Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session G01: Density Functional Theory and Beyond IIFocus Recordings Available
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Sponsoring Units: DCP Chair: Martin Mosquera, University of Montanna Room: McCormick Place W-175A |
Tuesday, March 15, 2022 11:30AM - 12:06PM |
G01.00001: Spin-Free Formalism of Spin-Density Functional Theory Invited Speaker: Mel Levy The spin-free approach greatly simplifies the mathematical structure of spin-density functional theory (SDFT). With this in mind, a new spin-free constrained-search formulation of SDFT will be presented (Phys. Rev. A 100, 062507 (2020)). A rigorous spin decomposition of the SDFT energy components naturally arises from this spin-free formalism of SDFT (Phys. Rev. A 104, 022815 (2021)). In addition, new spin-dependent coordinate-scaling relations are found and proven with this formalism. Exact mathematical constraints are instrumental for the construction of new density functional approximations. |
Tuesday, March 15, 2022 12:06PM - 12:18PM |
G01.00002: Title: Development of self-consistent pseudopotentials and PAW datasets for meta-GGA exchange-correlation functionals Natalie W Holzwarth, Marc Torrent, Michel Cote Within generalized density functional theory, recent developments of functionals which depend upon the kinetic energy density, such as the r2SCAN form,1 promise significant improvement in the computational representation of real material properties. In order to implement these forms within planewave codes, it is necessary to use pseudopotentials, ideally constructed with the same exchange-correlation functional, as has been implemented for the projector augmented wave (PAW) formalism in the ATOMPAW code.2 This was accomplished with the help of an efficient solver for the self-consistent radial bound states of each atom, based on cubic spline interpolation. |
Tuesday, March 15, 2022 12:18PM - 12:30PM |
G01.00003: Tuning strong correlation and charge transfer competition using fractional nuclear charge: emergence of exotic metal-insulator transitions in a 1D hydrogen-like chain Jianwei Sun, James W Furness, Ruiqi Zhang In chemistry and condensed matter physics the solution of simple paradigm systems, such as the hydrogen atom and the uniform electron gas, plays a critical role in understanding electron behaviors and developing electronic structure methods. The H2 molecule is a paradigm system for strong correlation with a spin-singlet ground state that localizes the two electrons onto opposite protons at dissociation. Here, we extend H2 to a new paradigm system by using fractional nuclear charges (FNC) to break the left-right nuclear symmetry, thereby enabling the competition between strong correlation and charge transfer. We use H2_FNC to connect the self-interaction and strong correlation errors of common density functional approximations, and show how a functional's accuracy for H2_FNC is reflected in its accuracy for transition metal monoxides. We further show the competition drive exotic metal-insulator transitions in a 1D FNC hydrogen chain at large nuclear separations. The extension therefore lays a foundation for improving practical electronic structure theories and provides a playground for analyzing how the competition appears and evolves with exotic properties. |
Tuesday, March 15, 2022 12:30PM - 12:42PM |
G01.00004: The exchange-correlation (XC) hole of the hydrogen molecule with fractional nuclear charge Lin Hou, Tom Irons, Andrew Teale, James W Furness, Jianwei Sun The exchange-correlation (XC) hole is fundamental for developing density functional approximations and understanding their behaviors in real material calculations. Although it is well defined, there are few XC holes calculated exactly for benchmarking density functionals, largely because of its dependence on the coupling constant [1] that scales the electron-electron Coulomb repulsion. Here, we calculate the coupling-constant-averaged XC hole of the hydrogen molecule at the CCSD level which is basis-set exact for 2 electron systems. We will extend the hydrogen molecule to have fractional nuclear charge which allows the left-right symmetry breaking and enables the strong correlation and charge transfer competition [2]. The effects of bond distance and the nuclei charge disproportionation on the XC hole will be examined. |
Tuesday, March 15, 2022 12:42PM - 12:54PM |
G01.00005: Comparisons of density-functional average-atom models and measures of the mean ionization state Timothy J Callow, Nathan E Rahat, Eli Kraisler, Attila Cangi Density-functional average-atom (AA) models are an important tool in simulations of the warm dense matter (WDM) regime, because they account for quantum interactions at favourable computational cost. AA models are typically based on a common premise - namely, an atom immersed in a plasma environment - but use a range of different assumptions and approximations, leading to inconsistent predictions for various properties. We compare results across several models, differing for example in their choice of boundary conditions and exchange-correlation functional, focussing on the mean ionization state (MIS), an important property in WDM. Furthermore, we compare different methods for evaluating the MIS: a simple energy threshold, and approaches based on the inverse participation function and electron localization function. We evaluate the relative merits of these approaches and, time-permitting, compare our AA results with full Kohn-Sham density-functional theory calculations. |
