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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records

Computational Spectroscopy of the Cr–Cr Bond in Coordination Complexes

In this work, we report the accurate computational vibrational analysis of the Cr–Cr bond in dichromium complexes using second-order multireference complete active space methods (CASPT2), allowing direct comparison with experimental spectroscopic data both to facilitate interpreting the low-energy region of the spectra and to provide insights into the nature of the bonds themselves. Recent technological development by the authors has realized such computation for the first time. Accurate simulation of the vibrational structure of these compounds has been hampered by their notorious multiconfigurational electronic structure that yields bond distances that do not correlate with bond order. Some measured Cr–Cr vibrational stretching modes, ν(Cr 2 ), have suggested weaker bonding, even for so-called ultrashort Cr–Cr bonds, while others are in line with the bond distance. Here, we optimize geometries and compute ν(Cr 2 ) with CASPT2 for three well-characterized complexes, Cr 2 (O 2 CCH 3 ) 4 (H 2 O) 2 , Cr 2 (mhp) 4 , and Cr 2 (dmp) 4 . We obtain CASPT2 harmonic ν(Cr 2 ) modes in good agreement with experiment at 282 cm –1 for Cr 2 (mhp) 4 and 353 cm –1 for Cr 2 (dmp) 4 , compute 50 Cr and 54 Cr isotope shifts, and demonstrate that the use of the so-called IPEA shift leads to improved Cr–Cr distances. Additionally, normal mode sampling was used to estimate anharmonicity along ν(Cr 2 ), leading to an anharmonic mode of 272 cm –1 for Cr 2 (mhp) 4 and 333 cm –1 for Cr 2 (dmp) 4 .

36 MATERIALS SCIENCE↗

Mid- to long-wave infrared computational spectroscopy with a graphene metasurface modulator

In recent years there has been much interest concerning the development of modulators in the mid- to long-wave infrared, based on emerging materials such as graphene. These have been frequently pursued for optical communications, though also for other specialized applications such as infrared scene projectors. Here we investigate a new application for graphene modulators in the mid- to long-wave infrared. We demonstrate, for the first time, computational spectroscopy in the mid- to long-wave infrared using a graphene-based metasurface modulator. Furthermore, our metasurface device operates at low gate voltage. To demonstrate computational spectroscopy, we provide our algorithm with the measured reflection spectra of the modulator at different gate voltages. We also provide it with the measured reflected light power as a function of the gate voltage. The algorithm then estimates the input spectrum. We show that the reconstructed spectrum is in good agreement with that measured directly by a Fourier transform infrared spectrometer, with a normalized mean-absolute-error (NMAE) of 0.021.

36 MATERIALS SCIENCE↗

Davis Computational Spectroscopy Workflow—From Structure to Spectra

Here, we describe an automated workflow that connects a series of atomic simulation tools to investigate the relationship between atomic structure, lattice dynamics, materials properties, and inelastic neutron scattering (INS) spectra. Starting from the atomic simulation environment (ASE) as an interface, we demonstrate the use of a selection of calculators, including density functional theory (DFT) and density functional tight binding (DFTB), to optimize the structures and calculate interatomic force constants. We present the use of our workflow to compute the phonon frequencies and eigenvectors, which are required to accurately simulate the INS spectra in crystalline solids like diamond and graphite as well as molecular solids like rubrene. We have also implemented a machine-learning force field based on Chebyshev polynomials called the Chebyshev interaction model for efficient simulation (ChIMES) to improve the accuracy of the DFTB simulations. We then explore the transferability of our DFTB/ChIMES models by comparing simulations derived from different training sets. We show that DFTB/ChIMES demonstrates ~100× reduction in computational expense while retaining most of the accuracy of DFT as well as yielding high accuracy for different materials outside of our training sets. The DFTB/ChIMES method within the workflow expands the possibilities to use simulations to accurately predict materials properties of increasingly complex structures that would be unfeasible with ab initio methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Photoelectron spectroscopy and computational investigations of the electronic structures and noncovalent interactions of cyclodextrin-closo-dodecaborate anion complexes x-CD·B12X122- (x = a, ß, y; X = H, F)

