dataesr/scientific-paragraphs-categorization huggingface dataset:
In the case of electron-phonon scattering, τ À1 nk!mkþq is obtained from Eq. (  2 ) by removing the summation over m and the integral over the Brillouin zone, i. e. P m R dq=Ω BZ. When both electron-phonon scattering and charged impurity scattering are taken into account, the partial scattering rate is written as the sum of the individual partial rates 1 τ nk!mkþq ¼ 1 τ ph nk!mkþq þ 1 τ imp nk!mkþq ; ( 11 ) where the superscripts refer to carrier-phonon (ph) and carrierimpurity (imp) scattering, respectively. In EPW, the carrier-impurity partial scattering rate 1=τ imp nk!mkþq is calculated under the following simplifying approximations: (i) each impurity is described by an idealized point charge, embedded in the dielectric continuum of the host material; (ii) the scattering rate from each impurity is evaluated within the first Born approximation; (iii) defects are sufficiently diluted that the scattering rates from different impurities are additive; (iv) impurities are randomly distributed, and this random distribution is formally taken into account by using the Kohn and Luttinger ensemble average  58.
Numerical tests show that this approach preserves the accuracy of more expensive full-grid calculations. FBW Eliashberg calculations are computationally more demanding than FSR calculations. In particular, to determine the chemical potential from Eq. (  25 ) one needs a Matsubara frequency cutoff of at least a few times the Kohn-Sham energy window, leading to a considerable increase in computational cost. To circumvent this issue, the default behavior of EPW is to keep the chemical potential fixed at the Fermi level unless it is instructed by the user to solve Eq. (  25 ). In this case, careful convergence tests with respect to the Matsubara frequency cutoff are warranted. Application example. To demonstrate the implementation of the superconducting module in EPW, we investigate the superconducting properties of hexagonal niobium diselenide (2H-NbSe 2 ).
(  64 ) of the "Methods" section]. The inversion of this last relation also allows one to interpolate the coefficients A nk throughout the Brillouin zone, which is useful to visualize how specific bands contribute to the polaron wavefunction (Fig. 4 ). Application example. To demonstrate the implementation of the polaron module in EPW, we investigate the electron and hole polarons in rocksalt NaCl, a prototypical polar insulator that hosts small hole polarons called V K centers  138, 139. We perform calculations using the PBE exchange and correlation functional  45  , ONCV pseudopotentials  47  , and a planewaves kinetic energy cutoff of 150 Ry. Ground-state and lattice-dynamical calculations are performed using a 12 × 12 × 12 uniform and unshifted Brillouin zone mesh for both k-and q-points.
Alternatively, n(ω) can be taken from experiments 143. Computational considerations. In the optics module of EPW, the imaginary part of the dielectric function is calculated using Eq. (  49 ). The summation over virtual states in Eqs. (  47 ) and (  48 ) are restricted to the manifold of valence and conduction bands included in the Wannierization procedure. The Dirac delta functions appearing in Eq. (  49 ) are replaced by Gaussian functions or Lorentzian functions with a finite broadening. The small parameter η in Eqs. (  47 ) and (  48 ) are used to avoid singular denominators which arise if, for a given photon energy ℏω, direct transitions are resonant with indirect transitions. These situations are encountered, for example, at the onset of direct transitions, i. e. when the photon energy matches the direct gap.
In these situations, the dielectric function and the absorption spectrum become sensitive to the choice of η: too small an η leads to a divergence of the spectrum, and too large an η leads to an excessive broadening. To probe the sensitivity of the spectra to this parameter, the optics module of EPW calculates Im[ϵ(ω)] for a range of broadening parameters between 1 meV and 0. 5 eV. Efforts are currently ongoing to eliminate these spurious singularities: we believe that they arise from an intrinsic limitation of second-order perturbation theory when direct and indirect transitions are in resonance; a more general theory that correctly describes these resonances is under development  145. In Eqs. (  47 ) and (  48 ), the velocity matrix elements are sensitive to the details of the electronic structure.
