Schedule for: 24w5171 - Towards Routine Orbital-free Large-Scale Quantum-Mechanical Modelling of Materials

A brief introduction with important logistical information, technology instruction, and opportunity for participants to ask questions.

Meeting Exchange-Correlation Challenges in Orbital-free DFT

S.B. Trickey*
QTP and Dept. of Physics, University of Florida, Gainesville FL 32611 USA and Center for Molecular Magnetic Quantum Materials, Univ. Florida, Gainesville FL 326111 USA ∗trickey@qtp.ufl.edu

Abstract
Most attention in the development of orbital-free DFT has focused on approximate functionals for the Kohn-Sham kinetic energy density τs[n]. Historically that priority was well-justified. Beyond the simplest Thomas-Fermi and von Weizs ̈acker kinetic energy density functionals (KEDFs) little was known. Moreover, the available approximate exchange correlation (XC) functionals were simple, dependent upon the density n and its spatial gradient ∇n at most.[1] But the advent of orbital-dependent XC approximations has altered the priorities. Popular meta-generalized gradient approximation (meta-GGA) XC functionals that are computationally efficient enough to be used in large-scale materials simulations are orbital dependent. (Worse, from the OFDFT perspective at least, is the relentless use - especially but not exclusively in quantum chemistry - of single-determinant exchange as a contribution to the XC approximation.)
Orbital-dependence in meta-GGA XC approximations enters through the use of τs in so-called iso-orbital indicator functionals. The OFDFT opportunity that arises is to use a KEDF to replace that τs dependence with a pure density functional, i.e. a KEDF. I will discuss progress and challenges of this “de-orbitalization” of meta-GGAs.[2-6]

References
[1] W. Mi, K. Luo, S.B. Trickey, and M. Pavanello , Chem. Rev. 123, 1239 (2023).
[2] H. Francisco R., A.C. Cancio, and S.B. Trickey, J. Phys. Chem. A, online 12 July 2024; doi:10.1021/acs.jcpa.4c02635 .
[3] H. Francisco R., A.C. Cancio, and S.B. Trickey, J. Chem. Phys. 159, 214103 (2023).
[4] D. Mej ́ıa Rodr ́ıguez and S.B. Trickey, Phys. Rev. B 102, 121109(R) (2020).
[5]D. Mej ́ıa-Rodr ́ıguez and S.B. Trickey, Phys. Rev. B 98, 115161 (2018).
[6]D. Mej ́ıa-Rodr ́ıguez and S.B. Trickey, Phys. Rev. A 96, 052512 (2017).

Supported in part by the Center for Molecular Magnetic Quantum Materials, an EFRC funded by the U.S. Dept. of Energy, Office of Science, Basic Energy Sciences under Award No. DE-SC0019330 and in part by U.S. NSF grant DMR-1912618.

Orbital-Free TDDFT Unleashed

Michele Pavanello
Departments of Physics and Chemistry, Rutgers University-Newark, Newark, NJ 07102

Abstract
Chemical reaction thermodynamics, kinetics, and nonequilibrium dynamics are crucial to accurately predict in chemical modeling. Despite advances, current models often fall short, being either too approximate to faithfully represent reality or too computationally expensive to yield timely results. This talk emphasizes the urgent need for next-generation electronic structure methods to support experimental efforts facing similarly complex challenges.
We introduce orbital-free Density Functional Theory (OF-DFT) and Time-Dependent Density Functional Theory (OF-TDDFT) as emerging methods for modeling materials in and out of equilibrium. OF-TDDFT, in particular, shows promise in modeling the plasmonic response [1,2] of complex systems. These methods are grounded in rigorous theoretical foundations, including the Hohenberg-Kohn theorems, the Runge-Gross theorem, and the van Leeuwen theorem, now extended to encompass orbital-free formulations [2].
In this talk, we will detail the theoretical and algorithmic innovations behind these methods (focusing especially on the Pavanello group’s work in the context of the current state-of-the-art) and demonstrate their practical applications using the open-source Python implementation, DFTpy [3]. Particular emphasis will be given to nonlocal functionals for OF-DFT [4-10] and nonadiabatic Pauli kernels and potentials for OF-TDDFT [11-13]. This software showcases the power of OF-DFT and OF-TDDFT for both production simulations and the prototyping of novel methods and workflows. With this robust computational arsenal, we are well-equipped to address today’s most challenging and timely electronic structure problems.

References
1. F. Della Sala, J. Chem. Phys. 157, 104101 (2022)
2. K. Jiang, M. Pavanello, Phys. Rev. B 103, 245102 (2021)
3. X. Shao, K. Jiang, W. Mi, A. Genova, M. Pavanello, WIREs: Comput. Mol. Sci., e1482c (2020)
4. W. Mi, A. Genova, M. Pavanello, J. Chem. Phys. 148, 18410 (2018)
5. W. Mi, M. Pavanello, Phys. Rev. B 100, 041105 (2019)
6. X. Shao, W. Mi, M Pavanello, J. Phys. Chem. Letters 12, 4134-4139 (2021)
7. X Shao, W Mi, M Pavanello, Phys. Rev. B 104, 045118 (2021)
8. Q. Xu, J. Lv, Y. Wang, and Y. Ma, Phys. Rev. B 101, 045110 (2020)
9. Q. Xu, Y. Wang, Y. Ma, Phys. Rev. B 100 (20), 205132 (2019)
10. W. Mi, K. Luo, S.B. Trickey, M. Pavanello, Chem. Rev. 123 (21), 12039-12104 (2023)
11. K. Jiang, X. Shao, M. Pavanello, Phys. Rev. B 104, 235110 (2021)
12. K. Jiang, X. Shao, M. Pavanello, Phys. Rev. B 106 (11), 115153 (2022)
13. T. G. White, S. Richardson, B. J. B. Crowley, L. K. Pattison, J. W. O. Harris, and G. Gregori, Phys. Rev. Lett. 111, 175002 (2013)

Using the Kato Cusp Condition to Improve Semi-local OF-DFT Functionals

Andrew M. Wibowo-Teale and Michael Hutcheon
School of Chemistry, University of Nottingham, UK, NG7 2RD

Abstract
We obtain near exact cusp behaviour in a self-consistent orbital-free density functional theory treatment of atomic and molecular systems, with standard kinetic energy functionals, by the introduction of a physically-motivated cost functional. The electron density, and it's gradient and Laplacian, are also nearly exact in the vicinity of nuclei, and shell structure emerges. This results in significantly reduced energy errors and provides a foundation for the development of next-generation kinetic energy functionals.