We report a joint negative ion photoelectron spectroscopy (NIPES) and computational study on the electronic structures and noncovalent interactions of a series of cyclodextrin-closo-dodecaborate dianion complexes, ?-CD·B12X122- (? = a, ß, ?; X = H, F). The measured vertical / adiabatic detachment energies (VDEs / ADEs) are 1.15/0.93, 3.55/3.20, 3.90/3.60, and 3.85/3.60 eV for B12H122- and its a-, ß-, ?-CD complexes, respectively; while the corresponding values are 1.90/1.70, 4.00/3.60, 4.33/3.95, and 4.30/3.85 eV for the X = F case. These results show that the inclusion of B12X122- into the CD cavities greatly increase the electronic stability of the dianions. The effect of electronic stabilization for ß-CD is roughly the same as for ?-CD, both being considerably stronger than that for a-CD. Density functional theory (DFT) based geometry optimization reveals that B12X122- are inserted into CDs increasingly deeper from a-CD to ?-CD. The calculated VDEs and ADEs agree with the experiments well, particularly, reproducing the electron binding energy (EBE) trends. The molecular orbital analyses indicate that the most loosely bound photodetached electrons origin from the guest B12X122- moieties. In addition to a shift of all signals to larger EBE, significant changes in the signal patterns are observed. At low EBE, this is due to the splitting of highly degenerate B12X122- orbitals, while at high EBE, photodetachment from CD oxygens contributes to the new bands. The guest B12X122- and host CD nocovalent, size-specific interaction based on the independent gradient model (IGM) and energy decomposition analysis (EDA), is dominated by electrostatic interactions. The analysis further unravels unambiguiously the existence of dihydrogen bonding and how it affects the total energy that stabilizes the host-guest complexes of CDs·B12H122- compared to the general hydrogen bonding interaction in CDs·B12F122-. This work clearly exhibits strong influences on the electronic structures of dodecaborates upon clustering with CDs, with both size (a-, ß-, ?-) and molecular (X = H or F) specificities, thus providing critical molecular-level information on the cyclodextrin-closo-dodecaborate interactions of interest to medical applications, e.g. Boron neutron capature therapy. The NIPES experiments done at PNNL were supported by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Bioscience (X.-B.W.) and was performed at the EMSL, a national scientific user facility sponsored by DOE’s Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. H.S. and Z.S. acknowledge the funding support of National Natural Science Foundation of China (Nos.11727810, 61720106009 and 21603074), the Science and Technology Commission of Shanghai Municipality (Nos. 19JC1412200), and the Program of Introducing Talents of Discipline to Universities 111 project (B12024). Z. L. thanks the China Scholarship Council (CSC) for financial support. We acknowledge the ECNU Multifunctional Platform for Innovation (001) and HPC Research Computing Team for providing computational and storage resources. J.W. acknowledges support from the Alexander von Humboldt foundation (Feodor Lynen Fellowship and Rückkehrerstipendium), a Freigeist fellowship of the Volkswagenfoundation and Prof. Vladimir A. Azov for helpful discussions.

Li, Zhipeng↗

Electronic structures and binding motifs of sodium polysulfide clusters NaSn- (n = 5-9): a joint negative ion photoelectron spectroscopy and computational investigation

