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Related Concept Videos

Resonance and Hybrid Structures02:16

Resonance and Hybrid Structures

According to the theory of resonance, if two or more Lewis structures with the same arrangement of atoms can be written for a molecule, ion, or radical, the actual distribution of electrons is an average of that shown by the various Lewis structures.
Resonance Structures and Resonance Hybrids
The Lewis structure of a nitrite anion (NO2−) may actually be drawn in two different ways, distinguished by the locations of the N–O and N=O bonds.
Atomic Orbitals02:44

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
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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...
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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...

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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Density functional resonance theory: complex density functions, convergence, orbital energies, and functionals.

Daniel L Whitenack1, Adam Wasserman

  • 1Department of Physics, Purdue University, 525 Northwestern Avenue, West Lafayette, Indiana 47907, USA. dwhitena@purdue.edu

The Journal of Chemical Physics
|May 8, 2012
PubMed
Summary

Density functional resonance theory (DFRT), a complex-scaled DFT method, reveals insights into electron decay and resonance energies. Careful implementation minimizes parameter dependence for accurate predictions of molecular properties.

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Area of Science:

  • Quantum Chemistry
  • Theoretical Chemistry
  • Computational Physics

Background:

  • Density Functional Theory (DFT) is a powerful quantum mechanical modeling method.
  • Complex scaling is a technique used to study resonances in quantum systems.
  • Density Functional Resonance Theory (DFRT) extends DFT to describe decaying states.

Purpose of the Study:

  • To thoroughly investigate the theoretical and practical aspects of Density Functional Resonance Theory (DFRT).
  • To establish connections between the complex density function and key physical quantities like resonance and threshold energies.
  • To explore the relationship between Kohn-Sham DFRT and ground-state DFT.

Main Methods:

  • Analysis of the asymptotic and local oscillatory behavior of the complex density function.
  • Investigation of the sensitivity of DFRT calculations to the complex-scaling parameter, θ.
  • Application of Kohn-Sham DFRT with optimized basis sets or grids to minimize θ-dependence.
  • Derivation of complex-scaling conditions relating ground-state DFT and DFRT functionals.

Main Results:

  • The asymptotic behavior of the complex density function correlates with complex resonance and threshold energies.
  • Local oscillations in the complex density indicate preferential electron decay directions.
  • θ-dependence in Kohn-Sham DFRT energies and lifetimes can be effectively removed.
  • The highest occupied Kohn-Sham orbital energy and lifetime in DFRT correspond to physical affinity and width.
  • Kohn-Sham system threshold energy is linked to the interacting system's threshold energy via a functional shift.

Conclusions:

  • DFRT provides a robust framework for studying electron decay phenomena and resonance states.
  • Proper implementation, including basis set selection, is crucial for reliable DFRT calculations.
  • DFRT offers a theoretical bridge between ground-state DFT and the description of unstable electronic states.