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List of Figures

  1. Excited condensed state electrons drive essential chemistry.
  2. Electron force field makes feasible simulations of large scale excited electron dynamics.
  3. (a) Excited condensed system evolves through many curve crossings, and can be approximately described by a mean field trajectory. (b) However, the mean field trajectory may incorrectly bisect well-separated adiabatic states.
  4. Summary of electron force field development.
  5. Character of electron depends on its proximity to nuclei.
  6. Gaussian and exact wave packet dynamics match for free particle and harmonic oscillator potentials.
  7. Exact and Gaussian wave packet dynamics for a double well potential.
  8. In sparse systems, electrons move mostly along adiabatic paths, with crossings limited to conical intersections with reduced dimensionality.
  9. $ \mathrm {H_{2}}$ potential energy surface (kcal/mol); eFF properly dissociates $ H_{2}$, but the simplicity of the basis leads to underbinding.
  10. Pauli repulsion comes from the kinetic energy increase upon making orbitals orthogonal to each other.
  11. Comparison of Pauli repulsion and electrostatic repulsion between two wavefunctions with $ s=1$.
  12. eFF geometries of simple substituted hydrocarbons
  13. eFF geometries of larger hydrocarbons, bond lengths in Angstroms
  14. Multiple bonds can split $ \sigma -\pi $ or form symmetric ``banana'' pairs.
  15. eFF reproduces curved bonds of cyclopropane, and pucker of five and six membered rings.
  16. eFF reproduces steric repulsions within alkanes
  17. eFF reproduces allylic strain interaction
  18. In eFF, methyl cation and radical are stable but methyl anion is unbound
  19. Protonation of helium and ammonia
  20. Carbocations can rearrange via hydride or methyl shifts.
  21. eFF distinguishes between allowed and forbidden hydrogen reactions.
  22. eFF can account for ionic and multicenter bonding.
  23. Previously proposed plasma phase transition [42,43] where hydrogen dissociates and ionizes simultaneously
  24. Dynamics snapshots showing deuterium dissociation as temperature is raised.
  25. Proton-proton pair distribution function shows gradual dissociation.
  26. Equation of state ($ r_{s}$ = 2 bohr) shows good agreement with best available theory.
  27. High densities suppress ionization that occurs at high temperature.
  28. Reproduction of the experimental shock Hugoniot curve obtained by gas gun and Z machine; Nova laser remains an outlier.
  29. Core holes relax via a two stage Auger decay process.
  30. Red points compare Boys localized Hartree-Fock orbital energies to eFF orbital energies.
  31. Removal of valence electrons from ethane results in selective bond breaking.
  32. Electron energies show Auger process in adamantane in detail.
  33. Auger dissociation of methane and ethane following creation of a core hole.
  34. Auger dissociation of neopentane and adamantane following creation of a core hole.
  35. We remove a core electron from a central carbon of a diamondoid particle.
  36. Trajectories of electrons after removal of a core electron.
  37. Excited electrons dissipate their energy into their surroundings.
  38. Pauli interaction between $ p$-like versus $ s$-like electrons.
  39. Pauli repulsion between $ s$-like electrons is modified to make electron sizes more similar and prevent electron-electron coalescence.
  40. Valence electrons of boron through neon arrange themselves into symmetric shells.
  41. The new eFF reproduces the correct periodic trend of ionization potentials for hydrogen through neon, while the old eFF is only suitable for describing hydrogen through carbon.
  42. The new eFF computes reasonable polarizabilities for first-row atoms. Oxygen and fluorine are exceptional cases, as the eFF gives those two atoms a permanent dipole moment which they should not have.
  43. eFF describes both open-shell and closed-shell atom hydrides properly.
  44. Atom hydride bond lengths and angles.
  45. Atom hydride bond dissociation energies.
  46. Measuring electron-nuclear distances and the angle between lone pairs.
  47. Comparison of eFF electron positions versus B3LYP localized orbital positions. There is good agreement, except that eFF lone pairs are further away from the nucleus than B3LYP lone pairs.