In addition, convergence of the phonon-assisted optical spectra for cubic boron arsenide 148 and cubic silicon carbide 149 was achieved with Brillouin zone grids of 32 × 32 × 32. When free-carrier absorption is considered, denser grids are required for converged spectra. For example, a grid of 48 × 48 × 48 is needed for converged phonon-assisted free-carrier absorption spectra in silicon 150. Application example. To demonstrate the implementation of the optics module in EPW, we examine phonon-assisted optical absorption in silicon. Gound-state DFT calculations are performed using the PBE exchange and correlation functional  45  , ONCV pseudopotentials  46, 61  , a planewaves kinetic energy cutoff of 60 Ry, and a 6 × 6 × 6 Brillouin zone sampling of both the k-point grid and the q-point grid.
This approach provides an alternative strategy for computing optical spectra to Eq. (  49 ) implemented in the indirect optics module of EPW. In the special displacement method, both temperature-dependent band structure renormalization and phonon-assisted processes are included on the same footing. Figure  6f  shows the imaginary part of the dielectric function of BaSnO 3 at 0 K (blue) and 300 K (green), including phonon-assisted processes. For comparison, we also show the calculation using the DFT ground-state structure (red), which misses phonon-assisted transitions. The spectra compare well with prior work using the special displacement method 181.
Implementation and HPC benchmarks In this section, we describe some of the implementation and parallel programming models of EPW. We first outline the computational workflow and basic capabilities of EPW. Then we describe our recent efforts to prepare EPW for exascale HPC systems with a focus on an explorative implementation of a highly scalable parallelization scheme, hybrid two-level MPI, and OpenMP parallelization. We present benchmarking results which demonstrate that, with this improved parallelization strategy, EPW can run at nearly full scale on the pre-exascale HPC system Frontera at the Texas Advanced Computing Center (TACC). Finally, we describe the I/O strategy employed in this explorative implementation, which is based on XML (eXtensible Markup Language) and HDF5 file formats. We emphasize that EPW continues to evolve with changes and improvements, and the reader is referred to the EPW website for its most up-to-date features and functionalities 182.
Computational workflow and basic capabilities. The EPW code is logically partitioned into two components. The first component serves as an interface to the PWscf and PHonon codes of Quantum ESPRESSO. The code imports ground-state charge density and wavefunctions with computational parameters from prior runs with pw. x, and dynamical matrices, variations of the Kohn-Sham potentials, and vibrational mode pattern files from a prior phonon calculation with ph. x. All these quantities are evaluated on coarse k-and q-points grids, and the phonon wavevectors are restricted to the irreducible wedge of the Brillouin zone. Then the code calls Wannier90 in library mode to calculate the unitary rotation matrices U mnk [Eq. (  64 ) of the "Methods" section] needed to transform Bloch states into maximally localized Wannier functions.
The vertical dashed lines indicate the direct and indirect band gap energies. A scissor shift of 1. 91 eV is employed to match the experimental gap  226. the full zone, evaluates electron-phonon matrix elements coarse k-and q-point grids, and it transforms the Hamiltonian, dynamical matrices, and electron-phonon matrix elements into the Wannier representation. At this point, the code can print relevant quantities for subsequent runs with epw. x, and it can continue to the interpolation part. The interpolation engine of EPW carries out Wannier interpolation of the Hamiltonian, dynamical matrices, and electron-phonon matrix elements on fine k-and q-point grids after reading these quantities in the Wannier representation, and then it calculates electron-phononrelated properties on these grids.
DISCUSSION Since the last technical paper in 2016  18  , the EPW code has considerably expanded in scope, to the point of becoming a robust and efficient software platform for developing, testing, and deploying methods addressing electron-phonon physics and related materials properties. It is then natural to ask which components and functionalities are still in need of improvement, what are emerging directions in this area, and more generally what comes next for the EPW project. On the functionality front, we expect to continue expanding the capabilities for transport, superconductivity, polarons, and optics described in the 'Results' section. For example, the transport module is based on the steady-state linearized Boltzmann transport equation; here, it would be desirable to generalize the methodology to high-field transport and to time-dependent driving fields.
Similarly, in the superconductivity module, the treatment of electron-electron repulsion could be improved by seamlessly integrating EPW with standard GW codes. The study of polaron physics from an ab initio many-body perspective is just beginning, therefore we can expect a number of developments in this area, from the study of polaron transport to their optical properties and their relation with the theory of band structure renormalization. Calculations of phonon-assisted optical transitions are currently restricted to optical absorption spectra, but the formalism can just as well be employed for investigating related phenomena such as for example Auger-Meitner recombination  184. Beyond these core modules of the EPW project, we anticipate growth in the calculation of electronic and optical properties using the special displacement method within the EPW/ZG code; for example, the current implementation focuses on harmonic systems, but generalizations to strongly anharmonic systems have recently been proposed 185.