Motivated by the significant biological functions of polysulfides in life processes and important applications of sodium polysulfides in battery sciences, herein we report a joint experimental and computational study on the electronic and geometric structures of a series of NaSn- (n = 5-9) clusters. The cryogenic, size-selective, negative ion photoelectron spectroscopy (NIPES) is employed to obtain their photoelectron spectra, in which distinctive spectral features with electron binding energy (EBE) up to 6.4 eV are unraveled. The EBE of the first peak in each spectrum for NaSn- (n =5-9), assigned to the transition from the ground state of anion to the ground state of each neutral radical, is observed to increase with cluster size. The vertical detachment energies (VDEs), determined from the first peak maximum, are 3.43 ± 0.02, 3.57 ± 0.02, 3.82 ± 0.03, 3.86 ± 0.02, and 4.00 ± 0.02 eV and the adiabatic detachment energies (ADEs), determined by the onset of the first peak, are 3.27 ± 0.05, 3.44 ± 0.05, 3.65 ± 0.05, 3.75 ± 0.05, and 3.93 ± 0.05 eV, for n = 5-9, respectively. A plural of low-lying isomers of anions are screened and identified with density functional theory calculations, showing that all featuring preference for a chain-like polysulfide moiety electrostatically interacted with a sodium cation. The calculated VDEs and ADEs using the high-level CCSD(T)/aug-cc-pVTZ method are in excellent agreement with experimental results, further confirming the identified isomers as most stable ones. Further analyses based on the excited-state transition, molecular orbitals and natural population charge are performed to assign all observed spectral bands along the binding energy axis, suggesting that the electron detachment process and observed excitations mainly derived from the polysulfide chain of NaSn- clusters. This work provides a fundamental understanding of the intrinsic molecular properties of sodium polysulfide systems, which widely exist in life science and sodium-sulfur cells.

Li, Zhipeng↗

FT-IR and Raman Spectroscopy and Computation of 5-Methylfurfural

5-Methylfurfural (5MF) was studied by vibrational (IR and Raman) spectroscopy and computational methods (DFT/B3LYP&MP2). FT-IR and FT-Raman spectra in KBr (at room temperature) were collected. The Gaussian 09 and Spartan 08 programs were used for conformational analysis and calculations of molecular structure, torsional barrier, and vibrational spectral data for the 5MF molecule. The obtained results were used in the analysis of experimental vibrational spectra of 5MF molecule.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Formation of Unusual Deprotomers of Citric Acid and Sodium Citrate Aggregates: A Photoelectron Spectroscopy and Computational Study

Given multiple distinct deprotonation sites and flexible structural conformation in citric acid (CA), the intrinsic interaction between protons, sodium cations and citrate anions deems complicated. In this work, we address this issue by combining photoelectron spectroscopy and theoretical modeling on a series of gaseous sodium citrate anion clusters with progressive substitution of protons with sodium cations [(CA-nH)·(n-1)Na]- (n = 1-3). Despite markedly different pKa values for the central (C, 3.28), terminal carboxylic (T, 5.98) and hydroxyl group (O, 18.44), our study reveals experimental observation of all three distinct deprotomers in [CA-1H]- with deprotonation from hydroxyl energetically competitive. Upon Na+ binding to the doubly or triply deprotonated CA, only one kind of deprotonation tautomer, respectively TC or TTC, is experimentally accessible. Moreover, a dianionic dimer [(CA-3H)·2Na]22- is observed. This work displays a diverse binding landscape among protons, sodium and citrate species in the gas phase, advancing our understanding of sodium citrate chemistry.

Yuan, Qinqin↗

High-Resolution Comonomer Sequencing of Blocky Brominated Syndiotactic Polystyrene Copolymers Using 13C NMR Spectroscopy and Computer Simulations

This work demonstrates the first high-resolution comonomer sequencing of Blocky brominated syndiotactic polystyrene (sPS-co-sPS-Br) copolymers based on pentad assign- ments of the quaternary carbon region of the nuclear magnetic resonance spectrum. Copolymers containing p-bromostyrene (Br-Sty) units were prepared in matched sets using postpolymerization bromination methods carried out in the heterogeneous gel state (Blocky) and homogeneous solution state (Random). Quantitative information from the quaternary carbon spectra, heteronuclear multiple bond correlation spectroscopy, electronic structure calculations, and simulated statistically random copolymers was correlated to confirm the carbon resonance assignments for all 20 possible pentad comonomer sequences. Using the experimental pentad sequence prevalences, a computer code was developed to simulate chains with microstructures typical of each sample as a means to visually represent the copolymer blockiness with quantitative precision. Based on the microstructure and distribution of run lengths in these chains, the simulations revealed that the Blocky copolymers contain a high degree of blockiness. By comparing the run lengths in the simulated chains to the average number of styrene units in a crystalline segment of sPS (found by small-angle X-ray scattering), copolymer crystallizability was predicted. For the simulated Blocky B-21% (21 mol % Br-Sty) chain, the probability of randomly selecting a styrene unit in a crystallizable block was 25.8%, while that in the simulated Random R-18% was zero, in excellent agreement with the experimental crystallization behavior measured by differential scanning calorimetry. Additionally, these predictions confirmed that the simulated chains accurately represent the ensemble of chains in their respective copolymer samples. Furthermore, each simulated Blocky chain contained one or more long sPS blocks that paralleled the measured 38-40 styrene units spanning a crystalline segment within the sPS/CCl4 gel. This finding affirmed that the long sPS segments originated from the precise lamellar structure within the heterogeneous gel morphology (i.e., block length is correlated with lamellar thickness). Overall, the ability to tailor the copolymer microstructure through control of the semicrystalline gel morphology opens the door to synthesizing ordered copolymers by postpolymerization functionalization processes with unprecedented levels of compositional control.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Photoelectron Spectroscopy and Computational Study on Microsolvated [B 10 H 10 ] 2– Clusters and Comparisons to Their [B 12 H 12 ] 2– Analogues

