Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “PBE”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A Numerical Modeling Framework for Flocculation and Cohesive Sediment Transport in the Wave Bottom Boundary Layer

Flocculation, a critical process in coastal and estuarine systems, plays a significant role in sediment transport, nutrient cycling, and ecological health. This study develops a cohesive sediment transport modeling framework tailored to the wave bottom boundary layer under dilute and equilibrium conditions, explicitly incorporating flocculation effects via a Population Balance Equation (PBE). Using Direct Numerical Simulation, six baseline cases, each with a distinct sediment concentration profile resulting from a constant settling velocity and critical erosion shear stress, are generated to drive the PBE flocculation model for given floc yield strength and stickiness. Results reveal that flocculation significantly influences sediment concentration profiles promoting three distinct stages, well‐mixed, transition to lutocline, and well‐developed lutocline. At low concentrations with well‐mixed profiles, cohesive floc properties are less significant, and turbulence is a main flocculation driver. In contrast, as concentration increases, cohesive floc properties become crucial, facilitating lutocline formation. Here, the analysis also highlights limitations of depth‐averaged settling velocity as a parameterization. It is suitable for well‐mixed and transitional profiles but fails in well‐developed lutoclines, where empirical formulations that explicitly incorporate turbulent shear rate and sediment concentration better capture variability. This study underscores the necessity of incorporating flocculation effects into sediment transport models to enhance predictions of sediment dynamics in wave bottom boundary layers.

Penaloza‐Giraldo, Jorge A. [Oak Ridge National Lab↗
DOE OSTI2024

Accelerating defect predictions in semiconductors using graph neural networks

First-principles computations reliably predict the energetics of point defects in semiconductors but are constrained by the expense of using large supercells and advanced levels of theory. Machine learning models trained on computational data, especially ones that sufficiently encode defect coordination environments, can be used to accelerate defect predictions. Here, we develop a framework for the prediction and screening of native defects and functional impurities in a chemical space of group IV, III–V, and II–VI zinc blende semiconductors, powered by crystal Graph-based Neural Networks (GNNs) trained on high-throughput density functional theory (DFT) data. Using an innovative approach of sampling partially optimized defect configurations from DFT calculations, we generate one of the largest computational defect datasets to date, containing many types of vacancies, self-interstitials, anti-site substitutions, impurity interstitials and substitutions, as well as some defect complexes. We applied three types of established GNN techniques, namely crystal graph convolutional neural network, materials graph network, and Atomistic Line Graph Neural Network (ALIGNN), to rigorously train models for predicting defect formation energy (DFE) in multiple charge states and chemical potential conditions. We find that ALIGNN yields the best DFE predictions with root mean square errors around 0.3 eV, which represents a prediction accuracy of 98% given the range of values within the dataset, improving significantly on the state-of-the-art. We further show that GNN-based defective structure optimization can take us close to DFT-optimized geometries at a fraction of the cost of full DFT. The current models are based on the semi-local generalized gradient approximation-Perdew–Burke–Ernzerhof (PBE) functional but are highly promising because of the correlation of computed energetics and defect levels with higher levels of theory and experimental data, the accuracy and necessity of discovering novel metastable and low energy defect structures at the PBE level of theory before advanced methods could be applied, and the ability to train multi-fidelity models in the future with new data from non-local functionals. The DFT-GNN models enable prediction and screening across thousands of hypothetical defects based on both unoptimized and partially optimized defective structures, helping identify electronically active defects in technologically important semiconductors.

