One-electron Systems Research Articles

Finite Nuclear Size Effect on the Relativistic Hyperfine Splittings of 2s and 2p Excited States of Hydrogen-like Atoms

Hyperfine splittings play an important role in quantum information and spintronics applications. They allow for the readout of the spin qubits, while at the same time providing the dominant mechanism for the detrimental spin decoherence. Their exact knowledge is thus of prior relevance. In this work, we analytically investigate the relativistic effects on the hyperfine splittings of hydrogen-like atoms, including finite-size effects of the nucleis’ structure. We start from exact solutions of Dirac’s equation using different nuclear models, where the nucleus is approximated by (i) a point charge (Coulomb potential), (ii) a homogeneously charged full sphere, and (iii) a homogeneously charged spherical shell. Equivalent modelling has been done for the distribution of the nuclear magnetic moment. For the 1s ground state and 2s excited state of the one-electron systems H1, H2, H3, and He+3, the calculated finite-size related hyperfine shifts are quite similar for the different structure models and in excellent agreement with those estimated by comparing QED and experiment. This holds also in a simplified approach where relativistic wave functions from a Coulomb potential combined with spherical-shell distributed nuclear magnetic moments promises an improved treatment without the need for an explicit solution of Dirac’s equation within the nuclear core. Larger differences between different nuclear structure models are found in the case of the anisotropic 2p3/2 orbitals of hydrogen, rendering these excited states as promising reference systems for exploring the proton structure.

Structural and theoretical exploration of an innovative unsymmetrical oxovanadium complex: Electrochemical analysis and in vitro antibacterial screening

2‑hydroxy-1-naphthaldehyde and 3,4-diaminotoluene were reacted with bis(acetylacetonato) oxovanadium to yield a novel NNOO -type chelate complex, VOL. The prepared complex is characterized by employing elemental analysis, electronic and infrared spectra. The expected structure was crystallized and identified by using the single-crystal X-ray diffraction method. The VOL complex crystallizes in the monoclinic system with the P21/c space group. Additionally, we affected a comprehensive analysis of VOV, VOIV and VOIII complexes focusing on their structural, electronic, and optical properties using DFT and TD-DFT calculations in gas. The computed parameters closely matched the experimental data, demonstrating good agreement. The electrochemical behavior of the VOL complex, investigated on a glassy carbon electrode (GCE) by means of cyclic voltammetry (CV), revealing a metal-centered one-electron redox systems corresponding to the VOIV/VOIII and VOV/VOIV at -1206 and 547 mV/SCE respectively. The in vitro antibacterial activities of the free ligand H2L and the corresponding VOL complex were evaluated against Gram-positive strains, Staphylococcus aureus and Streptococcus pyogenes, and Gram-negative strains, Escherichia coli, Proteus mirabilis and Klebseilla pneumoniae. The biological screening revealed that the VOL complex exhibits more potent activity than the free ligand.

Self-interaction corrected SCAN functional for molecules and solids in the numeric atom-center orbital framework.

Semilocal density-functional approximations (DFAs), including the state-of-the-art SCAN functional, are plagued by the self-interaction error (SIE). While this error is explicitly defined only for one-electron systems, it has inspired the self-interaction correction method proposed by Perdew and Zunger (PZ-SIC), which has shown promise in mitigating the many-electron SIE. However, the PZ-SIC method is known for its significant numerical instability. In this study, we introduce a novel constraint that facilitates self-consistent localization of the SIC orbitals in the spirit of Edmiston-Ruedenberg orbitals [Rev. Mod. Phys. 35, 457 (1963)]. Our practical implementation within the all-electron numeric atom-centered orbitals code FHI-aims guarantees efficient and stable convergence of the self-consistent PZ-SIC equations for both molecules and solids. We further demonstrate that our PZ-SIC approach effectively mitigates the SIE in the meta-generalized gradient approximation SCAN functional, significantly improving the accuracy for ionization potentials, charge-transfer energies, and bandgaps for a diverse selection of molecules and solids. However, our PZ-SIC method does have its limitations. It cannot improve the already accurate SCAN results for properties such as cohesive energies, lattice constants, and bulk modulus in our test sets. This highlights the need for new-generation DFAs with more comprehensive applicability.

