Diffusion Monte Carlo Simulations Research Articles

Quantum Monte Carlo Simulations of the Vibrational Wavefunction of the Aromatic Cyclo[10]carbon Using a Full Dimensional Permutationally Invariant Potential Energy Surface.

New experimental measurements [Sun et al., Nature 2023, 623, 972] of the cyclic C10 reveal a cumulenic pentagon-like D5h structure at ∼5 K. However, the long-standing presumption that a large zero-point vibrational energy combined with an extremely flat D5h ↔ D10h ↔ D5h isomerization pathway washes out the pentagonal D5h structure and yields a symmetric D10h decagon remains at odds with the experiment. We resolve this issue with our fitting approach based on a bond-order charge-density matrix expressed in permutationally invariant polynomials. We train the model on τHCTH/cc-pVQZ data morphed to reproduce a relativistic all-electron CCSDT(Q)/CBS D5h-D10h potential energy barrier (benchmarked previously by others). Large scale diffusion Monte Carlo simulations in full dimensionality show that the vibrational ground state of C10 has compositional character of more than 96% D5h, fully reflecting the experimental imaging data. Quantum mechanical variational calculations in 1-D further suggest persistence of the D5h symmetry structure at higher temperatures.

Tell Machine Learning Potentials What They Are Needed For: Simulation-Oriented Training Exemplified for Glycine.

Machine learning potentials (MLPs) are widely applied as an efficient alternative way to represent potential energy surfaces (PESs) in many chemical simulations. The MLPs are often evaluated with the root-mean-square errors on the test set drawn from the same distribution as the training data. Here, we systematically investigate the relationship between such test errors and the simulation accuracy with MLPs on an example of a full-dimensional, global PES for the glycine amino acid. Our results show that the errors in the test set do not unambiguously reflect the MLP performance in different simulation tasks, such as relative conformer energies, barriers, vibrational levels, and zero-point vibrational energies. We also offer an easily accessible solution for improving the MLP quality in a simulation-oriented manner, yielding the most precise relative conformer energies and barriers. This solution also passed the stringent test by diffusion Monte Carlo simulations.

Correlations between the Structures and Spectra of Protonated Water Clusters.

Badger's rule-like correlations between OH stretching frequencies and intensities and the OH bond length are used to develop a spectral mapping procedure for studies of pure and protonated water clusters. This approach utilizes the vibrationally averaged OH bond lengths, which were obtained from diffusion Monte Carlo simulations that were performed using the general potential developed by Yu and Bowman. Good agreement is achieved between the spectra obtained using this approach and previously reported spectra for H+(H2O)n clusters, with n = 3, 4, and 5, as well as their perdeuterated analogues. The analysis of the spectra obtained by this spectral mapping approach supports previous work that assigned the spectrum of H+(H2O)6 to a mixture of Eigen and Zundel-like structures. Analysis of the calculated spectra also suggests a reassignment of the frequency of one of the transitions that involves the OH stretching vibration of the OH bonds in the hydronium core in the Eigen-like structure of H+(H2O)6 from 1917 cm-1 to roughly 2100 cm-1. For D+(D2O)6, comparison of the measured spectrum to those obtained by using the spectral mapping approach suggests that the carrier of the measured spectrum is one or more of the isomers of D+(D2O)6 that contain a four-membered ring and two flanking water molecules. While there are several candidate structures, the two flanking water molecules most likely form a chain that is bound to the hydronium core.

The effects of axonal beading and undulation on axonal diameter estimation from diffusion MRI: Insights from simulations in human axons segmented from three-dimensional electron microscopy.

The increasing availability of high-performance gradient systems in human MRI scanners has generated great interest in diffusion microstructural imaging applications such as axonal diameter mapping. Practically, sensitivity to axon diameter in diffusion MRI is attained at strong diffusion weightings , where the deviation from the expected scaling in white matter yields a finite transverse diffusivity, which is then translated into an axon diameter estimate. While axons are usually modeled as perfectly straight, impermeable cylinders, local variations in diameter (caliber variation or beading) and direction (undulation) are known to influence axonal diameter estimates and have been observed in microscopy data of human axons. In this study, we performed Monte Carlo simulations of diffusion in axons reconstructed from three-dimensional electron microscopy of a human temporal lobe specimen using simulated sequence parameters matched to the maximal gradient strength of the next-generation Connectome 2.0 human MRI scanner ( 500 mT/m). We show that axon diameter estimation is accurate for nonbeaded, nonundulating fibers; however, in fibers with caliber variations and undulations, the axon diameter is heavily underestimated due to caliber variations, and this effect overshadows the known overestimation of the axon diameter due to undulations. This unexpected underestimation may originate from variations in the coarse-grained axial diffusivity due to caliber variations. Given that increased axonal beading and undulations have been observed in pathological tissues, such as traumatic brain injury and ischemia, the interpretation of axon diameter alterations in pathology may be significantly confounded.