Rahman, Md Habibur (ORCID:000000027705984X)↗
DOE OSTI2022

Structural and electronic properties of rare-earth chromites: A computational and experimental study

Here, in this work, the structural, optical, and electronic properties of rare-earth perovskites of the general formula R⁢ CrO 3 , where R⁢ represents the rare-earth Gd, Tb, Dy, Ho, Er, and Tm, have been studied in detail. These compounds were synthesized through a facile citrate route. X-ray diffraction, Raman spectroscopy, and UV-Visible spectroscopy were utilized to reveal the structural evolutions in R⁢ ⁢CrO 3 . The lattice parameters, Cr 3+ –O 2 –Cr 3+ bond angle, and CrO 6 octahedral distortions were found to strongly depend on the ionic radii of R⁢ . First-principles calculations based on density-functional theory within the generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) and strongly constrained and appropriately normed (SCAN) meta-GGA were also employed to calculate the structural and electronic properties of R⁢ ⁢CrO 3 . The ground-state energy, lattice constants, electronic structures, and density of states of R⁢ ⁢CrO 3 were calculated. These provide some insights into the electronic characteristics of the R⁢ ⁢CrO 3 compounds. The calculated values of lattice parameters and band gaps with Hubbard U correction (SCAN+ U ) agree well with values measured experimentally and show more accuracy in predicting the ground-state crystal structure and band structure compared to PBE+ U approximation. The band gap of R⁢ ⁢CrO 3 is found to be independent of the ionic radii of R⁢ from both experiments and calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Liquid-liquid phase transition of hydrogen and its critical point: Analysis from ab initio simulation and a machine-learned potential

We simulate high-pressure hydrogen in its liquid phase close to molecular dissociation using a machine-learned interatomic potential. The model is trained with density functional theory (DFT) forces and energies, with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional. We show that an accurate NequIP model, an E(3)-equivariant neural network potential, accurately reproduces the phase transition present in PBE. Moreover, the computational efficiency of this model allows for substantially longer molecular dynamics trajectories, enabling us to perform a finite-size scaling (FSS) analysis to distinguish between a crossover and a true first-order phase transition. Here, we locate the critical point of this transition, the liquid-liquid phase transition (LLPT), at 1200-1300 K and 155-160 GPa, a temperature lower than most previous estimates and close to the melting transition.

08 HYDROGEN↗
DOE OSTI2023

Polymer-Infiltrated Metal–Organic Frameworks for Thin-Film Composite Mixed-Matrix Membranes with High Gas Separation Properties

Thin-film composite mixed-matrix membranes (TFC-MMMs) have potential applications in practical gas separation processes because of their high permeance (gas flux) and gas selectivity. In this study, we fabricated a high-performance TFC-MMM based on a rubbery comb copolymer, i.e., poly(2-[3-(2H-benzotriazol-2-yl)-4-hydroxyphenyl] ethyl methacrylate)-co-poly(oxyethylene methacrylate) (PBE), and metal–organic framework MOF-808 nanoparticles. The rubbery copolymer penetrates through the pores of MOF-808, thereby tuning the pore size. In addition, the rubbery copolymer forms a defect-free interfacial morphology with polymer-infiltrated MOF-808 nanoparticles. Consequently, TFC-MMMs (thickness = 350 nm) can be successfully prepared even with a high loading of MOF-808. As polymer-infiltrated MOF is incorporated into the polymer matrix, the PBE/MOF-808 membrane exhibits a significantly higher CO 2 permeance (1069 GPU) and CO 2 /N 2 selectivity (52.7) than that of the pristine PBE membrane (CO 2 permeance = 431 GPU and CO 2 /N 2 selectivity = 36.2). Therefore, the approach considered in this study is suitable for fabricating high-performance thin-film composite membranes via polymer infiltration into MOF pores.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Ab Initio Structures and Energetics of Hydrated Flat and Terrace-Step Surfaces of Forsterite (Mg 2 SiO 4 )

Forsterite (Mg 2 SiO 4 ), a model divalent metal silicate mineral, has been extensively studied in the context of mineral carbonation. Although dissolution is a key step in this process, the mechanisms by which forsterite dissolves under high CO 2 conditions remain poorly understood. Atomistic simulations could aid in exploring these mechanisms, but it is essential first to understand the structures and energetics of the relevant forsterite surfaces. We present an ab initio study of the structure and surface energy at 0 K of the flat $(010), (110), (001), (111), (021), (101)$ and $(120)$ faces of forsterite using the density functional PBE Hamiltonian and a plane-wave basis set. Dry surfaces became stabilized upon hydration through the formation of bonds between surface Mg and O from water, as well as by the formation of hydrogen bonds. According to surface energy values, the stability order of the hydrated forsterite faces was found to be $(120) < (101) < (021) < (111) < (001) < (110) < (010)$. We also investigated the energetics of the terrace-step $(0\bar{41})$ surface as a model site for forsterite dissolution. Among all the facets, the $(0\bar{41})$ surface is the least stable termination in water. Hydration of Mg atoms on the $(0\bar{41})$ surface increases their susceptibility to dissolution. The presence of a step and its hydration destabilizes the terraces, making step retreat more likely than a dissolution front advancing along the [010] direction. This research will support future simulations to investigate forsterite dissolution in water under CO 2 -rich conditions.

