Accurate and general solutions to three-dimensional anisotropies: Applications to EPR spectra of triplets involving dipole-dipole, spin-orbit interactions and liquid crystals

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Abstract

Thanks to the squared Cartesian coordinates and its corresponding ternary diagram, several types of anisotropic physical quantities are expressed by a weighted mean of their principal values. Specifically, in terms of the electron paramagnetic resonance (EPR) spectra of triplet states under various conditions, the anisotropies in the resonance field (due to spin dipole-dipole interaction), in the spin polarization (due to spin-orbit intersystem crossing, SO-ISC), and in the distribution of molecular orientations (due to liquid crystal alignment) are all linearized. The spectral intensity becomes a path integral on the ternary diagram along the field isolines. These major simplifications afford, for the first time, analytical line shape formulas of arbitrarily polarized triplets as sums of elliptical integrals. Even with approximations applied, the analytical results agree almost perfectly with both simulated and experimental spectra and accurately capture the higher-order spectral effects such as peak shifts and net spin polarization. This Universal scheme is also promising for other spectroscopic techniques in which anisotropy plays a significant role.

Original languageEnglish
Pages (from-to)13853-13860
Number of pages8
JournalJournal of Physical Chemistry C
Volume114
Issue number32
DOIs
Publication statusPublished - Aug 19 2010

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Liquid Crystals
Spin polarization
spin-orbit interactions
Liquid crystals
Paramagnetic resonance
electron paramagnetic resonance
Orbits
Anisotropy
liquid crystals
dipoles
anisotropy
Molecular orientation
crystals
diagrams
Cartesian coordinates
polarization
simplification
atomic energy levels
line shape
alignment

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry
  • Electronic, Optical and Magnetic Materials
  • Surfaces, Coatings and Films
  • Energy(all)

Cite this

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title = "Accurate and general solutions to three-dimensional anisotropies: Applications to EPR spectra of triplets involving dipole-dipole, spin-orbit interactions and liquid crystals",
abstract = "Thanks to the squared Cartesian coordinates and its corresponding ternary diagram, several types of anisotropic physical quantities are expressed by a weighted mean of their principal values. Specifically, in terms of the electron paramagnetic resonance (EPR) spectra of triplet states under various conditions, the anisotropies in the resonance field (due to spin dipole-dipole interaction), in the spin polarization (due to spin-orbit intersystem crossing, SO-ISC), and in the distribution of molecular orientations (due to liquid crystal alignment) are all linearized. The spectral intensity becomes a path integral on the ternary diagram along the field isolines. These major simplifications afford, for the first time, analytical line shape formulas of arbitrarily polarized triplets as sums of elliptical integrals. Even with approximations applied, the analytical results agree almost perfectly with both simulated and experimental spectra and accurately capture the higher-order spectral effects such as peak shifts and net spin polarization. This Universal scheme is also promising for other spectroscopic techniques in which anisotropy plays a significant role.",
author = "Qixi Mi and Ratner, {Mark A} and Wasielewski, {Michael R}",
year = "2010",
month = "8",
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doi = "10.1021/jp103678m",
language = "English",
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journal = "Journal of Physical Chemistry C",
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publisher = "American Chemical Society",
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TY - JOUR

T1 - Accurate and general solutions to three-dimensional anisotropies

T2 - Applications to EPR spectra of triplets involving dipole-dipole, spin-orbit interactions and liquid crystals

AU - Mi, Qixi

AU - Ratner, Mark A

AU - Wasielewski, Michael R

PY - 2010/8/19

Y1 - 2010/8/19

N2 - Thanks to the squared Cartesian coordinates and its corresponding ternary diagram, several types of anisotropic physical quantities are expressed by a weighted mean of their principal values. Specifically, in terms of the electron paramagnetic resonance (EPR) spectra of triplet states under various conditions, the anisotropies in the resonance field (due to spin dipole-dipole interaction), in the spin polarization (due to spin-orbit intersystem crossing, SO-ISC), and in the distribution of molecular orientations (due to liquid crystal alignment) are all linearized. The spectral intensity becomes a path integral on the ternary diagram along the field isolines. These major simplifications afford, for the first time, analytical line shape formulas of arbitrarily polarized triplets as sums of elliptical integrals. Even with approximations applied, the analytical results agree almost perfectly with both simulated and experimental spectra and accurately capture the higher-order spectral effects such as peak shifts and net spin polarization. This Universal scheme is also promising for other spectroscopic techniques in which anisotropy plays a significant role.

AB - Thanks to the squared Cartesian coordinates and its corresponding ternary diagram, several types of anisotropic physical quantities are expressed by a weighted mean of their principal values. Specifically, in terms of the electron paramagnetic resonance (EPR) spectra of triplet states under various conditions, the anisotropies in the resonance field (due to spin dipole-dipole interaction), in the spin polarization (due to spin-orbit intersystem crossing, SO-ISC), and in the distribution of molecular orientations (due to liquid crystal alignment) are all linearized. The spectral intensity becomes a path integral on the ternary diagram along the field isolines. These major simplifications afford, for the first time, analytical line shape formulas of arbitrarily polarized triplets as sums of elliptical integrals. Even with approximations applied, the analytical results agree almost perfectly with both simulated and experimental spectra and accurately capture the higher-order spectral effects such as peak shifts and net spin polarization. This Universal scheme is also promising for other spectroscopic techniques in which anisotropy plays a significant role.

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