Critical screening parameters of one-electron systems with screened Coulomb potentials: circular Rydberg states

The critical screening parameters (λ c ) of one-electron systems in circular states under short-range screened Coulomb potentials (SCPs) are investigated using the generalized pseudospectral method. High-precision values of λ c are obtained for bound states with the principal quantum number n up to a thousand. The polynomial fittings based on the numerical values indicate that the high-Rydberg limits of the n 2-scaled critical screening parameters, i.e. , are equal to , , and , respectively, for the Debye–Hückel, Hulthén, and exponential cosine SCPs. It is surprisingly found that these high-Rydberg limits can be well-reproduced from Bohr’s correspondence principle together with the semi-classical model of the hydrogen atom. We further show that both the present numerical calculations and the semi-classical analysis can be extended to other short-range potentials such as the generalized exponential, Lennard–Jones, modified Pöschl–Teller, shifted Morse, Woods–Saxon, and Manning–Rosen potentials that attract wide interest in atomic, molecular, and nuclear physics.

Hyperpolarizabilities of hydrogenlike atoms in Debye and dense quantum plasmas.

The hyperpolarizabilities of the hydrogenlike atoms in Debye and dense quantum plasmas are calculated using the sum-over-states formalism based on the generalized pseudospectral method. The Debye-Hückel and exponential-cosine screened Coulomb potentials are employed to model the screening effects in, respectively, Debye and dense quantum plasmas. Our numerical calculation demonstrates that the present method shows exponential convergence in calculating the hyperpolarizabilities of one-electron systems and the obtained results significantly improve previous predictions in the strong screening environment. The asymptotic behavior of hyperpolarizability near the system bound-continuum limit is investigated and the results for some low-lying excited states are reported. By comparing the fourth-order corrected energies in terms of hyperpolarizability with the resonance energies using the complex-scaling method, we empirically conclude that the applicability of hyperpolarizability in perturbatively estimating the system energy in Debye plasmas lies in the range of [0,F_{max}/2], where F_{max} refers to the maximum electric field strength at which the fourth-order energy correction is equal to the second-order term.

A Density Functional Theory for the Average Electron Energy.

A formally exact density functional theory (DFT) determination of the average electron energy is presented. Our theory, which is based on a different accounting of energy functional terms, partially solves one well-known downside of conventional Kohn-Sham (KS) DFT: that electronic energies have but tenuous connections to physical quantities. Calculated average electron energies are close to experimental ionization potentials (IPs) in one-electron systems, demonstrating a surprisingly small effect of self-interaction and other exchange-correlation errors in established DFT methods. Remarkable agreement with ab initio quantum mechanical calculations of multielectron systems is demonstrated using several flavors of DFT, and we argue for the use of the average electron energy as a design criterion for density functional approximations.

ARSENY: A program for computing inelastic transitions via hidden crossings in one-electron atomic ion–ion collisions with classical description of nuclear motion