PBE Hamiltonian↗
DOE OSTI2025

Computational screening of fly ash zeolite sorbents for boric acid removal

In the United States, many impoundments at coal-fired power plants contain elevated contaminants like arsenic, boron, barium, and selenium. Zeolites synthesized from fly ash show promise as sorbents for these contaminants. However, optimizing sorption capacity is challenging due to numerous possible topologies, silicon to aluminum (Si/Al) ratios, and cation types. In this study, molecular simulations are used to design cationic zeolites for boric acid adsorption. Force field models based on quantum mechanical calculations (PBE + D2) for Na-, Ca-, Mn-, and Fe-exchanged chabazite and LTA are presented. The new D2FF force fields reproduce DFT energies with about half the error of UFF. Zeolite performance depends on Si/Al ratio and cation type, with low Si/Al ratio chabazite (CHA) and phillipsite (PHI) zeolite frameworks exchanged with Ca 2+ or Na + /Ca 2+ mixtures showing the highest adsorption. In conclusion, these findings suggest tailored fly ash-derived zeolites could provide effective boron removal from leachate ponds.

CCR impoundment↗
DOE OSTI2024

Self‐Consistent Convolutional Density Functional Approximations: Application to Adsorption at Metal Surfaces

The exchange-correlation (XC) functional in density functional theory is used to approximate multi-electron interactions. A plethora of different functionals are available, but nearly all are based on the hierarchy of inputs commonly referred to as “Jacob's ladder.” This paper introduces an approach to construct XC functionals with inputs from convolutions of arbitrary kernels with the electron density, providing a route to move beyond Jacob's ladder. We derive the variational derivative of these functionals, showing consistency with the generalized gradient approximation (GGA), and provide equations for variational derivatives based on multipole features from convolutional kernels. A proof-of-concept functional, PBEq, which generalizes the PBEα framework with mathematical equation being a spatially-resolved function of the monopole of the electron density, is presented and implemented. It allows a single functional to use different GGAs at different spatial points in a system, while obeying PBE constraints. Analysis of the results underlines the importance of error cancellation and the XC potential in data-driven functional design. After testing on small molecules, bulk metals, and surface catalysts, the results indicate that this approach is a promising route to simultaneously optimize multiple properties of interest.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Water‐mediated Decomposition Pathways of ε‐Hexanitrohexaazaisowurtzitane

The dominant initial decomposition mechanism of 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (HNIW) is understood from the literature to be the N─NO 2 bond scission unimolecular mechanism. Here we have found a water-mediated HONO release initial decomposition mechanism energetically competitive with the N─NO 2 bond scission mechanism modeled using ab initio nudged elastic band simulations. The activation energy of the water-mediated HONO mechanism was calculated to be 138.9 kJ/mol with the Perdew, Burke, and Ernzerhof (PBE) functional (177.8 with PBE0), while the double NO 2 release mechanism is 171.9 kJ/mol (203.3 with PBE0). Branching secondary, tertiary, and quaternary decomposition steps were also discovered including oxidation of HONO or H 2 O causing ring-opening that leads to C─N bond breaking and N 2 O or NO release. The reaction rate of HONO oxidation is much faster than HONO release, making the HONO concentration low. The Helmholtz free energy barrier of the double NO 2 release mechanism is lower than the water-mediated HONO release above 438 K (165°C) due to the vibrational contribution to the free energy. This helps explain why the literature reports more NO 2 release at higher temperatures. The present study reveals a physical mechanism for how water can catalyze the decomposition of HNIW at low enough temperatures, and reveals secondary, tertiary, and quaternary reaction mechanisms leading to NO x release. In conclusion, as water is realistically always present, the reported barriers are important for building kinetic models needed to ensure the safety and reliability of HNIW.