Lunch is served daily between 11:30am and 1:30pm in the Xianghu Lake National Tourist Resort

Large-Z Methodology Applied to Kinetic Functional Fevelopment

Olga Lopez-Acevedo
Instituto de Física, Universidad de Antioquia, Colombia

Abstract
Local pseudopotentials strongly influence the final precision of an Orbital-Free Density Functional Theory (OFDFT) calculation. How to improve kinetic functionals parametrization avoiding the use of fitting to calculations that require the use of pseudopotentials? The core of the problem is that the roots of OFDFT are in semiclassical Thomas-Fermi approximation, where each electron occupies constant volume in a position-momentum phase-space. The approximation is a perfectly reasonable assumption for homogeneous electron gas, but a flawed approximation for electrons near the atomic nucleus (Berthold-Georg Englert. Semiclassical Theory of Atoms, volume 300 of Lecture Notes in Physics,1988.). The use of methods like pseudo-potentials are therefore necessary because of the need of a different physical description of the core electrons. We showed (PRB 100 165111 2019) that the use of an exact constraint coming from semiclassical physics allows the removal of empirical parameters of gradient-based kinetic density orbital-free functionals. This method of parametrization is general enough so that it could be applied to parametrize kinetic functionals based on higher derivatives of the electronic density. Other large-Z limits exist, not only on atoms but also solids (JCP 151 244101 2019) that would allow to pursue of this methodology but require more attention.

Semilocal Kinetic Functional for Atoms and Diatoms

Kai Luo
Nanjing University of Science and Technology

Abstract
In this talk, I will summarize how we assess the current semilocal kinetic functionals and empirically put forward an augmented variant of Perdew-Constantin funtional [1]. It not only yields energies close to the references but also, more importantly, demonstrates qualitative predictions for stable molecules and provides reasonable quantitative estimates for bond lengths in diatomic systems[2]. K.L. was funded by the National Natural Science Foundation of China under grant no. 12104230. K.L. would like to thank S. B. Trickey for helpful discussions.

References
[1] J. P. Perdew, L. A. Constantin, Laplacian-level density functionals for the kinetic energy density and exchange-correlation energy. Phys. Rev. B (2007), 75, 155109,
[2] Tingwei Wang, Kai Luo, and Ruifeng Lu, Semilocal Kinetic Energy Density Functionals on Atoms and Diatoms, J. Chem. Theory Comput. 2024, 20, 12, 5176–5187

Renormalization Approaches for Kinetic Energy Functionals

Paul W. Ayers
Department of Chemistry and Chemical Biology, McMaster University, Hamilton ON, Canada

Abstract
Given that the gradient expansion does not converge for atomic and molecular systems, resummation methods seem appealing. We discuss some (nontraditional) resummation methods that are well-adapted to strongly divergent expansions and discuss their (alas, poor, but perhaps interesting) performance. In general, the problem of kinetic energy functionals seems extremely difficult, and some constraints on the kinetic energy functional may help explain why, while perhaps providing guidance for future investigations.

How Hard is It to Predict the Kohn-Sham Kinetic Energy Density for a Prototype Potential Using Deep Neural Networks? (remote)

Carlos Cárdenas1, Trinidad Novoa2, Paul W. Ayers3, Farnaz Heidar-Zadeh4
1 Departmento de Física, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Ñoñoa, Chile; 2. Laboratoire de Chimie Théorique (LCT) Sorbonne Université, CNRS, 4, Place Jussieu, Paris, Franc; 3. Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada; 4. Department of Chemistry, Queen’s University, Kingston, Ontario K7L 3N6, Canada.

Abstract
Accurate and efficient computation of the kinetic energy (KE) of many-electron systems has been a challenge for many years. To reduce the computational cost, the Orbital-free density functional theory (OFDFT) aims at finding an expression for the KE as a functional of the electron density, whose existence has been mathematically proven, to drastically decrease the computation cost. Alternatively, finding a functional for the non-interacting KE would let us evaluate large systems with the computational cost of OFDFT and accuracy of Kohn-Sham (KS) DFT. Here we show how deep neural networks (DNNs) can learn the functional form of the KS kinetic energy density (KED), which is then integrated to the total KS KE, for prototype one-dimensional symmetric double well potentials. We have used different functionals of the density as input features of the DNN, including a set of non-local descriptors inspired in the electron delocalization range function by Janesko et al., which have shown to notably improve the results. Our one-dimensional non-local model yields mean absolute errors of 0.102 a.u. and 0.053 a.u. for the KED and the KE, respectively. Additionally, an analysis of the relative importance of the input features shows that the delocalization length associated with the non-local descriptors plays a crucial role in the prediction of the KED.

Orbital-Free Methods & Software Development for Large-Scale First-Principles Simulations

Wenhui Mi1,2*, Cheng Ma1, Qiang Xu1, Xuecheng Shao1, Yanmchao Wang1, Michele Pavanello3 and Yanming Ma1,2
1. Key Laboratory of Material Simulation Methods & Software of Ministry of Education, College of Physics, Jilin University, Changchun 130012, China; 2. International Center of Future Science, Jilin University, Changchun 130012, China; 3. Department of Chemistry, Department of Physics, Rutgers University, Newark, New Jersey 07102,United States ; Email: mwh@jlu.edu.cn

Abstract
Kohn–Sham Density Functional Theory (KSDFT) is extensively used in chemistry, physics, and materials science due to its favorable balance between accuracy and computational cost for systems with up to a few hundred atoms. However, using KSDFT for larger system simulations is challenging due to its cubic scaling of computational cost. Orbital-free Density Functional Theory (OFDFT) provides an alternative approach by avoiding the explicit use of orbitals, which simplifies the method and allows for near-linear scaling with system size. This approach makes it feasible to simulate much larger systems and over longer time scales compared to conventional KSDFT. Despite these advantages, the absence of orbitals in OFDFT introduces difficulties in constructing accurate kinetic energy density functionals (KEDFs) and pseudopotentials, which has been a major barrier to its widespread application. To overcome these issues, we have developed a range of advanced nonlocal KEDFs, pseudopotential methods, and related software packages. These innovations have significantly broadened the applicability of OFDFT, enabling successful simulations of more complex systems beyond simple metals, such as semiconductors and quantum dots[1-2].

References
[1] W. Mi, K. Luo, S. B. Trickey, and M. Pavanello, Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations, Chem. Rev. 123, 12039 (2023).
[2] Q. Xu, C. Ma, W. Mi, Y. Wang, and Y. Ma, Recent Advancements and Challenges in Orbital Free Density Functional Theory, Wiley Interdiscip. Rev. Comput. Mol. Sci. 14, 1 (2024).

Breakfast is served daily between 7 and 9am in the Xianghu Lake National Tourist Resort

Orbital Free DFT: Good News for Exchange-Correlation Energy Functional Development and Bad News for Excited States

Weitao Yang
Duke University

Abstract
We use orbital free DFT to develop approximations to the exchange-correlation energy functional for conventional Kohn-Sham DFT calculations. This is latest development of the localized orbital scaling correction (LOSC) in overcoming systematic delocalization errors in commonly used density functional approximations (DFAs). LOSC is capable of correcting system energy, energy derivative and electron density in a size-consistent manner for all commonly used density functional approximations (DFAs). LOSC leads to systematically improved results, including the dissociation of ionic species, the band gaps of molecules, polymer chains and bulk systems, the energy and density changes upon electron addition and removal, and photoemission spectra, and energy-level alignments for interfaces. The inclusion of orbital relaxation, or screening, improve LOSC description of quasiparticle energies and band gaps for finite molecules, and is critical for bulk systems. It thus provides a single approximate functional that corrects the systematic errors of DFAs in total energy, electron density, and quasiparticle energies and band gaps, for finite and bulk systems. For excited states, we have recently established the theoretical foundation for the frequently used delta SCF method in DFT. We formulate excited-state theory using the defining variables of a noninteracting reference system, namely (1) the excitation quantum number ns and the potential, (2) the noninteracting wavefunction, or (3) the noninteracting one electron reduced density matrix. We show the equivalence of these three sets of variables and their corresponding energy functionals. The electron density alone is insufficient to characterize excited states – this is a fundamental drawback for orbital free DFT.

