Calculation Of Wave Functions Research Articles

Stationary scalar clouds around Kerr-Newman black holes

This study investigates scalar clouds around Kerr-Newman black holes within the Einstein-Maxwell-scalar model. Tachyonic instabilities are identified as the driving mechanism for scalar cloud formation. Employing the spectral method, we numerically compute wave functions and parameter space existence domains for both fundamental and excited scalar cloud modes. Our analysis demonstrates that black hole spin imposes an upper limit on the existence of scalar clouds, with excited modes requiring stronger tachyonic instabilities for their formation. These findings lay the groundwork for exploring the nonlinear dynamics and astrophysical implications of scalar clouds.

Positron annihilation spectroscopy guided by two-component density functional theory calculations distinguishes irradiation-induced vacancy type in 4H-SiC

Based on two-component density functional theory integrated with the projector augmented-wave basis and incorporating both calculated and experimental data from Positron Annihilation Spectroscopy (PAS), this study introduces a novel method for identifying and analyzing specific types of vacancies when multiple types of vacancies are coexisting. This method was then tested on 4H-SiC irradiated by 300 keV C4+ ion beams. By calculating charge density to analyze positron annihilation lifetime spectroscopy and calculating wave functions to analyze slow positron-beam Doppler broadening spectroscopy, for the first time, silicon monovacancies (VSi) and carbon monovacancies (VC) in irradiated 4H-SiC were quantitatively detected separately, allowing them to be distinguished with high accuracy. In addition, a decreasing trend in the relative percentage of VC with increasing irradiation dose, consistent with that expected when irradiating with carbon ions, was also observed, illustrating both the effectiveness and potential of this method for broader applications in material defect analysis. This study not only addresses the challenges of identifying multiple coexisting vacancy types using PAS but also extends the applicability and depth of PAS in fields such as nuclear energy, aerospace, and semiconductors.

Electronic excitations and spin interactions in chromium trihalides from embedded many-body wavefunctions

Although chromium trihalides are widely regarded as a promising class of two-dimensional magnets for next-generation devices, an accurate description of their electronic structure and magnetic interactions has proven challenging to achieve. Here, we quantify electronic excitations and spin interactions in CrX3 (X = Cl, Br, I) using embedded many-body wavefunction calculations and fully generalized spin Hamiltonians. We find that the three trihalides feature comparable d-shell excitations, consisting of a high-spin 4A2(t2g3eg0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({t}_{2g}^{3}{e}_{g}^{0})$$\\end{document} ground state lying 1.5–1.7 eV below the first excited state 4T2 (t2g2eg1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${t}_{2g}^{2}{e}_{g}^{1}$$\\end{document}). CrCl3 exhibits a single-ion anisotropy Asia = − 0.02 meV, while the Cr spin-3/2 moments are ferromagnetically coupled through bilinear and biquadratic exchange interactions of J1 = − 0.97 meV and J2 = − 0.05 meV, respectively. The corresponding values for CrBr3 and CrI3 increase to Asia = −0.08 meV and Asia= − 0.12 meV for the single-ion anisotropy, J1 = −1.21 meV, J2 = −0.05 meV and J1 = −1.38 meV, J2 = −0.06 meV for the exchange couplings, respectively. We find that the overall magnetic anisotropy is defined by the interplay between Asia and Adip due to magnetic dipole–dipole interaction that favors in-plane orientation of magnetic moments in ferromagnetic monolayers and bulk layered magnets. The competition between the two contributions sets CrCl3 and CrI3 as the easy-plane (Asia + Adip >0) and easy-axis (Asia + Adip <0) ferromagnets, respectively. The differences between the magnets trace back to the atomic radii of the halogen ligands and the magnitude of spin–orbit coupling. Our findings are in excellent agreement with recent experiments, thus providing reference values for the fundamental interactions in chromium trihalides.

L- and M-subshell ionization cross-sections of heavy atoms by electron and proton impact

Inner-shell ionization has many applications related to material analysis. However, full theoretical calculations in heavy multielectronic atoms are scarce. In this contribution, we assess proton and electron impact Li and Mi-subshell ionization cross-sections of heavy targets (72≤Z≤83) using two theoretical models. These calculations are based on the Distorted Plane Wave Born Approximation for electron impact and the shellwise local plasma approximation for the proton impact, combined with relativistic calculations of these deep subshells wave functions and binding energies. We analyze the L-shell ionization of W, Au, and Bi and the M-shell of Hf, Ta, W, Re, Os, Pt, Au, Pb, and Bi. Present values are compared with available experimental data from the literature, with disparate agreement. The convergence of proton and electron impact cross-sections at high-impact velocities is also discussed.

