Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session B58: DFT and Beyond IIFocus

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Sponsoring Units: DCP DCOMP DPOLY DCMP Chair: Adam Wasserman, Purdue Univ Room: Mile High Ballroom 3B 
Monday, March 2, 2020 11:15AM  11:51AM 
B58.00001: On the Constrained SearchCoordinate Scaling Formulations in DFT Invited Speaker: Mel Levy First, a review of the early history of DFT is given, including anecdotes, and the constrainedsearch formulation is presented within the context of this history. Then it is shown how this formulation leads to the derivation of key constraints for approximating density functionals. These constraints include those that involve the coordinate scaling of the total density, and of the individual up and down spin densities, where the use of spinfree wavefunctions for the derivations has very recently proven to be effective. 
Monday, March 2, 2020 11:51AM  12:03PM 
B58.00002: Essential difference between the machine learning and artificial KohnSham potentials Ryo Nagai, Kieron Burke, Ryosuke Akashi, Osamu Sugino The KohnSham density functional theory is widely used to predict physical or chemical properties of various materials with its practical accuracy and computational cost. Its accuracy depends on the exchangecorrelation functional. Although there exist many approximations for the functional, its entire structure is yet elusive since the reference databases and physical conditions available are limited. On the other hand, we develop another strategy; the functional structure is represented with a flexible neural network and its parameters are trained with machinelearning algorithms[1]. The NNbased functional becomes transferable enough by training with the density, which contains abundant information in the 3D space. 
Monday, March 2, 2020 12:03PM  12:15PM 
B58.00003: Machine learning accurate exchange and correlation functionals of the electronic density Sebastian Dick, Marivi Fernandez Serra Density Functional Theory (DFT) is the standard formalism to study the electronic structure of matter at the atomic scale. The balance between accuracy and computational cost that DFTbased simulations provide allows researchers to understand the structural and dynamical properties of increasingly large and complex systems at the quantum mechanical level. In KohnSham DFT, this balance depends on the choice of exchange and correlation functional, which only exists in approximate form. Here we propose a framework to create highly accurate density functionals by using supervised machine learning, termed NeuralXC. These machinelearned functionals are designed to lift the accuracy of local and semilocal functionals to that provided by more accurate methods while maintaining their efficiency. We show that the functionals learn a meaningful representation of the physical information contained in the training data, making them transferable across systems. We further demonstrate how a functional optimized for water can reproduce experimental results when used in molecular dynamics simulations. 
Monday, March 2, 2020 12:15PM  12:27PM 
B58.00004: Constrained Machine Learning deorbitalization of metaGGA exchangecorrelation functionals Kanun Pokharel, James Furness, Jianwei Sun Metageneralizedgradientapproximation (mGGA) exchangecorrelation functionals commonly take the orbital kinetic energy density τ(r) as an ingredient in their construction [1]. Such τ(r) dependent functionals have shown impressive performance for diverse problems, but orbital dependence of τ(r) complicates the exchangecorrelation potential and increases computational cost. Recently, Rodriguez et.al. constructed a mGGA with laplacian▽^{2}n without significantly degrading accuracy [2]. This suggests an intriguing but unclear relationship between τ(r) and ▽^{2}n . We exploit this relationship using machine learning combined with exact constraints to explore how neuralnetwork models can deorbitalize functionals and model fundamental components of KohnSham density functional theory. 
Monday, March 2, 2020 12:27PM  12:39PM 
B58.00005: Semiclassical Approximation to Sums of Eigenvalues with Application to DFT Pavel Okun, Kieron Burke I present a new mathematical framework developed by Kieron Burke and Michael V. Berry for estimating the sum of the lowest N eigenenergies of a onedimensional potential. I apply this method to several model onedimensional systems (harmonic oscillator, PoschlTeller well, quartic oscillator, linear well, and exponential well). This new method gives the sum of the energies as a semiclassical series, which can be shown to reproduce the DFT gradient expansion for slowly varying densities, and also produces a correction to the gradient expansion for finite systems with a discrete spectrum. Explicit corrections to the gradient expansion of the kinetic energy are derived which in simple cases greatly improve accuracy. All work is done assuming a system of noninteracting identical fermions. This research is funded by the NSF (CHE 1856165). 
Monday, March 2, 2020 12:39PM  12:51PM 
B58.00006: Progress in the Development of Advanced TemperatureDependent FreeEnergy Density Functionals Beyond the Generalized Gradient Approximation Deyan Mihaylov, Brenda McLellan, Valentin V Karasiev, Suxing Hu Recently, it has been shown that explicit dependence on temperature in the exchangecorrelation (XC) freeenergy density functional is important in density functional theory studies of warm dense matter [1]. As a first approximation, in the attempt to include thermal effects into XC, the finiteT KSDT local spindensity approximation functional was constructed by the analytical parametrization of the XC free energy of the homogeneous electron gas. Consequently, the nonempirical KDT16 [2] generalized gradient approximation (GGA) functional, which captures nonhomogeneity effects and shows better agreement with experiments, has been constructed. Here, we present recent progress in going beyond the GGA by developing finiteT extensions to the PBE0 and SCANL (the deorbitalized version of SCAN) XC functionals. We present preliminary results for optical reflectivity of shocked CH and warm dense He. 
