Diffusion Monte Carlo Simulations Research Articles

Tailoring Kinetics on a Topological Insulator Surface by Defect-Induced Strain: Pb Mobility on Bi2Te3.

Heteroepitaxial structures based on Bi2Te3-type topological insulators (TIs) exhibit exotic quantum phenomena. For optimal characterization of these phenomena, it is desirable to control the interface structure during film growth on such TIs. In this process, adatom mobility is a key factor. We demonstrate that Pb mobility on the Bi2Te3(111) surface can be modified by the engineering local strain, ε, which is induced around the point-like defects intrinsically forming in the Bi2Te3(111) thin film grown on a Si(111)-7 × 7 substrate. Scanning tunneling microscopy observations of Pb adatom and cluster distributions and first-principles density functional theory (DFT) analyses of the adsorption energy and diffusion barrier Ed of Pb adatom on Bi2Te3(111) surface show a significant influence of ε. Surprisingly, Ed reveals a cusp-like dependence on ε due to a bifurcation in the position of the stable adsorption site at the critical tensile strain εc ≈ 0.8%. This constitutes a very different strain-dependence of diffusivity from all previous studies focusing on conventional metal or semiconductor surfaces. Kinetic Monte Carlo simulations of Pb deposition, diffusion, and irreversible aggregation incorporating the DFT results reveal adatom and cluster distributions compatible with our experimental observations.

Smart darting diffusion Monte Carlo: Applications to lithium ion-Stockmayer clusters.

In a recent investigation [K. Roberts et al., J. Chem. Phys. 136, 074104 (2012)], we have shown that, for a sufficiently complex potential, the Diffusion Monte Carlo (DMC) random walk can become quasiergodic, and we have introduced smart darting-like moves to improve the sampling. In this article, we systematically characterize the bias that smart darting moves introduce in the estimate of the ground state energy of a bosonic system. We then test a simple approach to eliminate completely such bias from the results. The approach is applied for the determination of the ground state of lithium ion-n-dipoles clusters in the n = 8-20 range. For these, the smart darting diffusion Monte Carlo simulations find the same ground state energy and mixed-distribution as the traditional approach for n < 14. In larger systems we find that while the ground state energies agree quantitatively with or without smart darting moves, the mixed-distributions can be significantly different. Some evidence is offered to conclude that introducing smart darting-like moves in traditional DMC simulations may produce a more reliable ground state mixed-distribution.

Pseudopotential for the two-dimensional contact interaction

We propose a smooth pseudopotential for the contact interaction acting between ultracold atoms confined to two dimensions. The pseudopotential reproduces the scattering properties of the repulsive contact interaction up to 200 times more accurately than a hard disk potential, and in the attractive branch gives a tenfold improvement in accuracy over the square well potential. Furthermore, the potential enables diffusion Monte Carlo simulations of the ultracold gas to be run 15 times quicker than was previously possible.

Quantum Monte Carlo calculations of neutron matter with chiral three-body forces

Chiral effective field theory (EFT) enables a systematic description of low-energy hadronic interactions with controlled theoretical uncertainties. For strongly interacting systems, quantum Monte Carlo (QMC) methods provide some of the most accurate solutions, but they require as input local potentials. We have recently constructed local chiral nucleon-nucleon (NN) interactions up to next-to-next-to-leading order (N$^2$LO). Chiral EFT naturally predicts consistent many-body forces. In this paper, we consider the leading chiral three-nucleon (3N) interactions in local form. These are included in auxiliary field diffusion Monte Carlo (AFDMC) simulations. We present results for the equation of state of neutron matter and for the energies and radii of neutron drops. In particular, we study the regulator dependence at the Hartree-Fock level and in AFDMC and find that present local regulators lead to less repulsion from 3N forces compared to the usual nonlocal regulators.

Kinetic Monte Carlo Simulation of Oxygen Diffusion in Ytterbium Disilicate

ABSTRACTYtterbium disilicate is of interest as a potential environmental barrier coating for aerospace applications, notably for use in next generation jet turbine engines. In such applications, the transport of oxygen and water vapor through these coatings to the ceramic substrate is undesirable if high temperature oxidation is to be avoided. In an effort to understand the diffusion process in these materials, we have performed kinetic Monte Carlo simulations of vacancy-mediated and interstitial oxygen diffusion in Ytterbium disilicate. Oxygen vacancy and interstitial site energies, vacancy and interstitial formation energies, and migration barrier energies were computed using Density Functional Theory. We have found that, in the case of vacancy-mediated diffusion, many potential diffusion paths involve large barrier energies, but some paths have barrier energies smaller than one electron volt. However, computed vacancy formation energies suggest that the intrinsic vacancy concentration is small. In the case of interstitial diffusion, migration barrier energies are typically around one electron volt, but the interstitial defect formation energies are positive, with the result that the disilicate is unlikely to exhibit experience significant oxygen permeability except at very high temperature.

