Calculations of Vibronic states in solid and liquid hydrogen

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Calculations of Vibronic states in solid and
liquid hydrogen

• Application of van Kranendonk theory

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Outline

• Introduction (motivation of high pressure
  studies)
• Experimental results for excitations
• Van Kranendonk theory of excitations
• TB vibronic Hamiltonian
• Effect of intermolecular distance riations
• Effect of temperature
• Path integral method
• Numerical results

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Some research highlights on solid hydrogen

• Wigner-Huntington 1935 suggestion of possibility
  of achieving a monatomic Bravais crystal
  (metallic) of solid hydrogen (Pgt250 kbars25GPa,
  T0K)
• Neil Ashcroft 1968 prediction of high
  superconducting transition temperature of
  hydrogen in metallic state
• Lack of ability (to present) to achieve metallic
  hydrogen from static high pressure experiments up
  to 300 GPa.
• Discovery in 1996 of conducting state in shock
  compressed hydrogen high pressure and high
  temperature (Weir, Mitchell and Nellis)
• Theory of excitations and vibron Raman scattering
  by van Kranendonk and collaborators beginning in
  1958

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Electronic energy bands
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1935 paper by Wigner and Huntington
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Melting curve of hydrogen
From Bonev, Schwegler, Ogitsu and Galli, A
quantum fluid of metallic hydrogen suggested by
first principles calculations, letters to nature
(2004)
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Theories for vibrational-rotational excitations

• Dunham model of isolated molecule
• van Kranendonk theory of solid state
• Hamiltonian
• Wave function
• Raman intensity

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Experiments done for excitations

• Pure rotational
• Pure vibronic
• Phonon and elastic wave
• Mixtures (phonon vibron, etc.)
• Roton
• So-called overtones
• Experimental probes are
• Raman scattering
• Inelastic neutron scattering
• Infrared absorption
• Brillouin scattering

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Experimental Results from Hemleys group,
Geophysical Lab, Carnegie Institution of
Washington
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Overview of vibron-Raman P-T results
Gregoryanz, Goncharov, Mao and Hemley, PRL 2003
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One Vibron State
Note Each molecular function can be for a
different rotational state but for a 0-vibron
state except for one molecule
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Hamiltonian

• Tight binding formalism
• Phonon-vibron coupling terms included in
  renormalization of TB Hamiltonian parameters

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Low T results for vibrons
Experiments Eggert,Hemley,Mao De Kinder,Shoemaker
20 ortho T6K
50 ortho T77K
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Depiction of a vibronic state
Filledortho (L1), W4000 1/cm Unfilled para
(L0), W4006 1/cm
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Effect of intermolecular interactions

• The hopping term is known to vary with
  interatomic distance roughly as the van der Waals
  behavior 1/r6.
• Convolute 1/r6 (or 1/r6.8) with pair correlation
  function, g(r). Assume g(r) is zero for r less
  than some cut-off value and then Gaussian about
  equilibrium value of r breadth is calculated as
  function of temperature.
• Previously only zero-point renormalizations were
  discussed for the hopping term.