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Development and application of a particle-particle particle-mesh Ewald method for dispersion interactions
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10.1063/1.4764089
/content/aip/journal/jcp/137/17/10.1063/1.4764089
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/17/10.1063/1.4764089

Figures

Image of FIG. 1.
FIG. 1.

Total potential and split potential for r −6. When not using the Ewald sum, the whole area under the blue curve is solved in real space, whereas only the area under the green curve is solved in real space when using the Ewald sum. The error in the calculation is related to the area under the curves beyond the cutoff. Using the Ewald technique is thus more accurate.

Image of FIG. 2.
FIG. 2.

Real space error in the forces measured and estimated with Eq. (20) for (top) bulk system and (bottom) interfacial system. Measured errors are depicted as solid lines, estimated errors as dashed lines. From top to bottom, the real space cutoff is (blue) 2.0σ, (green) 3.0σ, and (red) 4.0σ. The estimate works well for the bulk system, but fails for the interfacial system.

Image of FIG. 3.
FIG. 3.

Measured and estimated reciprocal space errors for (top) a bulk system and (bottom) an interfacial system. The graphs on left show increasing interpolation order from P = 3 at the top to P = 6 at the bottom, with a fixed grid containing 32 grid points in each direction. The graphs on the right show grid density increasing from 22 points in each direction at the top to 26 points at the bottom, for fixed interpolation order P = 5. Measured errors are depicted as solid lines. Errors estimated with Eqs. (21) and (24) are depicted as dashed lines, those estimated with Eqs. (21) and (22) are depicted as dotted lines.

Image of FIG. 4.
FIG. 4.

Scaling of the Ewald sum and the PPPM method for dispersion interactions.

Image of FIG. 5.
FIG. 5.

Surface tension and density of hexane as a function of the total error in the calculated forces. The arrows point in the direction of increasing Ewald parameter.

Image of FIG. 6.
FIG. 6.

Surface tension, density, and errors in the forces in simulations of hexane. In the lower left graph, the red squares correspond to the real space error, while the triangles and circles correspond to the reciprocal space error when using the fine grid and coarse grid, respectively. The circles in the lower right graph correspond to the reciprocal space error. The Ewald parameter is β = 0.28 Å−1 in all figures on the right side. Dotted lines are error estimates calculated with Eqs. (20)–(22).

Image of FIG. 7.
FIG. 7.

Measured density profiles for simulations of LJ particles: (top) simulations with cutoff r c = 2.5σ and (bottom) simulations at a reduced temperature of T* = 1.1.

Image of FIG. 8.
FIG. 8.

Surface tensions and densities simulated when using a PPPM or a plain cutoff for dispersion. Results obtained when not using a long-range solver strongly depend on the chosen cutoff and approach the results of the simulation with the PPPM with increasing cutoff size.

Tables

Generic image for table
Table I.

Coefficients required for the calculation of the reciprocal space error estimate. Reprinted with permission from M. Deserno and C. Holm, J. Chem. Phys. 109, 7694 (1998). Copyright 1998 American Institute of Physics.

Generic image for table
Table II.

Results of the validation runs for the LJ particles. Uncertainties given in parentheses.

Generic image for table
Table III.

Results of the validation runs for the SPC/E water. Simulation marked with a dagger was run with higher precision.

Generic image for table
Table IV.

Results of the validation runs for the OPLS hexane.

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/content/aip/journal/jcp/137/17/10.1063/1.4764089
2012-11-06
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Development and application of a particle-particle particle-mesh Ewald method for dispersion interactions
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/17/10.1063/1.4764089
10.1063/1.4764089
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