We introduce a novel algorithm that leverages stochastic sampling techniques to compute the perturbative triples correction in the coupled-cluster (CC) framework. By combining elements of randomness and determinism, our algorithm achieves a favorable balance between accuracy and computational cost. The main advantage of this algorithm is that it allows for the calculation to be stopped at any time, providing an unbiased estimate, with a statistical error that goes to zero as the exact calculation is approached. We provide evidence that our semi-stochastic algorithm achieves substantial computational savings compared to traditional deterministic methods. Specifically, we demonstrate that a precision of 0.5 millihartree can be attained with only 10\% of the computational effort required by the full calculation. This work opens up new avenues for efficient and accurate computations, enabling investigations of complex molecular systems that were previously computationally prohibitive.

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The expectation value of the Hamiltonian using a model wave function is widely used to estimate the eigenvalues of electronic Hamiltonians. We explore here a modified formula for models based on long-range interaction. It scales differently the singlet and triplet component of the repulsion between electrons not present in the model (its short-range part). The scaling factors depend uniquely on the parameter used in defining the model interaction, and are constructed using only exact properties. We show results for the ground states and low-lying excited states of Harmonium with two to six electrons. We obtain important improvements for the estimation of the exact energy, not only over the model energy, but also over the expectation value of the Hamiltonian.

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Context. The James Webb Space Telescope (JWST) has captured the most detailed and sharpest infrared (IR) images ever taken of the inner region of the Orion Nebula, the nearest massive star formation region, and a prototypical highly irradiated dense photo-dissociation region (PDR).Aims. We investigate the fundamental interaction of far-ultraviolet (FUV) photons with molecular clouds. The transitions across the ionization front (IF), dissociation front (DF), and the molecular cloud are studied at high-angular resolution. These transitions are relevant to understanding the effects of radiative feedback from massive stars and the dominant physical and chemical processes that lead to the IR emission that JWST will detect in many Galactic and extragalactic environments.Methods. We utilized NIRCam and MIRI to obtain sub-arcsecond images over ~150″ and 42″ in key gas phase lines (e.g., Pa α, Br α, [FeII] 1.64 µm, H2 1−0 S(1) 2.12 µm, 0–0 S(9) 4.69 µm), aromatic and aliphatic infrared bands (aromatic infrared bands at 3.3–3.4 µm, 7.7, and 11.3 µm), dust emission, and scattered light. Their emission are powerful tracers of the IF and DF, FUV radiation field and density distribution. Using NIRSpec observations the fractional contributions of lines, AIBs, and continuum emission to our NIRCam images were estimated. A very good agreement is found for the distribution and intensity of lines and AIBs between the NIRCam and NIRSpec observations.Results. Due to the proximity of the Orion Nebula and the unprecedented angular resolution of JWST, these data reveal that the molecular cloud borders are hyper structured at small angular scales of ~0.1–1″ (~0.0002–0.002 pc or ~40–400 au at 414 pc). A diverse set of features are observed such as ridges, waves, globules and photoevaporated protoplanetary disks. At the PDR atomic to molecular transition, several bright features are detected that are associated with the highly irradiated surroundings of the dense molecular condensations and embedded young star. Toward the Orion Bar PDR, a highly sculpted interface is detected with sharp edges and density increases near the IF and DF. This was predicted by previous modeling studies, but the fronts were unresolved in most tracers. The spatial distribution of the AIBs reveals that the PDR edge is steep and is followed by an extensive warm atomic layer up to the DF with multiple ridges. A complex, structured, and folded H0/H2 DF surface was traced by the H2 lines. This dataset was used to revisit the commonly adopted 2D PDR structure of the Orion Bar as our observations show that a 3D “terraced” geometry is required to explain the JWST observations. JWST provides us with a complete view of the PDR, all the way from the PDR edge to the substructured dense region, and this allowed us to determine, in detail, where the emission of the atomic and molecular lines, aromatic bands, and dust originate.Conclusions. This study offers an unprecedented dataset to benchmark and transform PDR physico-chemical and dynamical models for the JWST era. A fundamental step forward in our understanding of the interaction of FUV photons with molecular clouds and the role of FUV irradiation along the star formation sequence is provided.

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Although selected configuration interaction (SCI) algorithms can tackle much larger Hilbert spaces than the conventional full CI (FCI) method, the scaling of their computational cost with respect to the system size remains inherently exponential. Additionally, inaccuracies in describing the correlation hole at small interelectronic distances lead to the slow convergence of the electronic energy relative to the size of the one-electron basis set. To alleviate these effects, we show that the non-Hermitian, transcorrelated (TC) version of SCI significantly compactifies the determinant space, allowing to reach a given accuracy with a much smaller number of determinants. Furthermore, we note a significant acceleration in the convergence of the TC-SCI energy as the basis set size increases. The extent of this compression and the energy convergence rate are closely linked to the accuracy of the correlation factor used for the similarity transformation of the Coulombic Hamiltonian. Our systematic investigation of small molecular systems in increasingly large basis sets illustrates the magnitude of these effects.

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