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Journal of Chemical Physics / Volume 135 / Issue 24 / ARTICLES / Theoretical Methods and Algorithms

J. Chem. Phys. 135, 244110 (2011); http://dx.doi.org/10.1063/1.3671386 (11 pages)

Quantum entanglement between electronic and vibrational degrees of freedom in molecules

Laura K. McKemmish1, Ross H. McKenzie2, Noel S. Hush3, and Jeffrey R. Reimers1

1School of Chemistry, The University of Sydney, NSW 2006, Australia
2School of Mathematics and Physics, The University of Queensland, QLD 4072, Australia
3School of Molecular Biosciences and School of Chemistry, The University of Sydney, NSW 2006, Australia

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(Received 6 July 2011; accepted 1 December 2011; published online 30 December 2011)

We consider the quantum entanglement of the electronic and vibrational degrees of freedom in molecules with tendencies towards double welled potentials. In these bipartite systems, the von Neumann entropy of the reduced density matrix is used to quantify the electron-vibration entanglement for the lowest two vibronic wavefunctions obtained from a model Hamiltonian based on coupled harmonic diabatic potential-energy surfaces. Significant entanglement is found only in the region in which the ground vibronic state contains a density profile that is bimodal (i.e., contains two separate local maxima). However, in this region two distinct types of density and entanglement profiles are found: one type arises purely from the degeneracy of energy levels in the two potential wells and is destroyed by slight asymmetry, while the other arises through strong interactions between the diabatic levels of each well and is relatively insensitive to asymmetry. These two distinct types are termed fragile degeneracy-induced entanglement and persistent entanglement, respectively. Six classic molecular systems describable by two diabatic states are considered: ammonia, benzene, BNB, pyridine excited triplet states, the Creutz-Taube ion, and the radical cation of the “special pair” of chlorophylls involved in photosynthesis. These chemically diverse systems are all treated using the same general formalism and the nature of the entanglement that they embody is elucidated.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. MODEL HAMILTONIAN AND ITS PARAMETERS
  3. NUMERICAL DETERMINATION OF THE HAMILTONIAN EIGENFUNCTIONS
  4. ENTANGLEMENT AS THE VON NEUMANN ENTROPY
  5. FRAGILE VS. PERSISTENT ENTANGLEMENT
  6. RELATION TO THE BOHM-AHARONOV TEST OF THE EINSTEIN-PODOLSKY-ROSEN PARADOX
  7. APPLICATIONS TO SOME MODEL MOLECULAR SYSTEMS
  8. CONCLUSIONS

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KEYWORDS and PACS

Keywords

entropy, organic compounds, potential energy surfaces, quantum entanglement, vibrational states, vibronic states

PACS

  • 33.20.Tp

    Vibrational analysis

  • 33.20.Wr

    Vibronic, rovibronic, and rotation-electron-spin interactions

  • 31.50.-x

    Potential energy surfaces

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3671386

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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