Diffusion Monte Carlo Simulations Research Articles

Quantum Defects for Sensing and Mechanistic Studies

Single wall carbon nanotubes (SWCNT) fluoresce in the near infrared (NIR) and have been assembled with biopolymers such as DNA to form highly sensitive molecular sensors. They change their fluorescence when they interact with analytes. Despite the progress in engineering of these sensors the underlying mechanisms are still not understood. Here, we identify processes and rate constants that explain the photophysical signal transduction by exploiting sp3 quantum defects in the sp2 carbon lattice of SWCNTs. As a model system we use ssDNA coated (6,5)-SWCNTs, which increase their NIR emission (E11, 990 nm) up to + 250 % in response to the important neurotransmitter dopamine. In contrast, SWCNTs coated with DNA but with a low number of NO2-Aryl sp3 quantum defects decrease both their E11 (-35%) and defect related E11* emission (- 50%) at 1130 nm. Consequently, the interaction with the analyte does not change the radiative exciton decay pathway alone. Furthermore, the fluorescence response of pristine SWCNTs increases with SWCNT length, suggesting that exciton diffusion is affected. The quantum yield of pristine (6,5)-SWCNTs increases in response to the analyte from 0.6 % to 1.3 % and points to a change in non-radiative rate constants. These experimental results are explained by a Monte Carlo simulation of exciton diffusion, which supports a change of two non-radiative decay pathways together with an increase of exciton diffusion (3 rate constant model). In summary, we demonstrate how perturbation of a system with quantum defects reveals the photophysical mechanism and provides opportunities for novel sensing concepts.

Diffusion mechanisms of DNA in agarose gels: NMR studies and Monte Carlo simulations.

We report on the diffusion mechanism of short, single-stranded DNA molecules with up to 100 nucleobases in agarose gels with concentrations of up to 2.0% with the aim to characterize the DNA-agarose interaction. The diffusion coefficients were measured directly, i.e., without any model assumptions, by pulsed field gradient nuclear magnetic resonance (PFG-NMR). We find that the diffusion coefficient decreases, as expected, with an increase in both DNA strand length and gel concentration. In addition, we performed Monte Carlo simulations of particle diffusion in a model network of polymer chains, considering our experimental conditions. Together, the Monte Carlo simulations and the PFG-NMR results show that the decrease in diffusion coefficients in the presence of the agarose gel is due to a temporary adhesion of the DNA molecules to the surface of gel fibers. The average adhesion time to a given gel fiber increases with the length of the DNA strands but is independent of the number of gel fibers. The corresponding magnitude of the binding enthalpies of DNA strands to gel fibers indicates that a mixture of van der Waals interactions and hydrogen bonding contributes to the decreased diffusion of DNA in agarose gels.

Fast Near Ab Initio Potential Energy Surfaces Using Machine Learning.

A machine-learning based approach for evaluating potential energies for quantum mechanical studies of properties of the ground and excited vibrational states of small molecules is developed. This approach uses the molecular-orbital-based machine learning (MOB-ML) method to generate electronic energies with the accuracy of CCSD(T) calculations at the same cost as a Hartree-Fock calculation. To further reduce the computational cost of the potential energy evaluations without sacrificing the CCSD(T) level accuracy, GPU-accelerated Neural Network Potential Energy Surfaces (NN-PES) are trained to geometries and energies that are collected from small-scale Diffusion Monte Carlo (DMC) simulations, which are run using energies evaluated using the MOB-ML model. The combined NN+(MOB-ML) approach is used in variational calculations of the ground and low-lying vibrational excited states of water and in DMC calculations of the ground states of water, CH5+, and its deuterated analogues. For both of these molecules, comparisons are made to the results obtained using potentials that were fit to much larger sets of electronic energies than were required to train the MOB-ML models. The NN+(MOB-ML) approach is also used to obtain a potential surface for C2H5+, which is a carbocation with a nonclassical equilibrium structure for which there is currently no available potential surface. This potential is used to explore the CH stretching vibrations, focusing on those of the bridging hydrogen atom. For both CH5+ and C2H5+ the MOB-ML model is trained using geometries that were sampled from an AIMD trajectory, which was run at 350 K. By comparison, the structures sampled in the ground state calculations can have energies that are as much as ten times larger than those used to train the MOB-ML model. For water a higher temperature AIMD trajectory is needed to obtain accurate results due to the smaller thermal energy. A second MOB-ML model for C2H5+ was developed with additional higher energy structures in the training set. The two models are found to provide nearly identical descriptions of the ground state of C2H5+.