First-principles modeling of three-body interactions in highly compressed solid helium

We present a set of three-body interaction models based on the Slater-Kirkwood (SK) potential that are suitable for the study of the energy, structural, and elastic properties of solid $^{4}\mathrm{He}$ at high pressure. Our effective three-body potentials are obtained from the fit to total energies and atomic forces computed with the van der Waals density functional theory method due to Grimme, and represent an improvement with respect to previously reported three-body interaction models. In particular, we show that some of the introduced SK three-body potentials reproduce closely the experimental equation of state and bulk modulus of solid helium up to a pressure of $\ensuremath{\sim}60$ GPa, when used in combination with standard pairwise interaction models in diffusion Monte Carlo simulations. Importantly, we find that recent predictions reporting a surprisingly small variation of the kinetic energy and Lindeman ratio on quantum crystals under increasing pressure are likely to be artifacts deriving from the use of incomplete interaction models. Also, we show that the experimental variation of the shear modulus, ${C}_{44}$, at pressures $0\ensuremath{\le}P\ensuremath{\le}25$ GPa can be quantitatively described by our set of SK three-body potentials. At higher compression, however, the agreement between our ${C}_{44}$ calculations and experiments deteriorates and thus we argue that higher order many-body terms in the expansion of the atomic interactions probably are necessary in order to better describe elasticity in very dense solid $^{4}\mathrm{He}$.

Emergence of a Kondo singlet state with Kondo temperature well beyond 1000 K in a proton-embedded electron gas

Hydrogen in metals has attracted much attention for a long time from both basic scientific and technological points of view. Its electronic state has been investigated in terms of a proton embedded in the electron gas mostly by the local density approximation (LDA) to the density functional theory. At high electronic densities, it is well described by a bare proton H^+ screened by metallic electrons (charge resonance), while at low densities two electrons are localized at the proton site to form a closed-shell negative ion H^- protected from surrounding metallic electrons by the Pauli exclusion principle. However, no details are known about the transition from H^+ to H^- in the intermediate-density region. Here, by accurately determining the ground-state electron distribution n(r) by the combination of LDA and diffusion Monte Carlo simulations with the total electron number up to 170, we obtain a complete picture of the transition, in particular, a sharp transition from short-range H^+ screening charge resonance to long-range Kondo-like spin-singlet resonance, the emergence of which is confirmed by the presence of an anomalous Friedel oscillation characteristic to the Kondo singlet state with the Kondo temperature T_K well beyond 1,000K. This study not only reveals interesting competition between charge and spin resonances, enriching the century-old paradigm of metallic screening to a point charge, but also discovers a long-sought novel high-T_K system, opening an unexpected route to room-temperature superconductivity in a Kondo lattice made of protons.

H2 Adsorption in a Porous Crystal: Accurate First-Principles Quantum Simulation.

A general method is presented for constructing, from ab initio quantum chemistry calculations, the potential energy surface (PES) for H2 absorbed in a porous crystalline material. The method is illustrated for the metal-organic framework material MOF-5. Rigid body quantum diffusion Monte Carlo simulations are used in the construction of the PES and to evaluate the quantum ground state of H2 in MOF-5, the zero-point energy, and the enthalpy of adsorption at 0 K.

Monte Carlo Study on Anomalous Carrier Diffusion in Inhomogeneous Semiconductors

We perform ensemble Monte Carlo simulations of electron diffusion in high mobility inhomogeneous InAs layers. Electrons move ballistically for short times while moving diffusively for sufficiently long times. We find that electrons show anomalous diffusion in the intermediate time domain. Our study suggests that electrons in inhomogeneous InAs could be used to experimentally explore generalized random walk phenomena, which, some studies assert, also occur naturally in the motion of animal foraging paths.