References
1. A. Cohen, P. Mori-Sanchez, and W. Yang. Insights into current limitations of density functional theory. Science, 321:792, 2008.
2. J. Cohen, P. Mori-Sanchez, and W. Yang. Challenges for Density Functional Theory. Chem. Rev. 112:289, 2012
3. C. Li, X. Zheng, N. Q. Su, and W. Yang, “Localized orbital scaling correction for systematic elimination of delocalization error in density functional approximations,” National Science Review, 5: 203–215, 2018.
4. Y. Mei, C. Li, N. Q. Su, and W. Yang, “Approximating Quasiparticle and Excitation Energies from Ground State Generalized Kohn–Sham Calculations,” J. Phys. Chem. A, vol. 123, no. 3, pp. 666–673, Jan. 2019
5. Y. Mei, J. Yu, Z. Chen, N. Q. Su, and W. Yang, “LibSC: Library for Scaling Correction Methods in Density Functional Theory,” J. Chem. Theory Comput., vol. 18, no. 2, pp. 840–850, Feb. 2022.
6. W. Yang and P.W. Ayers, “Foundation for the {\Delta}SCF Approach in Density Functional Theory” 2024. https://doi.org/10.48550/arXiv.2403.04604.
7. Williams, J. Z.; Yang, W. Localized Orbital Scaling Correction with Linear Response in Materials. arXiv June 12, 2024. https://doi.org/10.48550/arXiv.2406.07351.
8. Yu, J.; Mei, Y.; Chen, Z.; Yang, W. Accurate Prediction of Core Level Binding Energies from Ground-State Density Functional Calculations: The Importance of Localization and Screening. arXiv June 10, 2024. https://doi.org/10.48550/arXiv.2406.06345.

Development and Applications of the Density-Based Theory of Chemical Reactivity

Chunying Rong*1, Xin He2, Shubin Liu3
1Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research (Ministry of Education of China), Hunan Normal University, Changsha, Hunan 410081, China; 2 Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China; 3 Research Computing Center, University of North Carolina, Chapel Hill, North Carolina 27599-3420, United States

Abstract
Establishing a density-based conceptual framework to appreciate physicochemical properties is an unaccomplished task. In this talk, we at first provide an overview of the four pathways currently available in the literature to tackle the matter, including orbital-free density functional theory, conceptual density functional theory, direct use of density-associated quantities, and the information-theoretic approach. Then, highlight several recent advances of employing these approaches to realize new understandings for chemical concepts such as covalent bonding, noncovalent interactions, cooperation, frustration, electrophilicity, nucleophilicity, regioselectivity, and stereoselectivity. Finally, we provide a few possibilities for the future development of this relatively uncharted territory.

From Electron Delocalization to Predicting Superconductivity

CONTRERAS-GARCIA Julia, NOVOA Trinidad
Laboratoire de Chimie Théorique, 4 Pl Jussieu, 75005, Paris, France.
E-mail: julia.contreras_garcia@sorbonne-universite.fr

Abstract
A room temperaturesuperconductor is probably the most desired system in solid state physics. Sofar, the greatest advances, cuprates, pnictides and number of others wereobtained in a serendipitous way. As there is no clear theory for thesesuperconductors, it is difficult to predict where progress will be made. Incontrast the Bardeen-Cooper-Schrieffer (BCS) theory gives a clear guide forachieving high Tc, and hydrogen seems to be a main clue. Within this approach,the recently reported superconductivity at 190 K in compressed H2S[1] has been arguably the biggest discovery in the field since thesuperconducting cuprates nearly 30 years ago.
However, a microscopicunderstanding of why this particular material features such a strong couplingis still missing. We have recently shown that the underlying chemical structureand bonding need to be characterized for a good comprehension of the chemicalcomposition-superconductivity relation.
We have worked in characterizingthe bonding in superconductors by means of the Electron Localization Function[2] in two directions: globally, in order to characterize electrondelocalization [3] and locally, in order to characterize the degree of hydrogenmolecule formation [4].
We have constructed a databaseof binary and ternary hydrogen-based compounds with available criticaltemperatures. Thanks to machine learningalgorithms (decision trees), a very good correlation has been obtained forpredicting superconducting critical temperature in all these compounds.
These developments are nowavailable at a public code, Tcestime [5]; which allows to predict in a simpleand fast manner the critical temperature from a DFT calculation. A server tomake this calculation online is also available.
Further work is now beingcarried out in order to avoid the DFT calculations and obtain the bondingcharacterization from the atomic composition alone. We hope that thesedevelopments will open the possibility for a real high-throughput screening ofnew potential low pressure high critical temperature superconductors and, atthe same time, sets clear paths for chemically engineering better superconductors.

References
[1] A. P. Drozdov, M. I. Eremets, I. A. Troyan, V.Ksenofontov, and S. I. Shylin. Conventional superconductivi-ty at 203 kelvin athigh pressures in the sulfur hydride system. Nature 2015, 525, 73
[2] A. D. Becke and K. E. Edgecombe. A simple measureof electron localization in atomic and molecular systems. The Journal ofChemical Physics 1990, 92, 5397
[3] F. Belli, T. Novoa, J. Contreras-Garcia and I.Errea, Strong correlation between electronic bonding network and criticaltemperature in hydrogen-based superconductors. Natur. Comm. 2021, 12, 5381
[4] M. E. di Mauro, B. Braïda, I. Errea, T. Novoa, J.Contreras-García. Molecularity: a fast and efficient crite-rion for probingsuperconductivity. https://arxiv.org/abs/2403.07584
[5] https://github.com/juliacontrerasgarcia/Tcestime

Large-Scale Ab Initio Methods Based on Wave Propagation

Shengjun Yuan
School of Physics and Technology, Wuhan University, Wuhan, Hubei, 430072, China
E-mail: s.yuan@whu.edu.cn
http://yuan.whu.edu.cn/

Abstract
Common computational methods in condensed matter physics typically rely on the stationary Schrödinger equation, which involves diagonalizing the Hamiltonian and poses challenges for large systems. This talk primarily focuses on the methodology of transforming the problems from the stationary Schrödinger equation to the time-dependent Schrödinger equation, thereby circumventing the need for diagonalization and enabling large-scale ab initio calculations. The topics include two parts, the tight-binding method TBPM (www.tbplas.net) and the density functional method DFPM. Both methods abandon the explicit expression of eigenstates or orbitals but benefit from the random state propagation in real space.