Определение теплопроводности кремния с детальным учетом кинетики взаимодействия фононов

The thorough study of the heat carriers --- quasiparticles --- phonons interaction resulted in a pioneering method for calculating the thermal conductivity of nonmetallic solids. As the interactions of phonons are much more complicated than those of usual atoms and molecules, it is necessary to take into account the presence of two types of phonons with different properties; the decay of one phonon into two or the fusion of two phonons into one as a result of interaction; the presence of two types of interaction of phonons, one of which is elastic, the other is inelastic (moreover, the type of interaction results from solving the energy and quasi-momentum conservation equations). The existing methods for determining thermal conductivity, which typically involve solving the Boltzmann transport equation, use the iteration method, whose parameter is the average time between successive phonon interactions, and the calculation results provide little information on all types of interactions. In this research, we developed a method of direct Monte Carlo simulation of phonon diffusion with strict account for their interaction owing to the energy and quasi-momentum conservation laws. Calculations of the thermal conductivity coefficient for pure silicon in the temperature range of 100---300 K showed good agreement with the experiment and calculations of other authors, and also made it possible to consider the phonon kinetics in detail

Ground-state properties of an electron-phonon coupled quantum wire within the dynamic mean-field approximation

We investigate the ground-state properties of an electron-phonon (e-ph) coupled quantum wire in which the effect of coupling between longitudinal optical (LO) phonons and the wire electrons is considered, in addition to the conventional electron-electron (e-e) interactions. The e-ph coupling is included through the Fröhlich interaction potential and the dynamics of electron correlations using the quantum (dynamic) version of self-consistent mean-field approximation of Singwi et al (the qSTLS approach). Numerical results for static structure factor, pair-correlation function and static density susceptibility are presented over a wide range of electron number density parameter r s . We find that the electrons undergo Wigner crystallization at a critical electron density parameter r s c owing to the dynamics of severely correlated electrons. Notably at a fixed wire width, the inclusion of e-ph coupling tends to increase the value of r s c significantly in comparison to a situation in which only the e-e interactions are considered. Besides this, we compute the plasmon-phonon (pl-ph) coupled modes and the energy contribution of e-ph interactions (E e−ph ) to the ground-state energy of the quantum wire, also known as polaronic energy. We find that pl-ph coupled modes resonantly split into two branches, and ∣E e−ph ∣ monotonically increases with rise in r s then becomes almost constant as . Wherever interesting, we compare our results with the static STLS theory and the lattice regularized diffusion Monte Carlo (LRDMC) simulation data of Casula et al.

Carrier Diffusion in GaN : A Cathodoluminescence Study. III. Nature of Nonradiative Recombination at Threading Dislocations

We investigate the impact of threading dislocations with an edge component ($a$ or $a+c$ type) on carrier recombination and diffusion in $\mathrm{Ga}\mathrm{N}$(0001) layers close to the surface as well as in the bulk. To this end, we utilize cathodoluminescence imaging of the top surface of a $\mathrm{Ga}\mathrm{N}$(0001) layer with a deeply buried (In,$\mathrm{Ga}$)N quantum well. Varying the acceleration voltage of the primary electrons and comparing the signal from the layer and the quantum well enables us to probe carrier recombination at depths ranging from the close vicinity of the surface to the position of the quantum well. Our experiments are accompanied by fully three-dimensional Monte Carlo simulations of carrier drift, diffusion, and recombination in the presence of the surface, the quantum well, and the dislocation, taking into account the dislocation strain field and the resulting piezoelectric field at the dislocation outcrop. Near the surface, this field establishes an exciton dead zone around the dislocation, the extent of which is not related to the carrier diffusion length. However, reliable values of the carrier diffusion length can be extracted from the dipolelike energy shift observed in hyperspectral cathodoluminescence maps recorded around the dislocation outcrop at low acceleration voltages. For high acceleration voltages, allowing us to probe a depth where carrier recombination is unaffected by surface effects, we observe a much stronger contrast than expected from the piezoelectric field alone. This finding provides unambiguous experimental evidence for the strong nonradiative activity of edge threading dislocations in bulk $\mathrm{Ga}\mathrm{N}$ and hence also in buried heterostructures.

