Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On the breakdown of the Born-Oppenheimer approximation in LiH and LiD

Ville J. Härkönen

Abstract

We compute the ab-initio electron density beyond the strict Born-Oppenheimer approximation in crystalline LiH and LiD with density functional methods. By taking into account the quantum mechanical nature of the nuclei, an aspect absent in the strict Born-Oppenheimer approximation, we find significant corrections to electron density in the vicinity of nuclei equilibrium positions. We compare our results with earlier experimental findings that have suggested a breakdown of the Born-Oppenheimer approximation in these solids and obtain improved agreement between experiment and theory when quantum nuclear effects are included. A notable temperature dependence of electron density is found. The results indicate the existence of beyond strict Born-Oppenheimer effects in solids at normal pressures and suggest that such effects can be significant also in materials containing light elements other than hydrogen.

On the breakdown of the Born-Oppenheimer approximation in LiH and LiD

Abstract

We compute the ab-initio electron density beyond the strict Born-Oppenheimer approximation in crystalline LiH and LiD with density functional methods. By taking into account the quantum mechanical nature of the nuclei, an aspect absent in the strict Born-Oppenheimer approximation, we find significant corrections to electron density in the vicinity of nuclei equilibrium positions. We compare our results with earlier experimental findings that have suggested a breakdown of the Born-Oppenheimer approximation in these solids and obtain improved agreement between experiment and theory when quantum nuclear effects are included. A notable temperature dependence of electron density is found. The results indicate the existence of beyond strict Born-Oppenheimer effects in solids at normal pressures and suggest that such effects can be significant also in materials containing light elements other than hydrogen.
Paper Structure (14 sections, 19 equations, 3 figures, 2 tables)

This paper contains 14 sections, 19 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Theory
  3. Background
  4. Harmonic Approximation to Density
  5. Gaussian Approach to Density
  6. Calculational details
  7. Results
  8. Electron density
  9. Comparison with experimental radial densities
  10. Comparison with experimental structure factors
  11. Discussion and conclusions
  12. Data availability statement
  13. Acknowledgments
  14. Structure Factors

Figures (3)

  • Figure 1: Phonon dispersions for LiH and LiD and pseudo electron densities in 100-plane of the conventional unit cell (110-plane of the primitive cell) and in selected lines along the 100-plane. The electron densities are normalized to the number of electrons per unit cell. (a) The conventional unit cell with the 100-plane indicated with a green plane in the lower left corner (b) phonon dispersions for LiH and LiD (c) the difference of beyond strict BO and strict BO densities relative to $n_{\mathbf{x}}\left(\mathbf{y}\right)$ in percentage at 0 K, (d) electron densities along the line between lithium and hydrogen nuclei (pointed out in c), (e) between lithium nuclei and (f) between hydrogen nuclei. In (d), $\left\langle n_{d}\right\rangle$ denotes the diagonal contribution to $\left\langle n\right\rangle$ discussed in the text. We have left out the lines for LiD in (d) and (e) since in the vicinity of lithium nuclei the results are essentially identical.
  • Figure 2: Radial all electron densities by using Gaussian approach, nuclear densities, mean square displacements and electron density temperature dependence. (a) The nuclear one-body densities for hydrogen in LiH and the electron densities for hydrogen in LiH, the hydrogen atom, and the model of Eq. \ref{['eq:ElectronDensity_Eq_3']}. (b) The nuclear one-body densities for lithium in LiH and the electron densities for lithium in LiH and for the isolated lithium atom, solved numerically with the same DFT approach as in the crystalline case. For better visual, the inset shows the same curves near the nuclei equilibrium position. The axis for nuclear densities on the right. (c) The temperature dependence of electron densities at the nuclear equilibrium positions and mean square displacements in the inset, where the curve colors for elements matches those in the main plot.
  • Figure 3: Spherically averaged radial all electron densities in LiH. (a) For Li nucleus (b) for H and D nucleus. The experimental data at 293 K is from Ref. Vidal-EvidenceOnTheBreakdownOfTheBornOppenheimerApproximationInTheChargeDensityOfCrystalline7LiHD-1992.