In addition to the hybrid MPI/OpenMP parallelization, it will be necessary to leverage diverse GPU architectures and to enable the code for large-scale runs that will become possible with the exascale supercomputers that are being deployed worldwide. Another important direction will be to enhance the interoperability of EPW with other major electronic structure software packages such as Abinit 189 , VASP 190 , Siesta 191 , and GPAW 192. As several codes currently use the information generated by EPW for a variety of post-processing tasks, it will make sense to develop standardized data structures that adhere to the FAIR data principles. Regarding the programming model, transitioning toward object-oriented programming (OOP) will be useful due to the potential for high modularity, extensibility, and reusability, which will facilitate flexible and sustained software development  193.
We expect that targeted use of OOP will greatly increase the efficiency and productivity in the development and maintenance of code  194. Alongside these developments, we anticipate increased attention to the issue of automation and the capability of performing electron-phonon calculations at scale for high-throughput approaches, data science, and artificial intelligence/machine learning (AI/ML) applications. In summary, in this manuscript, we provided a comprehensive update on the current status, functionalities, and performance of the EPW code, we offered an overview of possible future directions for this and similar codes. We hope that, beyond capturing a snapshot of the current status of the EPW project, the present manuscript will contribute to making advanced electron-phonon calculations more accessible and more widely used in computational materials discovery and design.
ACKNOWLEDGEMENTS This research is supported by: the  Computational Materials Sciences Program  funded by the  U. S. Department of Energy, Office of Science, Basic Energy Sciences , under Award No. DE-SC0020129  (project coordination, scale-up, polaron module, transport module, optics module, special displacement module); the  National Science Foundation ,  Office of Advanced Cyberinfrastructure and Division of Materials Research  under Grants Nos. 2103991  and  2035518  (superconductivity module, interoperability); the  NSF Characteristic Science Applications for the Leadership Class Computing Facility program  under Grant No. 2139536  (preparation for LCCF); the  Fond National de la Recherche Scientifique of Belgium  (F. R. S. -FNRS ) and the  European Union 's  Horizon 2020 research and innovation program  under grant agreements No.
S. P. acknowledges computational resources provided by the  PRACE  award granting access to Discoverer in SofiaTech, Bulgaria (OptoSpin project id. 2020225411 ), and by the  Consortium des Équipements de Calcul Intensif (CÉCI) , funded by the  FRS-FNRS  under Grant No. 2. 5020. 11  and by the  Walloon Region , as well as computational resources awarded on the Belgian share of the EuroHPC LUMI supercomputer. K. B. acknowledges the support of the  U. S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Department of Energy Computational Science Graduate Fellowship  under Award Number  DE-SC0020347. The authors wish to thank  Zhenbang Dai ,  Nikolaus Kandolf ,  Viet-Anh Ha , and  Amanda Wang  for their contributions to the EPW project that are not discussed in this manuscript;  John Cazes  and  Hang Liu  at  TACC  for their support with the  Characteristic Science Applications  project,  Paolo Giannozzi  for his support with  Quantum ESPRESSO ; and  Stefano Baroni  for fruitful discussions.
Transmission Electron Microscopy (TEM) and Energy-Dispersive X-ray (EDX) Spectroscopy The TEM technique was employed to determine the morphology and structure of green-synthesized AgNPs. TEM images at the magnification of 50,000× and 100,000× revealed the spherical morphology of AgNPs with a polydispersity nature and no agglomeration as shown in Figure  3A  and B. Moreover, size calculations using Sigma Scan Pro software (Systat Software Inc. , San Jose, CA, USA) in conjunction with TEM revealed that AgNPs were in the range of 16 ± 2 nm, and our results are in accordance with the study conducted by Suriyakala et al. [77]. Likewise, a study conducted by Pei et al. [78]  reported the formation of spherical-shaped AgNPs using an aqueous extract of Coptis chinensis. Moreover, Khan et al. [79]  also reported the formation of spherical AgNPs using leaf extract of Hibiscus sabdariffa.