The 1S0 Pairing Gap in Neutron Matter

We report ab initio calculations of the S wave pairing gap in neutron matter calculated using realistic nuclear Hamiltonians that include two- and three-body interactions. We use a trial state, properly optimized to capture the essential pairing correlations, from which we extract ground state properties by means of auxiliary field diffusion Monte Carlo simulations. We extrapolate our results to the thermodynamic limit by studying the finite-size effects in the symmetry-restored projected Bardeen-Cooper-Schrieffer (PBCS) theory and compare our results to other ab initio studies done in the past. Our quantum Monte Carlo results for the pairing gap show a modest suppression with respect to the mean-field BCS values. These results can be connected to cold atom experiments, via the unitarity regime where fermionic superfluidity assumes a unified description, and they are important in the prediction of thermal properties and the cooling of neutron stars.

A combined first principles study of the structural, magnetic, and phonon properties of monolayer CrI3.

The first magnetic 2D material discovered, monolayer (ML) CrI3, is particularly fascinating due to its ground state ferromagnetism. However, because ML materials are difficult to probe experimentally, much remains unresolved about ML CrI3's structural, electronic, and magnetic properties. Here, we leverage Density Functional Theory (DFT) and high-accuracy Diffusion Monte Carlo (DMC) simulations to predict lattice parameters, magnetic moments, and spin-phonon and spin-lattice coupling of ML CrI3. We exploit a recently developed surrogate Hessian DMC line search technique to determine CrI3's ML geometry with DMC accuracy, yielding lattice parameters in good agreement with recently published STM measurements-an accomplishment given the ∼10% variability in previous DFT-derived estimates depending upon the functional. Strikingly, we find that previous DFT predictions of ML CrI3's magnetic spin moments are correct on average across a unit cell but miss critical local spatial fluctuations in the spin density revealed by more accurate DMC. DMC predicts that magnetic moments in ML CrI3 are 3.62 μB per chromium and -0.145 μB per iodine, both larger than previous DFT predictions. The large disparate moments together with the large spin-orbit coupling of CrI3's I-p orbital suggest a ligand superexchange-dominated magnetic anisotropy in ML CrI3, corroborating recent observations of magnons in its 2D limit. We also find that ML CrI3 exhibits a substantial spin-phonon coupling of ∼3.32 cm-1. Our work, thus, establishes many of ML CrI3's key properties, while also continuing to demonstrate the pivotal role that DMC can assume in the study of magnetic and other 2D materials.

Electrolyte clusters as hydrogen sponges: diffusion Monte Carlo simulations.

We carry out Diffusion Monte Carlo simulations of up to five hydrogen molecules aggregated with two Stockmayer clusters that solvate a single lithium ion. The first one contains six point dipole solvent particles with parameters tuned to emulate nitromethane. The second cluster is a relative large system investigated recently [G. DiEmma, S. Kalette, and E. Curotto, Chem. Phys. Lett. 2019, 725, 80-86]. In both cases we find that the aggregated hydrogen molecules perturb significantly the ground state of the host cluster and form a distorted tetrahedral cage around the Li+ ion. The fifth hydrogen molecule is absorbed by the larger Stockmayer cluster while remaining in the proximity of the solvated charge.

Transfer learned potential energy surfaces: accurate anharmonic vibrational dynamics and dissociation energies for the formic acid monomer and dimer.

