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The skeletal structure of polymers synthesized via radical polymerization is always branched. For example, the polymerization of ethylene by radical polymerization results in a low-density grade of polyethylene with a heavily branched skeletal structure. Here, the radical site abstracts hydrogen from the growing chain, and the radical site shifts from the end (a primary carbon center) to anywhere within the growing chain (a secondary carbon center). Consequently, the part of the chain from the...
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At room temperature, the chair conformer of cyclohexane undergoes rapid ring flipping between two equivalent chair conformers at a rate of approximately 105 times per second. These two chair conformers are in equilibrium. The rapid ring flipping results in the interconversion of the axial proton to an equatorial proton and an equatorial to the axial proton. Such interconversions are too rapid and cannot be detected on the NMR timescale. Hence, the NMR spectrometer cannot distinguish between the...
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Ziegler–Natta polymerization is another form of addition or chain‐growth polymerization used for synthesizing linear polymers over branched polymers. The catalyst used for polymerization is the Ziegler–Natta catalyst, named after Karl Ziegler and Giulio Natta, who developed it in 1953. This catalyst is an organometallic complex of titanium tetrachloride and triethyl aluminum, with the active form of the catalyst being an alkyl titanium compound. Using the Ziegler–Natta...
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The radical chain-growth polymerization mechanism consists of three steps: initiation, propagation, and termination of polymerization. The polymerization initiates when a free radical generated from the radical initiator adds to the unsaturated bond in the monomer. The unpaired electron of the free radical and one π electron in the unsaturated bond creates a σ bond between the free radical and the monomer. As a result, the other π electron in the unsaturated bond converts this species into...
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New insights into the 1D carbon chain through the RPA.

Benjamin Ramberger1, Georg Kresse1

  • 1University of Vienna, Faculty of Physics and Center for Computational Materials Sciences, Kolingasse 14-16, 1090 Vienna, Austria. georg.kresse@univie.ac.at.

Physical Chemistry Chemical Physics : PCCP
|February 25, 2021
PubMed
Summary
This summary is machine-generated.

We studied carbyne properties using DFT and RPA. RPA accurately predicts carbyne

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Area of Science:

  • Computational materials science
  • Condensed matter physics
  • Quantum chemistry

Background:

  • Carbyne, an infinite linear carbon chain, exhibits unique electronic and structural properties.
  • Understanding carbyne's behavior is crucial for advanced materials development.
  • Previous studies have utilized various theoretical methods with differing results.

Purpose of the Study:

  • To investigate the electronic and structural properties of carbyne.
  • To compare the accuracy of Density Functional Theory (DFT) and the Random Phase Approximation (RPA) for carbyne.
  • To assess carbyne behavior both in vacuum and within a carbon nanotube (CNT).

Main Methods:

  • Density Functional Theory (DFT) calculations.
  • Random Phase Approximation (RPA) for correlation energy.
  • Simulations performed in vacuum and within a (10,0) carbon nanotube.

Main Results:

  • In vacuum, RPA predicts a larger bond length alternation (0.13 Å) and higher optical mode frequency (~2000 cm-1) than DFT.
  • RPA results show excellent agreement with high-level quantum chemistry and diffusion Monte Carlo methods.
  • Inside a CNT, RPA predicts a significant bond length alternation (0.09 Å) and a red shift in vibrational frequencies, aligning with experimental data, while DFT shows sensitivity to k-point sampling and predicts no alternation at high density.
  • RPA reveals marked quantitative differences in phonon dispersion compared to DFT across the Brillouin zone.

Conclusions:

  • The Random Phase Approximation (RPA) provides reliable and accurate results for carbyne properties at moderate computational cost.
  • RPA is a valuable addition to correlated wavefunction methods, particularly for low-dimensional systems where semi-local DFT methods struggle.
  • Accurate prediction of carbyne's structural and vibrational properties, especially within nanotubes, is achievable with RPA.