On Entangled Singlet Pure Diradicals.

This work addresses a class of conjugated hydrocarbons that are expected to be singlet diradicals according to the topological Hückel Hamiltonian while possibly satisfying full on-bond electron pairing. These systems possess two degenerate singly occupied molecular orbitals (SOMOs), but aromaticity brought by properly positioned six-membered rings does prevent Jahn-Teller distortions. Density functional theory (DFT) calculations performed on two emblematic examples confirm the strong bond-length alternation in the closed-shell solutions and the clear spatial symmetry in the open-shell spin-unrestricted determinants, the latter solution always being found to have significantly lower energy. Since the SOMOs are here of different symmetry, the wave function is free from ionic valence-bond component, and spin decontamination of the unrestricted DFT solutions and wave function calculations at the CASSCF-plus-second-order-perturbation level confirm the expected pure diradical character of such molecules. In contrast to disjoint diradicals, the SOMOs of present systems have large amplitudes on neighbor atoms, and we propose to name them entangled pure diradicals, further providing some prescription rules for their design. Additional calculations point out the qualitative contrast between these molecules and the related diradicaloids.

Triplet-Singlet Emission of d-Block Metal Complexes Characterized by Spin-Orbit Natural Transition Orbitals.

Spin-orbit natural transition orbital (SO-NTO) methodology, recently developed in our group for complete and restricted active space (CAS/RAS) wavefunction calculations, is applied to analyze triplet-to-singlet emission in transition metal complexes. The lowest-energy (longest-wavelength) spin-forbidden transition is studied for for [Ir(pbt)2(acac)] and [Re(CO)4(pbt)] and the complexes [W(CO)4(bpy)] and [Mo(CO)4(bpy)]. For the latter complexes, spin-forbidden transitions from higher spin-triplet levels are additionally analyzed. SO-NTOs are compared with spin-free NTOs for the transitions under consideration. The major assignment of a spin-forbidden transition is obtained from the spin-free NTO analysis, while the source of intensity of the electronic transition is revealed by the SO-NTOs.

Measuring the nuclear magnetic quadrupole moment of optically trapped ytterbium atoms in the metastable state

We propose a scheme to measure a nuclear magnetic quadrupole moment (MQM), a CP -violating electromagnetic moment that appears in the nuclear sector, using the long-lived 3P2 metastable state in neutral 173Yb atoms. Laser-cooling and trapping techniques enable us to prepare ultracold 173Yb atoms in the 3P2 state trapped in an optical lattice or an optical tweezer array, providing an ideal experimental platform with long spin coherence time. In addition, our relativistic configuration interaction calculation for the 3P2 electronic wavefunction reveals a large magnetic field gradient generated by the atomic electrons in this state, which amplifies the measurable effect of an MQM. Our scheme could lead to an improvement of more than one order of magnitude in MQM sensitivity compared to the best previous measurement (Murthy et al 1989 Phys. Rev. Lett. 63, 965).

Small-Occupation Density Functional Correlation Energy Correction to Wave Function Approximations.

In this work, we introduce a novel hybrid approach, termed WFT-soDFT, designed to seamlessly incorporate DFT correlation into wave function ansatzes. This is achieved through a partitioning of the orbital space, distinguishing between large and small natural occupation numbers associated with wave function theory (WFT) and DFT correlation, respectively. The method uses a novel criterion for partitioning the orbital space and mapping the electron density in natural orbitals with a small occupation with the correlation energy of fast electrons within the homogeneous electron gas. Central to our approach is the introduction of a separation parameter ν, the choice of the WFT approach, and the correlation functional. Here, we combine the RASCI wave function with hole and particle truncation with a local density correlation functional to only account for small-occupation correlation energy. We investigate the performance of the method in the study of small but challenging chemical systems, for which WFT-soDFT demonstrates notable improvements over pristine wave function calculations. These findings collectively highlight the potential of the WFT-soDFT approach as a computationally affordable strategy to improve the accuracy of WFT electronic structure calculations.

A two-step quadrature-based variational calculation of ro-vibrational levels and wavefunctions of CO2 using a bisector-x molecule-fixed frame.