The vibrational dynamics of the formic acid monomer (FAM) and dimer (FAD) is investigated from machine-learned potential energy surfaces at the MP2 (PESMP2) and transfer-learned (PESTL) to the CCSD(T) levels of theory. The normal mode (MAEs of 17.6 and 25.1 cm−1) and second order vibrational perturbation theory (VPT2, MAEs of 6.7 and 17.1 cm−1) frequencies from PESTL for all modes below 2000 cm−1 for FAM and FAD agree favourably with experiment. For the OH stretch mode the experimental frequencies are overestimated by more than 150 cm−1 for both FAM and FAD from normal mode calculations. Conversely, VPT2 calculations on PESTL for FAM reproduce the experimental OH frequency to within 22 cm−1. For FAD the VPT2 calculations find the high-frequency OH stretch at 3011 cm−1, compared with an experimentally reported, broad (∼100 cm−1) absorption band with center frequency estimated at ∼3050 cm−1. In agreement with earlier reports, MD simulations at higher temperature shift the position of the OH-stretch in FAM to the red, consistent with improved sampling of the anharmonic regions of the PES. However, for FAD the OH-stretch shifts to the blue and for temperatures higher than 1000 K the dimer partly or fully dissociates using PESTL. Including zero-point energy corrections from diffusion Monte Carlo simulations for FAM and FAD and corrections due to basis set superposition and completeness errors yields a dissociation energy of D0 = −14.23 ± 0.08 kcal mol−1 compared with an experimentally determined value of −14.22 ± 0.12 kcal mol−1.

Candidate structure for the H2 -PRE phase of solid hydrogen

Experimental progress finally reached the metallic solid hydrogen phase, which was predicted by Wigner and Huntington over 80 years ago. However, the different structures in the phase diagram are still being debated due to the difficulty of diffraction experiments for high-pressured hydrogen. The determination of crystal structures under extreme condition is both of the basic condensed matter physics, and in planetary science: the behavior of giant gaseous planets (e.g., Jupiter and Saturn) strongly depends on the properties of inner high-pressured hydrogen. This work describes possible structures appearing under high pressures of $400\ensuremath{\sim}600$ GPa. We applied a structural search using particle swarm optimization with density functional theory (DFT) to propose several candidate structures. For these structures, we performed fixed-node diffusion Monte Carlo simulations combined with DFT zero-point energy corrections to confirm their relative stability. We found $P{2}_{1}/c\text{\ensuremath{-}}8$ as a promising candidate structure for the ${\mathrm{H}}_{2}$-PRE phase. $P{2}_{1}/c\text{\ensuremath{-}}8$ is predicted the most stable at 400 and 500 GPa. $P{2}_{1}/c\text{\ensuremath{-}}8$ reproduces qualitatively the IR spectrum peaks observed in the ${\mathrm{H}}_{2}$-PRE phase.

Metal-insulator transitions in bilayer electron-hole systems in transition metal dichalcogenides

We investigated metal-insulator transitions for double layer two-dimensional electron hole systems in transition metal dicalcogenides (TMDC) stacked on opposite sides of thin layers of boron nitride (BN). The interparticle interaction is calculated by including the screening due to the polarization charges at different interfaces, including that at the encapsultion and the substrate of experimental structures. We compute and compare the energies of the metallic electron-hole plasma and the newly proposed insulating exciton solid with fixed-node diffusion Monte Carlo simulation including the high valley degeneracy of the electron bands. We found that for some examples of current experimental structures, the transition electron/hole density is in an accessible range of g x 10^12 /cm*2 with g between 4.1 and 14.5 for spacer thicknesses between 2.5 and 7.5 nm. Our result raise the possibility of exploiting this effect for logic device applications.

Does powder averaging remove dispersion bias in diffusion MRI diameter estimates within real 3D axonal architectures?