Steele, Brad A. [Lawrence Livermore National Labor↗
DOE OSTI2023

Unveiling the mechanism of surface corrugation formation on a quasi free-standing bi-layer graphene via experimental and modeling investigations

Extensive studies have been conducted to accomplish the controls over the formation of surface corrugations on chemical vapor deposited (CVD) graphene. However, the underlying mechanism of the surface corrugation formation on graphene remains elusive, due to the difficulty delineating the growth-induced surface corrugations from wrinkles formed during graphene transfer with the use of a supporting layer casted on top of the sample. Here, in this study, “quasi free-standing” graphene was realized using the weakly-interacting h-BN layer during a wet transfer process to study the surface corrugation formation on graphene. The weak interaction of graphene with the supporting h-BN layer allows for the growth-induced surface corrugations to be released, enabling the investigation of the primary mechanism for the graphene corrugation behavior during the transfer process. The experimental measurements of surface corrugations were conducted using atomic force microscopy (AFM) to reveal that surface corrugations are formed following the graphene’s crystallographic directions. Density functional theory calculations using the projector augmented-wave (PAW) method and Perdew-Burke-Ernzerhof (PBE) exchange correlation functional were also conducted for two models of “atomic-scale ripples” and “nanoscale wrinkles” and showed that all of them are formed along the crystallographic axis of graphene, which is in good agreement with the experimental observations.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Bayesian prior construction for uncertainty quantification in first-principles statistical mechanics

First-principles statistical mechanics enables the prediction of thermodynamic and kinetic properties of materials, but is computationally expensive. Many approaches require surrogate models to calculate energies within Monte Carlo or molecular dynamics simulations. Inexpensive surrogates such as cluster expansions enable otherwise intractable calculations by interpolating data from higher accuracy methods, such as Density Functional Theory (DFT). Surrogate models introduce uncertainty into downstream calculations, in addition to any uncertainty inherent to DFT calculations. Bayesian frameworks address this by quantifying uncertainty and incorporating expert knowledge through priors. However, constructing effective priors remains challenging. This work introduces and describes practical strategies for building Bayesian cluster expansions, focusing on basis truncation, hyperparameter selection, and ground state replication. We analyze multiple basis truncation schemes, compare cross-validation to the evidence-approximation for hyperparameter optimization, and provide methods to find and enforce ground-state-preserving models through priors. Additionally, we compare the uncertainties between different approximations to DFT (LDA, PBE, SCAN) against the uncertainty introduced with the use of cluster expansion surrogate models. These approaches are demonstrated on the BCC Li x Mg 1-x and Li x Al 1-x alloys, which are both of interest for solid-state Li batteries. Our results provide guidelines for constructing and utilizing Bayesian cluster expansions, thereby improving the transparency of materials modeling. Furthermore, the approaches and insights developed in this work can be transferred to a wide range of cluster expansion surrogate models, including the atomic cluster expansion and related machine-learned interatomic potential architectures.

Alloy theory↗
DOE OSTI2026

Point defect energetics in gallium arsenide, a comprehensive density functional theory study

In materials, point defects often control or modify functional properties. To predict the performance of materials intended for application in optoelectronic devices, it is imperative to understand the properties of those point defects. For the first time, all six intrinsic defects of GaAs, a key optoelectronics material, and their charge transition levels are calculated using density functional theory with the HSE06 functional. For comparison, both PBE and r 2 SCAN calculations are also carried out. The HSE06 results are found to be in better agreement with experimental data than previous calculations. In conclusion, the importance of using the exact electron exchange present in hybrid functionals and larger supercells to accurately determine defect levels and ground state defect configurations is demonstrated.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Finite temperature properties of uranium mononitride

