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1. Asymptotics of eigenvalue sums when some turning points are complex

   https://doi.org/10.1088/1751-8121/ac8b45  

   Okun, Pavel; Burke, Kieron (September 2022, Journal of Physics A: Mathematical and Theoretical)

   Abstract Recent work has shown a deep connection between semilocal approximations in density functional theory and the asymptotics of the sum of the Wentzel–Kramers–Brillouin (WKB) semiclassical expansion for the eigenvalues. However, all examples studied to date have potentials with only real classical turning points. But systems with complex turning points generate subdominant (SD) terms beyond those in the WKB series. The simplest case is a pure quartic oscillator. We show how to generalize the asymptotics of eigenvalue sums to include SD contributions to the sums, if they are known for the eigenvalues. These corrections to WKB greatly improve accuracy for eigenvalue sums, especially for many levels. We obtain further improvements to the sums through hyperasymptotics. For the lowest level, our summation method has error below 2 × 10 −4 . For the sum of the lowest ten levels, our error is less than 10 −22 . We report all results to many digits and include copious details of the asymptotic expansions and their derivation. 

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2. Relativistic nucleon–nucleon potentials in a spin-dependent three-dimensional approach

   https://doi.org/10.1038/s41598-021-96924-1  

   Hadizadeh, M. R.; Radin, M.; Nazari, F. (December 2021, Scientific Reports)

   null (Ed.)

   Abstract The matrix elements of relativistic nucleon–nucleon ( NN ) potentials are calculated directly from the nonrelativistic potentials as a function of relative NN momentum vectors, without a partial wave decomposition. To this aim, the quadratic operator relation between the relativistic and nonrelativistic NN potentials is formulated in momentum-helicity basis states. It leads to a single integral equation for the two-nucleon (2 N ) spin-singlet state, and four coupled integral equations for two-nucleon spin-triplet states, which are solved by an iterative method. Our numerical analysis indicates that the relativistic NN potential obtained using CD-Bonn potential reproduces the deuteron binding energy and neutron-proton elastic scattering differential and total cross-sections with high accuracy. 

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3. Generalization of the tensor product selected CI method for molecular excited states

   Braunscheidel, Nicole M.; Abraham, Vibin; Mayhall, Nicholas J. (March 2023, arXivorg)

   In a recent paper (JCTC, 16, 6098 (2020)), we introduced a new approach for accurately approximating full CI ground states in large electronic active-spaces, called Tensor Product Selected CI (TPSCI). In TPSCI, a large orbital active space is first partitioned into disjoint sets (clusters) for which the exact local many-body eigenstates are obtained. Tensor products of these locally correlated many-body states are taken as the basis for the full, global Hilbert space. By folding correlation into the basis states themselves, the low-energy eigenstates become increasingly sparse, creating a more compact selected CI expansion. While we demonstrated that this approach can improve accuracy for a variety of systems, there is even greater potential for applications to excited states, particularly those which have some excitonic character. In this paper, we report on the accuracy of TPSCI for excited states, including a far more efficient implementation in the Julia programming language. In traditional SCI methods that use a Slater determinant basis, accurate excitation energies are obtained only after a linear extrapolation and at a large computational cost. We find that TPSCI with perturbative corrections provides accurate excitation energies for several excited states of various polycyclic aromatic hydrocarbons (PAH) with respect to the extrapolated result (i.e. near exact result). Further, we use TPSCI to report highly accurate estimates of the lowest 31 eigenstates for a tetracene tetramer system with an active space of 40 electrons in 40 orbitals, giving direct access to the initial bright states and the resulting 18 biexcitonic states. 

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4. Exact and approximate energy sums in potential wells

   https://doi.org/10.1088/1751-8121/ab69a6  

   Berry, M. V.; Burke, Kieron (February 2020, Journal of Physics A: Mathematical and Theoretical)

   Abstract Sums of theNlowest energy levels for quantum particles bound by potentials are calculated, emphasising the semiclassical regimeN  ≫  1. Euler-Maclaurin summation, together with a regularisation, gives a formula for these energy sums, involving only the levelsN  +  1,N  +  2…. For the harmonic oscillator and the particle in a box, the formula is exact. For wells where the levels are known approximately (e.g. as a WKB series), with the higher levels being more accurate, the formula improves accuracy by avoiding the lower levels. For a linear potential, the formula gives the first Airy zero with an error of order 10⁻⁷. For the Pöschl–Teller potential, regularisation is not immediately applicable but the energy sum can be calculated exactly; its semiclassical approximation depends on howNand the well depth are linked. In more dimensions, the Euler–Maclaurin technique is applied to give an analytical formula for the energy sum for a free particle on a torus, using levels determined by the smoothed spectral staircase plus some oscillatory corrections from short periodic orbits. 

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5. Machine learned potential for high-throughput phonon calculations of metal—organic frameworks

   https://doi.org/10.1038/s41524-025-01611-8  

   Elena, Alin_Marin; Kamath, Prathami_Divakar; Jaffrelot_Inizan, Théo; Rosen, Andrew_S; Zanca, Federica; Persson, Kristin_A (May 2025, npj Computational Materials)

   Abstract Metal–organic frameworks (MOFs) are highly porous and versatile materials studied extensively for applications such as carbon capture and water harvesting. However, computing phonon-mediated properties in MOFs, like thermal expansion and mechanical stability, remains challenging due to the large number of atoms per unit cell, making traditional Density Functional Theory (DFT) methods impractical for high-throughput screening. Recent advances in machine learning potentials have led to foundation atomistic models, such as MACE-MP-0, that accurately predict equilibrium structures but struggle with phonon properties of MOFs. In this work, we developed a workflow for computing phonons in MOFs within the quasi-harmonic approximation with a fine-tuned MACE model, MACE-MP-MOF0. The model was trained on a curated dataset of 127 representative and diverse MOFs. The fine-tuned MACE-MP-MOF0 improves the accuracy of phonon density of states and corrects the imaginary phonon modes of MACE-MP-0, enabling high-throughput phonon calculations with state-of-the-art precision. The model successfully predicts thermal expansion and bulk moduli in agreement with DFT and experimental data for several well-known MOFs. These results highlight the potential of MACE-MP-MOF0 in guiding MOF design for applications in energy storage and thermoelectrics. 

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