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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

### Abstract

A recently introduced solid-phase free-energy calculation method that is based upon overlap sampling with targeted free-energyperturbation is further developed and extended to systems with orientational degrees of freedom. Specifically we calculate the absolute free energy of the linear-molecular nitrogen model of Etter *et al.*, examining both the low-temperature low-pressure *α*-N_{2}structure and the orientationally disordered *β*-N_{2} phase. In each perturbation (for the *α*-N_{2} phase) to determine the free-energy difference between systems at adjacent temperatures, harmonic coordinate scaling is applied to both the translational and rotational degrees of freedom in the nitrogen molecule to increase the phase-space overlap of the two perturbing systems and consequently, improve the free-energy difference results. For the plastic *β*-N_{2} phase, a novel method that requires several perturbation paths is introduced to calculate its absolute free energy. Through these methods, the absolute free energies for both the *α*-N_{2} and *β*-N_{2} phase can be accurately and precisely determined. We find again that the anharmonic contribution to the free energy has weak dependence on system size. The transition properties for the *α*-N_{2} and *β*-N_{2} phase are also investigated. The *α-β*phase transition for the model at atmospheric pressure (0.1 MPa) is found to occur at 40.35 ± 0.01 K with volumetric and entropy changes of 0.44 ± 0.01 cm^{3}/mol and 1.99 ± 0.01 cal/mol.K respectively.

© 2011 American Institute of Physics

Received 29 April 2011
Accepted 07 July 2011
Published online 29 July 2011

Acknowledgments: Acknowledgment is made to the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research. Additional support has been provided by the U.S. National Science Foundation, Grant No. CHE-0626305. Computational resources were provided by the University at Buffalo Center for Computational Research.

Article outline:

I. BACKGROUND AND INTRODUCTION

II. FORMALISM AND METHOD

A. Rotational coordinates

B. Free-energy calculation for orientationally ordered α-N_{2} phase

C. Free-energy calculation for orientationally disordered *β*-N_{2} phase

1. TPTrans

2. RP

3. TP

D. Simulation details

III. RESULTS AND DISCUSSION

A. *A* _{ C } for *α*-N_{2}

B. Free-energy results and finite size effects for *α*-N_{2}

C. *A* _{ C } for *β*-N_{2}

D. Finite size effects for *β*-N_{2}

E. Examination of contributing terms in Helmholtz free energy

F. Relative stability of *α*-N_{2} and *β*-N_{2} phases

IV. CONCLUSIONS

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/content/aip/journal/jcp/135/4/10.1063/1.3615941

2011-07-29

2014-04-18

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