Uranium mononitride (UN) is a promising nuclear fuel that combines the advantageous properties of readily used UO 2 and uranium alloys, such as high melting temperature and high uranium density, and thermal conductivity, respectively. A better understanding of UN behavior at operating temperatures can be obtained from finite temperature data, such as elastic properties. To get this information, ab initio molecular dynamics (AIMD) simulations were performed at five different temperatures using constant volume (NVT) and constant pressure (NPT) ensembles. Initially, the performance of PBE functional in reproducing experimental crystallographic properties and magnetic ordering is assessed. The finite temperature phonon dispersions are calculated using NVT simulation results, which show a softening of the phonon modes with increasing temperature. The NPT results are used to obtain the thermal expansion of UN and finite temperature electronic properties. The calculated thermal expansion is compared with our measurements using neutron diffraction. Additionally, the temperature dependent elastic properties of UN are evaluated using the strain-stress method in AIMD simulations, indicating that UN becomes softer and more compressible with increasing temperature. Also, the calculated Young’s modulus slope is in very good agreement with the experiment. The finite temperature heat capacity and electronic thermal conductivity are calculated from AIMD simulations, which are in better agreement with the experiment than the heat capacity and thermal conductivity calculated using the structures relaxed at 0K. Finally, the thermal diffusivity from AIMD has opposite temperature dependence compared to experimental results, which we argued comes from the underestimated electronic thermal conductivity.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Ab initio modeling and thermodynamics of hydrated plutonium oxalates

An ab initio study on the plutonium oxalate hydrates: Pu 2 (C 2 O 4 ) 3 ·10H 2 O and Pu(C 2 O 4 ) 2 ·6H 2 O, using PBE exchange-correlation with D3 dispersion correction and Hubbard correction for the plutonium atoms, was performed and compared to experimental vibrational spectral and thermodynamic property values. Here we demonstrated that this technique can accurately predict the experimental infrared spectra Pu(III) oxalate hydrate, as well as the Raman peak of PuO 2 (used to calculate the thermodynamic properties of the oxalates). For Pu(IV) oxalate hydrate we found that our predicted structure agreed qualitatively with PXRD measurements, the only available experimental determination of the structure. Using this method at standard temperature and pressure, we predicted standard enthalpies of formation of -6,755 kJ mol -1 and -3,923 kJ mol -1 and standard Gibbs free energy of formation of -5,899 kJ mol -1 and -3,386 kJ mol -1 for Pu 2 (C 2 O 4 ) 3 ·10H 2 O and Pu(C 2 O 4 ) 2 ·6H 2 O, respectively.

36 MATERIALS SCIENCE↗
DOE OSTI2024

KCl-UCl 3 molten salts investigated by Ab Initio Molecular Dynamics (AIMD) simulations

Ab Initio Molecular Dynamics (AIMD) simulations are performed on molten KCl-UCl3 salt mixtures to determine energies, heat capacities, and densities. The density-dependent energy correction (DFT-dDsC), Grimme et al.'s DFT-D3, and Langreth & Lundqvist (vdW-cx) models are used for dispersion forces and combined with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation potential with a Hubbard U parameter for the 5f electrons of uranium. After validating predictions for the end-member systems to literature data, KCl-UCl 3 mixtures are studied at select temperatures. Densities and energies both deviate from ideal solution behavior, with the maximum deviation occurring around 36% UCl 3 for mixing energies and slightly lower (29% UCl3) for densities. Compared to the NaCl-UCl 3 system, which was previously investigated using the same simulation methodologies, the KCl-UCl 3 density and mixing energy deviations from ideal solution behavior are larger by almost a factor of two. No deviation from ideal solution behavior for heat capacity was observed. The AIMD predictions for mixing energies and densities agree qualitatively with experimental data, though the spread in data obtained from the various dispersion force models utilized, measurements, and empirical estimates makes strong conclusions difficult. The dependence of thermodynamic and thermophysical properties on composition is correlated with the local chemistry of the solution phase, in particular, the tendency of UCl 3 to form network structures.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Electrochemical leaching of spent LIBs: Kinetics, novel reactor, and modeling