Microhydrated closo-Boranes have attracted great interests due to their superchaotropic activity related to well-known Hofmeister effect and important applications in biomedical and battery fields. In this work, we report a combined negative ion photoelectron spectroscopy and quantum chemical investigation on hydrated closo-decaborate clusters [B 10 H 10 ] 2- ·nH 2 O (n = 1 – 7) with a direct comparison to their analogues [B 12 H 12 ] 2- ·nH 2 O and free water clusters. A single H 2 O molecule is found sufficient to stabilize the intrinsically unstable [B 10 H 10 ] 2- dianion. The first two water molecules strongly interact with the solute forming B-H···H-O dihydrogen bonds while additional water molecules show substantially reduced binding energies. Unlike [B 12 H 12 ] 2- ·nH 2 O possessing highly structured water network with the attached H 2 O molecules arranged in a unified pattern by maximizing B-H···H-O dihydrogen bonding, distinct structural arrangements of the water clusters within [B 10 H 10 ] 2– ·nH 2 O are achieved with the water cluster networks from trimer to heptamer resembling free water clusters. Such a distinct difference arises from the variations in size, symmetry, and charge distributions between these two dianions. Finally, the present finding again confirms the structural diversity of hydrogen-bonding networks in microhydrated closo-boranes and enrich our understanding of aqueous borate chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Interfacial Structure and Electric Field Probed by in Situ Electrochemical Vibrational Stark Effect Spectroscopy and Computational Modeling

Interfacial electric fields play crucial roles in electrochemistry, catalysis, and solar energy conversion. Understanding of the interfacial electric field effects has been hindered by the lack of a direct spectroscopic method to probe of the interfacial field at the molecular level. Here, we report the characterization of the field and interfacial structure at Au/diisocyanide/aqueous electrolyte interfaces, using a combination of in situ electrochemical vibrational sum frequency generation (SFG) spectroscopy, density functional theory (DFT) calculations, and molecular dynamics (MD) simulations. For 1,4-phenylene diisocyanide (PDI), 4,4'-biphenyl diisocyanide (BPDI), and 4,4"-p-terphenyl diisocyanide (TPDI), our results reveal that the frequency of the gold-bound NC stretch mode of the diisocyanide self-assembled monolayer (SAM) increases linearly with the applied potential, suggesting that SFG can be an in situ probe of the strength of the electric field at electrode/electrolyte interfaces. Using DFT-computed Stark tuning rates of model complexes, the electric field strength at the metal/SAM/electrolyte interfaces is estimated to be 108–109 V/m. The linear dependence of the vibrational frequency (and field) with applied potential is consistent with an electrochemical double-layer structure that consists of a Helmholtz layer in contact with a diffused layer. The Helmholtz layer thickness is approximately the same as the molecular length for PDI, suggesting a well-ordered SAM with negligible electrolyte penetration. For BPDI and TPDI, we found that the Helmholtz layer is thinner than the monolayer of molecular adsorbates, indicating that the electrolyte percolates into the SAM, as shown by molecular dynamics simulations of the Au/PDI/electrolyte interface. The reported analysis demonstrates that a combination of in situ SFG probes and computational modeling provides a powerful approach to elucidate the structure of electrochemical interfaces at the detailed molecular level.