“Plug-and-Play” potentials: Investigating quantum effects in (H2)2–Li+–benzene

Quantum and anharmonic effects are investigated in (H2)2-Li(+)-benzene, a model for hydrogen adsorption in metal-organic frameworks and carbon-based materials, using rigid-body diffusion Monte Carlo (RBDMC) simulations. The potential-energy surface (PES) is calculated as a modified Shepard interpolation of M05-2X/6-311+G(2df,p) electronic structure data. The RBDMC simulations yield zero-point energies (ZPE) and probability density histograms that describe the ground-state nuclear wavefunction. Binding a second H2 molecule to the H2-Li(+)-benzene complex increases the ZPE of the system by 5.6 kJ mol(-1) to 17.6 kJ mol(-1). This ZPE is 42% of the total electronic binding energy of (H2)2-Li(+)-benzene and cannot be neglected. Our best estimate of the 0 K binding enthalpy of the second H2 to H2-Li(+)-benzene is 7.7 kJ mol(-1), compared to 12.4 kJ mol(-1) for the first H2 molecule. Anharmonicity is found to be even more important when a second (and subsequent) H2 molecule is adsorbed; use of harmonic ZPEs results in significant error in the 0 K binding enthalpy. Probability density histograms reveal that the two H2 molecules are found at larger distance from the Li(+) ion and are more confined in the θ coordinate than in H2-Li(+)-benzene. They also show that both H2 molecules are delocalized in the azimuthal coordinate, ϕ. That is, adding a second H2 molecule is insufficient to localize the wavefunction in ϕ. Two fragment-based (H2)2-Li(+)-benzene PESs are developed. These use a modified Shepard interpolation for the Li(+)-benzene and H2-Li(+)-benzene fragments, and either modified Shepard interpolation or a cubic spline to model the H2-H2 interaction. Because of the neglect of three-body H2, H2, Li(+) terms, both fragment PESs lead to overbinding of the second H2 molecule by 1.5 kJ mol(-1). Probability density histograms, however, indicate that the wavefunctions for the two H2 molecules are effectively identical on the "full" and fragment PESs. This suggests that the 1.5 kJ mol(-1) error is systematic over the regions of configuration space explored by our simulations. Notwithstanding this, modified Shepard interpolation of the weak H2-H2 interaction is problematic and we obtain more accurate results, at considerably lower computational cost, using a cubic spline interpolation. Indeed, the ZPE of the fragment-with-spline PES is identical, within error, to the ZPE of the full PES. This fragmentation scheme therefore provides an accurate and inexpensive method to study higher hydrogen loading in this and similar systems.

Dynamic Monte Carlo simulation of non-equilibrium Brownian diffusion of single-chain macromolecules

We performed dynamic Monte Carlo simulations of biased diffusion of 3D phantom single lattice polymer. We observed spontaneous deformation of polymer coil when the external driving forces exceed a critical strength. In addition, longer chains require lower critical strengths, at which their activated velocities deviate from Newtonian-fluid behaviours and merge into a master curve exhibiting shear-thinning followed with shear thickening. We attributed the cause of deformation to the random updating of monomers. The latter represents the dynamic heterogeneity along the real polymer chain, and raises a nonlinear asymmetric accumulation of local acceleration and then an internal tension between chain middle and chain end, as evidenced by our previous Brownian Dynamics simulations. Our results unravel a single-molecular-level source of nonlinear dynamics, which has been overlooked in current theoretical considerations on the basis of Rouse ideal-chain model.

Vacancy-related diffusion correlation effects in a simple cubic random alloy and on the Na–K sublattice of alkali feldspar

Motivated by the need to analyse experimental data on ionic conductivity in alkali feldspar, we performed Monte Carlo (MC) simulations of vacancy diffusion in random binary systems. We employed an efficient procedure for the calculation of the vacancy correlation factor , which includes the computation of the associated partial correlation factors (PCFs) and . Test simulations on a simple cubic lattice show the improvements compared to previous MC data and the discrepancies with the Manning model. Vacancy correlation factors on the Na–K sublattice in the monoclinic structure of alkali feldspar proved to be dependent on crystal orientation. For the -direction, PCFs related to the four different jump types were calculated. We also examined the percolation behaviour for extreme ratios of the atomic jump frequencies. The results are found to agree with known data for the simple cubic lattice. In the case of feldspar, we provide the first useful estimates for the percolation threshold and the associated critical exponent using a simplified set of jump frequencies.

