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At least 19 records

Saddle point search with dynamic active volume

Sampling potential energy surface (PES) is critical for many problems in materials science, chemistry, physics, and biology and requires highly efficient saddle point searches (SPS). In the study, we introduce the concept of dynamic active volume (DAV) in addition to the active volume in self-evolving atomistic kinetic Monte Carlo (SEAKMC). The DAV method has further reduced the dimensionality of the PES at the elevation stage of a SPS. At the subsequent converging stage, the dynamic boundary in DAV is lifted to allow the system to converge to the right location of a saddle point. Coupled with the dimer method, the DAV method not only significantly reduces the time cost for a given search attempt, but also dramatically increases the probability of finding relevant saddle points for PES sampling. Further, a Python software package within the framework SEAKMC (SEAKMC_py) with the DAV method has been developed.

36 MATERIALS SCIENCE↗

Putative rhamnogalacturonan-II glycosyltransferase identified through callus gene editing bypasses embryo lethality

Rhamnogalacturonan II (RG-II) is a structurally complex and conserved domain of the pectin present in the primary cell walls of vascular plants. Borate crosslinking of RG-II is required for plants to grow and develop normally. Mutations that alter RG-II structure also affect crosslinking and are lethal or severely impair growth. Thus, few genes involved in RG-II synthesis have been identified. Here we developed a method to generate viable loss-of-function Arabidopsis (Arabidopsis thaliana) mutants in callus tissue via CRISPR/Cas9-mediated gene editing. We combined this with a candidate gene approach to characterize the male gametophyte defective 2 (MPG2) gene that encodes a putative family GT29 glycosyltransferase. Plants homozygous for this mutation do not survive. We showed that in the callus mutant cell walls, RG-II does not crosslink normally because it lacks 3-deoxy-D-manno-octulosonic acid (Kdo) and thus cannot form the α-L-Rhap-(1→5)-α-D-kdop-(1→ sidechain. We suggest that MGP2 encodes an inverting RG-II CMP-β-Kdo transferase (RCKT1). Our discovery provides further insight into the role of sidechains in RG-II dimerization. Our method also provides a viable strategy for further identifying proteins involved in the biosynthesis of RG-II.

59 BASIC BIOLOGICAL SCIENCES↗

Modeling Surface-Enhanced Raman Scattering of Au-Pyrazine and Au-Pyrazine-Au Nanorod Dimer Systems with the TD-DFTB Method

This study investigates Raman scattering from a pyrazine molecule adsorbed on gold nanorod surfaces using the time-dependent density functional tight-binding (TD-DFTB) method. We analyze surface enhanced Raman scattering (SERS) of the molecule for two configurations: one where the molecule is adsorbed on a single gold nanorod forming Au-pyrazine complex, and another where it forms a nano-junction Au-pyrazine-Au dimer system. These two configurations offer distinct chemical environments for the molecule and different local field enhancements, with the dimer systems generating enhanced hotspot regions at the junctions. We present results for nanojunction, Au-pyrazine-Au dimer structures, for variable nanogap sizes that lead to shift in the plasmon energy. The study identifies contributions to the SERS enhancements from chemical, electromagnetic, and resonance charge transfer mechanisms. Our results show that the chemical mechanism provides enhancement factors in the range of 10 2 –10 3 , while the electromagnetic enhancements are on the order of 10 3 –10 5 for monomer systems and 10 6 –10 8 for dimer structures. We present results for a nanorod with a length of 5.3 nm and a width of 0.52 nm, consisting of 121 gold atoms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Efficient formulation of multitime generalized quantum master equations: Taming the cost of simulating 2D spectra