Tensor-valued diffusion MRI of human acute stroke.

Tensor-valued diffusion encoding can disentangle orientation dispersion and subvoxel anisotropy, potentially offering insight into microstructural changes after cerebral ischemia. The purpose was to evaluate tensor-valued diffusion MRI in human acute ischemic stroke, assess potential confounders from diffusion time dependencies, and compare to Monte Carlo diffusion simulations of axon beading. Linear (LTE) and spherical (STE) b-tensor encoding with inherently different effective diffusion times were acquired in 21 acute ischemic stroke patients between 3 and 57 h post-onset at 3 T in 2.5 min. In an additional 10 patients, STE with 2 LTE yielding different effective diffusion times were acquired for comparison. Diffusional variance decomposition (DIVIDE) was used to estimate microscopic anisotropy (μFA), as well as anisotropic, isotropic, and total diffusional variance (MKA , MKI , MKT ). DIVIDE parameters, and diffusion tensor imaging (DTI)-derived mean diffusivity and fractional anisotropy (FA) were compared in lesion versus contralateral white matter. Monte Carlo diffusion simulations of various cylindrical geometries for all b-tensor protocols were used to interpret parameter measurements. MD was ˜40% lower in lesions for all LTE/STE protocols. The DIVIDE parameters varied with effective diffusion time: higher μFA and MKA in lesion versus contralateral white matter for STE with longer effective diffusion time LTE, whereas the shorter effective diffusion time LTE protocol yielded lower μFA and MKA in lesions. Both protocols, regardless of diffusion time, were consistent with simulations of greater beading amplitude and intracellular volume fraction. DIVIDE parameters depend on diffusion time in acute stroke but consistently indicate neurite beading and larger intracellular volume fraction.

Molecular Imaging with Aquaporin-Based Reporter Genes: Quantitative Considerations from Monte Carlo Diffusion Simulations.

Aquaporins provide a unique approach for imaging genetic activity in deep tissues by increasing the rate of cellular water diffusion, which generates a magnetic resonance contrast. However, distinguishing aquaporin signals from the tissue background is challenging because water diffusion is influenced by structural factors, such as cell size and packing density. Here, we developed a Monte Carlo model to analyze how cell radius and intracellular volume fraction quantitatively affect aquaporin signals. We demonstrated that a differential imaging approach based on subtracting signals at two diffusion times can improve specificity by unambiguously isolating aquaporin signals from the tissue background. We further used Monte Carlo simulations to analyze the connection between diffusivity and the percentage of cells engineered to express aquaporin and established a mapping that accurately determined the volume fraction of aquaporin-expressing cells in mixed populations. The quantitative framework developed in this study will enable a broad range of applications in biomedical synthetic biology, requiring the use of aquaporins to noninvasively monitor the location and function of genetically engineered devices in live animals.

Monte Carlo simulation of water diffusion through cardiac tissue models.

Monte Carlo diffusion simulations are commonly used to establish a reliable ground truth of tissue microstructure, including for the validation of diffusion-weighted MRI. However, selecting simulation parameters is challenging and affects validity and reproducibility. We conducted experiments to investigate critical conditions in Monte Carlo simulations, such as tissue representation complexity, simulated molecules, update duration, and compartment size. Results show significant changes in microstructure characteristics when parameters are altered, emphasizing the importance of careful control for a reliable ground truth.

Trihydrogen Cation Helium Clusters: A New Potential Energy Surface.

We present a new analytical potential energy surface (PES) for the interaction between the trihydrogen cation and a He atom, , in its electronic ground state. The proposed PES has been built as a sum of two contributions: a polarization energy term due to the electric field generated by the molecular cation at the position of the polarizable He atom, and an exchange-repulsion and dispersion interactions represented by a sum of "atom-bond" potentials between the three bonds of and the He atom. All parameters of this new PES have been chosen and fitted from data obtained from high-level ab-initio calculations. Using this new PES plus the Aziz-Slaman potential for the interaction between Helium atoms and assuming pair-wise interactions, we carry out classical Basin-Hopping (BH) global optimization, semiclassical BH with Zero Point Energy corrections, and quantum Diffusion Monte Carlo simulations. We have found the minimum energy configurations of small He clusters doped with , , with N=1-16. The study of the energies of these clusters allows us to find a pronounced anomaly for N=12, in perfect agreement with previous experimental findings, which we relate to a greater relative stability of this aggregate.

