Dupuis, Romain ; Benoit, M. ; Tuckerman, M. E. ; Merlin, M.
Equilibrium fractionation of stable isotopes is critically important in fields ranging from chemistry, including medicinal chemistry, electrochemistry, geochemistry, and nuclear chemistry, to environmental science. The dearth of reliable estimates of equilibrium fractionation factors, from experiment or from natural observations, has created a need for accurate computational approaches. Because isotope fractionation is a purely quantum mechanical phenomenon, exact calculation of fractionation factors is nontrivial. Consequently, a severe approximation is often made, in which it is assumed that the system can be decomposed into a set of independent harmonic oscillators. Reliance on this often crude approximation is one of the primary reasons that theoretical prediction of isotope fractionation has lagged behind experiment. A class of problems for which one might expect the harmonic approximation to perform most poorly is the isotopic fractionation between solid and solution phases.
In order to illustrate the errors associated with the harmonic approximation, we have considered the fractionation of Li isotopes between aqueous solution and phyllosilicate minerals, where we find that the harmonic approximation overestimates isotope fractionation factors by as much as 30% at 25 °C. Lithium is a particularly interesting species to examine, as natural lithium isotope signatures provide information about hydrothermal processes, carbon cycle, and regulation of the Earth’s climate by continental alteration. Further, separation of lithium isotopes is of growing interest in the nuclear industry due to a need for pure 6Li and 7Li isotopes. Moving beyond the harmonic approximation entails performing exact quantum calculations, which can be achieved using the Feynman path integral formulation of quantum statistical mechanics. In the path integral approach, a system of quantum particles is represented as a set of classical-like ring-polymer chains, whose interparticle interactions are determined by the rules of quantum mechanics. Because a classical isomorphism exists between the true quantum system and the system of ring-polymers, classical-like methods can be applied. Recent developments of efficient path integral approaches for the exact calculation of isotope fractionation now allow the case of the aforementioned dissolved Li fractionation properties to be studied in detail. Applying this technique, we find that the calculations yield results that are in good agreement with both experimental data and natural observations. Importantly, path integral methods, being fully atomistic, allow us to identify the origins of anharmonic effects and to make reliable predictions at temperatures that are experimentally inaccessible yet are, nevertheless, relevant for natural phenomena.
Dupuis, Romain; Dolaso, J. S. ; Benoit, M. ; Surga J.; Ayuela A.
Studies of the structure of hydroxides under pressure using neutron diffraction reveal that the high concentration of hydrogen is distributed in a disordered network. The disorder in the hydrogen-bond network and possible phase transitions are reported to occur at pressures within the range accessible to experiments for layered calcium hydroxides, which are considered to be exemplary prototype materials. In this study, the static and dynamical properties of these layered hydroxides are investigated using a quantum approach describing nuclear motion, shown herein to be required particularly when studying diffusion processes involving light hydrogen atoms. The effect of high-pressure on the disordered hydrogen-bond network shows that the protons tunnel back and forth across the barriers between three potential minima around the oxygen atoms. At higher pressures the structure has quasi two-dimensional layers of hydrogen atoms, such that at low temperatures this causes the barrier crossing of the hydrogen to be significantly rarefied. Furthermore, for moderate values of both temperature and pressure this process occurs less often than the usual mechanism of proton transport via vacancies, limiting global proton diffusion within layers at high pressure.
Fractionation of silicon isotopes in liquids: the importance of configurational disorder
Dupuis, Romain ; Benoit, M. ; Nardin, E. ; Méheut, M.