Discontinuous Galerkin Hartree-Fock Calculations for Predicting Accurate Electronic Structures of Mesoscopic-Scale Metal- Semiconductor Junctions with Millions of Atoms

Wei Hu, Xinming Qin and Jinlong Yang
University of Science and Technology of China, Hefei, Anhui, China
whuustc@ustc.edu.cn

Abstract
The evaluation of the exact Hartree-Fock exchange in hybrid density functional theory (DFT) is a crucial ingredient for accurately predicting electronic structures in molecules and solids. However, its application is currently limited to 5K atoms on leadership supercomputers due to its ultra-high computational complexity O(N 4 ). Herein, we propose a new discontinuous Galerkin Hartree-Fock (DGHF) method for large-scale hybrid functional electronic structure calculations. We present a massively parallel DGHF implementation on exascale supercomputers to reduce the high computational scaling of constructing the HFX matrix from O(N 4 ) to O(N). We showcase how DGHF can be used to predict accurate electronic structures of complex metal-semiconductor junctions with 2.5M atoms (17.2M electrons) using 35.9M cores on exascale Sunway supercomputer. This is the first time high-accuracy hybrid functional electronic structure calculations enable us to simulate next-generation electronic devices at mesoscopic scale (200 nm).

References
[1] Wei Hu, Jinlong Yang*, et al. “2.5 million-atom ab initio electronic-structure simulation of complex metallic heterostructures with DGDFT”. SC22: International Conference for High Performance Computing, Networking, Storage and Analysis, ACM Gordon Bell finalist (2022).

O(N) KS-DFT and Its Intersection with the Orbital-Free DFT

William Dawson (1), Jacob Leamer (2), Denys I. Bondar (2), Luigi Genovese (3), Takahito Nakajima (1)

(1) RIKEN Center for Computational Science; (2) Tulane University (3) CEA Grenoble

Abstract
Kohn-Sham Density Functional Theory (KS-DFT) is a popular method for modelling the properties of materials. However, the computational cost scales with the third power of the system size, which severely limits the scales of systems it can be applied to. In this workshop, most presenters hope to remove this bottleneck by developing Orbital-Free DFT methods. For this talk, we will present an alternative approach that reduces the cost to linear-scaling while staying in the Kohn-Sham ansatz. We will give an overview of O(N) KS-DFT techniques with a focus on our software packages [1, 2]. Then, we will turn our attention to developing O(N) method for metallic systems. We will present our most recent algorithm [3] and highlight its intersections with Orbital-Free methods.

References
[1] Ratcliff, L. E., W. Dawson, G. Fisicaro, D. Caliste, S. Mohr, A. Degomme, B. Videau et al. "Flexibilities of wavelets as a computational basis set for large-scale electronic structure calculations." J. Chem. Phys. 152, no. 19 (2020).
[2] Dawson, W., E. Kawashima, L. E. Ratcliff, M. Kamiya, L. Genovese, and T. Nakajima. "Complexity reduction in density functional theory: Locality in space and energy." J. Chem. Phys.158, no. 16 (2023).
[3] Leamer, J. M., W. Dawson, and D. I. Bondar. "Positivity preserving density matrix minimization at finite temperatures via square root." J. Chem. Phys. 160, no. 7 (2024).

Random Green’s Function Method: Probing the Density Matrix of Large-Scale System with Random Orbitals

Youqi Ke, Mingfa Tang and Qingyun Zhang, Zizhuang Liu
School of Physical Science and Technology, ShanghaiTech University, Shanghai, China

Abstract
Green’s function (GF) is a fundamental function and possesses wide applications in science and engineering. In quantum physics, the GF models the system's spatial and temporal response of a system, playing a vital role in fully quantum simulations. For example, the Keldysh's non-equilibrium GF (NEGF) and the retarded GF are the central quantities for calculating the respective non-equilibrium and equilibrium quantum systems. However, the conventional computation of retarded GF and NEGF features high computational complexity, and makes its application to large-scale systems very challenging. An accurate and linear-scaling (NE)GF is highly desirable for applications in the material and nano-electronics simulation. In the first part, I will present a linear-scaling (NE)GF based stochastic method with small number of random orbitals for calculating the large-scale electronic structure and quantum transport through large-scale nano-electronics. In the second part, I will show an accurate density matrix recovering technique based on GF measurement with few random orbitals, presenting a linear-scaling electronic structure method.

A Comprehensive Materials Database for Orbital-Free Density Functional Theory Developments (likely remote)

Johann Lüder (1,2,3), Sergei Manzhos (4)
1) Department of Materials and Optoelectronic Science, National Sun Yat-sen University, Kaohsiung, Taiwan
2) Center for Theoretical and Computational Physics, National Sun Yat-sen University, Kaohsiung, Taiwan
3) Center of Crystal Research, National Sun Yat-sen University, Kaohsiung, Taiwan
4) School of Materials and Chemical Technology, Tokyo Institute of Technology, Tokyo Japan

Abstract
Orbital-free Density Functional Theory (OFDFT) holds the promise of first-principles calculations with systems containing millions of atoms, but it is held back by, among others, a lack of accurate and reliable kinetic energy functionals. While analytic and empirical functionals have been successfully presented, OFDFT’s predictive powers have not yet reached those of Density Functional Theory (DFT). Hence, developments are ongoing and are becoming more influenced by machine learning approaches. However, machine-learning (ML) techniques are data intensive and data quality dependent, which can be a bottleneck for ML efforts, especially if data are unavailable and need to be generated, for instance, by DFT simulations. We present a DFT-based dataset tailored to the needs of OFDFT developers containing 433 materials for applications in machine-learning kinetic energy density functional development and benchmarks. In contrast to existing materials databases, we provide essential information required for kinetic energy functionals (KEF) and kinetic energy density functional (KEDF) developments, that is the electronic density, kinetic energy density, the total Kohn-Sham potential, and the gradients and Laplacian of the electronic density. The data furthermore contain structural information, total DFT energy, and its kinetic and potential energy contributions. The initial materials’ structures are taken from the Materials Project. We selected unary, binary and ternary compounds containing Li, Al, Mg, Si, As, Ga, Sb, Na, Sn, P, and/or In atoms and as well as off-equilibrium geometries, i.e. 18 strained structures, for each material providing additional data points for developers and tests. The DFT computations, including an isotropic volume relaxation for the ground state, were performed with local pseudopotentials in the Abinit package.
Our recent work on smoothened (partially averaged) [1] and averaged kinetic energy density (KED) to machine-learned kinetic energies by Gaussian Progress regression (GPR) [2] demonstrated the dataset’s practical use, which may motivate continuous efforts to push the current boundaries of OFDFT and provide a reference for future ML kinetic energy density functional developments.

References
1 Manzhos, S., Lüder, J., & Ihara, M. (2023). Machine learning of kinetic energy densities with target and feature smoothing: Better results with fewer training data. The Journal of Chemical Physics, 159(23). https://doi.org/10.1063/5.0175689
2 Lüder, J., Ihara, M., & Manzhos, S. (2024). A machine-learned kinetic energy model for light weight metals and compounds of group III-V elements. http://arxiv.org/abs/2407.11450

Application of Machine Learning to Conformational Analysis, Molecular Assembly and Conceptual DFT

Alberto Vela, Lucio Peña-Zarate, Oscar X. Guerrero-Gutiérrez, and Jorge Tiburcio
Department of Chemistry, Cinvestav-Zacatenco, CDMX, México
avela@cinvestav.mx

Abstract
The conformational flexibility of amino acids is crucial to gaining insight into how and why these essential building blocks participate in establishing the secondary and tertiary structures of peptides. Much experimental and theoretical effort has been devoted to determining, accurately and reliably, the conformational landscape of amino acids, starting with the simplest ones, glycine and alanine. Surprisingly, the theoretical prediction of the correct conformational ordering has been more complicated than expected, as seen in references [1] and [2], especially for DFT approaches. In this talk, I will present our tour de force in describing the conformational ordering of the simplest amino acids, glycine, α-alanine, and β-alanine, with well-known density functional approximations (DFAs) to the exchange-correlation energy, and using some of the DFAs that we have proposed in the last two decades, with dismaying results. Surprisingly, I will show that two machine learning approaches, ANI-1ccx[3] and DM21 [4], reproduce the observed conformational ordering correctly and do it at impressive speeds. I will show the capability of ML to describe the threading and unthreading processes prevailing in the assembly of molecular machines, as well as its explanation based on NCI and energy decomposition analysis. Finally, I will present the application of AIMNet to the calculation of chemical descriptors derived or justified within Conceptual-DFT. We thank Conahcyt for financial support.