In this paper, we propose a new two-step strategy for computing ro-vibrational energy levels and wavefunctions of a triatomic molecule and apply it to CO2. A two-step method [J. Tennyson and B. T. Sutcliffe, Mol. Phys., 1986, 58, 1067] uses a basis whose functions are products of K-dependent "vibrational" functions and symmetric top functions. K is the quantum number for the molecule-fixed z component of the angular momentum. For a linear molecule, a two-step method is efficient because the Hamiltonian used to compute the basis functions includes the largest coupling term. The most important distinguishing feature of the two-step method we propose is that it uses an associated Legendre basis and quadrature rather than a K-dependent discrete variable representation. This reduces the cost of the calculation and simplifies the method. We have computed ro-vibrational energy levels with J up to 100 for CO2, on an accurate available potential energy surface which is known as the AMES-2 PES and present a subset of those levels. We have converged most levels up to 20 000 cm-1 to 0.0001 cm-1.

Benchmarking DFT-based excited-state methods for intermolecular charge-transfer excitations.

Intermolecular charge-transfer is a highly important process in biology and energy-conversion applications where generated charges need to be transported over several moieties. However, its theoretical description is challenging since the high accuracy required to describe these excited states must be accessible for calculations on large molecular systems. In this benchmark study, we identify reliable low-scaling computational methods for this task. Our reference results were obtained from highly accurate wavefunction calculations that restrict the size of the benchmark systems. However, the density-functional theory based methods that we identify as accurate can be applied to much larger systems. Since targeting charge-transfer states requires the unambiguous classification of an excited state, we first analyze several charge-transfer descriptors for their reliability concerning intermolecular charge-transfer and single out the charge-transfer distance calculated based on the variation of electron density upon excitation (DCT) as an optimal choice for our purposes. In general, best results are obtained for orbital-optimized methods and among those, the maximum overlap method proved to be the most numerically stable variant when using the initial MOs as reference orbitals. Favorable error cancellation with optimally-tuned range-separated hybrid functionals and a rather small basis set can provide an economical yet reasonable wavefunction when using time-dependent density functional theory, which provides relevant information about the excited-state character to be used in the orbital-optimized methods. The qualitative agreement makes these fast calculations attractive for high-throughput screening applications.

First-principles study of luminescence and electronic properties of Ce-doped Y2SiO5.

The transition of energy from the 4f to the 5d state is a fundamental element driving various applications, such as phosphors and optoelectronic devices. The positioning of the 4f ground states and the 5d excited states significantly influences this energy shift. In our research, we delve into the placement of these states utilizing a hybrid density functional theory (DFT) combined with spin-orbit coupling (SOC) via the supercell method. Additionally, we scrutinize the transition energy, applying the constrained density functional theory (cDFT) approach in conjunction with the ΔSCF method. Our study illustrates that the synergy of cDFT and SOC generates a discrepancy of about 2% for Ce1 and 4% for Ce2 when comparing the calculated results to experimental data. Moreover, We have determined the positions of the 4f ground states to be 2.73eV above the Valence Band Maximum (VBM) for Ce1 and 2.70eV for Ce2. We also note a tight correlation between the 5d levels identified in the experimental data and the theoretical outcomes derived from wave function calculations at the CASPT2 accuracy level.

Magnetic Properties of Tetravalent Pu in the Perovskites BaPuO3 and SrPuO3.

BaPuO3 and SrPuO3 were synthesized, and their structures were refined in the orthorhombic space group Pbnm, a common distortion from the classic Pm3̅m cubic perovskite. Magnetic-susceptibility measurements, obtained as a function of temperature over the range of 1.8-320 K, exhibit temperature-dependent behavior, with evidence of long-range magnetic order at temperatures higher than their lanthanide and actinide analogues: BaPuO3 below 164(1) K and SrPuO3 below 76(1) K. Effective moments of 1.66(10)μB for BaPuO3 and 1.84(8)μB for SrPuO3 were obtained by fitting their paramagnetic susceptibilities using the Curie-Weiss law. Both are below the free-ion value of 2.68 μB expected for a Pu4+ 5I4 ground level. Ab initio wave function calculations, performed at the relativistic complete active space level including spin-orbit coupling and with an embedded cluster approach that neglects interactions between Pu centers, were used to generate embedded-cluster Pu4+ magnetic susceptibilities. The calculations agree well with experimental data at higher temperatures, providing evidence that a single-ion representation is sufficient to account for the observed paramagnetic behavior without the need to invoke charge transfer, disproportionation, strong covalent bonding, or other more complex electronic behavior.

Accessing Position Space Wave Functions in Band Structure Calculations of Periodic Systems─A Generalized, Adapted Numerov Implementation for One-, Two-, and Three-Dimensional Quantum Problems.

