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This paper addresses the challenges of solving the quantum many-body problem, particularly within nuclear physics, through the configuration interaction (CI) method. Large-scale shell model calculations often become computationally infeasible for systems with a large number of valence particles, requiring truncation techniques. We propose truncation methods for the nuclear shell model, in which angular momentum is conserved and rotational symmetry is restored. We introduce the monopole-interaction-based truncation and seniority truncation strategies, designed to reduce the dimension of the calculations. These truncations can be established by considering certain partitions based on their importance and selecting physically meaningful states. We examine these truncations for Sn, Xe, and Pb isotopes, demonstrating their effectiveness in overcoming computational limits. These truncations work well for systems with either a single type of valence nucleon or with both types. With these truncations, we are able to achieve good convergence for the energy at a very small portion of the total dimension.

(1) Background: Fragmentation after double and triple photoionization of the CCl4 molecule in the valence, Cl 2p, and C 1s regions have been reported; (2) Methods: We have used photoion-photoion (PIPICO) coincidence technique combined with synchrotron radiation. In addition, ab initio quantum mechanical calculations were done at multiconfigurational self-consistent and multireference configuration interaction to describe ground and inner-shell states; (3) Results: We have observed coincidences involving singly and doubly charged fragments coming from the doubly and triply ionized molecule. We have also found a well agreement between the quantum mechanical calculations and the total ion yield spectrum. It is shown that the Cl+ ion is the predominant product resulting from the fragmentation of the doubly and triply charged CCl4 molecule. The CCl+ + Cl+ pair is the dominant coincidence in the spectra from valence up to the C 1s edge; (4) Conclusions: The kinetic energy of the fragments is compatible with the Coulomb explosion model.

We propose a data-driven approach using a restricted Boltzmann machine (RBM) to solve the Schrödinger equation in configuration space. Traditional configuration interaction (CI) methods construct the wavefunction as a linear combination of Slater determinants, but this becomes computationally expensive due to the factorial growth in the number of configurations. Our approach extends the use of a generative model such as the RBM by incorporating a taboo list strategy to enhance efficiency and convergence. The RBM is used to efficiently identify and sample the most significant determinants, thus accelerating convergence and substantially reducing computational cost. This method achieves up to 99.99% of the correlation energy while using up to four orders of magnitude fewer determinants compared to full CI calculations and up to two orders of magnitude fewer than previous state of the art methods. Beyond efficiency, our analysis reveals that the RBM learns electron distributions over molecular orbitals by capturing quantum patterns that resemble radial distribution functions linked to molecular bonding. This suggests that the learned pattern is interpretable, highlighting the potential of machine learning for explainable quantum chemistry

Discrete Shannon entropy was introduced in view of the mathematical properties of multiconfiguration methods and then used to interpret the information in atomic states expressed by the multiconfiguration Dirac–Hartree–Fock wavefunction for Ni-like isoelectronic sequence. Moreover, the relationship between the concepts, including sudden change of Shannon entropy, information exchange, eigenlevel anticrossing, and strong configuration interaction, was clarified by induction on the basis of the present calculation of the energy structure for Ni-like isoelectronic sequence. It was found that there is an interesting connection between the change of Shannon entropies and eigenlevel anticrossings, along with the nuclear charge Z, which is helpful to conveniently locate the position of eigenlevel anticrossings and information exchanging and understand them from the point of view of information, besides the traditional physical concepts. Especially, it is concluded that in a given configuration space eigenlevel anticrossing is a sufficient and necessary condition for the sudden change of Shannon entropy, which is also a sufficient condition for information exchange.

We built a full-dimensional analytical potential energy surface of the ground electronic state of Li2H from ca. 20,000 ab initio multi-reference configuration interaction calculations, including core–valence correlation effects. The surface is flexible enough to accurately describe the three dissociation channels: Li (2s 2S) + LiH (1Σ+), Li2 (1Σg+) + H (1s 2S) and 2Li (2s 2S) + H (1s 2S). Using a local fit of this surface, we calculated pure (J = 0) vibrational states of Li2H up to the barrier to linearity (ca. 3400 cm−1 above the global minimum) using a vibrational self-consistent field/virtual state configuration interaction method. We found 18 vibrational states below this barrier, with a maximum of 6 quanta in the bending mode, which indicates that Li2H could be spectroscopically observable. Moreover, we show that some of these vibrational states are highly correlated already ca. 1000 cm−1 below the height of the barrier. We hope these calculations can help the assignment of experimental spectra. In addition, the first low-lying excited states of each B1, B2 and A2 symmetry of Li2H were characterized.