Anomalous Extracellular Diffusion in Rat Cerebellum

Extracellular space (ECS) is a major channel transporting biologically active molecules and drugs in the brain. Diffusion-mediated transport of these substances is hindered by the ECS structure but the microscopic basis of this hindrance is not fully understood. One hypothesis proposes that the hindrance originates in large part from the presence of dead-space (DS) microdomains that can transiently retain diffusing molecules. Because previous theoretical and modeling work reported an initial period of anomalous diffusion in similar environments, we expected that brain regions densely populated by DS microdomains would exhibit anomalous extracellular diffusion. Specifically, we targeted granular layers (GL) of rat and turtle cerebella that are populated with large and geometrically complex glomeruli. The integrative optical imaging (IOI) method was employed to evaluate diffusion of fluorophore-labeled dextran (MW 3000) in GL, and the IOI data analysis was adapted to quantify the anomalous diffusion exponent dw from the IOI records. Diffusion was significantly anomalous in rat GL, where dw reached 4.8. In the geometrically simpler turtle GL, dw was elevated but not robustly anomalous (dw = 2.6). The experimental work was complemented by numerical Monte Carlo simulations of anomalous ECS diffusion in several three-dimensional tissue models containing glomeruli-like structures. It demonstrated that both the duration of transiently anomalous diffusion and the anomalous exponent depend on the size of model glomeruli and the degree of their wrapping. In conclusion, we have found anomalous extracellular diffusion in the GL of rat cerebellum. This finding lends support to the DS microdomain hypothesis. Transiently anomalous diffusion also has a profound effect on the spatiotemporal distribution of molecules released into the ECS, especially at diffusion distances on the order of a few cell diameters, speeding up short-range diffusion-mediated signals in less permeable structures.

Quantum Monte Carlo study of the indirect Pauli exclusion effect in Bose-Fermi mixtures

We study the momentum distributions of a three-dimensional resonant Bose-Fermi mixture in the molecular limit at zero temperature. For concentration of the bosons with respect to the fermions less or equal to one, each boson is bound to a fermion and the system is composed of fermionic molecules plus excess fermions. Not only the bosonic condensate fraction goes to zero, signaling a quantum phase transition towards a normal phase, but a finite region of low momenta is depleted, depending on the concentration. This phenomenon is named indirect Pauli exclusion effect and is demonstrated via Fixed-Node Diffusion Monte Carlo simulations and T-matrix calculations.

Diffusion Monte Carlo Study of Para-Diiodobenzene Polymorphism Revisited.

We revisit our investigation of the diffusion Monte Carlo (DMC) simulation of para-diiodobenzene (p-DIB) molecular crystal polymorphism. [See J. Phys. Chem. Lett. 2010, 1, 1789-1794.] We perform, for the first time, a rigorous study of finite-size effects and choice of nodal surface on the prediction of polymorph stability in molecular crystals using fixed-node DMC. Our calculations are the largest that are currently feasible using the resources of the K-computer and provide insights into the formidable challenge of predicting such properties from first principles. In particular, we show that finite-size effects can influence the trial nodal surface of a small (1 × 1 × 1) simulation cell considerably. Therefore, we repeated our DMC simulations with a 1 × 3 × 3 simulation cell, which is the largest such calculation to date. We used a density functional theory (DFT) nodal surface generated with the PBE functional, and we accumulated statistical samples with ∼6.4 × 10(5) core hours for each polymorph. Our final results predict a polymorph stability that is consistent with experiment, but they also indicate that the results in our previous paper were somewhat fortuitous. We analyze the finite-size errors using model periodic Coulomb (MPC) interactions and kinetic energy corrections, according to the CCMH scheme of Chiesa, Ceperley, Martin, and Holzmann. We investigate the dependence of the finite-size errors on different aspect ratios of the simulation cell (k-mesh convergence) in order to understand how to choose an appropriate ratio for the DMC calculations. Even in the most expensive simulations currently possible, we show that the finite size errors in the DMC total energies are much larger than the energy difference between the two polymorphs, although error cancellation means that the polymorph prediction is accurate. Finally, we found that the T-move scheme is essential for these massive DMC simulations in order to circumvent population explosions and large time-step biases.

Ground Truth for Diffusion MRI in Cancer: A Model-Based Investigation of a Novel Tissue-Mimetic Material.

This work presents preliminary results on the development, characterisation, and use of a novel physical phantom designed as a simple mimic of tumour cellular structure, for diffusion-weighted magnetic resonance imaging (DW-MRI) applications. The phantom consists of a collection of roughly spherical, micron-sized core-shell polymer 'cells', providing a system whose ground truth microstructural properties can be determined and compared with those obtained from modelling the DW-MRI signal. A two-compartment analytic model combining restricted diffusion inside a sphere with hindered extracellular diffusion was initially investigated through Monte Carlo diffusion simulations, allowing a comparison between analytic and simulated signals. The model was then fitted to DW-MRI data acquired from the phantom over a range of gradient strengths and diffusion times, yielding estimates of 'cell' size, intracellular volume fraction and the free diffusion coefficient. An initial assessment of the accuracy and precision of these estimates is provided, using independent scanning electron microscope measurements and bootstrap-style simulations. Such phantoms may be useful for testing microstructural models relevant to the characterisation of tumour tissue.