Abstract Silicon isotopes are a promising tool to assess low-temperature geochemical processes such as weathering or chert precipitation. However, their use is hampered by an insufficient understanding of the fractionation associated with elementary processes such as precipitation or dissolution. In particular, the respective contributions of kinetic and equilibrium processes remain to be determined. In this work, equilibrium fractionation factors for silicon isotopes have been calculated using first-principles methods for quartz, kaolinite, and dissolved silicic acid (H4SiO4 and H3SiO4−) at 300 K. The two liquid systems are treated both as realistically as possible, and as consistently with the solids as possible. They are first simulated by ab initio molecular dynamics, then individual snapshots are extracted from the trajectories and relaxed, giving inherent structures (IS) and their fractionation properties are calculated. The fractionation properties of these IS are then calculated. A significant variability of the fractionation properties (σ= 0.4‰) is observed between the independent snapshots, emphasizing the importance of configurational disorder on the fractionation properties of solutions. Furthermore, a correlation is observed between the fractionation properties of these snapshots and the mean Si-O distances, consistent with calculations on minerals. This correlation is used to identify other parameters influencing the fractionation, such as the solvation layer. It is also used to reduce the number of configurations to be computed, and therefore the computational cost. At 300 K, we find a fractionation factor of + 2.1±0.2‰ between quartz and H4SiO4, + 0.4±0.2‰ between kaolinite and H4SiO4, and -1.6±0.3‰ between H3SiO4− and H4SiO4. These calculated solid-solution fractionations show important disagreement with natural observations in low-temperature systems, arguing against isotopic equilibration during silicon precipitation in these environments. On the other hand, the large fractionation associated with the de-protonation of silicic acid suggests the importance of speciation, and in particular pH, for the fractionation of silicon isotopes at low temperature.
Efficient calculation of free energy differences associated with isotopic substitution using Path Integral Molecular Dynamics
Marsalek, Ondrej ; Chen, Pei-Yang ; Dupuis, Romain ; Benoit, Magali ; Méheut, Merlin ; Bačić, Zlatko ; Tuckerman, Mark E.
The problem of computing free energy differences due to isotopic substitution in chemical systems is discussed. The shift in the equilibrium properties of a system upon isotopic substitution is a purely quantum mechanical effect that can be quantified using the Feynman path integral approach. In this paper, we explore two developments that lead to a highly efficient path integral scheme. First, we employ a mass switching function inspired by the work of Ceriotti and Markland [ J. Chem. Phys. 2013, 138, 014112] that is based on the inverse square root of the mass and which leads to a perfectly constant free energy derivative with respect to the switching parameter in the harmonic limit. We show that even for anharmonic systems, this scheme allows a single-point thermodynamic integration approach to be used in the construction of free energy differences. In order to improve the efficiency of the calculations even further, however, we derive a set of free energy derivative estimators based on the fourth-order scheme of Takahashi and Imada [ J. Phys. Soc. Jpn. 1984, 53, 3765]. The Takahashi–Imada procedure generates a primitive fourth-order estimator that allows the number of imaginary time slices in the path-integral approach to be reduced substantially. However, as with all primitive estimators, its convergence is plagued by numerical noise. In order to alleviate this problem, we derive a fourth-order virial estimator based on a transferring of the difference between second- and fourth-order primitive estimators, which remains relatively constant as a function of the number of configuration samples, to the second-order virial estimator. We show that this new estimator converges as smoothly as the second-order virial estimator but requires significantly fewer imaginary time points.
Development of Monte-Carlo simulations for nano-patterning surfaces associated with MM-EPES analysis: Application to different Si(111) nanoporous surfaces
EPES (elastic peak electron spectroscopy) allows measuring the percentage of elastic backscattered electrons ηe from a surface excited by primary electrons. However, this method must be combined with Monte Carlo simulations to get quantitative information. After a brief description of the algorithm used in this work (named MC2), we focused on the adaptation of this simulation for nanoporous surfaces (named MC2-NP). The theoretical results obtained put in evidence the dependence of ηe versus pore diameter (d), depth of the pores (h) and covering rate (CR) of the pores on the surface. Results obtained on surfaces having cylinder-shaped and cone-shaped holes with nanometer dimensions are presented too. To validate theoretical results obtained with MC2-NP, silicon(111) nanoporous surfaces have been prepared with an anodized aluminum oxide (AAO) template and by argon ion bombardment in an UHV chamber. Uniform nanohole arrays were formed as a replica of ordered lattice pattern of the template. Then EPES experimental measurements have been performed on planar and nanoporous Si(111) surfaces using a retarding field analyzer (RFA). The experimental results put in evidence that the percentage of the elastically backscattered electrons is influenced by the patterning of the surface. Then comparing values of ηe obtained experimentally with those obtained with MC2-NP simulations, we show the sensitivity of the EPES method for studying nanoporous surfaces. In this way, we expect fast estimation of nanohole’s dimensions by in-situ MM-EPES (Multi-Mode EPES) without other techniques such as for example scanning electron microscopy.
- Nanoporous alumina mask;
- Surface plasmon;
- Monte Carlo simulation