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Related Concept Videos

Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
Valence Bond Theory02:42

Valence Bond Theory

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...
Valence Bond Theory02:45

Valence Bond Theory

Overview of Valence Bond Theory
Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Valence Bond Theory and Hybridized Orbitals02:38

Valence Bond Theory and Hybridized Orbitals

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.
A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is...
MO Theory and Covalent Bonding02:40

MO Theory and Covalent Bonding

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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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Density functional theory embedding for correlated wavefunctions: improved methods for open-shell systems and

Jason D Goodpaster1, Taylor A Barnes, Frederick R Manby

  • 1Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.

The Journal of Chemical Physics
|December 20, 2012
PubMed
Summary

Wave-function theory-in-density-functional theory (WFT-in-DFT) embedding methods were enhanced for open-shell systems. New techniques improve accuracy for van-der-Waals dimers and transition-metal cations, reducing computational errors.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Electronic Structure Theory

Background:

  • Density functional theory (DFT) embedding offers an exact framework for combining wave-function theory (WFT) with lower-level electronic structure methods.
  • Accurate and stable WFT-in-DFT calculations are crucial for complex molecular systems.
  • Existing methods face challenges with open-shell systems and convergence in embedding potential calculations.

Purpose of the Study:

  • To develop improved techniques for WFT-in-DFT embedding calculations.
  • To enhance accuracy and stability, particularly for open-shell systems.
  • To enable reliable calculations for systems with van-der-Waals interactions and transition-metal cations.

Main Methods:

  • Development of spin-dependent embedding potentials in restricted and unrestricted orbital formulations.
  • Implementation of an orbital-occupation-freezing technique to improve convergence of optimized effective potential calculations.
  • Application of WFT-in-DFT embedding to the ethylene-propylene dimer and hexa-aquairon(II) cation.

Main Results:

  • WFT-in-DFT embedding accurately reproduced full CCSD(T) energies for the ethylene-propylene dimer, eliminating dispersion and partitioning errors.
  • Calculations on hexa-aquairon(II) showed reduced dependence on DFT exchange-correlation (XC) functionals when treating the metal atom at the WFT level.
  • Restricted open-shell WFT-in-DFT embedding demonstrated higher accuracy than unrestricted methods due to reduced spin contamination.

Conclusions:

  • The developed WFT-in-DFT embedding techniques significantly improve accuracy and stability for open-shell systems.
  • These advancements enable precise calculations of dispersion interactions and electronic properties in challenging molecular systems.
  • The study highlights the importance of spin-dependent potentials and restricted open-shell formulations for reliable WFT-in-DFT embedding.