Exciplexes with ionic dopants: stability, structure, and experimental relevance of M(+)((2)P)(4)He(n) (M = Sr, Ba).

M(+)((2)P)(4)Hen species, possibly involved in the post (2)P ← (2)S excitation dynamics of Sr(+) and Ba(+) in cold (4)He gas or droplets, are studied employing both high level ab initio calculations to determine the potential energy curves (PEC) and diffusion Monte Carlo (DMC) to obtain information on their ground state structure and energetics. PEC for the excited M(+)((2)P)He dimers were obtained using MRCI calculations with extended basis sets. Potential energy surfaces (PES) for M(+)((2)P)Hen were built with the DIM model including spin-orbit coupling via a perturbative procedure. DMC simulations indicated several exciplexes (n > 2) to be stable against He dissociation whatever the ion state, a finding that is at variance with what was previously suggested for Ba(+)((2)P1/2) due to the repulsive nature of the interaction potential obtained in [ Phys. Rev. A 2004 , 69 , 042505 ]. Our results, instead, support the suggestion made in [J. Chem. Phys. 2012, 137, 051102] for the existence of Ba(+)((2)P1/2)Hen exciplexes emitted following the excitation of the barium cation solvated into He droplets. In the (2)P1/2 state, the Ba ion also shows a peculiar behavior as a function of n with respect to the location and binding strength of the attached He atoms compared to Sr(+). Although the latter forms the usual equatorial He ring, Ba(+) deviates from this geometry for 1 ≤ n ≤ 4, with the radial distribution functions strongly depending on the number of solvent atoms. Finally, a putative species is proposed to explain the emission band at 523 nm that follows D1 or D2 excitation of Ba(+) in superfluid bulk helium.

Effects of Zero-Point Delocalization on the Vibrational Frequencies of Mixed HCl and Water Clusters.

We demonstrate the significant effect that large-amplitude zero-point vibrational motion can have on the high-frequency fundamental vibrations of molecular clusters, specifically small (HCl)n-(H2O)m clusters. Calculations were conducted on a many-body potential, constructed from a mix of new and previously reported semiempirical and high-level ab initio potentials. Diffusion Monte Carlo simulations were performed to determine ground-state wave functions. Visualization of these wave functions indicates that the clusters exhibit delocalized ground states spanning multiple stationary point geometries. The ground states are best characterized by planar ring configurations, despite the clusters taking nonplanar configurations at their global minima. Vibrational calculations were performed at the global minima and the Diffusion Monte Carlo predicted configurations and also using an approach that spans multiple stationary points along a rectilinear normal-mode reaction path. Significantly better agreement was observed between the calculated vibrational frequencies and experimental peak positions when the delocalized ground state was accounted for.

Specialized postsynaptic morphology enhances neurotransmitter dilution and high-frequency signaling at an auditory synapse.

Sensory processing in the auditory system requires that synapses, neurons, and circuits encode information with particularly high temporal and spectral precision. In the amphibian papillia, sound frequencies up to 1 kHz are encoded along a tonotopic array of hair cells and transmitted to afferent fibers via fast, repetitive synaptic transmission, thereby promoting phase locking between the presynaptic and postsynaptic cells. Here, we have combined serial section electron microscopy, paired electrophysiological recordings, and Monte Carlo diffusion simulations to examine novel mechanisms that facilitate fast synaptic transmission in the inner ear of frogs (Rana catesbeiana and Rana pipiens). Three-dimensional anatomical reconstructions reveal specialized spine-like contacts between individual afferent fibers and hair cells that are surrounded by large, open regions of extracellular space. Morphologically realistic diffusion simulations suggest that these local enlargements in extracellular space speed transmitter clearance and reduce spillover between neighboring synapses, thereby minimizing postsynaptic receptor desensitization and improving sensitivity during prolonged signal transmission. Additionally, evoked EPSCs in afferent fibers are unaffected by glutamate transporter blockade, suggesting that transmitter diffusion and dilution, and not uptake, play a primary role in speeding neurotransmission and ensuring fidelity at these synapses.

Vibrational ground state properties of the H+7/D+7 clusters

We present the first attempt for an analytical representation of the 15-dimensional potential energy surface (PES) of the H+7 cluster. Such surfaces are of particular interest in studying the unusual dynamics and spectroscopy of these cations. Diffusion Monte Carlo (PMC) and path-integral Monte Carlo (PMC) simulations based on this surface are employed to investigate the quantum effect and structural fluctuations of the vibrational ground state of H+7 and its deuterated isotopomer.