Ge, Aimin↗

Why Are 5-Thioglycopyranosyl Donors More Axially Selective than their Glycopyranosyl Counterparts? A Low and Variable Temperature NMR Spectroscopy and Computational Study

5-Thioglycopyranosyl donors differ in reactivity and selectivity from simple glycopyranosyl donors. An extensive study has been conducted on the nature and stability of the reactive intermediates generated on the activation of per-O-acetyl and per-O-methyl 5-thioglucopyranosyl donors and the corresponding glucopyranosyl donors. Variable temperature nuclear magnetic resonance (NMR) studies with per-O-methylated or per-O-acetyl glycosyl sulfoxides and trichloroacetimidates on activation with trifluoromethanesulfonic anhydride or trimethylsilyl triflate are reported. These show that following initial adduct formation with the promoter conversion of the 5-thioglucopyranosyl donors to the 5-thioglucopyranosyl triflates requires higher temperatures than that of the glucopyranosyl donors to the glucopyranosyl triflates. It is demonstrated that neighboring group participation is a less important phenomenon for the peracetylated thioglucosyl donors than for the peracetylated glucosyl donors. A simple thiocarbenium ion was generated by protonation of 2,3-dihydro-4H-thiopyran at low temperature and characterized by NMR spectroscopy. However, the corresponding 5-thioglucopyranosyl thenium ions were not observed in any of the NMR studies of the 5-thiopyranosyl donors: the electron-withdrawing C–O bonds around the thiopyranoside core discourage thiocarbenium ion formation, just as they discourage oxocarbenium ion formation. Density functional theory (DFT) calculations reveal the tetrahydrothiopyranyl thiocarbenium ion to be approximately 2.5 kcal/mol lower in energy than the corresponding tetrahydropyranyl oxocarbenium ion relative to the corresponding covalent triflates. However, the computations reveal a 5.8 kcal/mol activation barrier for conversion of the tetrahydrothiopyranyl triflate to the thiocarbenium ion, while formation of the oxocarbenium ion–triflate ion pair from tetrahydropyranyl triflate requires only 2.6 kcal·mol –1 . Overall, the greater axial selectivity of 5-thioglycopyranosyl donors compared to analogous glycopyranosyl donors derives from (i) the lower kinetic reactivity necessitating higher reaction temperatures, (ii) the greater stability of the thiocarbenium ion over the oxocarbenium ion facilitating equilibration under thermodynamic conditions, (iii) the greater magnitude of the anomeric effect in the 5-thiosugars, and (iv) decreased neighboring group participation in the per-esterified 5-thiosugars.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The unusual symmetry of hexafluoro-o-xylene—A microwave spectroscopy and computational study

The rotational constants and quartic centrifugal distortion coefficients of hexafluoro-o-xylene were precisely derived from the 8 GHz to 18 GHz gas phase microwave spectrum. In addition, the rotational constants of all singly substituted 13 C isotopologues were determined. Instead of the intuitively expected symmetry of C 2v , as in o-xylene, calculations with a variety of methods (B3LYP, CAM-B3LYP, ωB97XD, MP2, and coupled-cluster singles, doubles, and perturbative triples) predict a C 2 symmetry structure in which the two CF 3 groups rotate in opposite directions by about 16°. While the experimental results in this study are not capable of proving this unusual symmetry, they can support future microwave, gas phase electron diffraction or nuclear magnetic resonance studies. From the presented data, a preliminary r 0 structure was determined, reproducing the experimental rotational constants with deviations of no more than 15 kHz. Analysis of the interactions between the two CF 3 groups using an effective fragment potential approach identifies two major contributions to their interaction, due to exchange-repulsion and electrostatic repulsion, with electrostatic repulsion responsible for the barrier at the C 2v geometry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ultrafast x-ray pump x-ray probe transient absorption spectroscopy: A computational study and proposed experiment probing core-valence electronic correlations in solvated complexes