References
[1] D. Nguyen; A. C. Scheiner; J. W. Andzelm; S. Sirois; D. R. Salahub; A. T. Hagler, Journal of Computational Chemistry 1997, 18, 1609–1631.
[2] M. A. Ribeiro da Silva.; M. d. D. M. Ribeiro da Silva; A. F. L. Santos; M. V. Roux; C. Foces-Foces; R. Notario; R. Guzman-Mejia; E. Juaristi, Journal of Physical Chemistry B 2010, 114, 16471–16480.
[3] J. S. Smith; R. Zubatyuk; B. Nebgen; N. Lubbers; K. Barros; A. E. Roitberg; O. Isayev; S. Tretiak, Scientific Data 2020, 7, 1-10.
[4] J. Kirkpatrick; B. McMorrow; D. H. Turban; A. L. Gaunt; J. S. Spencer; A. G. Matthews; A. Obika; L. Thiry; M. Fortunato; D. Pfau; L. Román Castellanos; S. Petersen; A. W. R. Nelson; P. Kohli; P. Mori-Sánchez; D. Hassabis; A. J. Cohen, Science 2021, 374, 1385-1389.

Fragment-Based Deep Learning for Simultaneous Prediction of Polarizabilities and NMR Shieldings of Macromolecules and Their Aggregates

Dongbo Zhao,1 Yilin Zhao,2 Paul W. Ayers,2** Shubin Liu,3,4** and Dahua Chen1**
1Institute of Biomedical Research, Yunnan University, Kunming, Yunnan 650500, P. R. China
2Department of Chemistry and Chemical Biology, McMaster University, Hamilton ONL8S4M1, Canada
3Research Computing Center, University of North Carolina, Chapel Hill, North Carolina 27599-3420, United States
4Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, United States
**Email Address: chendh@ynu.edu.cn; ayers@mcmaster.ca; shubin@email.unc.edu

Abstract
Simultaneous prediction of the molecular response properties, such as polarizability and the NMR shielding constant, at a low computational cost is an unresolved issue. We propose to combine a linear-scaling generalized energy-based fragmentation (GEBF) method and deep learning (DL) with both molecular and atomic information-theoretic approach (ITA) quantities as effective descriptors. In GEBF, the total molecular polarizability can be assembled as a linear combination of the corresponding quantities calculated from a set of small embedded subsystems in GEBF. In the new GEBF-DL(ITA) protocol, one can predict subsystem polarizabilities based on the corresponding molecular wave function (thus electron density and ITA quantities) and DL model rather than calculate them from the computationally intensive coupled-perturbed Hartree−Fock or Kohn−Sham equations and finally obtain the total molecular polarizability via a linear combination equation. As a proof-of-concept application, we predict the molecular polarizabilities of large proteins and protein aggregates. GEBF-DL(ITA) is shown to be as accurate enough as GEBF, with mean absolute percentage error <1%. For the largest protein aggregate (>4000 atoms), GEBF-DL(ITA) gains a speedup ratio of 3 compared with GEBF. It is anticipated that when more advanced electronic structure methods are used, this advantage will be more appealing. Moreover, one can also predict the NMR chemical shieldings of proteins with reasonably good accuracy. Overall, the cost-efficient GEBF-DL(ITA) protocol should be a robust theoretical tool for simultaneously predicting polarizabilities and NMR shieldings of large systems.

Acknowledgement
This work was supported by the start-up funding of the Yunnan University, the Yunnan Fundamental Research Projects (grant no. 202101AU070012), the National Natural Science Foundation of China (grant no. 22203071), the High Level Talents Special Support Plan (to D.Z.), NSERC, Canada Research Chairs, and the Digital Research Alliance of Canada.
We are indebted to Benkun Hong and Profs. Wei Li and Shuhua Li of the Nanjing University and Lian Zhuo of the Hunan Normal University. Part of the computations were done on the high-performance computers of the Advanced Computing Center of Yunnan University.

References
[1] Zhao, D; Zhao, Y.; Xu, E.; Liu, W.; Ayers, P. W.; Liu, S.; Chen, D. J. Chem. Theory Comput. 2024, 20, 2655.
[2] Zhao, D; Zhao, Y.; He, X.; Li, Y.; Ayers, P. W.; Liu, S. J. Chem. Theory Comput. 2023, 19, 6461.
[3] Zhao, D; Zhao, Y.; He, X.; Ayers, P. W.; Liu, S. Phys. Chem. Chem. Phys. 2023, 25, 2131.

Machine Learning Orbital-Free Density Functional Theory for Atomic Nuclei

Pengwei Zhao
School of Phsics, Peking University, Beijing, China

Abstract
Research on quantum mechanical many-body problems is essential in a wide variety of scientific fields including nuclear physics. Nuclei are self-bound systems, and the shell effects are intimately connected to nuclear deformation, which arises from the spontaneous symmetry breaking of the nuclear mean field in the intrinsic framework. Density functional theory (DFT) is the only microscopic approach that can be used to describe nuclides all over the nuclear chart [1]. For a precise and self-consistent description of nuclear shell and deformation effects, the Kohn-Sham DFT is the most widely used framework for the study of nuclear structure and dynamics.
In a series of our recent works [1,2], machine learning is employed to build an energy density functional for self-bound nuclear systems for the first time. By learning the kinetic energy as a functional of the nucleon density alone, a robust and accurate orbital-free density functional for nuclei is established. Self-consistent calculations that bypass the Kohn-Sham equations provide the ground-state densities, total energies, and root-mean-square radii with a high accuracy in comparison with the Kohn-Sham solutions. No existing orbital-free density functional theory comes close to this performance for nuclei.

References
[1] Y. L. Yang, Y. K. Wang, P. W. Zhao, Z. P. Li, Phys. Rev. C 104, 054312 (2021).
[2] X. H. Wu, Z. X. Ren, P. W. Zhao, Phys. Rev. C 105, L031303 (2022).
[3] X. H. Wu, Z. X. Ren, P. W. Zhao, submitted.