Noninvasive estimation of axon diameter with diffusion MRI holds the potential to investigate the dynamic properties of the brain network and pathology of neurodegenerative diseases. Recent studies use powder averaging to account for complex white matter architectures, but these have not been validated for real axonal geometries from regions that contain fibre crossings. Here, we present 120−304μm long segmented axons from X-ray nano-holotomography volumes of a splenium and crossing fibre region of a vervet monkey brain. We show that the axons in the complex crossing fibre region, which contains callosal, association, and corticospinal connections, exhibit a wider diameter distribution than those of the splenium region. To accurately estimate the axon diameter in these regions, therefore, sensitivity to a wide range of diameters is required. We demonstrate how the q-value, b-value, signal-to-noise ratio and the assumed intra-axonal parallel diffusivity influence the range of measurable diameters with powder average approaches. Furthermore, we show how Gaussian distributed noise results in a wider range of measurable diameter at high b-values than Rician distributed noise, even at high signal-to-noise ratios of 100. The number of gradient directions is also shown to impose a lower bound on measurable diameter. Our results indicate that axon diameter estimation can be performed with only few b-shells, and that additional shells do not improve the accuracy of the estimate. For strong gradients available on human Connectom and preclinical scanners, Monte Carlo simulations of diffusion confirm that powder averaging techniques succeed in providing accurate estimates of axon diameter across a range of diameters, sequence parameters and diffusion times, even in complex white matter architectures. At relatively low b-values, the diameter estimate becomes sensitive to axonal microdispersion and the intra-axonal parallel diffusivity shows time dependency at both in vivo and ex vivo intrinsic diffusivities.

Ultrahigh-b diffusion-weighted imaging for quantitative evaluation of myelination in shiverer mouse spinal cord.

To perform a quantitative evaluation of myelination on WT and myelin-deficient (shiverer) mouse spinal cords using ultrahigh-b diffusion-weighted imaging (UHb-DWI). UHb-DWI of ex vivo on spinal cord specimens of two shiverer (C3HeB/FeJ-shiverer, homozygous genotype for MbPshi ) and six WT (Black Six, C3HeB/FeJ) mice were acquired using 3D multishot diffusion-weighted stimulated-echo EPI, a homemade RF coil, and a small-bore 7T MRI system. Imaging was performed in transaxial plane with 75 × 75 μm2 in-plane resolution, 1-mm-slice thickness, and radial DWI using bmax = 42,890 s/mm2 . Histological evaluation was performed on upper thoracic sections using optical and transmission electron microscopy. Numerical Monte Carlo simulations (MCSs) of water diffusion were performed to facilitate interpretation of UHb-DWI signal-b curves. The white matter ultrahigh-b radial DWI (UHb-rDWI) signal-b curves of WT mouse cords behaved biexponentially with high-b diffusion coefficient DH < 0.020 × 10-3 mm2 /s. However, as expected with less myelination, the signal-b of shiverer mouse cords behaved monoexponentially with significantly greater DH = 0.162 × 10-3 , 0.142 × 10-3 , and 0.164 × 10-3 mm2 /s at anterodorsal, posterodorsal, and lateral columns, respectively. The axial DWI signals of all mouse cords behaved monoexponentially with D = (0.718-1.124) × 10-3 mm2 /s. MCS suggests that these elevated DH are mainly induced by increased water exchange at the myelin sheath. Microscopic results were consistent with the UHb-rDWI findings. UHb-DWI provides quantitative differences in myelination of spinal cords from myelin-deficit shiverer and WT mice. UHb-DWI may become a powerful tool to evaluate myelination in demyelinating disease models that may translate to human diseases, including multiple sclerosis.

Using Diffusion Monte Carlo Wave Functions to Analyze the Vibrational Spectra of H7O3+ and H9O4.

An approach for evaluating spectra from ground state probability amplitudes (GSPA) obtained from diffusion Monte Carlo (DMC) simulations is extended to improve the description of excited state energies and allow for coupling among vibrational excited states. This approach is applied to studies of the protonated water trimer and tetramer, and their deuterated analogs. These ions provide models for solvated hydronium, and analysis of these spectra provides insights into spectral signatures of proton transfer in aqueous environments. In this approach, we obtain a separable set of internal coordinates from the DMC ground state probability amplitude. A basis is then developed from products of the DMC ground state wave function and low-order polynomials in these internal coordinates. This approach provides a compact basis in which the Hamiltonian and dipole moment matrix are evaluated and used to obtain the spectrum. The resulting spectra are in good agreement with experiment and in many cases provide comparable agreement to the results obtained using much larger basis sets. In addition, the compact basis allows for interpretation of the spectral features and how they evolve with cluster size and deuteration.