Modern 4-wave mixing spectroscopies are expensive to obtain experimentally and computationally. In certain cases, the unfavorable scaling of quantum dynamics problems can be improved using a generalized quantum master equation (GQME) approach. However, the inclusion of multiple (light–matter) interactions complicates the equation of motion and leads to seemingly unavoidable cubic scaling in time. In this paper, we present a formulation that greatly simplifies and reduces the computational cost of previous work that extended the GQME framework to treat arbitrary numbers of quantum measurements. Specifically, we remove the time derivatives of quantum correlation functions from the modified Mori–Nakajima–Zwanzig framework by switching to a discrete-convolution implementation inspired by the transfer tensor approach. We then demonstrate the method’s capabilities by simulating 2D electronic spectra for the excitation-energy-transfer dimer model. In our method, the resolution of data can be arbitrarily coarsened, especially along the t2 axis, which mirrors how the data are obtained experimentally. Even in a modest case, this demands O(103) fewer data points. We are further able to decompose the spectra into one-, two-, and three-time correlations, showing how and when the system enters a Markovian regime where further measurements are unnecessary to predict future spectra and the scaling becomes quadratic. This offers the ability to generate long-time spectra using only short-time data, enabling access to timescales previously beyond the reach of standard methodologies.

Chemistry↗

Characterization of Deformational Isomerization Potential and Interconversion Dynamics with Ultrafast X-ray Solution Scattering

Dimeric complexes composed of d 8 square planar metal centers and rigid bridging ligands provide model systems to understand the interplay between attractive dispersion forces and steric strain in order to assist the development of reliable methods to model metal dimer complexes more broadly. [Ir 2 (dimen) 4 ] 2+ (dimen = para-diisocyanomenthane) presents a unique case study for such phenomena, as distortions of the optimal structure of a ligand with limited conformational flexibility counteract the attractive dispersive forces from the metal and ligand to yield a complex with two ground state deformational isomers. Here, in this work, we use ultrafast X-ray solution scattering (XSS) and optical transient absorption spectroscopy (OTAS) to reveal the nature of the equilibrium distribution and the exchange rate between the deformational isomers. The two ground state isomers have spectrally distinct electronic excitations that enable the selective excitation of one isomer or the other using a femtosecond duration pulse of visible light. We then track the dynamics of the nonequilibrium depletion of the electronic ground state population—often termed the ground state hole—with ultrafast XSS and OTAS, revealing a restoration of the ground state equilibrium in 2.3 ps. This combined experimental and theoretical study provides a critical test of various density functional approximations in the description of bridged d 8 –d 8 metal complexes. The results show that density functional theory calculations can reproduce the primary experimental observations if dispersion interactions are added, and a hybrid functional, which includes exact exchange, is used.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Effective Fragment Molecular Orbital Method: Achieving High Scalability and Accuracy for Large Systems

The effective fragment molecular orbital (EFMO) method has been developed to predict the total energy of a very large molecular system accurately (with respect to the underlying quantum mechanical method) and efficiently by taking advantage of the locality of strong chemical interactions and employing a two-level hierarchical parallelism. The accuracy of the EFMO method is partly attributed to the accurate and robust intermolecular interaction prediction between distant fragments, in particular, the many-body polarization and dispersion effects, which require the generation of static and dynamic polarizability tensors by solving the coupled perturbed Hartree–Fock (CPHF) and time-dependent HF (TDHF) equations, respectively. Solving the CPHF and TDHF equations is the main EFMO computational bottleneck due to the inefficient (serial) and I/O-intensive implementation of the CPHF and TDHF solvers. In this work, the efficiency and scalability of the EFMO method are significantly improved with a new CPU memory-based implementation for solving the CPHF and TDHF equations that are parallelized by either message passing interface (MPI) or hybrid MPI/OpenMP. Here, the accuracy of the EFMO method is demonstrated for both covalently bonded systems and noncovalently bound molecular clusters by systematically examining the effects of basis sets and a key distance-related cutoff parameter, R cut . R cut determines whether a fragment pair (dimer) is treated by the chosen ab initio method or calculated using the effective fragment potential (EFP) method (separated dimers). Decreasing the value of Rcut increases the number of separated (EFP) dimers, thereby decreasing the computational effort. It is demonstrated that excellent accuracy (<1 kcal/mol error per fragment) can be achieved when using a sufficiently large basis set with diffuse functions coupled with a small R cut value. With the new parallel implementation, the total EFMO wall time is substantially reduced, especially with a high number of MPI ranks. Given a sufficient workload, nearly ideal strong scaling is achieved for the CPHF and TDHF parts of the calculation. For the first time, EFMO calculations with the inclusion of long-range polarization and dispersion interactions on a hydrated mesoporous silica nanoparticle with explicit water solvent molecules (more than 15k atoms) are achieved on a massively parallel supercomputer using nearly 1000 physical nodes. In addition, EFMO calculations on the carbinolamine formation step of an amine-catalyzed aldol reaction at the nanoscale with explicit solvent effects are presented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structural Characterization of Disulfide-Linked p53-Derived Peptide Dimers

