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Efficient calculation of α- and β-nitrogen free energies and coexistence conditions via overlap sampling with targeted perturbation
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10.1063/1.3615941
/content/aip/journal/jcp/135/4/10.1063/1.3615941
http://aip.metastore.ingenta.com/content/aip/journal/jcp/135/4/10.1063/1.3615941

Figures

Image of FIG. 1.
FIG. 1.

(a) Coordinate definition for linear-molecule orientation. is the molecular orientation vector, which rotates an angle θ off its nominal orientation . , , and are mutually orthogonal. represents the projection of vector on the plane that is perpendicular to . (b) Graphical illustration of the relationship between the rotation angle and the spherical surface area. is the nominal molecular orientation. The shaded blue spherical cap represents the surface area, 2π(1 − cosθ), around within the angle θ.

Image of FIG. 2.
FIG. 2.

Illustration of the alternating layers of unit cell A and B for the artificial “low-temperature” β-N2 phase structure.

Image of FIG. 3.
FIG. 3.

Molecular geometry of Etters et al.'s nitrogen model. Size of nitrogen atom centers is not drawn to scale.

Image of FIG. 4.
FIG. 4.

χ i vs. temperature for α-N2. Legend indicates the molecular density in Å−3.

Image of FIG. 5.
FIG. 5.

Plots of ⟨cos θ⟩ probability distribution for molecular densities, ρ−3], of (a) 0.0230, (b) 0.0225, (c) 0.0220, (d) 0.0215, and (e) 0.0210. Legend indicates the temperature in Kelvin.

Image of FIG. 6.
FIG. 6.

Plot of βA/N vs. 1/N for α-N2 phase at ρ = 0.0230 Å−3 and T = 30 K, where N is the number of particles and βA/N is from Eq. (2).

Image of FIG. 7.
FIG. 7.

TPTrans path. χ i vs. temperature in Kelvin. Legend indicates molecular density in Å−3.

Image of FIG. 8.
FIG. 8.

Free energy difference for initial, orientation-coupling perturbation of RP perturbation path, as function of molecular density, ρ.

Image of FIG. 9.
FIG. 9.

RP path. χ i vs. constraint angle, θmax , in degrees. Legend indicates molecular density in Å−3.

Image of FIG. 10.
FIG. 10.

TP path.χ i vs. temperature in Kelvin. Legend indicates molecular density in Å−3.

Image of FIG. 11.
FIG. 11.

βA C /N vs. 1/N plot for different perturbation paths at ρ = 0.0230 Å−3 with 432-, 1024-, and 2000-particle system sizes. The perturbation paths presented in the plot are (a) TPTrans, (b) RP, and (c) TP.

Image of FIG. 12.
FIG. 12.

Plot of βA/N vs. 1/N for β-N2 phase at ρ = 0.0230 Å−3 and T = 45 K, where βA/N is from Eq. (16). The harmonic contribution represents that formulated at the outset of the TPtrans path, and thus is defined with respect to the system with rigid molecular orientations.

Image of FIG. 13.
FIG. 13.

Plot of Gibbs free energy vs. temperature. Legend indicates the pressure for each set of curves.

Image of FIG. 14.
FIG. 14.

P-T diagram of solid-phase nitrogen. α-N2 is stable at lower temperatures and β-N2 is at higher temperatures. The uncertainty reported for the data from this work is about the size of the symbols.

Tables

Generic image for table
Table I.

Potential parameters.

Generic image for table
Table II.

Examination of contributing terms in Helmholtz free-energy calculation per particle [in unit Kelvin] for α-N2 and β-N2 phase at ρ = 0.0230 Å−3, and T = 49 K. The last digit in the parentheses is the 67% confidence limit.

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/content/aip/journal/jcp/135/4/10.1063/1.3615941
2011-07-29
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Efficient calculation of α- and β-nitrogen free energies and coexistence conditions via overlap sampling with targeted perturbation
http://aip.metastore.ingenta.com/content/aip/journal/jcp/135/4/10.1063/1.3615941
10.1063/1.3615941
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