In this work, a generalized, adapted Numerov implementation capable of determining band structures of periodic quantum systems is outlined. Based on the input potential, the presented approach numerically solves the Schrödinger equation in position space at each momentum space point. Thus, in addition to the band structure, the method inherently provides information about the state functions and probability densities in position space at each momentum space point considered. The generalized, adapted Numerov framework provided reliable estimates for a variety of increasingly complex test suites in one, two, and three dimensions. The accuracy of the proposed methodology was benchmarked against results obtained for the analytically solvable Kronig-Penney model. Furthermore, the presented numerical solver was applied to a model potential representing a 2D optical lattice being a challenging application relevant, for example, in the field of quantum computing.

Non-orthogonal Configuration Interaction Study on the Effect of Thermal Distortions on the Singlet Fission Process in Photoexcited Pure and B,N-Doped Pentacene Crystals.

The present computational work analyzes singlet fission (SF) as a pathway for multiplication of photogenerated excitons in crystalline polyacenes. Our study explores the well-known crystalline pentacene (C22H14) and the prospective and potentially interesting doped B,N-pentacene (BC20NH14). At the molecular level, the singlet fission process involves a pair of neighboring molecules and is based on the coupling between an excited singlet state (S1S0) and two singlet-coupled triplets (1T1T1), which, typically, is influenced by an intermolecular charge transfer state. Taking data from periodic density functional theory and ab initio wave function calculations, we applied the non-orthogonal configuration interaction method to determine electronic coupling parameters. The comparison of the results for both equilibrium structures reveal smaller SF coupling for pentacene than for B,N-pentacene by a factor of ∼5. Introduction of the dynamic behavior to the crystals (vibrations, thermal motion) provides a more realistic picture of the effect of the disorder at the molecular level on the SF efficiency. The coupling values associated to out-of-equilibrium structures show that most of the S1S0/1T1T1 couplings remain virtually constant or slightly increase for pentacene when molecular disorder is introduced. Homologous calculations on B,N-pentacene show a generalized decrease in the coupling values, notably if large phonon displacements are considered. A few of the structures analyzed feature much larger SF coupling if some distortion results in (nearly) degenerate charge transfer and excited singlet and triplet states. For these particular situations, an acceleration of the SF process could occur although in competition with electron-hole separation as an alternative pathway.

Pair-correlation function study of the proton-electron system: A method to calculate the contact hyperfine couplings within two-component density functional theory

The quantum effect of light atoms such as hydrogen in materials is usually considered as lattice vibration from an abinitio perspective. Some recent studies have also tried to quantize the hydrogen from the outset within two-component density functional theory and parametrize the two-body correlation energy by vibrational states calculation, then calculate the wave function of the proton directly. Since there is no experimental verification of the calculated wave function, we further develop a pair-correlation function of the proton-electron system by quantum Monte Carlo, thus it is possible to estimate the hyperfine couplings of the proton from the calculated wave function directly. The pair-correlation function form is tested in some basic systems with different functionals and shows its good potential in the study of the contact interactions incorporating the quantum effect of light nuclei such as hydrogen.

Near-Unity Energy Transfer from Uranyl to Europium in a Heterobimetallic Organic Framework with Record-Breaking Quantum Yield.

Lanthanide organic frameworks (Ln-MOFs) have attracted increasing research enthusiasm as photoluminescent materials. However, limited luminescence efficiency stemming from restricted energy transfer efficiency from the organic linker to the metal center hinders their applications. Herein, a uranyl sensitization approach was proposed to boost the luminescence efficiency of Ln-MOFs in a distinct heterobimetallic uranyl-europium organic framework. The record-breaking photoluminescence quantum yield (PLQY, 92.68%) among all reported Eu-MOFs was determined to benefit from nearly 100% energy transfer efficiency between UO22+ and Eu3+. Time-dependent density functional theory and ab initio wave-function theory calculations confirmed the overlap of excited state levels between UO22+ and Eu3+, which is responsible for the efficient energy transfer process. Coupled with intrinsically strong stopping power toward X-ray of the uranium center, SCU-UEu-2 features an ultralow detection limit of 1.243 μGyair/s, outperforming the commercial scintillator LYSO (13.257 μGyair/s) and satisfying the requirement of X-ray diagnosis (below 5.5 μGyair/s) in full.

Reproducibility of calculations on Li species with correlation-consistent basis sets

We have found that two different basis set series, both labeled cc-pVxZ, are widely available and widely used for calculation on Li compounds such that calculations that should be the same are different, causing a reproducibility problem. Here we study the magnitude of the disagreement of these nominally-the-same basis sets for wave function and density functional calculations of Li clusters. We find deviations among the basis sets of as large as 22 millihartrees. In most cases one obtains lower energies with the noncanonical choices. Therefore, it is important to specify which version of the basis set is used for calculations.

