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At least 1,063 records · Page 59

Benchmarking quantum trial wavefunctions for phaseless auxiliary-field quantum Monte Carlo

The phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) method is a stochastic imaginary-time projection technique for computing ground-state properties of strongly correlated quantum systems, with accuracy that depends critically on the choice of trial wavefunction. Here, we investigate ph-AFQMC with trial states prepared using parameterized quantum circuits. In this work, we present a comprehensive benchmarking study of quantum trial wavefunctions spanning unitary coupled-cluster, Hamiltonian-informed, Jastrow-inspired, and adaptively constructed ansatze. The benchmarking evaluates accuracy, expressibility, and scalability of these ansatze within the QC-AFQMC framework. We test these ansatze on linear hydrogen chains under bond stretching and find that several ansatz families produce chemically accurate ph-AFQMC energies across the dissociation curve. We have performed simulations using the CUDA-Q quantum development platform on the GPU partition of the Perlmutter supercomputer. When comparing ansatze at similar numbers of variational parameters, we find that different ansatz families yield comparable ph-AFQMC results despite exhibiting substantially different variational energies, optimization costs, and circuit depths. Our results indicate that the variational energy of an ansatz is not always a reliable indicator of its quality for ph-AFQMC and reveal instances of over-parameterization. In the strongly correlated regime, trial wavefunctions obtained from adaptive ansatze, exemplified here by ADAPT-VQE with the UCCSD operator pool, can outperform their fixed-ansatz counterparts (UCCSD) in terms of projected energies while using substantially more compact circuits, providing a flexible route to optimize quantum resources within the ph-AFQMC framework.

Rofougaran, Rod [LBNL, Berkeley; Columbia U.; PNL,↗

Manifold Learning-Based Polynomial Chaos Expansions for High-Dimensional Surrogate Models

In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of a set of high-dimensional data representing quantities of interest of the computational or analytical model. For this purpose, we employ Grassmannian diffusion maps, a two-step nonlinear dimension reduction technique which allows us to reduce the dimensionality of the data and identify meaningful geometric descriptions in a parsimonious and inexpensive manner. Polynomial chaos expansion is then used to construct a mapping between the stochastic input parameters and the diffusion coordinates of the reduced space. An adaptive clustering technique is proposed to identify an optimal number of clusters of points in the latent space. The similarity of points allows us to construct a number of geometric harmonic emulators which are finally utilized as a set of inexpensive pretrained models to perform an inverse map of realizations of latent features to the ambient space and thus perform accurate out-of-sample predictions. Thus, the proposed method acts as an encoder-decoder system which is able to automatically handle very high-dimensional data while simultaneously operating successfully in the small-data regime. The method is demonstrated on two benchmark problems and on a system of advection-diffusion-reaction equations which model a first-order chemical reaction between two species. In all test cases, the proposed method is able to achieve highly accurate approximations which ultimately lead to the significant acceleration of UQ tasks.

42 ENGINEERING↗

Detecting anomalous packets in network transfers: investigations using PCA, autoencoder and isolation forest in TCP

Large-scale scientific workflows rely heavily on high-performance file transfers. These transfers require strict quality parameters such as guaranteed bandwidth, no packet loss or data duplication. To have successful file transfers, methods such as predetermined thresholds and statistical analysis need to be done to determine abnormal patterns. Network administrators routinely monitor and analyze network data for diagnosing and alleviating these, making decisions based on their experience. However, as networks grow and become complex, monitoring large data files and quickly processing them, makes it improbable to identify errors and rectify these. Abnormal file transfers have been classified by simply setting alert thresholds, via tools such as PerfSonar and TCP statistics (Tstat). This paper investigates the feasibility of unsupervised feature extraction methods for identifying network anomaly patterns with three unsupervised classification methods—principal component analysis, autoencoder and isolation forest. Here, we collect file transfer statistics from two experiment sets—synthetic iPerf generated traffic and 1000 Genome workflow runs, with synthetically introduced anomalies. Our results show that while PCA and a simple autoencoder finds it difficult to detect clusters, the tree-variant isolation forest is able to identify anomalous packets by breaking down TCP traces into tree classes early.