Tuesday, March 15, 2022 12:54PM - 1:06PM |
G01.00006: Generalizable machine-learned density functionals using a spin-adapted Kohn-Sham regularizer Ryan D Pederson, Bhupalee Kalita, Li Li, Kieron Burke The generalization performance of an exchange-correlation (XC) functional approximation largely determines its practical usefulness in density functional theory (DFT) calculations. For training machine-learned XC functional models, the Kohn-Sham regularizer (KSR) method has been shown to greatly improve generalization [1]. To extend this approach, we propose a spin-adapted version of KSR with local, semilocal, and nonlocal neural network model approximations for the XC energy functional. Using 1-dimensional (1D) analog model systems, we assess generalizability by training on a handful of 1D atomic systems and testing on a set of 1D equilibrium-bonded molecules. The performance of the various trained neural XC models is analyzed. In particular, we find that our nonlocal XC model obtains near chemical accuracy for ground-state properties of 1D molecules in the test set. |
Tuesday, March 15, 2022 1:06PM - 1:18PM |
G01.00007: Kohn-Sham regularizer in the bond-dissociation limit Bhupalee Kalita, Ryan D Pederson, Li Li, Kieron Burke With standard exchange-correlation (XC) approximations, Kohn-Sham density functional theory (KS-DFT) fails to correctly describe the breaking of a chemical bond. A nonlocal machine-learned XC can provide a good description of such strongly correlated systems when carefully embedded with prior knowledge and trained on accurate results. By training on just two separations, the Kohn-Sham regularizer (KSR) with a nonlocal neural network approximation to the XC energy density is shown to reproduce the entire binding energy curve of one-dimensional H2 with chemical accuracy [1]. We analyze the ingredients of this nonlocal approximation and assess the importance of including prior knowledge in constructing machine-learned functionals. We further evaluate the generalizability of the performance of KSR local, semilocal and nonlocal neural XC approximations for one-dimensional strongly correlated molecules with limited training. We also analyze the machine-learned XC potentials, especially for stretched heteronuclear diatomic molecules where the exact XC potential has a characteristic localized upshift in the region around the more electronegative atom. |
Tuesday, March 15, 2022 1:18PM - 1:30PM |
G01.00008: Size transferability of machine-learning based density functional theory surrogates Lenz Fiedler, Gabriel A Popoola, Normand A Modine, Aidan P Thompson, Attila Cangi Density Functional Theory (DFT) is the most common tool for investigating materials under extreme conditions, yet its scaling behavior with respect to both system size and temperature prohibits large scale simulations in such regimes. Progress in this regard would enable accurate modeling of planetary interiors or radiation damage in fusion reactor walls. |
Tuesday, March 15, 2022 1:30PM - 1:42PM |
G01.00009: Analysis of the Large Z Exchange Expansion of Neutral Atoms Beyond the Leading Order Jeremy J Redd, Antonio C Cancio, Kieron Burke, Nathan Argaman Lieb-Simon zeta-scaling, which describes the scaling of neutral closed-shell atoms as Z approaches infinity, has been used with marked success to provide theoretical constraints on density functionals and to help generate perturbative expansions with Z. The exact large Z expansion for the exchange energy has never been explicitly calculated beyond the leading order Z5/3 term. It is typically considered that the next term is of order Z, however in general terms of order Z4/3 and ZlogZ are possible. We test these considerations via calculations using the Optimized Effective Potential (OEP) method for atoms up to Z=120, and the LDA and popular GGAs up to Z=978. This data shows that the LDA exchange analyzed down columns of the periodic table has a leading order of Z4/3. From analysis of the beyond-LDA contributions to the OEP exchange energy we conclude that there is no additional Z4/3 contribution from exact exchange, but rather, that there is a distinct dependence on ZlogZ. Current GGAs repoduce the limiting trend in Z qualitatively but not quantitatively. We do find reasonably good agreement with theoretical estimates based on analyzing the inner shells of very large Z atoms. |
Tuesday, March 15, 2022 1:42PM - 1:54PM |
G01.00010: GEO: How to quantify and understand errors in geometries Kieron Burke, Stefan Vuckovic Nearly all electronic structure calculations contain errors in both energies and equilibrium geometries. I will show results only for molecules, but all the methodology could also be applied to materials. For molecules, quantifying errors in possibly dozens of bond angles and bond lengths is a Herculean task. Recently, we proposed the geometric energy offset (GEO) framework for quantifying and analysing errors in molecular geometries based on a single and natural measure. GEO links many disparate aspects of geometry errors: a new ranking of different methods, quantitative insight into errors in specific geometric parameters, and insight into trends with different methods. GEO can also reduce the cost of high-level geometry optimizations and shows when geometric errors distort the overall error of a method. GEO applies to all methods of simulation, including DFTB, and even classical force fields. |
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