Introducing Novel Materials with Diffuse Electrons for Applications in Redox Catalysis and Quantum Computing via Theoretical Calculations

Diamond-like structures, where carbon atoms have been replaced with Li+ and C–C bonds with diamines, have currently been introduced as new materials, which can host diffuse electrons in the periphery of each lithium tetra-amine center. These materials display a diverse range of properties behaving as metals or semiconductors depending on the diamine chain length. Multi-reference wavefunction and density functional theory calculations were employed to study the electronic structure of these materials. Initially, gas phase calculations are performed on isolated (NH3)3LiNH2(CH2)1–10H2NLi(NH3)3 molecular strings. One diffuse electron surrounds the periphery of each −NH2Li(NH3)3 terminus. The two terminal electrons couple into a triplet and open-shell singlet states, which are nearly degenerate for long chains and as closed shell singlets for short. At intermediate lengths, the wavefunction of the ground-state singlet state mixes both open- and closed-shell configurations raising doubts about which configuration should be considered for density functional theory calculations. Observations from gas phase calculations accurately predict properties from the condense phase density functional theory calculations carried out for proposed crystalline Li-diamine materials, offering an avenue for further development and insight. Spin-polarized and unpolarized calculations are performed for the whole range of hydrocarbon sizes reporting geometrical and electronic band structures, spin density contours, and density of states. Diffuse electrons can be used for redox reactions or can serve as qubits for quantum computing. Future work will focus on decorating the hydrocarbon backbone with functional groups and/or bulky units, in order to facilitate or block the association between neighboring electrons for more controlled quantum computing applications and propose materials for selective redox catalysis.

On the Rational Design of Core/(Multi)-Crown Type-II Heteronanoplatelets.

Solution-processed two-dimensional nanoplatelets (NPLs) allowing lateral growth of a shell (crown) by not affecting the pure confinement in the vertical direction provide unprecedented opportunities for designing heterostructures for light-emitting and -harvesting applications. Here, we present a pathway for designing and synthesizing colloidal type-II core/(multi-)crown hetero-NPLs and investigate their optical properties. Stoke's shifted broad photoluminescence (PL) emission and long PL lifetime (∼few 100 ns) together with our wavefunction calculations confirm the type-II electronic structure in the synthesized CdS/CdSe1-xTex core/crown hetero-NPLs. In addition, we experimentally obtained the band-offsets between CdS, CdTe, and CdSe in these NPLs. These results helped us designing hetero-NPLs with near-unity PL quantum yield in the CdSe/CdSe1-xTex/CdSe/CdS core/multicrown architecture. These core/multicrown hetero-NPLs have two type-II interfaces unlike traditional type-II NPLs having only one and possess a CdS ending layer for passivation and efficient suppression of stacking required for optoelectronic applications. The light-emitting diode (LED) obtained using multicrown hetero-NPLs exhibits a maximum luminance of 36,612 cd/m2 and external quantum efficiency of 9.3%, which outcompetes the previous best results from type-II NPL-based LEDs. These findings may enable designs of future advanced heterostructures of NPLs which are anticipated to show desirable results, especially for LED and lasing platforms.

Finding optimal basis states for variation after projection nuclear wave functions* *Supported by the National Natural Science Foundation of China (11975314), the Key Laboratory of Nuclear Data foundation (JCKY2022201C158), and the Continuous Basic Scientific Research Project (WDJC-2019-13, BJ2000250)

The variation after projection (VAP) method is expected to be an efficient way of obtaining the optimized nuclear wave functions, which can be as close as possible to the exact shell model ones. However, we found that there are two additional problems that may seriously affect the convergence of the VAP iteration. The first problem is the existence of irrelevant projected basis states. At a VAP iteration, the Hill-Wheeler (HW) equation is composed of all updated projected basis states. If one of these projected basis states does not mix with a calculated wave function of interest, which is obtained by solving this HW equation, it is likely that this basis state will never mix with this wave function even after the VAP iteration converges. The other problem is the poor orthonormality among the projected basis states, which seriously affects the accuracy of the calculated VAP wave function. In the present work, solutions for these two problems are proposed, and examples are presented to test the validity. With the present solutions, the most important projected basis states can be reliably obtained, and the fully optimized VAP wave functions can be accurately and efficiently calculated.