Neural network-based inverse model for diffuse reflectance spectroscopy.

In diffuse reflectance spectroscopy, the retrieval of the optical properties of a target requires the inversion of a measured reflectance spectrum. This is typically achieved through the use of forward models such as diffusion theory or Monte Carlo simulations, which are iteratively applied to optimize the solution for the optical parameters. In this paper, we propose a novel neural network-based approach for solving this inverse problem, and validate its performance using experimentally measured diffuse reflectance data from a previously reported phantom study. Our inverse model was developed from a neural network forward model that was pre-trained with data from Monte Carlo simulations. The neural network forward model then creates a lookup table to invert the diffuse reflectance to the optical coefficients. We describe the construction of the neural network-based inverse model and test its ability to accurately retrieve optical properties from experimentally acquired diffuse reflectance data in liquid optical phantoms. Our results indicate that the developed neural network-based model achieves comparable accuracy to traditional Monte Carlo-based inverse model while offering improved speed and flexibility, potentially providing an alternative for developing faster clinical diagnosis tools. This study highlights the potential of neural networks in solving inverse problems in diffuse reflectance spectroscopy.

Sheet and void porous media models for brain interstitial space.

The interstitial space (ISS) component of brain extracellular space resembles an unconsolidated porous medium. Previous analysis of the diffusion of small molecules in this domain shows that the typical porosity is 0.2 and typical tortuosity 1.6. An ensemble of cubic cells separated by uniform sheets of ISS cannot generate the measured tortuosity, even if some of the tortuosity value is attributed to interstitial viscosity, so more complex models are needed. Here two models are analysed: the corner cubic void (CCV) and the edge tunnel void (ETV). Both models incorporate dead spaces formed from local expansions of the ISS to increase geometrical tortuosity. Using Monte Carlo simulation of diffusion it is found that in the range of normal porosities, the square of the tortuosity is a linear function of the ratio of void to sheet volumes for the CCV model and this model can generate the experimentally observed tortuosities. For abnormally high porosities, however, the linear relation fails. The ETV model shows a quartic functional relation and can only generate the observed tortuosity if interstitial viscosity is present. The CCV model is used to analyse the recently described changes in porosity between asleep and awake brain states.

CACTUS: a computational framework for generating realistic white matter microstructure substrates.

Monte-Carlo diffusion simulations are a powerful tool for validating tissue microstructure models by generating synthetic diffusion-weighted magnetic resonance images (DW-MRI) in controlled environments. This is fundamental for understanding the link between micrometre-scale tissue properties and DW-MRI signals measured at the millimetre-scale, optimizing acquisition protocols to target microstructure properties of interest, and exploring the robustness and accuracy of estimation methods. However, accurate simulations require substrates that reflect the main microstructural features of the studied tissue. To address this challenge, we introduce a novel computational workflow, CACTUS (Computational Axonal Configurator for Tailored and Ultradense Substrates), for generating synthetic white matter substrates. Our approach allows constructing substrates with higher packing density than existing methods, up to 95% intra-axonal volume fraction, and larger voxel sizes of up to 500μm3 with rich fibre complexity. CACTUS generates bundles with angular dispersion, bundle crossings, and variations along the fibres of their inner and outer radii and g-ratio. We achieve this by introducing a novel global cost function and a fibre radial growth approach that allows substrates to match predefined targeted characteristics and mirror those reported in histological studies. CACTUS improves the development of complex synthetic substrates, paving the way for future applications in microstructure imaging.

Monitoring optoporated process on mammalian cells by real-time measurement of membrane resealing time.

Resealing time based loading efficiency of optoporation is the key parameter for drug or gene delivery. This work describes a comparatively simple optical approach to directly measure the cell membrane resealing time of the gold nanoparticle mediated photoporation. To establish a membrane potential detection optical system, which can provide a direct measurement of resealing time of the optoporated cells. Voltage sensitive dye has been used to label the gold nanoparticle covered cell before laser activation and the resealing time was estimated from the voltage change due to the fluorescence light intensity change before and after laser activation. The approach has been validated by the simulated data based on diffusion model and Monte Carlo simulation and the experimental data obtained from a flow cytometry analysis. The measured resealing time after perforation varied from 28.6 to 163.8s on Hela cells when the irradiation fluence was increased, with a correlation coefficient () of 0.9938. This result is in agreement with the resealing time (1-2min) of photothermal porated Hela cells measured by electrical impedance method. The intracellular delivery efficiency of extracellular macromolecular under the same irradiation fluence depends mainly on diffusion velocity rather than pore size. The method described here can be used to directly measure resealing time of optoporated cells for accurately estimating the loading efficiency on discovering the mechanism of optoporation.

