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Crystal Field Theory - Octahedral Complexes02:58

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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...
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For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar.
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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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Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

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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,...
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Ladder Diagrams: Complexation Equilibria01:07

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Ladder diagrams are useful for evaluating equilibria involving metal-ligand complexes. The vertical scale of the ladder diagram represents the concentration of unreacted or free ligand, pL. The horizontal lines on the scale depict the log of stepwise formation constants for metal-ligand complexes and indicate the dominant species in all the regions.
The formation constant, K1, for the formation of Cd(NH3)2+ complex from cadmium and ammonia is 3.55 × 102. Log K1 (i.e. pNH3) is 2.55, and...
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Metal-Ligand Bonds

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The hemoglobin in the blood, the chlorophyll in green plants, vitamin B-12, and the catalyst used in the manufacture of polyethylene all contain coordination compounds. Ions of the metals, especially the transition metals, are likely to form complexes.
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Exploring the Accuracy Limits of PNO-Based Local Coupled-Cluster Calculations for Transition-Metal Complexes.

Ahmet Altun1, Christoph Riplinger2, Frank Neese1

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This study enhances the domain-based local pair natural orbital coupled-cluster method with singles, doubles, and perturbative triples (DLPNO-CCSD(T)) for accurate calculations on first-row transition metals. It addresses semicore orbital correlation and dynamic correlation-induced orbital relaxation errors.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Method Development

Background:

  • The domain-based local pair natural orbital coupled-cluster method with singles, doubles, and perturbative triples (DLPNO-CCSD(T)) is crucial for accurate calculations of large systems.
  • However, its application to first-row transition metals with complex electronic structures presents challenges.
  • Key error sources include semicore orbital correlation and dynamic correlation-induced orbital relaxation effects.

Purpose of the Study:

  • To identify and mitigate the primary error sources affecting DLPNO-CCSD(T) accuracy for first-row transition metals.
  • To develop a computational strategy for eliminating semicore correlation errors and improving method efficiency.
  • To introduce a diagnostic for assessing deviations from canonical CCSD(T) due to orbital relaxation.

Main Methods:

  • Development of a computational strategy to eliminate errors from 3s and 3p semicore orbital correlation.
  • Implementation of a diagnostic tool to estimate dynamic correlation-induced orbital relaxation (DCIOR) effects.
  • Refinement of the local MP2 guess to better describe orbital relaxation.

Main Results:

  • A novel computational strategy successfully eliminates DLPNO errors associated with semicore correlation effects.
  • The efficiency of the DLPNO-CCSD(T) method is enhanced.
  • A diagnostic is introduced to quantify DCIOR effects, enabling estimation of deviations from canonical CCSD(T).

Conclusions:

  • The developed strategy significantly improves the accuracy and efficiency of DLPNO-CCSD(T) for first-row transition metals.
  • The new diagnostic provides valuable insights into the reliability of DLPNO-CCSD(T) for systems with significant orbital relaxation.
  • This work advances the applicability of high-level coupled-cluster methods to challenging chemical systems.