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Electronic Structure of Atoms02:28

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An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum...
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Tetrahedral Complexes
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An applied magnetic field causes loosely bound π-electrons in organic molecules to circulate, producing a local or induced diamagnetic field over a large spatial volume. As the molecules tumble in solution, the field generated by π-electrons in spherical substituents results in a zero net field. However, the net field generated by π-electrons in non-spherical substituents is not zero. The effect of this induced field depends on the orientation of the molecule with respect to B0,...
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Valence shell electron-pair repulsion theory (VSEPR theory) enables us to predict the molecular structure around a central atom from an examination of the number of bonds and lone electron pairs in its Lewis structure. The VSEPR model assumes that electron pairs in the valence shell of a central atom will adopt an arrangement that minimizes repulsions between these electron pairs by maximizing the distance between them. The electrons in the valence shell of a central atom form either bonding...
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A General Sparse Tensor Framework for Electronic Structure Theory.

Samuel Manzer1,2, Evgeny Epifanovsky3, Anna I Krylov4

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Developing efficient linear-scaling algorithms is crucial for large-scale electronic structure theory. This study introduces a symbolic block-sparse tensor library to simplify code development and enhance performance for complex molecular simulations.

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Area of Science:

  • Computational chemistry
  • Materials science
  • Quantum mechanics

Background:

  • Linear-scaling algorithms are essential for extending electronic structure theory to larger molecules.
  • The complexity of modern linear-scaling methods poses challenges for code development and maintenance.
  • A lack of robust software abstractions for block-sparse tensor operations hinders progress.

Purpose of the Study:

  • To develop a highly efficient symbolic block-sparse tensor library.
  • To provide high-level software constructs for treating complex tensor operations.
  • To simplify the development and maintenance of linear-scaling methods.

Main Methods:

  • Implementation of a symbolic C++ language library for tensor operations.
  • Support for arbitrary multi-dimensional sparsity in input and output tensors.
  • Avoidance of cumbersome machine-generated code.

Main Results:

  • The developed library offers efficient handling of block-sparse tensor operations.
  • The implementation supports multi-dimensional sparsity across all tensors.
  • Demonstrated very high performance for linear-scaling sparse tensor contractions.

Conclusions:

  • The symbolic block-sparse tensor library facilitates the development of advanced linear-scaling algorithms.
  • This abstraction simplifies complex computational chemistry problems.
  • The library achieves high performance, enabling the study of larger molecular systems.