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Hybridization of Atomic Orbitals I03:24

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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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When two or more atoms come together to form a molecule, their atomic orbitals combine and molecular orbitals of distinct energies result. In a solid, there are a large number of atoms, and therefore a large number of atomic orbitals that may be combined into molecular orbitals. These groups of molecular orbitals are so closely placed together to form continuous regions of energies, known as the bands.
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Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
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The range is one of the measures of variation. It can be defined as the difference between a dataset's highest and lowest values. For example, in the study of seven 16-ounce soda cans, the filled volume of soda was measured, thus producing the following amount (in ounces) of soda:
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A general range-separated double-hybrid density-functional theory.

Cairedine Kalai1, Julien Toulouse1

  • 1Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France.

The Journal of Chemical Physics
|May 3, 2018
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Summary
This summary is machine-generated.

A new range-separated double-hybrid (RSDH) scheme offers accurate chemical predictions. This method combines Hartree-Fock exchange and MP2 correlation with density functionals, showing promise for general chemical applications.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry

Background:

  • Existing hybrid and double-hybrid schemes have limitations.
  • Range separation is a key concept in electronic structure theory.

Purpose of the Study:

  • Develop a generalized range-separated double-hybrid (RSDH) scheme.
  • Improve accuracy for chemical properties using a novel computational approach.

Main Methods:

  • Developed a two-parameter Coulomb-attenuating-method (CAM)-like decomposition.
  • Combined Hartree-Fock exchange with second-order Møller-Plesset (MP2) correlation.
  • Incorporated density functionals and developed semi-local approximations.

Main Results:

  • The RSDH scheme demonstrated minimal basis dependence.
  • Achieved high accuracy for atomization energies and reaction barrier heights.
  • Showed comparable or superior performance to existing MP2 methods for weak interactions.

Conclusions:

  • The RSDH scheme represents a new, minimally empiric family of double hybrids.
  • This method offers a promising tool for broad applications in computational chemistry.
  • RSDH provides accurate predictions for diverse chemical properties.