97 MATHEMATICS AND COMPUTING↗

Leveraging graph clustering techniques for cyber‐physical system analysis to enhance disturbance characterisation

Abstract Cyber‐physical systems have behaviour that crosses domain boundaries during events such as planned operational changes and malicious disturbances. Traditionally, the cyber and physical systems are monitored separately and use very different toolsets and analysis paradigms. The security and privacy of these cyber‐physical systems requires improved understanding of the combined cyber‐physical system behaviour and methods for holistic analysis. Therefore, the authors propose leveraging clustering techniques on cyber‐physical data from smart grid systems to analyse differences and similarities in behaviour during cyber‐, physical‐, and cyber‐physical disturbances. Since clustering methods are commonly used in data science to examine statistical similarities in order to sort large datasets, these algorithms can assist in identifying useful relationships in cyber‐physical systems. Through this analysis, deeper insights can be shared with decision‐makers on what cyber and physical components are strongly or weakly linked, what cyber‐physical pathways are most traversed, and the criticality of certain cyber‐physical nodes or edges. This paper presents several types of clustering methods for cyber‐physical graphs of smart grid systems and their application in assessing different types of disturbances for informing cyber‐physical situational awareness. The collection of these clustering techniques provide a foundational basis for cyber‐physical graph interdependency analysis.

97 MATHEMATICS AND COMPUTING↗

The Model Assessment Wizard (MAW): A Visualization System for Ontology Constraint Violations

Validation and verification of engineering models is important to understand potential weaknesses and issues in the model. This is accomplished through the application of constraint logic to the model. These models and the constraints put upon them can be represented through a graph structure. Here we give a visualization system to aid users understanding, locating, and fixing constraint violations in their systems. We give users several ways to narrow down on the specific errors and parts of the graph they’re interested in. Users have the opportunity to choose the types of errors that will be shown in the graph. Clustering is applied to the graph to help users narrow down their searches. Several other graph interactions are given to support discovery of constraint violations.

97 MATHEMATICS AND COMPUTING↗

An in-silico NMR laboratory for nuclear magnetic shieldings computed via finite fields: Exploring nucleus-specific renormalizations of MP2 and MP3

Here we developed and implemented a method-independent, fully numerical, finite difference approach to calculating nuclear magnetic resonance shieldings, using gauge-including atomic orbitals. The resulting capability can be used to explore non-standard methods, given only the energy as a function of finite-applied magnetic fields and nuclear spins. For example, standard second-order Møller-Plesset theory (MP2) has well-known efficacy for 1H and 13C shieldings and known limitations for other nuclei such as 15N and 17O. It is, therefore, interesting to seek methods that offer good accuracy for 15N and 17O shieldings without greatly increased compute costs, as well as exploring whether such methods can further improve 1H and 13C shieldings. Using a small molecule test set of 28 species, we assessed two alternatives: κ regularized MP2 (κ-MP2), which provides energy-dependent damping of large amplitudes, and MP2.X, which includes a variable fraction, X, of third-order correlation (MP3). The aug-cc-pVTZ basis was used, and coupled cluster with singles and doubles and perturbative triples [CCSD(T)] results were taken as reference values. Our κ-MP2 results reveal significant improvements over MP2 for 13C and 15N, with the optimal κ value being element-specific. κ-MP2 with κ = 2 offers a 30% rms error reduction over MP2. For 15N, κ-MP2 with κ = 1.1 provides a 90% error reduction vs MP2 and a 60% error reduction vs CCSD. On the other hand, MP2.X with a scaling factor of 0.6 outperformed CCSD for all heavy nuclei. These results can be understood as providing renormalization of doubles amplitudes to partially account for neglected triple and higher substitutions and offer promising opportunities for future applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Neutrons in Structural Biology: Challenges and Opportunities (Workshop Report)

