Relativistic quantum theory and algorithms: a toolbox for modeling many-fermion systems in different scenarios

• URL: http://arxiv.org/abs/2110.00775v1
• Date: Sat, 2 Oct 2021 10:20:50 GMT
• Title: Relativistic quantum theory and algorithms: a toolbox for modeling many-fermion systems in different scenarios
• Authors: Simone Taioli and Stefano Simonucci
• Abstract summary: We discuss the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements. We show the application of our relativistic quantum mechanical framework to the assessment of the elastic differential scattering cross section of electrons impinging on molecular targets.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this chapter we focus first on the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements for which relativistic effects become significant. In particular, we discuss the mean-field approximation of the Dirac equation for many-electron systems, and its self-consistent numerical solution by using either radial mesh or Gaussian basis sets. The former technique is appropriate for spherical symmetric problems, such as atoms, while the latter approach is better suited to study non-spherical non-periodic polycentric systems, such as molecules and clusters. We also outline the pseudopotential approximation in relativistic context to deal with the electron-ion interaction in extended systems, where the unfavourable computational scaling with system size makes it necessary. As test cases we apply our theoretical and numerical schemes to the calculation of the electronic structure i) of the gold atom, and ii) of the superatom W@Au, where the inclusion of spin-orbit effects is crucial to the accurate understanding of the electronic properties. Furthermore, we describe the extension of our relativistic approach to deal with nuclear reactions driven by the weak force, such as the electron capture and $\beta$-decay, also at finite temperature in astrophysical scenarios, using the Fermi-Dirac statistics. The latter processes are indeed major drivers of the nucleosynthesis of the elements in stars and, thus, their understanding is crucial to model the chemical evolution of the Universe. Finally, we show the application of our relativistic quantum mechanical framework to the assessment of the elastic differential scattering cross section of electrons impinging on molecular targets, notably liquid water.

Related papers

• Electronic Correlations in Multielectron Silicon Quantum Dots [0.3793387630509845]
  Silicon metal-oxide-semiconductor based quantum dots present a promising pathway for realizing practical quantum computers. Hartree-Fock theory is an imperative tool for the electronic structure modelling of multi-electron quantum dots. We present a Hartree-Fock-based method that accounts for these complexities for the modelling of silicon quantum dots.
  arXiv  Detail & Related papers  (2024-07-05T06:46:38Z)
• Neural Pfaffians: Solving Many Many-Electron Schrödinger Equations [58.130170155147205]
  Neural wave functions accomplished unprecedented accuracies in approximating the ground state of many-electron systems, though at a high computational cost. Recent works proposed amortizing the cost by learning generalized wave functions across different structures and compounds instead of solving each problem independently. This work tackles the problem by defining overparametrized, fully learnable neural wave functions suitable for generalization across molecules.
  arXiv  Detail & Related papers  (2024-05-23T16:30:51Z)
• Relativistic EELS scattering cross-sections for microanalysis based on Dirac solutions [2.3421105223430483]
  electron energy-loss spectroscopy (EELS) comes from the complex inelastic scattering process. To quantify EELS, the common practice is to compare the cross-sections integrated within an energy window. We make these tabulated GOS available under an open-source license to the benefit of both academic users as well as allowing integration into commercial solutions.
  arXiv  Detail & Related papers  (2024-05-16T14:46:34Z)
• Measuring Electron Correlation. The Impact of Symmetry and Orbital Transformations [0.0]
  Measures of electron correlation used in wavefunction theory, density functional theory and quantum information theory are briefly reviewed. We focus on a more traditional metric based on dominant weights in the full configuration solution. The impact of symmetry is discussed and we emphasize that the distinction between determinants, configuration state functions and configurations as reference functions is useful.
  arXiv  Detail & Related papers  (2023-01-30T11:59:23Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Spectral density reconstruction with Chebyshev polynomials [77.34726150561087]
  We show how to perform controllable reconstructions of a finite energy resolution with rigorous error estimates. This paves the way for future applications in nuclear and condensed matter physics.
  arXiv  Detail & Related papers  (2021-10-05T15:16:13Z)
• Relativistic aspects of orbital and magnetic anisotropies in the chemical bonding and structure of lanthanide molecules [60.17174832243075]
  We study the electronic and ro-vibrational states of heavy homonuclear lanthanide Er2 and Tm2 molecules by applying state-of-the-art relativistic methods. We were able to obtain reliable spin-orbit and correlation-induced splittings between the 91 Er2 and 36 Tm2 electronic potentials dissociating to two ground-state atoms.
  arXiv  Detail & Related papers  (2021-07-06T15:34:00Z)
• Mapping quantum chemical dynamics problems onto spin-lattice simulators [0.5249805590164901]
  We provide a framework which allows for the solution of quantum chemical nuclear dynamics by mapping these to quantum spin-lattice simulators. Our approach represents a paradigm shift in the methods used to study quantum nuclear dynamics.
  arXiv  Detail & Related papers  (2021-03-12T17:32:52Z)
• Many Electrons and the Photon Field -- The many-body structure of nonrelativistic quantum electrodynamics [0.0]
  We show how to turn electronic-structure methods into polaritonic-structure methods that are accurate from the weak to the strong-coupling regime. We discuss how to adopt standard algorithms of electronic-structure methods to adhere to the new hybrid Fermi-Bose statistics.
  arXiv  Detail & Related papers  (2021-02-23T11:00:06Z)
• Time-resolved Interparticle Coulombic Decay spectra including nuclear degrees of freedom [49.1574468325115]
  We explore the ultra-rapid electronic motion spanning attoseconds to femtoseconds, demonstrating that it is equally integral and relevant to the discipline. The advent of ultrashort attosecond pulse technology has revolutionized our ability to directly observe electronic rearrangements in atoms and molecules.
  arXiv  Detail & Related papers  (2021-02-10T16:51:48Z)
• Graph Neural Network for Hamiltonian-Based Material Property Prediction [56.94118357003096]
  We present and compare several different graph convolution networks that are able to predict the band gap for inorganic materials. The models are developed to incorporate two different features: the information of each orbital itself and the interaction between each other. The results show that our model can get a promising prediction accuracy with cross-validation.
  arXiv  Detail & Related papers  (2020-05-27T13:32:10Z)

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.