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The scope of this article is to present an overview of the Density Functional based Tight Binding (DFTB) method and its applications. The paper introduces the basics of DFTB and its standard formulation up to second order. It also addresses methodological developments such as third order expansion, inclusion of non-covalent interactions, schemes to solve the self-interaction error, implementation of long-range short-range separation, treatment of excited states via the time-dependent DFTB scheme, inclusion of DFTB in hybrid high-level/low level schemes (DFT/DFTB or DFTB/MM), fragment decomposition of large systems, large scale potential energy landscape exploration with molecular dynamics in ground or excited states, non-adiabatic dynamics. A number of applications are reviewed, focusing on -(i)- the variety of systems that have been studied such as small molecules, large molecules and biomolecules, bare or functionalized clusters, supported or embedded systems, and -(ii)- properties and processes, such as vibrational spectroscopy, collisions, fragmentation, thermodynamics or non-adiabatic dynamics. Finally outlines and perspectives are given. GRAPHICAL ABSTRACT

Context. JWST has taken the sharpest and most sensitive infrared (IR) spectral imaging observations ever of the Orion Bar photodis-sociation region (PDR), which is part of the nearest massive star-forming region the Orion Nebula, and often considered to be the ‘prototypical’ strongly illuminated PDR. Aims. We investigate the impact of radiative feedback from massive stars on their natal cloud and focus on the transition from the H II region to the atomic PDR – crossing the ionisation front (IF) –, and the subsequent transition to the molecular PDR – crossing the dissociation front (DF). Given the prevalence of PDRs in the interstellar medium and their dominant contribution to IR radiation, understanding the response of the PDR gas to far-ultraviolet (FUV) photons and the associated physical and chemical processes is fundamental to our understanding of star and planet formation and for the interpretation of any unresolved PDR as seen by JWST. Methods. We used high-resolution near-IR integral field spectroscopic data from NIRSpec on JWST to observe the Orion Bar PDR as part of the PDRs4All JWST Early Release Science programme. We constructed a 3″ × 25″’ spatio-spectral mosaic covering 0.97– 5.27 μm at a spectral resolution R of ~2700 and an angular resolution of 0.075″–0.173″. To study the properties of key regions captured in this mosaic, we extracted five template spectra in apertures centred on the three H₂ dissociation fronts, the atomic PDR, and the H II region. This wealth of detailed spatial-spectral information was analysed in terms of variations in the physical conditions-incident UV field, density, and temperature – of the PDR gas. Results. The NIRSpec data reveal a forest of lines including, but not limited to, He I, H I , and C I recombination lines; ionic lines (e.g. Fe III and Fe II); O I and N I fluorescence lines; aromatic infrared bands (AIBs, including aromatic CH, aliphatic CH, and their CD counterparts); pure rotational and ro-vibrational lines from H₂; and ro-vibrational lines from HD, CO, and CH⁺, with most of them having been detected for the first time towards a PDR. Their spatial distribution resolves the H and He ionisation structure in the Huygens region, gives insight into the geometry of the Bar, and confirms the large-scale stratification of PDRs. In addition, we observed numerous smaller-scale structures whose typical size decreases with distance from θ¹ Ori C and IR lines from C I , if solely arising from radiative recombination and cascade, reveal very high gas temperatures (a few 1000 K) consistent with the hot irradiated surface of small-scale dense clumps inside the PDR. The morphology of the Bar, in particular that of the H₂ lines, reveals multiple prominent filaments that exhibit different characteristics. This leaves the impression of a ‘terraced’ transition from the predominantly atomic surface region to the CO-rich molecular zone deeper in. We attribute the different characteristics of the H₂ filaments to their varying depth into the PDR and, in some cases, not reaching the C⁺/C/CO transition. These observations thus reveal what local conditions are required to drive the physical and chemical processes needed to explain the different characteristics of the DFs and the photochemical evolution of the AIB carriers. Conclusions. This study showcases the discovery space created by JWST to further our understanding of the impact radiation from young stars has on their natal molecular cloud and proto-planetary disk, which touches on star and planet formation as well as galaxy evolution.

Massive stars disrupt their natal molecular cloud material through radiative and mechanical feedback processes. These processes have profound effects on the evolution of interstellar matter in our Galaxy and throughout the universe, from the era of vigorous star formation at redshifts of 1–3 to the present day. The dominant feedback processes can be probed by observations of the Photo-Dissociation Regions (PDRs) where the far-ultraviolet photons of massive stars create warm regions of gas and dust in the neutral atomic and molecular gas. PDR emission provides a unique tool to study in detail the physical and chemical processes that are relevant for most of the mass in inter- and circumstellar media including diffuse clouds, proto-planetary disks, and molecular cloud surfaces, globules, planetary nebulae, and star-forming regions. PDR emission dominates the infrared (IR) spectra of star-forming galaxies. Most of the Galactic and extragalactic observations obtained with the James Webb Space Telescope (JWST) will therefore arise in PDR emission. In this paper we present an Early Release Science program using the MIRI, NIRSpec, and NIRCam instruments dedicated to the observations of an emblematic and nearby PDR: the Orion Bar. These early JWST observations will provide template data sets designed to identify key PDR characteristics in JWST observations. These data will serve to benchmark PDR models and extend them into the JWST era. We also present the Science-Enabling products that we will provide to the community. These template data sets and Science-Enabling products will guide the preparation of future proposals on star-forming regions in our Galaxy and beyond and will facilitate data analysis and interpretation of forthcoming JWST observations.

The density functional based tight binding (DFTB) is a semiempirical method derived from the density functional theory (DFT). It inherits therefore its problems in treating van der Waals clusters. A major error comes from dispersion forces, which are poorly described by commonly used DFT functionals, but which can be accounted for by an a posteriori treatment DFT-D. This correction is used for DFTB. The self-consistent charge (SCC) DFTB is built on Mulliken charges which are known to give a poor representation of Coulombic intermolecular potential. We propose to calculate this potential using the class IV/charge model 3 definition of atomic charges. The self-consistent calculation of these charges is introduced in the SCC procedure and corresponding nuclear forces are derived. Benzene dimer is then studied as a benchmark system with this corrected DFTB (c-DFTB-D) method, but also, for comparison, with the DFT-D. Both methods give similar results and are in agreement with references calculations (CCSD(T) and symmetry adapted perturbation theory) calculations. As a first application, pyrene dimer is studied with the c-DFTB-D and DFT-D methods. For coronene clusters, only the c-DFTB-D approach is used, which finds the sandwich configurations to be more stable than the T-shaped ones.