Gaining a thorough understanding of biological systems requires building our knowledge about biological processes from the level of atoms and electrons, and up to whole organisms. Such comprehensive knowledge will allow for a predictive understanding of complex biological systems behavior. It will guide us in the design and development of novel therapeutics and vaccines to tackle existing health threats and to prepare for future pandemics, and it will provide information necessary to create new biomaterials and bio-inspired technologies through manipulation of biological macromolecules, their assemblies, single cells and even microorganisms. Reaching these goals will require a synergistic combination of multiple experimental techniques with molecular calculations and predictive simulations, and the design and development of new techniques and capabilities that bridge current knowledge and technology gaps. Neutron scattering provides unique information about the biomacromolecular structure and function and can play a major role in achieving these goals. A workshop was held to engage the scientific community in identifying pressing challenges in biochemistry, structural biology, enzymology and structure-guided drug design not solved with the current neutron scattering technologies or utilizing other structural biology techniques such as X-ray crystallography, NMR, and cryo-EM. The workshop brought together structural biology, biochemistry and computational experts, as well as early career researchers and students, creating a forum for discussing scientific advancement and collaboration. The workshop included a one-day satellite training workshop where graduate students and postdoctoral researchers were educated in the application of neutron crystallography and small-angle scattering in structural biology. Furthermore, the Instrument Scientific Advisory Board (ISAB) for the development of a macromolecular neutron diffractometer at ORNL’s Second Target Station was introduced at the workshop. The major outcome was that neutrons can provide atomic-level understanding of biomacromolecular structure, function and dynamics which is of paramount importance for addressing the identified challenges. Neutron crystallography, in particular, can resolve long-standing biochemical issues regarding enzyme function by delineating the underlying chemistry and can have a major impact on the design of small-molecule therapeutics, especially in combination with molecular computation (quantum chemistry and molecular dynamics simulations) and the emerging artificial intelligence (AI)-assisted drug design technologies. The unique properties of neutrons, including their high sensitivity to hydrogen and their non-destructive nature, make them ideal probes of biological matter. There is a palpable need in the scientific community to expand and enhance the impact of neutron sciences on biology. Neutron crystallography is the only structural biology method capable of determining positions of all hydrogen atoms in proteins, nucleic acids and their complexes at near-physiological temperatures and of unstable species at cryogenic temperatures. Moreover, neutron analysis is non-ionizing, non-destructive and does not perturb the structure or redox chemistry of active site metal centers and clusters in proteins, which can be invaluable for studying radiation-sensitive metalloprotein complexes. Further, neutron energies used in scattering applications are similar to atomic motions, permitting neutron spectroscopies to characterize the dynamics of biomacromolecules on the picosecond to microsecond timescales. The different sensitivities of neutrons to protium (H) and deuterium (D) isotopes of hydrogen allow enhanced visibility of specific parts of biological complexes through isotopic labeling. The impact of neutrons will be most powerful when neutron scattering is combined with complementary experimental techniques that use photons and electrons, and with high-performance computing. The interconnection and mutuality of the experimental and theoretical capabilities will drive discoveries in biological and health sciences to generate more complete picture of complex biological systems. The major limitation in the field of biological neutron crystallography has been signal-to-noise, demanding large samples that are difficult to produce for the majority of biomacromolecules and limiting the applicability of this technique in biological sciences. A neutron crystallography instrument at the Second Target Station will revolutionize biological science with neutrons by engaging a large scientific community of structural biologists, enabling successful neutron diffraction experiments from radically smaller biomacromolecular crystals, resolving unanswered biochemical questions, and meaningfully contributing to rational drug design. The meeting highlighted 10 grand challenges that will be addressed with this advanced capability over the next decade and beyond, and the recommendations required to help address them are given below.

59 BASIC BIOLOGICAL SCIENCES↗

Unsupervised atomic data mining via multi-kernel graph autoencoders for machine learning force fields

Constructing a chemically diverse dataset while avoiding sampling bias is critical to training efficient and generalizable force fields. However, in computational chemistry and materials science, many common dataset generation techniques are prone to oversampling regions of the potential energy surface. Furthermore, these regions can be difficult to identify and isolate from each other or may not align well with human intuition, making it challenging to systematically remove bias in the dataset. While traditional clustering and pruning (down-sampling) approaches can be useful for this, they can often lead to information loss or a failure to properly identify distinct regions of the potential energy surface due to difficulties associated with the high dimensionality of atomic descriptors. In this work, we introduce the Multi-kernel Edge Attention-based Graph Autoencoder (MEAGraph) model, an unsupervised approach for analyzing atomic datasets. MEAGraph combines multiple linear kernel transformations with attention-based message passing to capture geometric sensitivity and enable effective dataset pruning without relying on labels or extensive training. Demonstrated applications on niobium, tantalum, and iron datasets show that MEAGraph efficiently groups similar atomic environments, allowing for the use of basic pruning techniques for removing sampling bias. This approach provides an effective method for representation learning and clustering that can be used for data analysis, outlier detection, and dataset optimization.

