Kinetic energy of solid neon by Monte Carlo with improved Trotter and finite-size extrapolation

Cuccoli, Alessandro; Macchi, Alessandro; Pedrolli, Gaia; Tognetti, V.; Vaia, Ruggero

doi:10.1103/physrevb.56.51

Cited by 18 publications

(14 citation statements)

References 22 publications

(47 reference statements)

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“…This approximation leads also to simple long-range corrections for the pressure and internal energies. 35,36 The virial estimator was used for the calculation of the kinetic energy. 37 Solid phase simulations were started with the atoms on their ideal face-centered-cubic (fcc) positions, while the liquid and gas phase simulations were initialized by using random positions.…”

Section: Methodology a Computational Conditionsmentioning

confidence: 99%

Quantum path-integral study of the phase diagram and isotope effects of neon

Ramı́rez

Herrero

2008

The Journal of Chemical Physics

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The phase diagram of natural neon has been calculated for temperatures in the range of 17-50 K and pressures between 10(-2) and 2 x 10(3) bar. The phase coexistence between solid, liquid, and gas phases has been determined by the calculation of the separate free energy of each phase as a function of temperature. Thus, for a given pressure, the coexistence temperature was obtained by the condition of equal free energy of coexisting phases. The free energy was calculated by using nonequilibrium techniques such as adiabatic switching and reversible scaling. The phase diagram obtained by classical Monte Carlo simulations has been compared to that obtained by quantum path-integral simulations. Quantum effects related to the finite mass of neon cause that coexistence lines are shifted toward lower temperatures when compared to the classical limit. The shift found in the triple point amounts to 1.5 K, i.e., about 6% of the triple-point temperature. The triple-point isotope effect has been determined for (20)Ne, (21)Ne, (22)Ne, and natural neon. The simulation data show satisfactory agreement to previous experimental results, which report a shift of about 0.15 K between triple-point temperatures of (20)Ne and (22)Ne. The vapor pressure isotope effect has been calculated for both solid and liquid phases at triple-point conditions. The quantum simulations predict that this isotope effect is larger in the solid than in the liquid phase, and the calculated values show nearly quantitative agreement to available experimental data.

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Section: Methodology a Computational Conditionsmentioning

confidence: 99%

Quantum path-integral study of the phase diagram and isotope effects of neon

Ramı́rez

Herrero

2008

The Journal of Chemical Physics

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“…The most popular is the Lennard-Jones pair potential given in Eq. (52), with parameters ǫ and σ slightly differing in several works [72][73][74][75][76][77][78] . Other model potentials have been employed for the effective interaction between noble-gas atoms, such as Aziz-type pair potentials 9,79,80 and three-body interactions [81][82][83][84] .…”

Section: Noble-gas Solidsmentioning

confidence: 99%

“…Path-integral simulations have been used to study structural, thermodynamic, and vibrational properties of heavier noble-gas solids 73,75,80,[100][101][102] . This technique has turned out to be well-suited to analyze isotopic effects in different properties of these solids 75 .…”

Section: B Heavier Elementsmentioning

confidence: 99%

Path-integral simulation of solids

Herrero

Ramı́rez

2014

J. Phys.: Condens. Matter

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The path-integral formulation of the statistical mechanics of quantum many-body systems is described, with the purpose of introducing practical techniques for the simulation of solids. Monte Carlo and molecular dynamics methods for distinguishable quantum particles are presented, with particular attention to the isothermal-isobaric ensemble. Applications of these computational techniques to different types of solids are reviewed, including noble-gas solids (helium and heavier elements), group-IV materials (diamond and elemental semiconductors), and molecular solids (with emphasis on hydrogen and ice). Structural, vibrational, and thermodynamic properties of these materials are discussed. Applications also include point defects in solids (structure and diffusion), as well as nuclear quantum effects in solid surfaces and adsorbates. Different phenomena are discussed, as solid-to-solid and orientational phase transitions, rates of quantum processes, classical-to-quantum crossover, and various finite-temperature anharmonic effects (thermal expansion, isotopic effects, electron-phonon interactions). Nuclear quantum effects are most remarkable in the presence of light atoms, so that especial emphasis is laid on solids containing hydrogen as a constituent element or as an impurity.

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“…Moreover accurate Trotter extrapolations are in order and finite-size effects are more and more important. We have used the procedure introduced by us 2,9 by which we correct the raw PIMC data, subtracting the exact contributions of the harmonic part for finite P and N , and adding both the exact harmonic results for infinite P and N , In this way, an accuracy of 0.2% is reached for the zeroth moment, which rises to 1% for the fourth moment. This corresponds to a maximum uncertainty of 4% for δ 2k .…”

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confidence: 99%

Spectral shapes of solid neon

Pedrolli¹,

Cuccoli²,

Macchi³

et al. 1998

J. Phys.: Condens. Matter

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We present a Path Integral Monte Carlo calculation of the first three moments of the displacementdisplacement correlation functions of solid neon at different temperatures for longitudinal and transverse phonon modes. The Lennard-Jones potential is considered. The relevance of the quantum effects on the frequency position of the peak and principally on the line-width of the spectral shape is clearly pointed out. The spectrum is reconstructed via a continued fraction expansion; the approximations introduced using the effective potential quantum molecular dynamics are discussed.Rare gas solids (RGS) are the simplest real systems in which we can study lattice vibrations. Argon and the heavier RGS can be well approximated as a set of harmonic oscillators at lowest temperatures, while the classical behaviour is reached before the melting point. Quantum corrections on the thermodynamic quantities, like kinetic energy and specific heat, can be taken into account by means of the effective potential approach (EP) 1 only for small quantum coupling g, (g < 0.25) defined as the ratio between the characteristic frequency and the strength of the binding potential. For neon (g = 0.694) anharmonic effects are present even for determining the ground state 2,3 . Indeed, precise calculations of kinetic energy, to be compared with accurate experiments done by Deep Inelastic Neutron Scattering (DINS) 4 , needed a rather sophisticated Path Integral Monte Carlo (PIMC) computation, being the EP approach inadequate. These results show that quantum effects are very important also at rather high temperatures 2 . Information about phonon dynamics is given by spectral shape, namely the space and time Fourier transform of the (symmetrized) displacement-displacement correlation function:withx α i is α-th component of the displacement of the i-th atom from its equilibrium position. Even though this quantity has been investigated since long time 5 , complete information is not available for various rare gas solids and in particular for neon. The perturbative many-body approach can give frequency and lifetime of phonons only at low temperatures. Classical molecular dynamics (CMD) can describe the behaviour of argon and krypton at highest temperatures, but it is no more valid for lower temperatures or stronger coupling. As shown in the following, the spectra of neon present significant quantum effects up to the melting point and the high quantum coupling prevents us to use the EP method in the entire temperature range.We approach the calculation of the spectra of neon as given in equation (1), by PIMC, evaluating the first three even frequency moments, ω 2n αβ k

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Kinetic energy of solid neon by Monte Carlo with improved Trotter and finite-size extrapolation

Cited by 18 publications

References 22 publications

Quantum path-integral study of the phase diagram and isotope effects of neon

Quantum path-integral study of the phase diagram and isotope effects of neon

Path-integral simulation of solids

Spectral shapes of solid neon

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