Femtosecond X-ray pump X-ray probe experiments are currently possible at free electron lasers such as the linac coherent light source (LCLS), which opens new opportunities for studying solvated transition metal-ligand complexes. In order to make the most effective use of these kinds of experiments, it is necessary to determine which chemical properties an X-ray pump pulse will measure. In this paper, we have combined electron cascade calculations and excited-state time-dependent density functional theory calculations to predict the initial state prepared by an X-ray pump and the subsequent X-ray probe spectra at the Fe K-edge in the solvated model transition metal complex, K 4 Fe II (CN) 6 . We find several key spectral features that report on the ligand-field splitting, solvent-solute interactions, and the 3p and 3d electron interactions. We then show how these features could be measured in an experiment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Emerging Atomistic Modeling Methods for Heterogeneous Electrocatalysis

Heterogeneous electrocatalysis lies at the center of various technologies that could help enable a sustainable future. However, its complexity makes it challenging to accurately and efficiently model at an atomic level. Herein, we review emerging atomistic methods to simulate the electrocatalytic interface with special attention devoted to the components/effects that have been challenging to model, such as solvation, electrolyte ions, electrode potential, reaction kinetics, and pH. Additionally, we review relevant computational spectroscopy methods. Then, we showcase several examples of applying these methods to understand and design catalysts relevant to green hydrogen. We also offer experimental views on how to bridge the gap between theory and experiments. Finally, we provide some perspectives on opportunities to advance the field.

36 MATERIALS SCIENCE↗

Evaluating the Importance of Conformers for Understanding the Vacuum-Ultraviolet Spectra of Oxiranes: Experiment and Theory

Vacuum-ultraviolet (VUV) absorption spectroscopy enables electronic transitions that offer the unambiguous identification of molecules. As target molecules become more complex, multifunctional species present a great challenge to both experimental and computational spectroscopy. This research reports both experimental and theoretical studies of oxiranes. Computationally, the nuclear ensemble approach has been used to accurately predict experimental spectra for a variety of molecules. However, this approach incurs great computational cost, as ensembles generally consist of thousands of geometries. The present study aims to drastically reduce the ensemble by evaluating the significance of the conformers to the predicted spectra. This approach was applied to 11 substituted oxiranes using the Conformer Rotamer Ensemble Sampling Tool (CREST) of Grimme to generate an ensemble of unique conformers determined by their Boltzmann populations. Five TD-DFT functionals (BMK, CAM-B3LYP, M06-2X, MN15, ωB97X-D) and EOM-CCSD were used to simulate the spectrum of each substituted oxirane ensemble. Computed spectra were then compared to the experiment using both qualitative and quantitative metrics. Based on these metrics, it was observed that certain conformers may not be necessary to characterize this set of oxiranes despite the temperature (323 K) of the experiment. A single conformer can then be used with TD-DFT and EOM-CCSD to replicate the experimental spectra of these medium-sized combustion species.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Roadmap on methods and software for electronic structure based simulations in chemistry and materials

This Roadmap article provides a succinct, comprehensive overview of the state of electronic structure methods and software for molecular and materials simulations. Seventeen distinct sections collect insights by 51 leading scientists in the field. Each contribution addresses the status of a particular area, as well as current challenges and anticipated future advances, with a particular eye towards software related aspects and providing key references for further reading. Foundational sections cover density functional theory and its implementation in real-world simulation frameworks, Green's function based many-body perturbation theory, wave-function based and stochastic electronic structure approaches, relativistic effects and semiempirical electronic structure theory approaches. Subsequent sections cover nuclear quantum effects, real-time propagation of the electronic structure, challenges for computational spectroscopy simulations, and exploration of complex potential energy surfaces. The final sections summarize practical aspects, including computational workflows for complex simulation tasks, the impact of current and future high-performance computing architectures, software engineering practices, education and training to maintain and broaden the community, as well as the status of and needs for electronic structure based modeling from the vantage point of industry environments. Overall, the field of electronic structure software and method development continues to unlock immense opportunities for future scientific discovery, based on the growing ability of computations to reveal complex phenomena, processes and properties that are determined by the make-up of matter at the atomic scale, with high precision.

36 MATERIALS SCIENCE↗