Composition Characterization. XPS measurements were performed using a Kratos AXIS Supra X-ray Photoelectron Spectrometer equipped with monochromatic Al Kα radiation (E ex = 1486. 6 eV). The analysis area was approximately 700 × 300 μm. Charge correction was done by referencing the adventitious C-C peak to 284. 8 eV. DFT Calculations. The calculations were performed under the Kohn-Sham formulation  20, 21  as implemented in the Vienna Ab-initio Simulation Package (VASP). 22  The projector augmented wave (PAW) method  23, 24  was used to describe the interaction between the ion cores and the electrons. The electron exchange-correlation was treated by the generalized gradient approximation (GGA) based on the Perdew-Burke-Ernzerhof (PBE) functional. The rotationally invariant GGA+U approach introduced by Dudarev et al.
CCDC 2257540, 2257555, 2257548, and 2238869 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www. ccdc. cam. ac. uk/ data_request/cif, or by emailing data_request@ccdc. cam. ac. uk, or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033. Accession Codes ■ AUTHOR INFORMATION Corresponding Authors.
Characterization XPS surface analysis was performed on a ThermoFisher Scientific K-ALPHA spectrometer with a monochromatized Al Ka source (hn = 1486. 6 eV). The powdered samples were pressed onto small indium foils or directly examined on the Transmission Electron Microscopy (TEM) grids with a 200 mm X-ray spot size. The overall spectra (0-1100 eV) were obtained with a constant pass energy of 200 eV and high-resolution spectra at 40 eV. Charge neutralization was applied during analysis and sputtering was achieved with 3 keV Ar + ions at an angle of incidence, y, of 451 to the normal of the sample. Highresolution spectra were quantified and/or fitted with the software AVANTAGE provided by ThermoFisher Scientific (Scofield sensitivity factors were used for quantification). The binding energy (BE) of the spectra was corrected with that of adventitious carbon C1s (C-C, C-H) at 284.
Acknowledgements The authors acknowledge the  China Scholarship Council  for a PhD Grant to FZ and QB. This project has received financial support from the  CNRS  through the  MITI interdisciplinary programs (Action MITI: Nouveaux Materiaux   2020-2021 ). All the TEM observations were performed on the microscopes of the  Plateforme Aquitaine de Caracterisation des Materiaux (PLACAMAT ,  UMS 3626 ,  CNRS-Univ. deBordeaux, Pessac, France)  and the  Bordeaux Imaging Centre. MHD and QB want to acknowledge  Jerome Majimel  for preliminary TEM, and  Christine Labruge  `re from  UMS   3626  for XPS data.
During the last fifteen years, we and other research groups reported many investigations on Mg(II) metalloporphyrins  [2] [3] [4] [5] [6]. These magnesium(II) porphyrinic species are known to exhibit higher fluorescence quantum yields and longer excited state lifetimes compared to those of other metalloporphyrins such as Zn (II) porphyrin complexes  [7]. Mg(II) porphyrins have been tested in many areas such as catalysis  [8] [9] [10] [11] [12] , sensors  [13, 14]  and environmental applications  [15, 16]. It is also noteworthy that all known structures of cadmium(II) porphyrin complexes are pentacoordinate because of the large size of the Cd 2+ ion which cannot fit the size of a porphyrin macrocycle. An inspection of the Cambridge Structural Database (CSD Version 5. 43, last update September 2022)  [17]  shows that magnesium(II) porphyrin complexes can be pentacoordinated or hexacoordinated.
Emission spectroscopy The emission spectra were recorded at room temperature with a Horiba Scientific Fluoromax-4 spectrofluorometer. The luminescence lifetime measurements were performed for excitation at λ = 450 nm using the second harmonic of a titanium-sapphire laser (picosecond Tsunami laser spectra physics 3950-M1BB and 39868-03 pulse picker doubler) at an 800 kHz repetition rate. Fluotime 200 from AMS technologies was used for the decay acquisition. It consists of a GaAs microchannel plate photomultiplier tube (Hamamatsu model R3809U-50) followed by a time-correlated single photon counting system from Picoquant (PicoHarp300). The ultimate time resolution of the system is close to 30 ps. The luminescence decays were analysed with the FLUOFIT software available from Picoquant. The mission quantum yields were determined at room temperature in dichloromethane solutions by using the optically dilute method.