Monday, March 2, 2020 12:51PM  1:03PM 
B58.00007: SymmetryBreaking Polymorphous Descriptions for Correlated Materials without Interelectronic U Yubo Zhang, James Furness, Ruiqi Zhang, Zhi Wang, Alex Zunger, Jianwei Sun Correlated materials with openshell d and fions having degenerate band edge states show a rich variety of interesting properties. The textbook view for the electronic structure of these materials is that meanfield approaches are inappropriate, as the interelectronic interaction U is required to open a band gap between the occupied and unoccupied degenerate states while retaining symmetry. We show that the meanfield band theory can lift such degeneracies when nontrivial unit cell representations (polymorphous networks) are allowed to break symmetry, in conjunction with a recently developed nonempirical exchange and correlation density functional without an onsite interelectronic interaction U. We rationalize how density functional theory (DFT) in the polymorphous representation achieves band gap opening in correlated materials through a separate mechanism to the MottHubbard approach. We show the method predicts magnetic moments and gaps for four classical 3d transitionmetal monoxides in both the antiferromagnetic and paramagnetic phases, offering a highlyefficient alternative to symmetryconserving approaches for studying a range of functionalities in open d and fshell complex materials. 
Monday, March 2, 2020 1:03PM  1:15PM 
B58.00008: A step in the direction of resolving the paradox of PerdewZunger selfinteraction correction Rajendra Zope, Yoh Yamamoto, Carlos Diaz, Tunna Baruah, Juan Peralta, Koblar Alan Jackson, Biswajit Santra, John P. Perdew Selfinteraction (SI) error, which results when exchangecorrelation contributions to the total energy are approximated, limits the reliability of many density functional approximations. The PerdewZunger SI correction (PZSIC), when applied in conjunction with the local spin density approximation (LSDA), improves the description of many properties, but overall, this improvement is limited. Here we propose a modification to PZSIC that uses an isoorbital indicator to identify regions where local SI corrections should be applied. Using this localscaling SIC (LSIC) approach with LSDA, we analyze predictions for a wide range of properties including, for atoms, total energies, ionization potentials, and electron affinities, and for molecules, atomization energies, dissociation energy curves, reaction energies, and reaction barrier heights. LSIC preserves the results of PZSICLSDA for properties where it is successful and provides dramatic improvements for many of the other properties studied. Atomization energies calculated using LSIC are better than those of the Perdew, Burke, and Ernzerhof (PBE) generalized gradient approximation (GGA). LSIC also restores the uniform gas limit for the exchange energy that is lost in PZSICLSDA. 
Monday, March 2, 2020 1:15PM  1:27PM 
B58.00009: KohnSham effective potentials from FLOSIC using RyabinkinKohutStaroverov method Carlos Diaz, Luis Basurto, Rajendra Zope Density functional or beyond methods are often used in combination with photoelectron spectroscopy to obtain physical insights about the electronic structure of molecules and solids. The KohnSham eigenvalues are not electron removal energies except for the highest occupied one, but they often, though not always, provide good approximations to electron binding energies (EBEs). Eigenvalues of the range separated hybrid functionals using tuned separation parameter generally provide good approximations to EBEs due to mitigation of selfinteraction (SI) errors. We adapt and implement the RyabinkinKohutStaroverov method to obtain effective local potentials from the selfinteraction corrected FermiLowdin orbitals and density in the FLOSIC code. The density of states and HOMOLUMO gaps obtained using this approach show much closer agreement with experimental values compared to those obtained with a range of DFA or functionals. 
Monday, March 2, 2020 1:27PM  1:39PM 
B58.00010: Performance of scaled selfinteraction correction to semilocal functionals Puskar Bhattarai, Chandra Shahi, Kamal Wagle, Biswajit Santra, John P. Perdew Most semilocal functionals suffer from selfinteraction error (SIE). Perdew and Zunger (PZ)^{1} applied selfinteraction correction (SIC) to each delocalized KohnSham orbital by subtracting the SIE from each occupied orbital. The FermiLowdin orbital selfinteraction correction (FLOSIC) uses sizeextensive localized FermiLowdin orbitals that improve the results for the properties like barrier heights that involves strong SIE, as in stretched bonds. However, it worsens the equilibrium properties such as atomization energies, as FLOSIC applied to a functional violates the exact constraints and the appropriate norms that the semilocal approximations satisfy^{2}. Here, we apply a scaled PZ SIC to LSDA, PBE, and SCAN and calculated different properties such as electron affinity, ionization potential, barrier height, atomization energy, and bond length of some representative test sets. We find that the scaled SIC works well for both the equilibrium properties and for the features that involve stretched bonds or noded densities. 
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