Semi-local Kinetic Energy Density Functionals using Kolmogorov-Arnold Networks

Luis Rincon
Grupo de Quimica Computacional y Teorica, Universidad San Francisco de Quito, Colegio Politecnico, Quito 17-1200-841, Ecuador

Abstract
Therecent introduction of Kolmogorot-Arnold Networks (KAN)1 suggests that it is possible torevisit and improve the performance of previously semi-local machine-learningkinetic energy density functionals. Comparedto traditional Neural Network topologies, KANs are more interpretable andrequire less parameters. In this work, KANsare used to evaluate correctionsto the second order gradient expansion of the kinetic energy functional that rely solely on the normalized reduced gradient andnormalized reduced Laplacian.2 Numerical assessments of the present methodology wereperformed for an atomic dataset that contain 18 atoms and the full QM-9database that correspond to 133885 organic structures with up to nine heavyatoms (CONF atoms). The results demonstrate that KANs recover the accuracy ofprevious Neural Networks architectures with an order the magnitude less nodes(neurons).

References
1. Z. Liu, Y. Wang, S. Vaidya, F. Ruehle, J. Halverson,M. Soljačić, T. Y. Hou and M. Tegmark, ‘KAN: Kolmogorov-Arnold Networks’,arXiv: 2404.19756,2 May 2024
2. L.Rincón, L.E Seijas, R. Almeida and FJavier Torres, ‘Towards the construction of an accurate kinetic energy densityfunctional and its functional derivative through physics-informed neuralnetworks’, J. Phys. Commun. 7 061001 (2023)

Kinetic Energy Density-Based Machine Learning Models of Kinetic Energy Using Gradient Expansion Based Features

Johann Lueder (1), Manabu Ihara (2), Sergei Manzhos (2)*
1) Department of Materials and Optoelectronic Science, National Sun Yat-sen University, Kaohsiung, Taiwan
2) School of Materials and Chemical Technology, Tokyo Institute of Technology, Tokyo Japan
E-mail: Sergei.Manzhos@gmail.com

Abstract
We will overview our recent results in machine learning (ML) of kinetic energy densities (KED) and kinetic energies (KE) from descriptors based on terms of the gradient expansion and the product of the density and Kohn-Sham effective potential [1]. We show that this approach allows reproducing energy volume dependence of light metals and compounds made of group III-V elements around equilibrium geometry with good accuracy [2-3].
We use smoothened (partially averaged) descriptors to learn smoothened KEDs. This approach is useful when reference materials are few, resulting in abundant data yet palliating the issue of very uneven data distribution that is characteristic of the KEDF paradigm [2]. Smoothing not only facilitates ML (which is sensitive to data distribution), it is advantageous when an ML algorithm is costly to train on many data even when such data are abundant, as is the case of Gaussian process regression (GPR) used here. When the training set contains many materials, the KEDF paradigm may become too data-intensive; in this case working with fully averaged descriptors is advantageous. Working with averaged KED rather than integral KE is then still advantageous as it helps palliate the effect of different unit call sizes in terms of data distribution. In this way we machine-learn KEs multiple phases of unary, binary, and ternary compounds containing Li, Al, Mg, Si, As, Ga, Sb, Na, Sn, P, and In - a total of 433 materials. We also find that unary compounds sample a wider region of the descriptor space than binary and ternary compounds, and it is therefore important to include them in the training set; a GPR model trained on a small number of unary compounds is able to extrapolate relatively well to binary and ternary compounds but not vice versa [3, 4].

References
[1] J. Chem. Phys., 153, 074104 (2020)
[2] J. Chem. Phys., 159, 234115 (2023)
[3] https://arxiv.org/pdf/2407.11450
[4] https://github.com/sergeimanzhos/GPRKE/

Harnessing Chemical Understanding with Wave Function Theory, Density Functional Theory, Machine Learning, and Quantum Computers

Shubin Liu
Research Computing Center, University of North Carolina, Chapel Hill NC 27599-3420; Department of Chemistry, University of North Carolina, Chapel Hill NC 27599-3290

Abstract
In this talk, we overview the status of how theory and computation can be exploited to obtain chemical understanding from wave function theory and density functional theory, and then outlook the likely impact of machine learning (ML) and quantum computers (QC) to appreciate traditional chemical concepts. It is maintained that the development and maturation of ML and QC methods in theoretical and computational chemistry represent two paradigm shifts about how the Schrödinger equation can be solved. New chemical understanding can be harnessed in these two new paradigms by making respective use of ML features and QC qubits. Before that happens, however, we still have hurdles to face and obstacles to overcome in both ML and QC arenas. Possible pathways to tackle these challenges are proposed. We anticipate that hierarchical modeling, in contrast to multiscale modeling, will emerge and thrive, becoming the workhorse of in silico simulations in the next few decades.

References
1. Shubin Liu, Harvesting Chemical Understanding with Machine Learning and Quantum Computers. ACS Phys Chem Au 2024, 4(2), 135-142.
2. Shubin Liu (ed.), Conceptual Density Functional Theory: Towards a New Chemistry Reactivity Theory. April 2022, Wiley-VCH GmbH, Weinheim, Germany.
3. Shubin Liu (ed), Exploring Chemical Concepts Through Theory and Computation. May 2024, Wiley-VCH GmbH, Germany.

Machine Learning Assisted Kinetic Energy Density Functionals Implemented in ABACUS

Liang Sun, Mohan Chen
HEDPS, CAPT, School of Physics and College of Engineering, Peking University, Beijing 100871, People’s Republic of China

Abstract
We introduced a novel ML-based physical-constrained non-local KEDF (MPN KEDF), which (a) contains non-local information, (b) obeys a series of exact physical constraints, and (c) achieves convergence via careful design of descriptors, neural network output, post-processing, and loss function, etc. The MPN KEDF exceeded the accuracy of semi-local KEDFs and approached the accuracy of non-local KEDFs in simple metals and their alloys. We conclude that incorporating non-local information and exact physical constraints is crucial to improving the accuracy, transferability, and stability of ML-based KEDFs.
Building on this success, we further developed a multi-channel ML-based physical-constrained non-local KEDF (CPN KEDF), extending the MPN KEDF methodology to semiconductor systems. The CPN KEDF integrates information from several channels, each designed to capture features at distinct scales. We discovered that the multi-channel architecture is essential for the CPN KEDF to accurately represent the electronic structure of semiconductors. Specifically, the CPN5 KEDF, with five different channels, outperformed semi-local KEDFs and neared the accuracy of non-local KEDFs in semiconductor systems. Notably, it demonstrated excellent reproduction of covalent bonding structures, which is challengeable for conventional analytical KEDFs. Both the MPN and CPN KEDFs have been integrated into ABACUS, an open-source ab initio computational package, making these advancements accessible to the broader scientific community.

Electron Localization-Delocalization Matrices (LDMs): A Powerful Predictive Molecular Descriptor

Chérif F. Matta,1,2
1 Dept. of Chemistry and Physics, Mount Saint Vincent University, Halifax, NS, Canada, B3M 2J6.
2 Dept. of Chemistry, Saint Mary's University, Halifax, NS, Canada, B3H 3C3.
e-mail: cherif.matta@msvu.ca

Abstract
An electron localization-delocalization matrix (LDM) is a representation of the complete molecular graph. A complete graph links all pairs of vertices (atoms) in the molecule, unlike the usually incomplete chemical structure, where only a line is drawn when atoms share a chemical bond. The edges of the molecular graph represented by an LDM are electron exchange channels that exist between each pair of atoms. Therefore, an LDM condenses a considerable amount of electronic structure information at atomic and diatomic resolution. By inserting the localization and delocalization indices obtained from a Quantum Theory of Atoms in Molecules (QTAIM) wavefunction analysis as matrix elements, the LDM represents a bridge between quite separate branches of theoretical chemistry, i.e., quantum chemistry on the one hand and chemical graph theory on the other. LDMs are found to be powerful predictors of molecular properties as diverse as pKa, boiling points, substituent effects, aromaticity, corrosion inhibitor activity (including the discovery of active species), mosquito repellency, λmax (UV), enzyme catalysis, etc. [1-6].