Electrochemistry Cyclic voltammetry (CV) experiments were performed with a CH-660B potentiostat (CH Instruments). All analytical experiments were conducted at room temperature under an argon atmosphere (argon stream) in a standard one compartment, three-electrode electrochemical cell. Tetra-n-butylammonium perchlorate (TBAP) was used as a supporting electrolyte (0. 2 M) in dichloromethane previously distilled over calcium hydride under argon. An automatic ohmic drop compensation procedure was systematically implemented before the CV data were recorded with electrolytic solutions containing the studied compounds at concentrations of ca. 10 -3 M. CH Instruments vitreous carbon (ϕ = 3 mm) working electrodes were polished with 1 mm diamond paste before each recording. The Ag/AgNO 3 0. 01 M (TBAP 0.
X-ray structure determination A dark blue single crystal of dimensions 0. 40 × 0. 20 × 0. 12 mm of complex (1) was chosen for an X-ray diffraction study. Crystal evaluation and data collection were performed on a Bruker-AXS-Enraf-Nonius Kappa APEXII diffractometer equipped with a CCD area detector with Mo Kα radiation of wavelength (λ = 0. 71073 Å) at 200(2) K during data collection. The data were scaled and corrected for absorption correction using SADABS-2004/1  (Bruker, 2004)   [23, 24]  and refined by full-matrix least-squares techniques based on F 2 by using the SHELXL-2014 program  [25]. All non-hydrogen atoms were refined with anisotropic atomic displacement parameters. C-bound hydrogen atoms were  > 2σ(F o )] 4025 Parameters 349 S [Goodness of fit] 1. 123 R 1 a , wR 2 b [F o > 4σ(F o )] R 1 = 0.
Hirshfeld Surface Analysis A Hirshfeld surface analysis on complex 1 was performed with the CrystalExplorer17. 5 program  [34]   The two-dimensional fingerprint plots are depicted in Table  S7. The Hirshfeld surface analysis shows that in the crystal lattice of 1 are five major types of intermolecular non-conventional H bonds: H…H = 41. 8%, Br…H = 22. 6%, C…H = 21. 1%, N…H = 5. 1% and O…H = 2. 2% on the d norm surface. The shape-index map of complex 1 (Figure  11-a ) was generated in the range -1 to 1 Å. Concave red regions symbolize hydrogen-acceptor groups and convex blue regions symbolize hydrogen-donor groups  interaction on the sharp-index map and are represented by adjacent red and blue triangles. This confirms the Cg … Cg π intermolecular interaction in the crystal lattice of 1 where Cg is the centroid of a five of six-member ring (Figure  9 , Table  S2 ).
MEP and optimized structure of [Mg(TBrPP)(4-pypo-κO) 2 ] (1) The geometry of complex 1 is optimized at the DFT-D3/B3LYP/ GENECP level of theory  [41] [42] [43]. based on the Cif file obtained from the X-ray diffraction analysis of 1. The H, C, N, O, Br, and the Mg center metal are optimized at 6-311G(d, p), LanL2DZ  [44] , and 6-311G(d, p)  [45] , respectively. The 3D molecular system was visualized by the Vesta package  [46]. The calculated stable structure is shown in Figure  14. The.
QTAIM and NCI-RDG analyses Since the electronic and the geometrical parameters may not be enough to explain clearly the intermolecular interactions between the two (4-pypo-κO) axial ligands and the [Mg(TBrPP)] moiety we have studied the electronic density parameters of our complex using the quantum theory of atom in molecule (QTAIM)  [48] [49] [50]. The deficiency of the electronic charges in the interatomic path was identified by using the Non-Covalent Interactions (NCI) index  [51, 52]. The NCI-RDG analysis was performed in order to get a visual representation of weak interactions within a system. The Multiwfn program  [53]  was used to execute the QTAIM topological parameters using the bond critical points (BCPs) in our compound from the wfn file generated from the chk file of the Gaussian 09 package  [54].
Poroelastic characterization of collagen gels We prepared collagen gels at a concentration of 2. 4 mg/ml using thermal gelation at 37°C during 45 min using the protocol described in  (27). Collagen gels were either used in their native conformation (non-cross-linked) or cross-linked (CL) with paraformaldehyde at a concentration of 4% for 10 hours  (28). The pressure response in the cavity was recorded for actuation pressures in the range of 100 to 1000 Pa (red and blue datasets with positive values in Fig. 3, A  and B ). In these settings, collagen properties are probed in tension because the material bulges and expands in the cavity due hydrostatic stress (top inset in Fig. 3A ). The kinetics of pressure relaxation took about 60 s, and, after this transient phase, the pressure was the same in the inlet and in the air cavity.