Disulfide bonds provide a convenient method for chemoselective alteration of peptide and protein structure and function. We previously reported that mild oxidation of a p53-derived bisthiol peptide (CTFANLWRLLAQNC) under dilute non-denaturing conditions led to unexpected disulfide-linked dimers as the exclusive product. The dimers were antiparallel, significantly α-helical, resistant to protease degradation, and easily reduced back to the original bisthiol peptide. Here, in this work, we examine the intrinsic factors influencing peptide dimerization using a combination of amino acid substitution, circular dichroism (CD) spectroscopy, and X-ray crystallography. CD analysis of peptide variants suggests critical roles for Leu6 and Leu10 in the formation of stable disulfide-linked dimers. The 1.0 Å resolution crystal structure of the peptide dimer supports these data, revealing a leucine-rich LxxLL dimer interface with canonical knobs-into-holes packing. Two levels of higher-order oligomerization are also observed in the crystal: an antiparallel “dimer of dimers” mediated by Phe3 and Trp7 residues in the asymmetric unit and a tetramer of dimers mediated by Trp7 and Leu10. In CD spectra of Trp-containing peptide variants, minima at 227 nm provide evidence for the dimer of dimers in dilute aqueous solution. Importantly, and in contrast to the original dimer model, the canonical leucine-rich core and robust dimerization of most peptide variants suggests a tunable molecular architecture to target various proteins and evaluate how folding and oligomerization impact various properties, such as cell permeability.

36 MATERIALS SCIENCE↗

CO 2 Activation with Manganese Tricarbonyl Complexes through an H–Atom Responsive Benzimidazole Ligand

Herein, we report the synthesis and characterization of two manganese tricarbonyl complexes, Mn I (HL)(CO) 3 Br (1 a-Br) and Mn I (MeL)(CO) 3 Br (1 b-Br) (where HL=2-(2’-pyridyl)benzimidazole; MeL=1-methyl-2-(2’-pyridy)benzimidazole) and assayed their electrocatalytic properties for CO 2 reduction. A redox-active pyridine benzimidazole ancillary ligand in complex 1 a-Br displayed unique hydrogen atom transfer ability to facilitate electrocatalytic CO 2 conversion at a markedly lower reduction potential than that observed for 1 b-Br. Notably, a one-electron reduction of 1 a-Br yields a structurally characterized H-bonded binuclear Mn(I) adduct (2 a’) rather than the typically observed Mn(0)-Mn(0) dimer, suggesting a novel method for CO 2 activation. Furthermore, combining advanced electrochemical, spectroscopic, and single crystal X-ray diffraction techniques, we demonstrate the use of an H-atom responsive ligand may reveal an alternative, low-energy pathway for CO 2 activation by an earth-abundant metal complex catalyst.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Unraveling Electronic and Vibrational Coherences Following a Charge Transfer Process in a Photosystem II Reaction Center

A reaction center is a unique biological system that performs the initial charge separation within a Photosystem II (PSII) multiunit enzyme, which eventually drives the catalytic water-splitting in plants and algae. The possible role of quantum coherences coinciding with the energy and charge transfer processes in PSII reaction center is one of the active areas of research. Here, we study these quantum coherences by using a numerically exact method on an excitonic dimer model, including linear vibronic coupling and employing optimal parameters from experimental two-dimensional coherent spectroscopic measurements. This enables us to precisely capture the excitonic interaction between pigments and the dissipation of the energy from electronic and charge-transfer (CT) states to the protein environment. We employ the time nonlocal (TNL) quantum master equation to calculate the population dynamics, which yields numerically reliable results. The calculated results show that, due to the strong dissipation, the lifetime of electronic coherence is too short to have direct participation in the charge transfer processes. However, there are long-lived vibrational coherences present in the system at frequencies close to the excitionic energy gap. These are strongly coupled with the electronic coherences, which makes the detection of the electronic coherences with conventional techniques very challenging. Additionally, we unravel the strong excitonic interaction of radical pair (PD1 and PD2) in the reaction center, which results in a long-lived electronic coherence of >100 fs, even at room temperature. Our work provide important physical insight to the charge separation process in PSII reaction center, which may be helpful for better understanding of photophysical processes in other natural and artificial light-harvesting systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Catalytic carbon–carbon bond cleavage in lignin via manganese–zirconium-mediated autoxidation