Materials science↗

Covariance matrices for variance-suppressed simulations

ABSTRACT Cosmological N-body simulations provide numerical predictions of the structure of the Universe against which to compare data from ongoing and future surveys, but the growing volume of the Universe mapped by surveys requires correspondingly lower statistical uncertainties in simulations, usually achieved by increasing simulation sizes at the expense of computational power. It was recently proposed to reduce simulation variance without incurring additional computational costs by adopting fixed-amplitude initial conditions. This method has been demonstrated not to introduce bias in various statistics, including the two-point statistics of galaxy samples typically used for extracting cosmological parameters from galaxy redshift survey data, but requires us to revisit current methods for estimating covariance matrices of clustering statistics for simulations. In this work, we find that it is not trivial to construct covariance matrices analytically for fixed-amplitude simulations, but we demonstrate that ezmock (Effective Zel’dovich approximation mock catalogue), the most efficient method for constructing mock catalogues with accurate two- and three-point statistics, provides reasonable covariance matrix estimates for such simulations. We further examine how the variance suppression obtained by amplitude-fixing depends on three-point clustering, small-scale clustering, and galaxy bias, and propose intuitive explanations for the effects we observe based on the ezmock bias model.

79 ASTRONOMY AND ASTROPHYSICS↗

Comparing the Performance of Julia on CPUs versus GPUs and Julia-MPI versus Fortran-MPI: a case study with MPAS-Ocean (Version 7.1)

Abstract. Some programming languages are easy to develop at the cost of slow execution, while others are fast at runtime but much more difficult to write. Julia is a programming language that aims to be the best of both worlds – a development and production language at the same time. To test Julia's utility in scientific high-performance computing (HPC), we built an unstructured-mesh shallow water model in Julia and compared it against an established Fortran-MPI ocean model, the Model for Prediction Across Scales–Ocean (MPAS-Ocean), as well as a Python shallow water code. Three versions of the Julia shallow water code were created: for single-core CPU, graphics processing unit (GPU), and Message Passing Interface (MPI) CPU clusters. Comparing identical simulations revealed that our first version of the Julia model was 13 times faster than Python using NumPy, where both used an unthreaded single-core CPU. Further Julia optimizations, including static typing and removing implicit memory allocations, provided an additional 10–20× speed-up of the single-core CPU Julia model. The GPU-accelerated Julia code was almost identical in terms of performance to the MPI parallelized code on 64 processes, an unexpected result for such different architectures. Parallelized Julia-MPI performance was identical to Fortran-MPI MPAS-Ocean for low processor counts and ranges from 2× faster to 2× slower for higher processor counts. Our experience is that Julia development is fast and convenient for prototyping but that Julia requires further investment and expertise to be competitive with compiled codes. We provide advice on Julia code optimization for HPC systems.

54 ENVIRONMENTAL SCIENCES↗

Shape-driven, emergent behavior in active particle mixtures

Abstract Active particle systems can vary greatly from one-component systems of spheres to mixtures of particle shapes at different composition ratios. We investigate computationally the combined effect of anisotropy and stoichiometry on the collective behavior of two-dimensional active colloidal mixtures of polygons. We uncover three emergent phenomena not yet reported in active Brownian particle systems. First, we find that mixtures containing hexagons exhibit micro-phase separation with large grains of hexagonal symmetry. We quantify a measurable, implicit ‘steric attraction’ between the active particles as a result of shape anisotropy and activity. This calculation provides further evidence that implicit interactions in active systems, even without explicit attraction, can lead to an effective preferential attraction between particles. Next, we report stable fluid clusters in mixtures containing one triangle or square component. We attribute the fluidization of the dense cluster to the interplay of cluster destabilizing particles, which introduce grain boundaries and slip planes into the system, causing solid-like clusters to break up into fluid clusters. Third, we show that fluid clusters can coexist with solid clusters within a sparse gas of particles in a steady state of three coexisting phases. Our results highlight the potential for a wide variety of behavior to be accessible to active matter systems and establish a route to control active colloidal systems through simple parameter designs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Chapter 21. Atomic-Level Dislocation Dynamics in Irradiated Metals