The use of electrons as main reagent for the recovery and recycling of critical metals from spent lithium-ion batteries (LIBs) is a process electrification strategy that can be used to close the life-cycle loop of LIBs through more sustainable methods. Electrochemical leaching, a process that uses a reductant that is constantly regenerated electrochemically for the leaching of lithium-ion battery black mass (LIBBM), has shown high extraction efficiencies and sustainable scores. However, slow kinetics, reactor design challenges and lack of deeper understanding of the underlying processes are barriers to the optimization, scale-up, and market adoption of this technology. In this paper, a kinetic study and mathematical model for dissolving LIBBM is presented to better understand the underlying mechanisms aiming to reduce the processing time and make predictions for future design and scale-up. The effect of acid and electrochemically mediated reductant concentrations, LIBBM loading, and cathode/reactor designs were explored. As a result, the leaching time was reduced from 7h to under 1h at a pulp density of 73 g/L, without external heating. A novel reactor with parallel baffle electrodes (PBE) was developed, which significantly reduced the leaching time by improving convection in a stirred slurry electrochemical reactor. Dimensionless numbers were deduced from an unsteady state model, which can be used in dimensional analysis for future process design and scale-up.

25 ENERGY STORAGE↗
DOE OSTI2024

Invariant Molecular Representations for Heterogeneous Catalysis

Catalyst screening is a critical step in the discovery and development of heterogeneous catalysts, which are vital for a wide range of chemical processes. In recent years, computational catalyst screening, primarily through density functional theory (DFT), has gained significant attention as a method for identifying promising catalysts. However, the computation of adsorption energies for all likely chemical intermediates present in complex surface chemistries is computationally intensive and costly due to the expensive nature of these calculations and the intrinsic idiosyncrasies of the methods or data sets used. This study introduces a novel machine learning (ML) method to learn adsorption energies from multiple DFT functionals by using invariant molecular representations (IMRs). To do this, we first extract molecular fingerprints for the reaction intermediates and later use a Siamese-neural-network-based training strategy to learn invariant molecular representations or the IMR across all available functionals. Our Siamese network-based representations demonstrate superior performance in predicting adsorption energies compared with other molecular representations. Notably, when considering mean absolute values of adsorption energies as 0.43 eV (PBE-D3), 0.46 eV (BEEF-vdW), 0.81 eV (RPBE), and 0.37 eV (scan+rVV10), our IMR method has achieved the lowest mean absolute errors (MAEs) of 0.18 0.10, 0.16, and 0.18 eV, respectively. These results emphasize the superior predictive capacity of our Siamese network-based representations. The empirical findings in this study illuminate the efficacy, robustness, and dependability of our proposed ML paradigm in predicting adsorption energies, specifically for propane dehydrogenation on a platinum catalyst surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Quantum Vibronic Effects on the Electronic Properties of Molecular Crystals

We present a study of molecular crystals, focused on the effect of nuclear quantum motion and anharmonicity on their electronic properties. We consider a system composed of relatively rigid molecules, a diamondoid crystal, and one composed of floppier molecules, NAI-DMAC, a thermally activated delayed fluorescence compound. We compute fundamental electronic gaps at the density functional theory (DFT) level of theory, with the Perdew–Burke–Erzenhof (PBE) and strongly constrained and approximately normed (SCAN) functionals, by coupling first-principles molecular dynamics with a nuclear quantum thermostat. We find a sizable zero-point renormalization (ZPR) of the band gaps, which is much larger in the case of diamondoids (0.6 eV) than for NAI-DMAC (0.22 eV). We show that the frozen phonon (FP) approximation, which neglects intermolecular anharmonic effects, leads to a large error (~50%) in the calculation of the band gap ZPR. Instead, when using a stochastic method, we obtain results in good agreement with those of our quantum simulations for the diamondoid crystal. However, the agreement is worse for NAI-DMAC where intramolecular anharmonicities contribute to the ZPR. Our results highlight the importance of accurately including nuclear and anharmonic quantum effects to predict the electronic properties of molecular crystals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