Abstract Efforts to produce aromatic monomers through catalytic lignin depolymerization have historically focused on aryl–ether bond cleavage. A large fraction of aromatic monomers in lignin, however, are linked by various carbon–carbon (C–C) bonds that are more challenging to cleave and limit the yields of aromatic monomers from lignin depolymerization. Here, we report a catalytic autoxidation method to cleave C–C bonds in lignin-derived dimers and oligomers from pine and poplar. The method uses manganese and zirconium salts as catalysts in acetic acid and produces aromatic carboxylic acids as primary products. The mixtures of the oxygenated monomers are efficiently converted to cis,cis -muconic acid in an engineered strain of Pseudomonas putida KT2440 that conducts aromatic O -demethylation reactions at the 4-position. This work demonstrates that autoxidation of lignin with Mn and Zr offers a catalytic strategy to increase the yield of valuable aromatic monomers from lignin.

09 BIOMASS FUELS↗

Role of electron correlation on the adenine dimer interaction for non-equilibrium geometries: a benchmark Quantum Monte Carlo study

The accurate description of non-covalent interactions is critical for understanding the structure, dynamics, and eventual function of biomolecules. The adenine dimer serves as a benchmark system for computational methods due to its role in nucleic acid structures and its rich conformational landscape. In this study, we employ benchmark diffusion quantum Monte Carlo (DMC) methods to investigate the relative energies and role of electron correlation on a set of adenine dimer conformations generated via a search of the potential energy landscape using the global optimizer algorithm. Relative DMC energies are compared against a wide range of density functional theory (DFT) approximation results. We find that although most of the DFT functionals perform well for low-energy structures, their accuracy varies significantly for higher-energy conformations, including stacked and T-shaped structures. A large fraction of the variation is due to the treatment of the van der Waals interaction. BLYP, B3LYP, and PBE0 significantly improve with added D4 dispersion, while the recent r2SCAN-D4 and ωB97M-V functionals show the least scatter and closest agreement with the DMC. These findings highlight the delicate nature of these interactions in biomolecular systems and provide guidance for simulations of their structure and dynamics and for the development of machine learned interatomic potentials.