Primary damage and microstructure evolution in structural nuclear materials operating under conditions of a high flux of energetic atomic particles and high temperature and stress lead to the formation of a high concentration, non-homogeneous distribution of defect clusters in the form of dislocation loops, voids, gas-filled bubbles and radiation-induced precipitates of nanometer scale. They cause changes in many material properties. Being obstacles to dislocation glide, they strongly affect the mechanical properties, with an increase in yield and flow stresses and a reduction in ductility. Atomic-scale computer simulations can provide details of how these effects are influenced by the obstacle structure, applied stress, strain rate and temperature. Processes such as obstacle cutting, transformation, absorption and drag are observed. Some recent results for body-centered and face-centered cubic metals are described in this review and, where appropriate, comparisons are drawn with predictions based on the elasticity theory of crystal defects. Perspectives on how to use this information at higher scales and in particular in mesoscale, dislocation dynamics simulations are also discussed.

Osetskiy, Yury N.↗

Uncovering acoustic signatures of pore formation in laser powder bed fusion

Abstract We present a machine learning workflow to discover signatures in acoustic measurements that can be utilized to create a low-dimensional model to accurately predict the location of keyhole pores formed during additive manufacturing processes. Acoustic measurements were sampled at 100 kHz during single-layer laser powder bed fusion (LPBF) experiments, and spatio-temporal registration of pore locations was obtained from post-build radiography. Power spectral density (PSD) estimates of the acoustic data were then decomposed using non-negative matrix factorization with custom $$\varvec{k}$$ k -means clustering (NMF $$\varvec{k}$$ k ) to learn the underlying spectral patterns associated with pore formation. NMF $$\varvec{k}$$ k returned a library of basis signals and matching coefficients to blindly construct a feature space based on the PSD estimates in an optimized fashion. Moreover, the NMF $$\varvec{k}$$ k decomposition led to the development of computationally inexpensive machine learning models which are capable of quickly and accurately identifying pore formation with classification accuracy of supervised and unsupervised label learning greater than 95% and 90%, respectively. The intrinsic data compression of NMF k , the relatively light computational cost of the machine learning workflow, and the high classification accuracy makes the proposed workflow an attractive candidate for edge computing toward in-situ keyhole pore prediction in LPBF.

36 MATERIALS SCIENCE↗

Computational study of the electrostatic potential and charges of multivalent ionic liquid molecules

The electrostatic interactions in ionic liquids (ILs) can be difficult to quantify, but this information is very valuable for improving intermolecular potentials for performing molecular-level simulations. Although polarizable forcefields can provide improved accuracy, the computational efficiency of fixed charge molecular models is often preferred for larger systems. Here, we propose a multi-scale screening approach for analyzing the charge scaling behavior and other electrostatic properties of ILs, which is more attainable than previous analysis methods that rely on the IL crystalline structures. Based on isolated molecules and small clusters, we study the electrostatic potential properties and charges of multivalent IL molecules using density-functional theory calculations and ab initio molecular dynamics simulations. The charges of the IL molecules are calculated and compared using several different charge estimation techniques. Although there are some differences among the estimated partial charges on the atoms, the total anion and cation charges are very similar. In conclusion, the charge scaling factors are substantial, and they are only slightly affected by the IL cluster size model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Probing the Role of Multi-scale Heterogeneity in Graphite Electrodes for Extreme Fast Charging

Electrode-scale heterogeneity can combine with complex electrochemical interactions to impede lithium-ion battery performance, particularly during fast charging. This research investigates the influence of electrode heterogeneity at different scales on the lithium-ion battery electrochemical performance under operational extremes. We employ image-based mesoscale simulation in conjunction with a three-dimensional electrochemical model to predict performance variability in 14 graphite electrode X-ray computed tomography data sets. Our analysis reveals that the tortuous anisotropy stemming from the variable particle morphology has a dominating influence on the overall cell performance. Cells with platelet morphology achieve lower capacity, higher heat generation rates, and severe plating under extreme fast charge conditions. On the contrary, the heterogeneity due to the active material clustering alone has minimal impact. Our work suggests that manufacturing electrodes with more homogeneous and isotropic particle morphology will improve electrochemical performance and improve safety, enabling electromobility.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Permutation-adapted complete and independent basis for atomic cluster expansion descriptors

