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Related Concept Videos

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,...
Electronic Structure of Atoms02:28

Electronic Structure of Atoms


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 numbers:  n, l, ml, and...
VSEPR Theory02:37

VSEPR Theory

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...
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...
Predicting Molecular Geometry02:27

Predicting Molecular Geometry

VSEPR Theory for Determination of Electron Pair Geometries
VSEPR Theory and the Effect of Lone Pairs04:01

VSEPR Theory and the Effect of Lone Pairs

Effect of Lone Pairs of Electrons on Molecule Geometry

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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Published on: May 27, 2020

A tractable and accurate electronic structure method for static correlations: the perfect hextuples model.

John A Parkhill1, Martin Head-Gordon

  • 1Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA. john.parkhill@gmail.com

The Journal of Chemical Physics
|July 17, 2010
PubMed
Summary

The new perfect hextuples (PH) model offers a computationally efficient approximation for complex molecular systems. This method accurately captures static correlations in molecules, improving upon previous models for electronic structure calculations.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Electronic Structure Theory

Background:

  • The valence orbital-optimized coupled-cluster (VOO-CC) formalism provides a hierarchy of approximations for accurate electronic structure calculations.
  • Existing models like perfect pairing (PP) and perfect quadruples (PQ) capture correlations for one and two electron pairs, respectively.

Purpose of the Study:

  • To introduce the perfect hextuples (PH) model as the next stage in local approximations for CASSCF.
  • To develop a computationally tractable method for correlating three electron pairs within the VOO-CC framework.

Main Methods:

  • The PH model is an approximation to VOO-CC, specifically truncating at hextuples to include correlations among three electron pairs.
  • Implementation includes techniques to reduce computational scaling from the 14th power (VOO-CCDTQ56) to the 6th power, with further reduction to 5th order.
  • The method was applied to active spaces twice the size of CASSCF limits without symmetry constraints.

Main Results:

  • The PH model demonstrates significantly reduced computational cost compared to higher-order VOO-CC methods.
  • It accurately models static correlations in molecules with up to triple bonds in a size-consistent manner.
  • For organic reactions, PH results generally achieve chemical accuracy comparable to CASSCF.

Conclusions:

  • The PH model represents a significant advancement in the PP, PQ, PH hierarchy for electronic structure calculations.
  • It enables the study of larger active spaces and complex chemical phenomena like symmetry breaking and various reaction mechanisms.
  • The method's efficiency and accuracy make it a valuable tool for computational chemistry research.