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A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
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The protons in unsubstituted alkanes are strongly shielded with chemical shifts below 1.8 ppm. Methine, methylene, and methyl protons appear at approximately 1.7, 1.2 and 0.7 ppm, while the proton signal from methane appears at 0.23 ppm. An electronegative substituent, such as chlorine, withdraws the electron density from the protons, increasing their chemical shift. Progressive substitution of the hydrogens in methane by chlorine shifts the proton signals increasingly downfield, to 3.05 ppm in...
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Vibration overtone hyperpolarizability measured for H2.

Rachel M Ellis1, David P Shelton1

  • 1Department of Physics and Astronomy, University of Nevada, Las Vegas, Nevada 89154-4002, USA.

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The second hyperpolarizability (γ) of hydrogen molecules was measured using electric field induced second harmonic generation. Experimental results for resonant vibrational contributions to γ were found to be higher than theoretical predictions.

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Area of Science:

  • Molecular Spectroscopy
  • Quantum Chemistry
  • Nonlinear Optics

Background:

  • The second hyperpolarizability (γ) is a crucial molecular property influencing nonlinear optical phenomena.
  • Accurate measurement of γ is essential for understanding molecular response to electric fields.
  • Previous studies have focused on non-resonant contributions, necessitating investigation into resonant effects.

Purpose of the Study:

  • To experimentally measure the second hyperpolarizability (γ) of the H₂ molecule.
  • To investigate the resonant vibrational contributions to γ at specific overtone transitions.
  • To compare experimental findings with theoretical predictions for γ.

Main Methods:

  • Gas-phase electric field induced second harmonic generation (EFISHG) technique.
  • Measurements performed at the one-photon resonance frequencies of H₂ 3-0 Q(J) overtone transitions (v, J = 0, J → 3, J for J = 0, 1, 2, and 3).
  • Calibration using previously determined non-resonant γ values; measurement of pressure broadening and frequency shift.

Main Results:

  • The resonant contribution to the second hyperpolarizability (γ) of H₂ was measured with 2% accuracy.
  • Measured γ resonance strength exceeded theoretical predictions by 4%-14%.
  • Pressure broadening and frequency shift data for the overtone transitions were obtained.

Conclusions:

  • Experimental measurements provide valuable data for validating theoretical models of molecular hyperpolarizability.
  • Discrepancies between experimental and theoretical γ values highlight the need for refined theoretical approaches.
  • This study advances the understanding of resonant vibrational contributions to molecular nonlinear optical properties.