### Abstract

We present two efficient iterative Monte Carlo algorithms in the grand canonical ensemble with which the chemical potentials corresponding to prescribed (targeted) partial densities can be determined. The first algorithm works by always using the targeted densities in the kT log (ρ i) (ideal gas) terms and updating the excess chemical potentials from the previous iteration. The second algorithm extrapolates the chemical potentials in the next iteration from the results of the previous iteration using a first order series expansion of the densities. The coefficients of the series, the derivatives of the densities with respect to the chemical potentials, are obtained from the simulations by fluctuation formulas. The convergence of this procedure is shown for the examples of a homogeneous Lennard-Jones mixture and a NaCl-Ca Cl2 electrolyte mixture in the primitive model. The methods are quite robust under the conditions investigated. The first algorithm is less sensitive to initial conditions.

Original language | English |
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Article number | 124102 |

Journal | The Journal of Chemical Physics |

Volume | 128 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2008 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*The Journal of Chemical Physics*,

*128*(12), [124102]. https://doi.org/10.1063/1.2839302

**Simulating prescribed particle densities in the grand canonical ensemble using iterative algorithms.** / Malasics, Attila; Gillespie, Dirk; Boda, D.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 128, no. 12, 124102. https://doi.org/10.1063/1.2839302

}

TY - JOUR

T1 - Simulating prescribed particle densities in the grand canonical ensemble using iterative algorithms

AU - Malasics, Attila

AU - Gillespie, Dirk

AU - Boda, D.

PY - 2008

Y1 - 2008

N2 - We present two efficient iterative Monte Carlo algorithms in the grand canonical ensemble with which the chemical potentials corresponding to prescribed (targeted) partial densities can be determined. The first algorithm works by always using the targeted densities in the kT log (ρ i) (ideal gas) terms and updating the excess chemical potentials from the previous iteration. The second algorithm extrapolates the chemical potentials in the next iteration from the results of the previous iteration using a first order series expansion of the densities. The coefficients of the series, the derivatives of the densities with respect to the chemical potentials, are obtained from the simulations by fluctuation formulas. The convergence of this procedure is shown for the examples of a homogeneous Lennard-Jones mixture and a NaCl-Ca Cl2 electrolyte mixture in the primitive model. The methods are quite robust under the conditions investigated. The first algorithm is less sensitive to initial conditions.

AB - We present two efficient iterative Monte Carlo algorithms in the grand canonical ensemble with which the chemical potentials corresponding to prescribed (targeted) partial densities can be determined. The first algorithm works by always using the targeted densities in the kT log (ρ i) (ideal gas) terms and updating the excess chemical potentials from the previous iteration. The second algorithm extrapolates the chemical potentials in the next iteration from the results of the previous iteration using a first order series expansion of the densities. The coefficients of the series, the derivatives of the densities with respect to the chemical potentials, are obtained from the simulations by fluctuation formulas. The convergence of this procedure is shown for the examples of a homogeneous Lennard-Jones mixture and a NaCl-Ca Cl2 electrolyte mixture in the primitive model. The methods are quite robust under the conditions investigated. The first algorithm is less sensitive to initial conditions.

UR - http://www.scopus.com/inward/record.url?scp=41549083325&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41549083325&partnerID=8YFLogxK

U2 - 10.1063/1.2839302

DO - 10.1063/1.2839302

M3 - Article

C2 - 18376903

AN - SCOPUS:41549083325

VL - 128

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 12

M1 - 124102

ER -