References
1. Matta CF, Ayers PW, Cook R. Electron Localization-Delocalization Matrices, Springer, Berlin, (2024).
2. Cook R. Struct. Chem. 28, 1527-1538 (2017).
3. Sumar I, Cook R, Ayers PW, Matta CF. Phys. Script. 91, Artículo # 013001 (2016).
4. Sumar I, Cook R, Ayers PW, Matta CF. Comput. Theor. Chem. 1070, 55-67 (2015).
5. Sumar I, Ayers PW, Matta CF. Chem. Phys. Lett. 612, 190-197 (2014).
6. Matta CF. J. Comput. Chem. 35, 1165-1198 (2014).

The critical frequency in Quantum Hydrodynamic Theory

Fabio Della Sala (1, 2)
1) Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100, Lecce, Italy
2) Center for Biomolecular Nanotechnologies, Istituto Italiano di Tecnologia, Via Barsanti 14, 73010 Arnesano (LE), Italy
E-mail: fabio.dellasala@unisalento.it

Abstract
The Quantum-Hydrodynamic Theory (QHT) can be considered a reformulation of the Time-Dependent Density-Functional Theory (TD-DFT) in which all electrons move in phase[1,2]. Thus, it is well suited to describe collective excitations in plasmonic systems, e.g. metal nanoparticles (NP). The QHT is an orbital-free approach and it llows to compute the absorption spectrum directly from the ground-state density. The accuracy of the QHT absorption spectrum depends on the approximation of the kinetic energy (KE) functional. Conventional KE approximations are based on gradient-corrected KE functionals, such as the Thomas-Fermi-von Weiszäcker (TFvW), which can reproduce accurately the main plasmon peak.
It has been shown that for the QHT-TFvW approach a critical frequency exists [2,3], so that the absorption spectrum is not stable above it and it strongly depends on the exponential decay of the ground-state density. Using the Laplacian-Level (LL) KE functionals [4] no critical frequency exists, the absorption spectra is always stable.
The properties of the QHT methods will be discussed considering excitation energies, oscillator strengths and induced densities for a large benchmark of jellium nanoparticles and nanoshells, in comparison with reference TDDFT results.

References
[1] M. Bonitz, Zh. A. Moldabekov, T. S. Ramazanov, T. S. Phys. Plasmas 2019, 26, 090601 (2019).
[2] F. Della Sala, J. Chem. Phys. 157, 104101 (2022).
[3] C. Ciracì, F. Della Sala, Phys. Rev. B 93, 205405 (2016).
[4] H. M. Baghramyan, F. Della Sala, C. Ciracì, Phys. Rev. X 11, 011049 (2021).

Alchemical Derivatives for Orbital-Free Energies

Guido von Rudorff
University of Kassel

Abstract
Alchemical Perturbation Density Functional Theory (APDFT) [1] is one particular method from the Quantum Alchemy family where the derivatives of the total energy can be expressed as a simple functional of the density derivatives. The connection between the energy derivatives and the electron density derivatives which also recover the true self-consistent density[2] of all close isoelectronic systems and, therefore, all one-electron properties, might be a starting point for future developments of both orbital-free methods as well as an application of methods which can yield (electron density) response functions.
Quantum Alchemy is a family of methods which assess large numbers of isoelectronic systems perturbatively from a single quantum chemistry reference calculation. As a perturbative approach, many diverse properties such as energies, orbital eigenvalues, electron densities, photoelectron circular dichroism parameters and protonation energies can be predicted with the simple closed form expression of quantum alchemy. At heart, a Taylor approximation is built from the first low-order response functions of the property w.r.t. changes in the nuclear charges and geometry. End-to-end, this is typically five orders of magnitude cheaper than quantum chemistry methods of comparable accuracy, which will further improve with differentiable quantum chemistry calculations.

References
[1] Alchemical perturbation density functional theory, von Rudorff, von Lilienfeld, Phys Rev Res 2020. https://doi.org/10.1103/physrevresearch.2.023220
[2] Arbitrarily Accurate Quantum Alchemy, von Rudorff, J Chem Phys, 2021. https://doi.org/10.1063/5.0073941
[3] Optimal photoelectron circular dichroism of a model chiral system, J Chem Phys, 2024. https://doi.org/10.1063/5.0209161

FFLUX: a Force Field Based on an Electron-Density Based Energy-Decomposition

Paul L.A. Popelier, M.Brown, M.Burn, L.Cabrera, G.Hawe, P. Bandyopadhyay, B.Isamura, M. Nosratjoo, B. Symons, M. Bane and M.Vincent
Department of Chemistry, University of Manchester, M13 9PL Manchester, Britain
pla@manchester.ac.uk.

Abstract
The electron density serves as a central information platform being fed from three possible sources: (i) orbitals and basis functions, (ii) a grid, or (iii) X-ray diffraction experiment. If an atom inside a quantum system is defined based on the electron density then this atom is independent from the source that fed it. This is an important advantage, making this atom more universal. The Quantum Theory of Atoms in Molecules (QTAIM) [1] proposes such an atom, and does so in a minimal way, well linked to quantum mechanics. This quantum atom is a prime candidate to serve as a cornerstone for a novel type of force field, closer to the underlying quantum mechanics and taking advantage of this atom’s rigorous chemical transferability. This approach[2] is called FFLUX.
We pioneered[3] the use of Gaussian Process Regression in the design of atomic potentials. Contrary to efforts of other research groups, we started first with the machine learning (ML) of accurate electrostatics (e.g. for all 20 amino acids[4]). It is manifest to work with multipole moments if only nuclear sites are used. Next followed accurate ML predictions of the atomic energies. At the heart of this method are quantum atoms for which a single partitioning method provides all atomic properties. Thus, the ML learns physically-based atomic properties and does not partition the total system.
Sustained in-house software development led to the ML training program FEREBUS[5] supported by ICHOR[6] and the molecular dynamics program DL_FFLUX, which is an offspring of British software package DL_POLY. Active learning combined with a AIMD-based sample set produces models with fewer training point than neural network do for small molecules[7]. Improved training now tackles molecules (e.g. paracetamol) up to ~30 atoms[8]. The recent parallellisation[9] of DL_FFLUX enables the simulation of condensed matter, whether molecular crystals[10] or liquid water[11], all with high-rank polarisable electrostatics. The next major step will be to link models in order to describe oligopeptides and later even proteins. Meanwhile, innovative ML techniques are being introduced[12] to improve the prediction errors.