  48. Electron densities along lone pairs and bond pairs; a comparison between eFF electron densities and B3LYP localized orbital electron densities.
  49. Electron arrangements in carbon-carbon single, double, and triple bonds.
  50. Bond dissociation energies and geometry parameters of ethane, ethylene, and acetylene.
  51. Improved geometries for old eFF ``problem hydrocarbons''.
  52. Key geometric parameters of substituted alkanes and alkenes.
  53. Comparison of old versus new eFF geometric parameters for simple substituted alkanes and alkenes.
  54. Optimized eFF and B3LYP alkenes superimposed, with root-mean-squared deviations (RMSD) given in parenthesis (angstroms).
  55. eFF overestimates the energy gained from turning double bounds into single bonds; prototype $ [2+2]$ and $ [4+2]$ cycloadditions are shown, eFF (B3LYP) energy differences in kcal/mol.
  56. eFF alkynes are unstable relative to alkene diradicals. eFF (B3LYP) distances in angstroms.
  57. eFF shows no resonance stabilization of conjugated double bonds.
  58. Gallery of heteroatom single, double, and triple bonds.
  59. Bonds between heteroatoms are too strong and too short, possibly due to insufficient repulsion between lone pairs.
  60. Repulsion between neon atoms in eFF is too small.
  61. Hydrogen bonds in eFF are too strong and too short, probably from a combination of too-small Pauli repulsion and too-large monomer dipoles.
  62. Interaction energy of the water dimer, with the estimated effects of changing monomer dipole moments and Pauli repulsions to be the correct values.
  63. The new eFF creates spurious stable minima corresponding to unphysical arrangements of hydrogen atoms.
  64. Icosahedral boron cluster $ B_{12}$ is stable with the new eFF, and matches a B3LYP optimized geometry well; however an amorphous boron-centered structure is found to be even more stable.
  65. Uniform electron gas represented as different packings of localized electrons.
  66. Uniform electron gas energy versus density. eFF with exchange matches Hartree-Fock, while eFF with exchange and correlation matches exact quantum Monte Carlo energies.
  67. Density versus electron size. Adding correlation causes the electrons to grow larger.
  68. Survey of electron packings considered, showing a variety of packing fractions and coordinations.
  69. Energetics of different electron packings, with non-close-packed configurations marked red, and close-packed configurations marked black. All close-packed arrangements have similar energies which are near the exact values.
  70. Spin-averaged electron-electron pair distribution function, showing partial explicit segregation of electrons in eFF.
  71. Spin-resolved electron-electron pair distribution functions, showing that eFF keeps same-spin electrons apart, but allows opposite-spin electrons to mingle.
  72. Electron trajectories in a uniform electron gas ($ r_{s}$ = 2 bohr) at low and high temperature.
  73. At low temperatures, the heat capacity of a metal goes to zero because only electrons near the Fermi level are excited.
  74. eFF uniform electron gas has the heat capacity of a solid crystal, not a metal with Fermi-Dirac statistics. The heat capacity in this figure is given by the slope, since we are plotting total energy versus temperature.
  75. Plasma oscillations are excited uniformly over the range of temperatures considered.
  76. We modify the exchange interaction to fit properly the interaction energy of $ \mathrm {He_{2}}$ and HeH.
  77. Comparison of the new exchange potential to previous Pauli potentials, showing that the new potential has a reasonable amount of repulsion.
  78. We scale the correlation function to match the long range falloff of the GVB correlation energy in $ \mathrm {H_{2}}$.
  79. Comparison of $ \mathrm {H_{2}}$ potential energy curves; we limit the correlation function to correcting correlation, not deficiencies in the basis.
  80. Gallery of systems with nuclei and s-like electrons.
  81. eFF with exchange shows good agreement with Hartree-Fock for bond lengths and dissociation energies of s-electron systems.
  82. eFF reproduces some energy and bond length changes caused by adding correlation.
  83. Atomic correlation energies, eFF reproduces major trends.


Julius 2008-04-29