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Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
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Characterization of Surface Modifications by White Light Interferometry: Applications in Ion Sputtering, Laser Ablation, and Tribology Experiments
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Communication: an existence test for dividing surfaces without recrossing.

Ryan Gotchy Mullen1, Joan-Emma Shea2, Baron Peters1

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|February 12, 2015
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The Grote-Hynes theory (GHT) and multidimensional variational transition state theory (VTST) equivalence is tested. A new trajectory-based method identifies when GHT and VTST are not equivalent, showing no perfect dividing surface exists.

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Area of Science:

  • Chemical kinetics
  • Theoretical chemistry
  • Statistical mechanics

Background:

  • The equivalence between Grote-Hynes theory (GHT) and multidimensional variational transition state theory (VTST) is a long-standing debate in chemical dynamics.
  • Both theories aim to accurately predict reaction rates but rely on different theoretical underpinnings regarding the nature of the dividing surface.

Purpose of the Study:

  • To develop and implement a practical test to determine the conditions under which GHT and VTST are equivalent.
  • To investigate the existence of a perfect dividing surface, a prerequisite for GHT-VTST equivalence.
  • To provide data-supported conclusions on the relationship between GHT and VTST.

Main Methods:

  • Employing deterministic microcanonical (NVE) trajectories to simulate reaction dynamics.
  • Analyzing trajectory behavior to identify instances of surface recrossing.
  • Implementing a test to detect the absence of a perfect dividing surface.

Main Results:

  • The developed test successfully identifies scenarios where a perfect dividing surface does not exist.
  • Data obtained from the test provides evidence regarding the limitations of GHT-VTST equivalence.
  • The study offers concrete examples where the two theories diverge.

Conclusions:

  • The claim of GHT equivalence to VTST is not universally valid.
  • The existence of a perfect dividing surface is critical for GHT-VTST equivalence.
  • The implemented trajectory-based test is a valuable tool for assessing the relationship between GHT and VTST in specific chemical systems.