallel/antiparallel to a universal axis of magnetization. In this meeting, I will present local spin analyses results obtained using different DFT functionals. Local projection operators are used to decompose the expectation value $ 
Monday, March 14, 2016 12:39PM  1:15PM 
B31.00006: The LiebOxfourd bound and the exchangecorrelation kernel from the strictlycorrelated electrons functional Invited Speaker: Paola GoriGiorgi I will present some recent results based on the strictlycorrelated electrons (SCE) functional: 1) a rigorous method to set lower bounds to the optimal particlenumber dependent constant appearing in the LiebOxford bound, and 2) an investigation of exact properties in the time domain, including an analytical expression for the kernel in onedimension, with an analysis of its behavior for the case of bondbreaking excitations. [Preview Abstract] 
Monday, March 14, 2016 1:15PM  1:27PM 
B31.00007: Exchangecorrelation functionals from a local interpolation along the adiabatic connection Stefan Vuckovic, Tom Irons, Andrew Teale, Andreas Savin, Paola GoriGiorgi We use the adiabatic connection formalism to construct a density functional by doing an interpolation between the weak and the strong coupling regime. Combining the information from the two limits, we are able to construct an exchangecorrelation (xc) density functional free of the bias towards weakly correlated system, which is present in the majority of approximate xc functionals. Previous attempts in doing the interpolation between the two regimes, such as the interaction strength interpolation (ISI), had a fundamental flaw: the lack of sizeconsistency, as the corresponding functional depends nonlinearly on the global (integrated over all space) ingredients. To recover sizeconsistency in such a framework, we move from the global to local quantities. We use the energy densities as local quantities in the gauge of the electrostatic potential of the xc hole. We use the ``strictlycorrelated electrons'' (SCE) approach to compute the energy densities in the strongcoupling limit and the Lieb maximization algorithm to extract the energy densities from the lowcoupling regime. We then test the accuracy of the local interpolation schemes by using the nearly exact local energy densities. In this talk I am going to present our results with the emphasis on strongly correlated systems. [Preview Abstract] 
Monday, March 14, 2016 1:27PM  1:39PM 
B31.00008: The exact density functional for two electrons in one dimension Aron Cohen, Paula MoriSanchez The exact universal density functional $F[\rho]$ is calculated for real space twoelectron densities in one dimension $\rho(x)$ with a softCoulomb interaction. It is calculated by the Levy constrained search $F[\rho]=\min_{\Psi\rightarrow\rho}\langle\Psi\hat{T}+\hat{V}_{ee}\Psi\rangle$ over wavefunctions of a twodimensional Hilbert space $\Psi(x_{1},x_{2})\rightarrow\rho(x_{1})$ and can be directly visualized. We do an approximate constrained search via density matrices and a direct approximation to natural orbitals. This allows us to make an accurate approximation to the exact functional that is calculated using a search over potentials. We investigate the exact functional and the performance of many approximations on some of the most challenging electronic structure in twoelectron systems, from stronglycorrelated electron transfer to the description of a localizeddelocalized transition. The exact KohnSham potential, $v_s(x)$, and exact KohnSham eigenvalues, $\epsilon_i$, are calculated and this allows us to discuss the bandgap problem versus the perspective of the exact density functional $F[\rho]$ for all numbers of electrons. We calculate the derivative discontinuity of the exact functional in an example of a MottInsulator, onedimensional stretched H$_2$. [Preview Abstract] 
Monday, March 14, 2016 1:39PM  1:51PM 
B31.00009: Landscape of the exact energy functional for a simplified universe Paula MoriSanchez, Aron Cohen One of the great challenges of electronic structure theory is the quest for the exact functional of density functional theory (DFT). Its existence is proven, but it is a complicated multivariable functional that is almost impossible to conceptualize. In this talk we study the asymmetric twosite Hubbard model because it has only a twodimensional universe of density matrices, hence the exact functional becomes a simple function of two variables whose three dimensional energy landscape can be visualized and explored. A walk on this unique landscape, tilted to an angle defined by the oneelectron Hamiltonian, gives a valley whose minimum is the exact total energy. This is contrasted with the landscape of some approximate functionals, explaining their failure for electron transfer in the strongly correlated limit. We show concrete examples of purestate density matrices that are not $v$representable due to the underlying nonconvex nature of the energy landscape. The exact functional is calculated for all numbers of electrons, including fractional, allowing the derivative discontinuity to be visualized and understood. The fundamental gap for all possible systems is obtained solely from the derivatives of the exact functional. [Preview Abstract] 
Monday, March 14, 2016 1:51PM  2:03PM 
B31.00010: Spontaneous charge carrier localization in extended onedimensional systems Vojt\v{e}ch Vl\v{c}ek, Helen Eisenberg, Gerd SteinleNeumann, Roi Baer Charge carrier localization in extended atomic systems can be driven by disorder, point defects or distortions of the ionic lattice. Herein we give firstprinciples theoretical computational evidence that it can also appear as a purely electronic effect in otherwise perfectly ordered periodic structures and we show that electronic eigenstates can spontaneously localize upon excitation. Optimallytuned range separated density functional calculations reveal that in transpolyacetylene and polythiophene the hole density localizes on a length scale of several nanometers. This is due to exchange induced translational symmetry breaking of the charge density. Ionization potentials, optical absorption peaks, excitonic binding energies and the optimallytuned range parameter itself all become independent of polymer length when it exceeds the critical localization length scale. These firstprinciples findings show, for the first time, that charge localization is not caused by lattice distortion but rather it is their cause, changing the physical models of polaron formation and dynamics, helping to explain experimental findings that polarons in conjugated polymers form instantaneously after exposure to ultrafast light pulses. [Preview Abstract] 
Monday, March 14, 2016 2:03PM  2:15PM 
B31.00011: Selfconsistent calculation of Hubbard U parameters within linearscaling DFT Glenn Moynihan, Gilberto Teobaldi, David D. O'Regan DFT+U has proven to be a computationally efficient method for correcting for the underestimation of electron localization effects, or for the absent derivative discontinuity, inherent in conventional density functionals. Invoking an approximate interpretation of DFT+U as a corrective penalty functional for the spurious curvature of the totalenergy with respect to subspace occupancy, the Hubbard U parameter may be calculated [1,2], in which case DFT+U may be considered to be fully firstprinciples approach. We describe our approach for computing the Hubbard U and Hund’s J parameters within ONETEP, a linearscaling DFT code which comprises a complete DFT+U+J [3] implementation including ionic forces and a flexible choice of population analyses [4,5]. We discuss issues of charge preservation and selfconsistency, and we demonstrate the capability of our method by means of numerical tests on the groundstate properties of selected molecules that present challenges for approximate DFT. [1] W. E. Pickett, et al., Phys. Rev. B, 58, 1201 (1998). [2] H. J. Kulik, et al., Phys. Rev. Lett. 97, 103001 (2006). [3] B. Himmetoglu, et al., Phys. Rev. B 84, 115108 (2011). [4] D. D. O’Regan, et al., Phys. Rev. B 85, 085107 (2012). [5] D. D. O’Regan, et al., Phys. Rev. B 83, 245124 (2011). [Preview Abstract] 
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