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A comparison of methods for melting point calculation using molecular dynamics simulations
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10.1063/1.3702587
/content/aip/journal/jcp/136/14/10.1063/1.3702587
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/14/10.1063/1.3702587

Figures

Image of FIG. 1.
FIG. 1.

A schematic of the pseudo-supercritical path for melting point calculations.

Image of FIG. 2.
FIG. 2.

The calculated enthalpy (top panel) and free energy (middle panel) against temperature for pure argon liquid and solid phases. The free energy difference between solid and liquid phases ΔG was computed to be 0.0233 Kcal/mol at 90 K and the shifted free energy curves are shown in the bottom panel. The melting point was determined to be 82.8 K.

Image of FIG. 3.
FIG. 3.

The thermodynamic integrations for each step along the PSCP path calculated for argon at 90 K. The sum of all integration terms gives the free energy difference between solid and liquid phases at the reference temperature.

Image of FIG. 4.
FIG. 4.

The thermodynamic integrations for each step along the PSCP path for argon at 90 K computed by starting the simulation from the solid state. The computed results for each step agree with the corresponding step shown in Figure 3 where the simulation was started from liquid phase (note the difference in sign). Essentially, the same free energy difference ΔG was obtained from both calculations, confirming the reversibility of the PSCP path.

Image of FIG. 5.
FIG. 5.

The free energy difference (in Kcal/mol) between states along the PSCP path computed for argon at 90 K by starting the simulations from the liquid phase (blue) or the solid phase (red). The two numbers for the C-WC step are for contributions associated with scaling down the intermolecular interaction and the turning on/off of the tethering potential, respectively. The computed free energy change for each step along the path is independent of direction that the thermodynamic integration was carried out, demonstrating the reversibility of the method. The same melting point of 82.8 K was predicted, regardless of the integration direction.

Image of FIG. 6.
FIG. 6.

The average equilibrium box volume of argon system as a function of temperature obtained from interface/NPT ensemble simulations. The melting point was determined to be between 82 K and 83 K where a sharp volume increase (or density decrease) was observed. The experimental melting point is indicated by a dashed line.

Image of FIG. 7.
FIG. 7.

Melting point calculation results for argon using the solid-liquid interface system with NVE ensemble simulations. The horizontal black line indicates the pressure of 1 atm and the vertical dashed line indicates the experimental melting point. TOP: The results when NVE simulations were started from 83 K and 85 K initial conditions. The equilibrated P-T curves cross with P = 1 atm line. The average melting point was found to be 82.7 K. BOTTOM: Simulation results from four different initial configurations prepared at different temperatures. All data points were fitted by a linear function and the melting point was determined to be 82.8 K.

Image of FIG. 8.
FIG. 8.

The calculated melting points for argon using the voids method. The observed melting point decreases with increasing number of voids and reaches a flat region after 100 voids. The melting point was estimated to be 89.4 K by taking the average of the flat region. The experimental melting point is indicated by a dashed line.

Image of FIG. 9.
FIG. 9.

The free energy difference (in Kcal/mol) between states along the PSCP path computed for [BMIM][Cl] at 380 K by starting the simulations from the liquid phase (blue) or the solid phase (red). The two numbers for the C-WC step are for contributions associated with scaling down the intermolecular interaction and the turning on/off of the tethering potential, respectively. The computed free energy change for L-WL and WL-DWF steps are the same (absolute values) no matter which direction the integration was carried out. For the other two steps, however, the free energy change was found to be larger if the integration was carried out from C to WC or from WC to DWF, respectively. This is consistent with the observation that when the simulation was carried out in the other direction, the ordered state was not reached so that the simulations ended up at some intermediate states (indicated by short dotted lines) and corresponding to smaller free energy change.

Image of FIG. 10.
FIG. 10.

The thermodynamic integration results (in Kcal/mol) computed along a two intermediate states PSCP path for argon at 90 K. Removing the weak crystal state from the path, the free energy change connecting the crystal and dense weak fluid states is different when the integration is computed in different directions. The crystal phase was actually not reached at the end of the simulation started from dense weak fluid state (indicated by short dotted line), indicating the importance of the weak crystal phase enforced by the tethering potential in ensuring the PSCP path to be reversible.

Image of FIG. 11.
FIG. 11.

The average equilibrium box volume of [BMIM][Cl] system as a function of temperature calculated from interface/NPT ensemble simulations. The melting of the crystal occurred between 450 K and 500 K, where a sharp volume increase (or density decrease) was observed. The two lines were fit to the solid and liquid phase data points, respectively. The experimental melting point is indicated by a vertical dashed line.

Image of FIG. 12.
FIG. 12.

Melting point calculation results for [BMIM][Cl] using the interface/NVE method. The horizontal black line indicates a pressure of 1 atm and the vertical dashed line the experimental melting point. NVE simulations were initiated from three configurations prepared at different temperatures. Three sets of P-T points crossed with P = 1 atm line at different temperatures varying by ∼50 K, indicating strong dependence of the observed melting point on the initial simulation setup.

Image of FIG. 13.
FIG. 13.

The calculated melting point for orthorhombic [BMIM][Cl] using the voids method. The computed system density as a function of temperature is shown in the upper panel with the experimental melting point of 338 K indicated by a vertical line. The liquid phase density is included as solid black line. The observed melting point as a function of number of voids is shown in the lower panel. The dashed line indicates the experimental melting point. Unlike argon case, no clear flat region was observed before the crystal structure collapsed with more than 36 voids.

Tables

Generic image for table
Table I.

Summary of calculated melting points (in K) for argon and [BMIM][Cl] using various simulation methods.

Generic image for table
Table II.

Individual contributions to the solid-liquid free energy difference (in Kcal/mol) for [BMIM][Cl] at 380 K and 1 atm using the revised PSCP method with scaled tethering potential strength. For the C → WC step, the first column refers to the intermolecular potential and the second column refers to the tethering potential (see text for detail).

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/content/aip/journal/jcp/136/14/10.1063/1.3702587
2012-04-13
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A comparison of methods for melting point calculation using molecular dynamics simulations
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/14/10.1063/1.3702587
10.1063/1.3702587
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