Quantum self-bound droplets in Bose-Bose mixtures: Effects of higher-order quantum and thermal fluctuations

We systematically study the effects of higher-order quantum and thermal fluctuations on the stabilization of self-bound droplets in Bose mixtures employing the time-dependent Hartree-Fock-Bogoliubov theory. We calculate the ground-state energy, the droplet equilibrium density, the depletion and anomalous density of the droplets as well as the critical temperature as a function of the relevant parameters. Our findings are compared with previous analytical predictions and diffusion Monte Carlo simulations. We employ our theory together with the local density approximation for quantum and thermal fluctuations to obtain an extended finite-temperature Gross-Pitaevskii equation. The density profiles and breathing modes of the droplet are deeply examined in terms of the interaction strength and the temperature by numerically solving the developed generalized Gross-Pitaevskii equation.

Fine structure of spatial diode photoresponse profiles measured while scanning a narrow strip-shaped illumination spot with FPA diode

The three-dimensional Monte Carlo simulation of charge-carrier diffusion in a mercury-cadmium-tellurium based focal plane array (FPA) was used to calculate the spatial diode photoresponse profiles measured while scanning a narrow strip-shaped illumination spot with a selected FPA diode in the limit of largest and lowest diode photocurrents. The simulation was performed for a standard 2D n-on-p FPA with square photodiodes. Fine features in measured spot-scan profiles due to the presence of FPA structure were identified, and the de-pendence of these features on the boundary conditions for diffusing charge carriers at the n-type diode regions was demonstrated. An explanation to the shape of the profiles, fully con-sistent with the computational procedure of the problem, is given.

Probing the ground-state structural transition in small lithium clusters by quantum Monte Carlo simulations.

The ground-state structural transition in small lithium clusters Lin (n = 4 - 6) is analyzed based on the many-body expansion of the interaction energy using the total energy calculated by the fixed-node diffusion Monte Carlo (FN-DMC) simulations. The results show that the transition from 2D to 3D structure occurs through an intricate competition of attractive and repulsive interaction energies. As the structure dimensionality increases from 2D to 3D, the electron-correlation contribution to the interaction energy in the isomer of the ground-state structure is always the largest.

Noncovalent Interactions by the Quantum Monte Carlo Method: Strong Influence of Isotropic Jastrow Cutoff Radii.

We present a paradigmatic example of a strong effect of Jastrow cutoff radii setup on the accuracy of noncovalent interaction energy differences within one-determinant Slater-Jastrow fixed-node diffusion Monte Carlo (1FNDMC) simulations using isotropic Jastrow terms and effective-core potentials. Analysis of total energies, absolute and relative errors, and local energy variance of energy differences vs the reference results suggests a simple procedure to marginalize the related biases. The presented data showcase improvements in dispersion-bounded systems within such a 1FNDMC method.

GPU-Accelerated Neural Network Potential Energy Surfaces for Diffusion Monte Carlo.

Diffusion Monte Carlo (DMC) provides a powerful method for understanding the vibrational landscape of molecules that are not well-described by conventional methods. The most computationally demanding step of these calculations is the evaluation of the potential energy. In this work, a general approach is developed in which a neural network potential energy surface is trained by using data generated from a small-scale DMC calculation. Once trained, the neural network can be evaluated by using highly parallelizable calls to a graphics processing unit (GPU). The power of this approach is demonstrated for DMC simulations on H2O, CH5+, and (H2O)2. The need to include permutation symmetry in the neural network potentials is explored and incorporated into the molecular descriptors of CH5+ and (H2O)2. It is shown that the zero-point energies and wave functions obtained by using the neural network potentials are nearly identical to the results obtained when using the potential energy surfaces that were used to train the neural networks at a substantial savings in the computational requirements of the simulations.