Path Integral Monte Carlo Calculations of Equation of State of Hydrogen

doi:10.19596/j.cnki.1001-246x.7855

Abstract

Abstract: We computed equations of state of hydrogen in warm dense matter regime by using DPIMC method. In large part of the regime, pressure difference between DPIMC and RPIMC is less than 10%. In low temperature regime, some difference beyond 20%. We pointed out two clerical errors in pressure of RPIMC. In dissociation and ionization regime, pressures of DPIMC lie between results of TF and TFC model. In dissociation regime, the largest pressure difference between DPIMC and RPIMC is 15%. In ionization regime, pressures of DPIMC are agree with RPIMC. In low density regime, internal energies of DPIMC are close to those of RPIMC, less than those of QMD and those of IG model. In high density regime, pressures of DPIMC lie between results of TFC and IG model, internal energies of DPIMC less than those of IG model.

Key words: DPIMC method, hydrogen, equation of state, warm dense matter

CLC Number:

ZHANG Qili, LIU Haifeng, LI Qiong, SONG Hongzhou, ZHANG Gongmu. Path Integral Monte Carlo Calculations of Equation of State of Hydrogen[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 36(4): 379-385.

References

[1] MCCRORY R L, et al. Progress in direct-drive inertial confinement fusion[J]. Phys Plasmas, 2008, 15:055503.
[2] MEYERHOFER D D. High-performance inertial confinement fusion target implosions on OMEGA[J]. Nucl Fusion, 2011, 51:053010.
[3] LINDL J D. Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain[J]. Phys Plasmas, 1995, 2:3933.
[4] HUBBARB W B. Interiors of the giant planets[J]. Science, 1981, 214:145.
[5] STEVENSON D J. Interiors of the giant planets[J]. Annu Rev Earth Planet Sci, 1982, 10:257.
[6] ZHAO Y, ZHANG G, ZHANG Q, et al. Equation of state of detonation products for HMX explosive[J]. Chinese Journal of Computational Physics, 2017, 34(2):155-159.
[7] FOULKES W M C, MITAS L, NEEDS R J, et al. Quantum Monte Carlo simulations of solids[J]. Rev Mod Phys, 2001, 73:33.
[8] CEPERLEY D M. Path integrals in the theory of condensed helium[J]. Rev Mod Phys, 1995, 65:279.
[9] 李名锐, 周刚, 李志康, 等. 液氘单次冲击压缩的QMC模拟研究[J].高压物理学报,2015,29(1):1-8.
[10] KITAMURA H, TSUNEYUKI SH, TADASHI O, et al. Quantum distribution of protons in solid molecular hydrogen at megabar pressure[J]. Nature, 2000, 404:259-262.
[11] JOHNSON K A, ASHCROFT N W. Structure and bandgap closure in dense hydrogen[J]. Nature, 2000, 403:632-635.
[12] WANG Y, PERDEW J P. Correlation hole of the spin-polarized electron gas, with exact small-wave-vector and high-density scaling[J]. Phys Rev B, 1991, 44:13298.
[13] LENOSKY T J, BICKHAM S R, KRESS J D. Density-functional calculations of the Hugoniot of shocked liquid deuterium[J]. Phys Rev B, 2000, 61:1.
[14] DESJARLAIS M P. Density-functional calculations of the liquid deuterium Hugoniot, reshock, and reverberation timing[J]. Phys Rev B, 2003, 68:064204.
[15] 张其黎, 张弓木, 赵艳红, 等. 氘、氦及其混合物状态方程第一原理研究[J]. 物理学报, 2015, 64:094702.
[16] KNUDSON M D, DESJARLAIS M P, BECKER A, et al. Direct observation of an abrupt insulator-to-metal transition in dense liquid deuterium[J]. Science, 2015, 348(6242):1455.
[17] MILITZER B, CEPERLEY D M. Path integral Monte Carlo calculation of the deuterium hugoniot[J]. Phys Rev Lett, 2000, 85:1890-1893.
[18] TUBMAN N M, LIBERATORE E, PIERLEONI C, et al. Molecular-atomic transition along the deutrium Hugoniot curve with coupled electron-ion Monte Carlo simulations[J]. Phys Rev Lett, 2015, 115:45301.
[19] FILINOV V S, FORTOV V E, BONITZ M. Fermionic path integral Monte Carlo results for the uniform electron gas at finite temperature[J]. arXiv:1407.3600v1[cond-mat.str-el], 2014.
[20] LI Q, LIU H F, ZHANG G M, et al. The thermodynamical instability induced by pressure ionization in fluid helium[J]. Phys Plasmas, 2016, 23:112709.
[21] WANG C, ZHANG P. Wide range equation of state for fluid hydrogen from density function theory[J]. Phys Plasmas, 2013, 20:092703.
[22] HU S X, MILITZER B, GONCHAROV V N. First-principles equation-of-state table of deuterium for inertial confinement fusion applications[J]. Phys Rev B, 2011, 84:224109.
[23] PIERLEONI C, CEPERLEY D M, HOLZMANN M. Coupled electron-ion Monte Carlo calculations of dense metallic hydrogen[J]. Phys Rev Lett, 2004, 93(14):146402.
[24] MORALES M A, PIERLEONI C, CEPERLEY D M. Equation of state of metallic hydrogen from coupled electron-ion Monte Carlo simulations[J]. Phys Rev E, 2010, 81:021202.
[25] KNUDSON M D,DESJARLAIS M P. High-precision shock wave measurements of deuterium:Evaluation of exchange-correlation functionals at the molecular-to-atomic transition[J]. Phys Rev Lett, 2017, 118:035501.
[26] KERLEY G I. A theoretical equation of state for deuterium[R]. Technical Report No. LA-4776, Los Alamos Scientific Laboratory, 1972.
[27] KERLEY G I. Equation of state for hydrogen and deuterium[R]. Technical Report No. SAND2003-3613, Sandia National Laboratories, 2003.
[28] BECKER A, LORENZEN W, FORTNEY J J, et al. Ab initio equations of state for hydrogen (H-REOS.3) and helium (He-REOS.3) and their implications for the interior of brown dwarfs[J]. The AstroPhy J Supp Ser, 2014, 215:21.
[29] LIU H F, SONG H F, ZHANG Q L, et al. Validation for equation of state in wide regime:Copper as prototype[J]. Matter and Radiation at Extremes, 2016, 1:123-131.
[30] FILINOV V S, FORTOV V E, BONITZ M. Pair distribution functions of dense partially ionized hydrogen[J]. Phys Lett A, 2000, 274:228-235.
[31] FILINOV V S, BONITZ M, EBELING W. Thermodynamics of hot dense H-plasmas:Path integral Monte Carlo simulations and analytical approximations[J]. Plasmas Phys Control Fusion, 2001, 43:743-759.