The exponentially correlated Hylleraas–configuration interaction method (E-Hy-CI) is a generalization of the Hylleraas–configuration interaction method (Hy-CI) in which the single rij of an Hy-CI wave function is generalized to a form of the generic type rijνije−ωijrij. This work continues the exploration, begun in the first two papers in this series (on the helium atom and on ground and excited S states of Li II), of whether wave functions containing both linear and exponential rij factors converge more rapidly than either one alone. In the present study, we examined not only 1s2 1S states but 1s2p 1P states for the He I, Li II, Be III, C V and O VII members of the He isoelectronic sequence as well. All 1P energies except He I are better than previous results. The wave functions obtained were used to calculate oscillator strengths, including upper and lower bounds, for the He-sequence lowest (resonance) 1S→1P transition. Interpolation techniques were used to make a graphical study of the oscillator strength behavior along the isoelectronic sequence. Comparisons were made with previous experimental and theoretical results. The results of this study are oscillator strengths for the 1s2 1S→ 1s2p1P He isoelectronic sequence with rigorous non-relativistic quantum mechanical upper and lower bounds of (0.001–0.003)% and probable precision ≤ 0.0000003, and were obtained by extending the previously developed E-Hy-CI formalism to include the calculation of transition moments (oscillator strengths).

The structural, electronic, and spectroscopic properties of high- and intermediate-spin transition metal phthalocyaninato complexes (MPc; M = V, Cr, Mn and Fe) have been theoretically investigated to look into the origin, symmetry and strength of the M–Pc bonding. DFT calculations coupled to the Ziegler’s extended transition state method and to an advanced charge density and bond order analysis allowed us to assess that the M–Pc bonding is dominated by σ interactions, with FePc having the strongest and most covalent M–Pc bond. According to experimental evidence, the lightest MPcs (VPc and CrPc) have a high-spin ground state (GS), while the MnPc and FePc GS spin is intermediate. Insights into the MPc unoccupied electronic structure have been gained by modelling M L2,3-edges X-ray absorption spectroscopy data from the literature through the exploitation of the current Density Functional Theory variant of the Restricted Open-Shell Configuration Interaction Singles (DFT/ROCIS) method. Besides the overall agreement between theory and experiment, the DFT/ROCIS results indicate that spectral features lying at the lowest excitation energies (EEs) are systematically generated by electronic states having the same GS spin multiplicity and involving M-based single electronic excitations; just as systematically, the L3-edge higher EE region of all the MPcs herein considered includes electronic states generated by metal-to-ligand-charge-transfer transitions involving the lowest-lying π* orbital (7eg) of the phthalocyaninato ligand.

In this contribution I would like to discuss briefly the recent developments of the nuclear configuration interaction shell model approach. As examples, we apply the model to calculate the structure and decay properties of low-lying states in neutron-deficient nuclei around 100Sn and 208Pb that are of great experimental and theoretical interests.

Configuration interaction (CI) effects can greatly influence the way in which extreme ultraviolet (EUV) and soft X-ray (SXR) spectra of heavier ions are dominated by emission from unresolved transition arrays (UTAs), the most intense of which originate from Δn = 0, 4p64dN+1−4p54dN+2+4p64dN4f1 transitions. Changing the principle quantum number n, from 4 to 5, changes the origin of the UTA from Δn = 0, 4p64dN+1−4p54dN+2+4p64dN4f1 to Δn = 0, 5p65dN+1−5p55dN+2+5p65dN5f1 transitions. This causes unexpected and significant changes in the impact of configuration interaction from that observed in the heavily studied n = 4 – n = 4 arrays. In this study, the properties of n = 5 – n = 5 arrays have been investigated theoretically with the aid of Hartree-Fock with configuration interaction (HFCI) calculations. In addition to predicting the wavelengths and spectral details of the anticipated features, the calculations show that the effects of configuration interaction are quite different for the two different families of Δn = 0 transitions, a conclusion which is reinforced by comparison with experimental results.

Recent experimental work by Belmonte et al. (2014) has given rates for some 4p–4d transitions that are significantly at variance with the previous experimental work of Rudko and Tang (1967) recommended in the NIST tabulations. To date, there are no theoretical rates with which to compare. In this work, we provide such theoretical data. We have undertaken a substantial and systematic configuration interaction calculation, with an extrapolation process applied to ab initio mixing coefficients, which gives energy differences in agreement with experiment. The length and velocity forms give values that are within 10%–15% of each other. Our results are in sufficiently close agreement with those of Belmonte et al. that we can confidently recommend that their results are much more accurate than the early results of Rudko and Tang, and should be adopted in place of the latter.