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Related Concept Videos

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
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The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
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According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.
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The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while...
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Related Experiment Video

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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Geminal embedding scheme for optimal atomic basis set construction in correlated calculations.

S Sorella1, N Devaux2, M Dagrada2

  • 1International School for Advanced Studies (SISSA), Via Beirut 2-4, 34014 Trieste, Italy and INFM Democritos National Simulation Center, Trieste, Italy.

The Journal of Chemical Physics
|January 3, 2016
PubMed
Summary

We developed an efficient embedding method to create optimal basis sets for electronic structure calculations. This approach significantly reduces computational parameters for accurate many-body wave function representation in complex systems.

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Area of Science:

  • Computational Chemistry
  • Quantum Mechanics

Background:

  • Electronic structure calculations are crucial for understanding material properties.
  • Accurate representation of many-body wave functions requires significant computational resources.
  • Developing efficient and adaptive basis sets is essential for advancing computational chemistry.

Purpose of the Study:

  • To introduce an efficient method for constructing optimal and system-adaptive basis sets.
  • To reduce the number of variational parameters in many-body wave function calculations.
  • To enable controlled optimization of wave functions for large systems.

Main Methods:

  • An embedding scheme is used, isolating a reference atom from its environment.
  • The system is described by a Slater determinant or antisymmetrized geminal power (AGP) extension.
  • Primitive basis sets are contracted into geminal embedded orbitals (GEOs).
  • Variational Monte Carlo with a Jastrow factor is employed for energy minimization.

Main Results:

  • A dramatic reduction in variational parameters for a given accuracy was achieved.
  • The resulting GEO basis sets facilitate controlled optimization of many-body wave functions.
  • The method was applied to the water molecule, cerium volume collapse, and high-pressure liquid hydrogen.

Conclusions:

  • The developed method provides an efficient pathway for constructing accurate basis sets.
  • This approach is suitable for electronic structure calculations of bulk materials with many electrons and atoms.
  • The GEO basis sets offer a significant advancement in computational quantum chemistry.