In many recent applications, particularly in the field of atom-centered descriptors for interatomic potentials, tensor products of spherical harmonics have been used to characterize complex atomic environments. When coupled with a radial basis, the atomic cluster expansion (ACE) basis is obtained. However, symmetrization with respect to both rotation and permutation results in an overcomplete set of ACE descriptors with linear dependencies occurring within blocks of functions corresponding to particular generalized Wigner symbols. All practical applications of ACE employ semi-numerical constructions to generate a complete, fully independent basis. While computationally tractable, the resultant basis cannot be expressed analytically, is susceptible to numerical instability, and thus has limited reproducibility. Here we present a procedure for generating explicit analytic expressions for a complete and independent set of ACE descriptors. The procedure uses a coupling scheme that is maximally symmetric w.r.t. permutation of the atoms, exposing the permutational symmetries of the generalized Wigner symbols, and yields a permutation-adapted rotationally and permutationally invariant basis (PA-RPI ACE). Theoretical support for the approach is presented, as well as numerical evidence of completeness and independence. A summary of explicit enumeration of PA-RPI functions up to rank 6 and polynomial degree 32 is provided. The PA-RPI blocks corresponding to particular generalized Wigner symbols may be either larger or smaller than the corresponding blocks in the simpler rotationally invariant basis. Finally, we demonstrate that basis functions of high polynomial degree persist under strong regularization, indicating the importance of not restricting the maximum degree of basis functions in ACE models a priori.

74 ATOMIC AND MOLECULAR PHYSICS↗

Machine Learning Approaches for Nuclear Material Accounting Data from Irradiation and Reprocessing

We are currently exploring data analysis methods for their ability to strengthen the synthesis and evaluation of information generated within domestic and international safeguard regimes. Safeguard data typically includes rich heterogenous datasets amenable to advanced data analytics methods, such as machine learning. We have converted transactional data containing both numerical and categorical attributes from a domestic nuclear material control and accountability (NMC&A) system into a low-dimensional numerical structure via linear principal component analysis. This data representation allows for global structure discovery via cluster analysis, which can characterize the typical behavior of each of the primary types of transaction events. Furthermore, the structure of the top principal components captures the “typical behavior” of the data and is thus amenable to anomaly detection through statistical hypothesis testing. We explored this capability by generating erroneous permutations of the data and computing the Q-residual quantity increase associated with the information loss when these data are projected into the low-dimensional principal component analysis space representative of typical transactions.Future work will focus on identifying data transformations (e.g., graph networks) that more closely align with the inherent structure of these transactions to explain more salient information and disambiguate the underlying nuclear process—in this case, irradiation and reprocessing—from artifacts of NMC&A system transactional record keeping data.

Drescher, Adam↗

Local Pair Natural Orbital-Based Coupled-Cluster Theory through Full Quadruples (DLPNO–CCSDTQ)

In this work, we implement a local pair natural orbitalbased coupled-cluster method through the full treatment of quadruple excitations (CCSDTQ). The domain-based local pair natural orbital (DLPNO) approach, which has successfully been applied to lower levels of coupled-cluster theory, is utilized in our algorithm, and thus our algorithm is called DLPNO-CCSDTQ. For simplicity in the working equations and in the implementation, we t 1 -dress the twoelectron integrals as well as Fock matrix elements. Our method can recover CCSDTQ-CCSDT and CCSDTQ-CCSDT(Q) energy differences on the order of 0.01−0.05 kcal mol −1 , even at a loose quadruples natural orbital (QNO) occupation number cutoff of 3.33 × 10 −6 . To highlight the capabilities of our code and its potential future applications, we showcase computations that would be intractable with canonical CCSDTQ, such as the benzene dimer, (H 2 O) 17 , and adamantane. With sufficient computing resources, computations up to 15 heavy atoms (40 atoms overall) may be feasible for fully bonded 3D systems.

Cluster chemistry↗