Washburn, Laurel [ORNL] (ORCID:0000000324179335)↗

2023 American Society for Mass Spectrometry (ASMS) 71st Annual Conference on Mass Spectrometry and Allied Topics

Introduction (120 words max) Understanding metal-cluster chemistry occuring at solvent boundaries in the aqueous and organic phases has applications in environments from cellular processes to nuclear fuel reprocessing. Transport of metal ions at the boundaries from aqueous to organic phases involves forming a metal-ligand complex, and wherever the initial metal coordination environment is significantly different from the final one, the metal transitions through a series of transient species in passing from one phase to another. Here an investigation of the role of coordination in the chemistry of the transient species using gas-phase measurements that are free of solvent effects to better understand the binding of complexes of metals with triphenylphosphine chalcogenide ligands, examining metal-ligand homo- and hetero-dimers to better understand transient species. Methods (120 word max) Mass spectrometry and collision induced dissociation (CID) experiments were performed with a Bruker (Billerica, MA, USA) micrOTOF-Q II quadrupole time-of-flight mass spectrometer (QTOF) and Bruker amaZon speed ETD (ion trap). High resolution/high mass accuracy spectra were generated using the QTOF. External calibration was performed with Agilent (Santa Clara, CA, USA) ESI-L Low Concentration tuning mix. Both mass spectrometers were equipped with either the electrospray ionization source or nanospray sources. Metal samples were prepared between 40 – 60 uM of the metal-ligand complex in 25% water and 75% acetonitrile. Metal-ion clusters were isolated and subjected to collision induced dissociation. Density functional theory calculations were performed. Preliminary Data or Plenary Speakers Abstract (300 words max) Metal ion clusters with triphenylphosphine chalcogenide ligands were observed for group I metals with triphenylphosphine chalcogenide samples in the mass spectrum upon electrospray ionization. For each metal ligand complex of interest, the parent ion was isolated and collision induced dissociation fragmentation spectra were acquired. We observed clusters of group I metal with triphenylphosphine oxide, triphenyl phosphine sulfide, and triphenylphosphine selenide, with homodimers and heterodimer formation. In samples where the ligands were mixed, we observed mixed sodium ligand clusters at varying amounts. These mixed ligand clusters were fragmented. Metal clusters of mixed ligand dimers containing triphenylphosphine oxide showed preferential loss of the other ligand, either triphenylphosphine sulfide or triphenyl selenide. In samples with mixed triphenylphosphine sulfide and triphenylphosphine selenium ligands, sodium bound similarly between the ligands, and losses were more evenly split, showing loss ratio upon CID with losses of triphenylphosphine sulfide:triphenylphosphine selenide 43:57 ratio observed on CID. These results suggest that the oxide binds significantly more strongly than either the selenium or sulfur triphenylphosphine ligand, and the sulfur and selenium ligands are more evenly bound. Calculations were performed using density functional theory to calculate likely structures and bond energies between the group I metal and the ligands. Novel Aspect Novel analysis of sodium bound dimers with chalcogenide triphenylphosphine ligands were investigated using mass spectrometry and theoretical calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Reactions of U(DMSO) 8 (ClO 4 ) 4 with Terpyridine Yield Dimeric Hydrolysis Products and Induce C–C Coupling

Reactions have been carried out using UIV(DMSO) 8 (ClO 4 ) 4 with 2,2′:6′,2″-terpyridine (terpy) under nonaqueous conditions. At room temperature in acetonitrile, the combination of the U(IV) starting material with terpy resulted in a mixture containing [UO 2 (DMSO) 2 terpy][ClO 4 ] 2 ·MeCN, while increasing the water content led to the hydrolysis products [(UO 2 (DMSO)terpy) 2 (μ 2 –O)][ClO 4 ] 2 and [(UO 2 terpy) 2 (μ 2 –OH) 2 ][ClO 4 ] 2 ·MeCN·H 2 O. Performing the reaction at slightly elevated temperature with no added water led to the formation of [UO 2 sexipyridine][ClO 4 ] 2 ·MeCN. This new uranyl complex contains the hexadentate ligand 2,2′:6′,2″:6″,2″:6‴,2⁗:6⁗,2⁗′-sexipyridine, which formed in situ from the tetravalent uranium starting material, where photoexcited uranyl or in situ generated peroxide could have induced C–C coupling. Analysis of bonding in the dimeric uranyl species via quantum chemical methods revealed a small increase in covalency of the bridging oxo unit and a slightly greater stability compared to the bridging hydroxo compound, which causes a significant shift in the uranyl symmetric stretch in the Raman spectrum. Structural, spectroscopic, and computational comparisons are made across the series of compounds, providing insight into the bonding and reactivity of uranium in nonaqueous media.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Coherent photoexcitation of entangled triplet pair states

The functional properties of organic semiconductors are defined by the interplay between optically bright and dark states. Organic devices require rapid conversion between these bright and dark manifolds for maximum efficiency, and one way to achieve this is through multiexciton generation (S 1 → 1 TT). Here, the dark state 1 TT is typically generated from bright S 1 after optical excitation; however, the mechanistic details are hotly debated. Here we report a 1 TT generation pathway in which it can be coherently photoexcited, without any involvement of bright S 1 . Using <10-fs transient absorption spectroscopy and pumping sub-resonantly, 1 TT is directly generated from the ground state. Applying this method to a range of pentacene dimers and thin films of various aggregation types, we determine the critical material properties that enable this forbidden pathway. Through a strikingly simple technique, this result opens the door for new mechanistic insights into 1 TT and other dark states in organic materials.

