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Subsections

Generating extended systems

Hydrogen box

This routine places hydrogen atoms on a rectangular lattice, with alternating layers shifted in such a way that they form hydrogen molecules upon minimization. Section 2.5 has an example of this script being used to generate starting structures for calculating thermodynamic properties of warm dense hydrogen.

The script takes as input $ n_{x}$, $ n_{y}$, $ n_{z}$, which are the number of unit cells to place along the x, y, and z directions; and $ r_{s}$, where the density of hydrogen atoms is $ \rho = (4/3 \pi r_{s}^{3})^{-1}$.

  h2_box_cfg [nx] [ny] [nz] [rs]

Figure 5.1: Hydrogen box generated with $ n_{x} = n_{y} = n_{z} = 2$, $ r_{s}$ = 2 bohr.


Uniform electron gas

The uniform electron gas is an idealized representation of a metal or plasma, where electrons exist in a uniform neutralizing background charge. This system is defined by a single parameter, the Wigner-Seitz radius $ r_{s}$, related to the electron density $ \rho = (4/3 \pi r_{s}^{3})^{-1}$.

eFF describes the uniform electron gas as a close-packed lattice of localized electrons analogous to a Wigner crystal packing. We find that an NaCl packing is favored, where opposite spin electrons occupy the sodium and chloride sites, although other lattices are close in energy, suggesting that the uniform electron gas in eFF is fluxional. The energetics with respect to $ r_{s}$ are similar to those calculated from Hartree-Fock theory, but not from an exact calculation including electron correlation.

The script takes as input $ n_{x}$, $ n_{y}$, $ n_{z}$, which are the number of unit cells to place along the x, y, and z directions; and $ r_{s}$, described above. It generates the NaCl uniform electron gas packing.

  uniform_electron_gas_cfg [nx] [ny] [nz] [rs]

Figure 5.2: Uniform electron gas generated with $ n_{x} = n_{y} = n_{z} = 2$, $ r_{s}$ = 1 bohr, electrons scaled by 0.2.


Lithium

We described the eFF representation of lithium in Section 2.6, and used it as a starting point to optimize dendritic bulk forms of lithium. To summarize, the $ \mathrm{Li^{+}}$ ions and valence electrons occupy an NaCl-like geometry, with the ions and electrons taking the place of the sodium and chloride. Lattice constants and elastic properties are well-reproduced, but the cohesive energy is too high.

The script takes as input $ n_{x}$, $ n_{y}$, $ n_{z}$, which are the number of unit cells to place along the x, y, and z directions. The eFF optimized lattice constant of 8.352 bohr (versus 8.32 bohr experimental) is used.

  lithium_solid_cfg [nx] [ny] [nz]

Figure 5.3: Lithium solid generated with $ n_{x} = n_{y} = n_{z} = 2$, electrons scaled by 0.2.


Lithium hydride

Lithium hydride in eFF and experiment adopts a NaCl-like geometry, with $ \mathrm{Li^{+}}$ and $ \mathrm{H^{-}}$ taking the place of sodium and chloride. The script takes as input $ n_{x}$, $ n_{y}$, $ n_{z}$, which are the number of unit cells to place along the x, y, and z directions. The eFF optimized lattice constant of 6.785 bohr (versus 7.72 bohr experimental) is used.

  lithium_hydride_solid_cfg [nx] [ny] [nz]

Figure 5.4: Lithium hydride solid generated with $ n_{x} = n_{y} = n_{z} = 2$, electrons scaled by 0.2.


Beryllium

Beryllium in eFF and experiment exists as a hexagonal-close packed structure. We observe strong bonding between atoms in XY plane, the result of closed-shell electron pairs that occupy alternating threefold sites between $ \mathrm{Be^{2+}}$ ions. The bonding between layers is strong as well, the result of vertical columns of alternating electrons and nuclei in the Z direction. As in lithium, Lattice constants and elastic properties are well-reproduced, but the cohesive energy is too high.

The script takes as input $ n_{x}$, $ n_{y}$, $ n_{z}$, which are the number of unit cells to place along the x, y, and z directions. The eFF optimized lattice constants of a = 4.592 bohr (versus 4.33 bohr experimental) and c = 7.025 bohr (versus 6.78 bohr experimental) are used.

  beryllium_solid_cfg [nx] [ny] [nz]

Figure 5.5: Beryllium solid generated with $ n_{x} = n_{y} = n_{z} = 2$, electrons scaled by 0.2.


Diamond

Diamond in eFF and experiment contains atom-centered core electrons and bond-centered sigma electrons, and nuclei on a diamond (A4) lattice.

The script takes as input $ n_{x}$, $ n_{y}$, $ n_{z}$, which are the number of unit cells to place along the x, y, and z directions. The eFF optimized lattice constant of 7.335 bohr (versus 6.740 bohr experimental) is used.

  diamond_cfg [nx] [ny] [nz]

Figure 5.6: Diamond generated with $ n_{x} = n_{y} = n_{z} = 2$, electrons scaled by 0.2.


next up previous contents index
Next: Generating hydrocarbons Up: Helper scripts Previous: Helper scripts   Contents   Index
Julius 2008-04-29