Approximate Functionals in Hypercomplex Kohn-Sham Theory
- URL: http://arxiv.org/abs/2102.08790v2
- Date: Wed, 23 Feb 2022 17:30:44 GMT
- Title: Approximate Functionals in Hypercomplex Kohn-Sham Theory
- Authors: Neil Qiang Su
- Abstract summary: The recently developed hypercomplex Kohn-Sham (HCKS) theory shows great potential to overcome the static/strong correlation issue in density functional theory (DFT)
This work focuses on approximate functionals in HCKS, seeking to gain more insights into functional development from the comparison between Kohn-Sham (KS) DFT and HCKS.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The recently developed hypercomplex Kohn-Sham (HCKS) theory shows great
potential to overcome the static/strong correlation issue in density functional
theory (DFT), which highlights the necessity of further exploration of the HCKS
theory toward better handling many-electron problem. This work mainly focuses
on approximate functionals in HCKS, seeking to gain more insights into
functional development from the comparison between Kohn-Sham (KS) DFT and HCKS.
Unlike KS-DFT, HCKS can handle different correlation effects by resorting to a
set of auxiliary orbitals with dynamically varying fractional occupations.
These orbitals of hierarchical correlation (HCOs) thus contain distinct
electronic information for better considering the exchange-correlation effect
in HCKS. The test on the triplet-singlet gaps shows that HCKS has much better
performance as compared to KS-DFT in use of the same functionals, and the
systematic errors of semi-local functionals can be effectively reduced by
including appropriate amount of the HCO-dependent Hartree-Fock (HF) exchange.
In contrast, KS-DFT shows large systematic errors, which are hardly reduced by
the functionals tested in this work. Therefore, HCKS creates new channels to
address to the strong correlation issue, and further development of functionals
that depend on HCOs and their occupations is necessary for the treatment of
strongly correlated systems.
Related papers
- NeuralSCF: Neural network self-consistent fields for density functional theory [1.7667864049272723]
Kohn-Sham density functional theory (KS-DFT) has found widespread application in accurate electronic structure calculations.
We propose a neural network self-consistent fields (NeuralSCF) framework that establishes the Kohn-Sham density map as a deep learning objective.
arXiv Detail & Related papers (2024-06-22T15:24:08Z) - Quantum-Enhanced Neural Exchange-Correlation Functionals [0.193482901474023]
KohnSham Density Functional Theory (KS-DFT) provides the exact ground state energy and electron density of a molecule, contingent on the asyet unknown universal exchange-correlation (XC) functional.
Recent research has demonstrated that neural networks can efficiently learn to represent approximations to that functional, offering accurate generalizations to molecules not present during the training process.
With the latest advancements in quantum-enhanced machine learning (ML), evidence is growing that Quantum Neural Network (QNN) models may offer advantages in ML applications.
arXiv Detail & Related papers (2024-04-22T15:07:57Z) - TC-LIF: A Two-Compartment Spiking Neuron Model for Long-Term Sequential
Modelling [54.97005925277638]
The identification of sensory cues associated with potential opportunities and dangers is frequently complicated by unrelated events that separate useful cues by long delays.
It remains a challenging task for state-of-the-art spiking neural networks (SNNs) to establish long-term temporal dependency between distant cues.
We propose a novel biologically inspired Two-Compartment Leaky Integrate-and-Fire spiking neuron model, dubbed TC-LIF.
arXiv Detail & Related papers (2023-08-25T08:54:41Z) - Variational principle to regularize machine-learned density functionals:
the non-interacting kinetic-energy functional [0.0]
We propose a new and efficient regularization method to train density functionals based on deep neural networks.
The method is tested on (effectively) one-dimensional systems, including the hydrogen chain, non-interacting electrons, and atoms of the first two periods.
For the atomic systems, the generalizability of the regularization method is demonstrated by training also an exchange--correlation functional.
arXiv Detail & Related papers (2023-06-30T12:07:26Z) - Neural-network quantum states for ultra-cold Fermi gases [49.725105678823915]
This work introduces a novel Pfaffian-Jastrow neural-network quantum state that includes backflow transformation based on message-passing architecture.
We observe the emergence of strong pairing correlations through the opposite-spin pair distribution functions.
Our findings suggest that neural-network quantum states provide a promising strategy for studying ultra-cold Fermi gases.
arXiv Detail & Related papers (2023-05-15T17:46:09Z) - IPCC-TP: Utilizing Incremental Pearson Correlation Coefficient for Joint
Multi-Agent Trajectory Prediction [73.25645602768158]
IPCC-TP is a novel relevance-aware module based on Incremental Pearson Correlation Coefficient to improve multi-agent interaction modeling.
Our module can be conveniently embedded into existing multi-agent prediction methods to extend original motion distribution decoders.
arXiv Detail & Related papers (2023-03-01T15:16:56Z) - D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory [79.50644650795012]
We propose a deep learning approach to solve Kohn-Sham Density Functional Theory (KS-DFT)
We prove that such an approach has the same expressivity as the SCF method, yet reduces the computational complexity.
In addition, we show that our approach enables us to explore more complex neural-based wave functions.
arXiv Detail & Related papers (2023-03-01T10:38:10Z) - Momentum Diminishes the Effect of Spectral Bias in Physics-Informed
Neural Networks [72.09574528342732]
Physics-informed neural network (PINN) algorithms have shown promising results in solving a wide range of problems involving partial differential equations (PDEs)
They often fail to converge to desirable solutions when the target function contains high-frequency features, due to a phenomenon known as spectral bias.
In the present work, we exploit neural tangent kernels (NTKs) to investigate the training dynamics of PINNs evolving under gradient descent with momentum (SGDM)
arXiv Detail & Related papers (2022-06-29T19:03:10Z) - Generalizability of density functionals learned from differentiable
programming on weakly correlated spin-polarized systems [2.896251429985507]
Kohn-Sham regularizer (KSR) is a machine learning approach that optimize a physics-informed exchange-correlation functional.
We evaluate the generalizability of KSR by training on atomic systems and testing on molecules at equilibrium.
Our nonlocal functional outperforms any existing machine learning functionals by predicting the ground-state energies of the test systems with a mean absolute error of 2.7 milli-Hartrees.
arXiv Detail & Related papers (2021-10-28T02:03:04Z) - eQE 2.0: Subsystem DFT Beyond GGA Functionals [58.720142291102135]
subsystem-DFT (sDFT) can dramatically reduce the computational cost of large-scale electronic structure calculations.
The key ingredients of sDFT are the nonadditive kinetic energy and exchange-correlation functionals which dominate it's accuracy.
eQE 2.0 delivers excellent interaction energies compared to conventional Kohn-Sham DFT and CCSD(T)
arXiv Detail & Related papers (2021-03-12T22:26:36Z) - Unity of Kohn-Sham Density Functional Theory and Reduced Density Matrix
Functional Theory [0.0]
This work presents a theory to unify the two independent theoretical frameworks of Kohn-Sham (KS) density functional theory (DFT) and reduced density matrix functional theory (RDMFT)
The generalization of the KS orbitals to hypercomplex number systems leads to the hypercomplex KS (HCKS) theory, which extends the search space for the density in KS-DFT to a space that is equivalent to natural spin orbitals with fractional occupations in RDMFT.
arXiv Detail & Related papers (2021-01-31T06:39:14Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.