14 SOLAR ENERGY↗

Rapidly convergent quantum Monte Carlo using a Chebyshev projector

The multireference coupled-cluster Monte Carlo (MR-CCMC) algorithm is a determinant-based quantum Monte Carlo (QMC) algorithm that is conceptually similar to Full Configuration Interaction QMC (FCIQMC). It has been shown to offer a balanced treatment of both static and dynamic correlation while retaining polynomial scaling, although application to large systems with significant strong correlation remained impractical. In this paper, we document recent algorithmic advances that enable rapid convergence and a more black-box approach to the multireference problem. These include a logarithmically scaling metric-tree-based excitation acceptance algorithm to search for determinants connected to the reference space at the desired excitation level and a symmetry-screening procedure for the reference space. We show that, for moderately sized reference spaces, the new search algorithm brings about an approximately 8-fold acceleration of one MR-CCMC iteration, while the symmetry screening procedure reduces the number of active reference space determinants with essentially no loss of accuracy. We also introduce a stochastic implementation of an approximate wall projector, which is the infinite imaginary time limit of the exponential projector, using a truncated expansion of the wall function in Chebyshev polynomials. Notably, this wall-Chebyshev projector can be used to accelerate any projector-based QMC algorithm. We show that it requires significantly fewer applications of the Hamiltonian to achieve the same statistical convergence. We benchmark these acceleration methods on the beryllium and carbon dimers, using initiator FCIQMC and MR-CCMC with basis sets up to cc-pVQZ quality.

Zhao, Zijun↗

Challenges for density functional theory in simulating metal–metal singlet bonding: A case study of dimerized VO2

VO2 is renowned for its electric transition from an insulating monoclinic (M1) phase, characterized by V–V dimerized structures, to a metallic rutile (R) phase above 340 K. This transition is accompanied by a magnetic change: the M1 phase exhibits a non-magnetic spin-singlet state, while the R phase exhibits a state with local magnetic moments. Simultaneous simulation of the structural, electric, and magnetic properties of this compound is of fundamental importance, but the M1 phase alone has posed a significant challenge to the density functional theory (DFT). In this study, we show none of the commonly used DFT functionals, including those combined with on-site Hubbard U to treat 3d electrons better, can accurately predict the V–V dimer length. The spin-restricted method tends to overestimate the strength of the V–V bonds, resulting in a small V–V bond length. Conversely, the spin-symmetry-breaking method exhibits the opposite trends. Each of these two bond-calculation methods underscores one of the two contentious mechanisms, i.e., Peierls lattice distortion or Mott localization due to electron–electron repulsion, involved in the metal–insulator transition in VO2. To elucidate the challenges encountered in DFT, we also employ an effective Hamiltonian that integrates one-dimensional magnetic sites, thereby revealing the inherent difficulties linked with the DFT computations.

Chemistry↗

Reproducibility of fixed-node diffusion Monte Carlo across diverse community codes: The case of water–methane dimer

Fixed-node diffusion quantum Monte Carlo (FN-DMC) is a widely trusted many-body method for solving the Schrödinger equation, known for its reliable predictions of material and molecular properties. Furthermore, its excellent scalability with system complexity and near-perfect utilization of computational power make FN-DMC ideally positioned to leverage new advances in computing to address increasingly complex scientific problems. Even though the method is widely used as a computational gold standard, reproducibility across the numerous FN-DMC code implementations has yet to be demonstrated. This difficulty stems from the diverse array of DMC algorithms and trial wave functions, compounded by the method’s inherent stochastic nature. Here, this study represents a community-wide effort to assess the reproducibility of the method, affirming that yes, FN-DMC is reproducible (when handled with care). Using the water–methane dimer as the canonical test case, we compare results from eleven different FN-DMC codes and show that the approximations to treat the non-locality of pseudopotentials are the primary source of the discrepancies between them. In particular, we demonstrate that, for the same choice of determinantal component in the trial wave function, reliable and reproducible predictions can be achieved by employing the T-move, the determinant locality approximation, or the determinant T-move schemes, while the older locality approximation leads to considerable variability in results. These findings demonstrate that, with appropriate choices of algorithmic details, fixed-node DMC is reproducible across diverse community codes—highlighting the maturity and robustness of the method as a tool for open and reliable computational science.

Della Pia, Flaviano [Univ. of Cambridge (United Ki↗