Quantum Monte Carlo study of the role of p -wave interactions in ultracold repulsive Fermi gases

Single-component ultracold atomic Fermi gases are usually described using noninteracting many-fermion models. However, recent experiments reached a regime where $p$-wave interactions among identical fermionic atoms are important. In this paper, we employ variational and fixed-node diffusion Monte Carlo simulations to investigate the ground-state properties of single-component Fermi gases with short-range repulsive interactions. We determine the zero-temperature equation of state, and elucidate the roles played by the $p$-wave scattering volume and the $p$-wave effective range. A comparison against recently derived second-order perturbative results shows good agreement in a broad range of interaction strength. We also compute the quasiparticle effective mass, and we confirm the perturbative prediction of a linear contribution in the $p$-wave scattering volume, while we find significant deviations from the beyond-mean-field perturbative result, already for moderate interaction strengths. Finally, we determine ground-state energies for two-component unpolarized Fermi gases with both interspecies and intraspecies hard-sphere interactions, finding remarkable agreement with a recently derived fourth-order expansion that includes $p$-wave contributions.

Durability life prediction and horizontal bearing characteristics of CFRP composite piles in marine environments

In this paper, the durability life and horizontal bearing characteristics of carbon fiber reinforced polymers (CFRP) composite piles in marine environments are studied. The durability life of CFRP composite piles is divided into the initial corrosion stage of reinforcement and the crack propagation stage of concrete protection layer. The chloride diffusion model and Monte Carlo simulation method are used to predict the initial corrosion time of CFRP composite piles. Based on the thick-walled cylinder theory, the critical corrosion depth of the reinforced steel corresponding to the cracking of concrete protective layer is deduced. The durability life prediction model of crack propagation stage is established. The flexural stiffness reduction factor of CFRP composite piles with different replacement ratios is obtained by conducting the model pile bending tests. The attenuation law of bending stiffness and horizontal bearing characteristics of CFRP composite piles in marine environments are analyzed. The results show that the higher the replacement ratio of CFRP bar, the slower the reduction rate of flexural stiffness of CFRP composite pile is. Under the same buried depth, the pile bending moment and shear force of CFRP composite piles decrease with the increase of CFRP reinforcement replacement ratio. The horizontal displacement of CFRP composite piles increases with the increase of CFRP reinforcement replacement ratio.

How Many Excitons Can Combine?

Quantum diffusion Monte Carlo simulation demonstrated the formation of polyexcitons in two-dimensional multi-valley semiconductor systems, where all exciton pairs were energetically bound by equal-strength “chemical bonds.”

Machine learning based on-the-fly kinetic Monte Carlo simulations of sluggish diffusion in Ni-Fe concentrated alloys

Defect diffusion in concentrated alloys plays a key role on governing their unique mechanical and physical properties. In such alloys, defect diffusion depends on its complex local atomic environment and varies from site to site due to the chemical disorder. On-the-fly determination of the defect migration barrier at every site using the standard nudged elastic band (NEB) method is computationally expensive and often impractical. In this work, we couple machine learning and kinetic Monte Carlo (KMC) to study vacancy-mediated sluggish diffusion in concentrated Ni-Fe model alloys. Based on about 32,000 pre-calculated NEB barriers, an artificial neural network (ANN) based machine learning model is developed to accurately predict the vacancy migration barriers for arbitrary local atomic environments, including both random solution configurations and alloys with short-range orders. The ANN model is then coupled with KMC (ANN-KMC) to determine the vacancy migration barriers on-the-fly, enabling an efficient study of the vacancy diffusion in the full composition range at a wide range of temperatures. In addition, a composition and temperature dependent jump attempt frequency model is developed. Upon calibration, the ANN-KMC modeling can predict nearly identical vacancy diffusivities as those obtained from independent molecular dynamics (MD) and temperature accelerated dynamics (TAD) simulations at their accessible temperatures. The sluggish diffusion mechanisms in this specific alloy system at both high and low temperatures are discussed based on the ANN-KMC results.

Fixed-node diffusion Monte Carlo simulation of small ionized carbon clusters

The structural and energetic features of small cationic carbon clusters with up to ten atoms are investigated using the Hartree–Fock, density functional theory, and fixed-node diffusion Monte Carlo simulations. The results show that the cationic carbon clusters present significant structural changes with relevant Jahn–Teller distortion compared to the neutral ones. A satisfactory agreement with available experimental results is observed for ionization potential, relative binding energy, and atomic dissociation energy. Our calculations present quantitative investigations on the electron correlation effects in the cationic carbon clusters and show the important roles of the electron correlation in the stability of these clusters.

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+.