References
[1] Bader, R. F. W., Atoms in Molecules. A Quantum Theory. Oxford Univ. Press, GB, 1990.
[2] Popelier, P. L. A., Int.J.Quant.Chem. 2015, 115, 1005-1011.
[3] Handley, C. M.; Hawe, G. I.; Kell, D. B.; Popelier, P., Phys.Chem.Chem.Phys. 2009, 11, 6365.
[4] Fletcher, T. L.; Popelier, P. L. A., J.Chem.Theor.Comput. 2016, 12 (6), 2742-2751.
[5] Burn, M. J.; Popelier, P. L. A., Digital Discovery 2023, 2, 152-164.
[6] Burn, M. J.; Popelier, P. L. A., Materials Advances 2022, 3, 8729-8739.
[7] Burn, M. J.; Popelier, P. L. A., J.Chem.Phys. 2020, 153, 054111.
[8] Burn, M. J.; Popelier, P. L. A., J.Chem.Theory Comp. 2023, 19, 1370-1380.
[9] Symons, B. C. B.; Bane, M. K.; Popelier, P. L. A., J.Chem.Theor.Comp. 2021, 17, 7043-7055.
[10] Brown, M. L.; Skelton, J. M.; Popelier, P. L. A., J.Chem.Theor.Comp. 2023, 19 (21), 7946.
[11] Symons, B. C. B.; Popelier, P. L. A., J.Chem.Theory Comp. 2022, 18 5577−5588.
[12] Isamura, B. K.; Popelier, P. L. A., Artificial Intelligence Chemistry 2023, 1 (2), 100021.

Orbital-Free Density-Potential Functional Theory for Electronic Structure

Martin-Isbjoern Trappe
Centre for Quantum Technologies, National University of Singapore

Abstract
Density-potential-functional theory (DPFT), where the variational variables are both the density and an effective potential, is an alternative formulation of orbital-free density functional theory. Recently, we extended the list of applications of DPFT (from mainly quantum gases in one- and two-dimensional settings) to electronic structure. We build on systematic Suzuki-Trotter factorizations of the quantum-mechanical propagator and on the Wigner function formalism, respectively, to derive nonlocal as well as semilocal functional approximations without resorting to system-specific approximations or ad hoc measures of any kind. The cost for computing the basic versions of these semiclassical ground-state single-particle density scales (quasi)linearly with particle number, and we illustrate that the developed density formulas become relatively more accurate for larger particle numbers. Most importantly, the Suzuki-Trotter-based expressions can be improved systematically: We present the beginnings of a technology that is comparable in accuracy to Kohn-Sham DFT and scales (at worst) quadratically with particle number. With its universal applicability this DPFT approach offers alternatives to existing orbital-free methods for mesoscopic quantum systems and may be suitable for modeling the electronic structure of large systems.

Fast and Stable Framework for Nonlocal Kinetic Energy Density Functional Reconstruction in OF-DFT Calculations

Yongshuo Chen1*, Cheng Ma1, Boning Cui1, Qiang Xu1, Wenhui Mi1,2 and Yanming Ma1,2
1. Key Laboratory of Material Simulation Methods & Software of Ministry of Education, College of Physics, Jilin University, Changchun 130012, China; 2. International Center of Future Science, Jilin University, Changchun 130012
*Email: lanse627@qq.com, yongshuo4@gmail.com

Abstract
Nonlocal kinetic energy functionals that incorporate a density-dependent kernel have significantly enhanced the accuracy of Orbital-Free Density Functional Theory (OF-DFT). Although more complex kinetic energy functionals can provide even greater accuracy, they often entail substantial increases in computational costs. To address this challenge, we have developed a new scheme for reconstructing of kinetic energy density functionals (KEDFs) using the “tight-binding” approximation. We selected two nonlocal KEDFs with density-dependent kernels (LDAK-MGPA and revHC) for benchmarking the performance of this approach on standard structures of elements like Li, Mg, Al, Ga, Si, and III-V semiconductors, as well as Mg8 and Si50 clusters. Results indicated that the new framework can considerably reduce the computational cost of OFDFT and enhance numerical stability without sacrificing any accuracy. This framework will provide a promising framework for developing more sophisticated KEDF for realistic materials simulations with OFDFT.

Advanced Computational Modelling of Interfaces and Grain Boundaries in Fuel Cells and Batteries

Kulbir Kaur Ghuman
Institut national de la recherché (INRS), Centre Énergie Matériaux Télécommunications, Université du Québec, Canada National Institute of Scientific Research (INRS), Energy, Materials, and Telecommunications Center, University of Quebec, Canada

Abstract
Addressing the critical challenges posed by climate change hinges on our ability to identify champion materials that can be used to construct sustainable, and environmentally friendly devices. With this aim in mind, my research leverages leading-edge computational techniques and a multidisciplinary approach to understand the intricate behaviors exhibited by complex polycrystalline materials utilized in fuel cells and batteries, subsequently optimizing them for the development of next-generation devices. Materials used in solid oxide fuel cells (SOFCs) and lithium-ion batteries are typically polycrystalline, exhibiting variations in grain sizes, orientations, dopant segregation, and defect distribution, often with a high density of grain boundaries and interfaces that significantly impact their performance, particularly in terms of ionic conductivity. In this presentation, I will present our latest discoveries concerning the microstructural and ionic behaviors observed at grain boundaries and interfaces within prominent materials such as Yttria Stabilized Zirconia (YSZ) used in SOFCs, and Li-La-Ti-O (LLTO) employed in batteries. Through integrating classical and quantum simulations, our work has developed realistic models of these materials, providing explanations for observed experimental phenomena. Finally, I will discuss some of the challenges in identifying the overall impact of all the microstructural defects present in polycrystalline materials and the role that advanced computational modelling tools can play in resolving them.

Nonlocal Free-Energy Density Functional Enables a Broad Range of Warm Dense Matter Simulations via ATLAS

Cheng Ma1, Qiang Xu1, Min Chen1, Wenhui Mi1,2 Yanchao Wang1, and Yanming Ma1,2
1. Key Laboratory of Material Simulation Methods & Software of Ministry of Education, College of Physics, Jilin University, Changchun 130012, China; 2. International Center of Future Science, Jilin University, Changchun 130012, China; Email: macheng@calypso.cn

Abstract
Due to the favorable scaling with both system size and temperature, finite-temperature orbital-free density functional theory (FT-OFDFT) holds considerable promise for investigating the properties of warm dense matter. According to the generally accepted scenario, the quality of FT-OFDFT strongly depends on a noninteracting free-energy-density functional. Recently, we derived a new nonlocal free-energy density functional, named XWMF, using line integrals for FT-OFDFT and implementing it in ATLAS[1-2]. The XWMF has been benchmarked using a variety of warm dense matter systems, including Si, Al, H, He, and H-He mixture, and has demonstrated exceptional accuracy and numerical stability.

References
[1] C. Ma, M. Chen, Y. Xie, Q. Xu, W. Mi, Y. Wang, and Y. Ma, Nonlocal free-energy density functional for a broad range of warm dense matter simulations Phys. Rev. B 110, 085113 (2024)
[2] W. Mi, X. Shao, C. Su, Y. Zhou, S. Zhang, Q. Li, H. Wang, L. Zhang, M. Miao, Y. Wang, and Y. Ma, ATLAS: a real-space finite-difference implementation of orbital-free density functional theory, Comput. Phys. Commun. 200, 87 (2016).