The ARSENY program is intended to compute cross-sections of inelastic transitions via hidden crossings upon slow one-electron atomic ion–ion collisions using the approximation of classical description of nuclear motion in the collision energy region E<20 KeV/nucleon. Particular attention is paid to the calculation of the analytical properties of adiabatic potential energy curves of the two-center Coulomb problem for complex values of the internuclear distance. Complex branch points and hidden crossings are calculated and their significance for the dynamics of one-electron collisional systems is revealed. Benchmark calculations of cross sections for charge exchange, excitation, and ionization in slow He2++H(1s) collisions are presented and compared with experimental data. Program summaryProgram Title: ARSENYCPC Library link to program files:https://doi.org/10.17632/n43srxwdnm.1Licensing provisions: CC By 4.0Programming language: FORTRAN 90/95. Compilers: Intel(R) Visual Fortran Compiler 19.0.4.245 [IA-32]Nature of problem: The processes of charge exchange, excitation, and ionization in one-electron atomic ion–ion collisions in a low-temperature plasma are actively studied in astrophysics and tokamak Charge-eXchange Recombination Spectroscopy (CXRS) Edge diagnostics in ITER [1–7]. Numerical calculations of cross sections for charge exchange, excitation, and ionization for slow one-electron atomic ion–ion collisions within the approximation of classical description of nuclear motion have been conventionally implemented, in particular, by the electron-nuclear dynamics approach [8] and the close-coupled channel method using basis functions of the two-center Coulomb problem (see, e.g., [9–13]). However, with real-valued internuclear distance these approaches did not allow for the dynamical structure of discrete-discrete and discrete-continuous transitions in the two-center Coulomb problem. This disadvantage manifests itself in the disagreement between the theoretical and experimental cross-sections at small velocity of ions [13–15]. In a number of papers [1,14,16–20] the dynamical structure of the transitions is considered in terms of hidden crossing of potential curves, when using the analytic continuation to a complex plane of the internuclear distance. This approach is implemented in the ARSENY program aimed at computing cross sections of inelastic discrete-discrete and discrete-continuous transitions via hidden crossings for slow one-electron atomic ion–ion collisions within the approximation of classical description of nuclear motion announced in [1]. Benchmark calculations of cross sections for charge exchange, excitation, and ionization in slow He2++H(1s) collisions are presented and compared with experimental data.Solution method: The potential energy curves E=E(R) and the separation constant λ=λ(R) depending on the real-valued and complex-valued parameter R of the two-center Coulomb problem are calculated from the minimization condition for a quadratic functional corresponding to a pair of nonlinear equations with respect to a pair of unknowns E(R) and λ(R) by iterating three-term recurrent relations [21,22] using a mean least square method [23]. These equations are obtained from the known recurrent relations for the expansion coefficients of quasiradial and quasiangular spheroidal Coulomb functions. The series of branching points Rc sought for in the complex plane of internuclear distance R and the hidden crossings of complex potential energy curves E(R) are calculated by an iterative method using the known analytical behavior in the form of a square root of difference E(R)−E(Rc) in the vicinity of the unknown branch points Rc. Calculations of cross-sections of inelastic transitions via hidden crossings for the slow one-electron atomic ion–ion collisions within the approximation of classical description of nuclear motion are carried out by integration over the impact parameter of the nonadiabatic transition probability expressed in terms of the Stückelberg parameter determined integral of difference of imaginary parts of each pair of complex potential energy curves E(R) by a contour around the branching point Rc [18,19].Additional comments including restrictions and unusual features: In calculations of cross sections and required branch points, about 220 adiabatic states of the lower part of the discrete spectrum of the two-center problem are used.

Rigorous analysis of the effects of electron–phonon interactions on magnetic properties in the one-electron Kondo lattice model

The Kondo lattice model (KLM) is a typical model describing heavy fermion systems. In this paper, we consider the interaction of phonons with the system described by the one-electron KLM. Magnetic properties of the ground state of this model are revealed in a rigorous form. Furthermore, we derive the effective Hamiltonian in the strong coupling limit (\(J\rightarrow \infty \)) for the strength of the spin-exchange interaction J; we examine the magnetic properties of the ground state of the effective Hamiltonian and prove that the Aizenman–Lieb theorem concerning the magnetization holds for the effective Hamiltonian at finite temperatures. Generalizing the obtained results, we clarify a mechanism for the stability of magnetic properties of the ground state in the one-electron KLM system.

How good are recent density functionals for ground and excited states of one-electron systems?

Sun et al. [J. Chem. Phys. 144, 191101 (2016)] suggested that common density-functional approximations (DFAs) should exhibit large energy errors for excited states as a necessary consequence of orbital nodality. Motivated by self-interaction corrected density-functional calculations on many-electron systems, we continue their study with the exactly solvable 1s, 2p, and 3d states of 36 hydrogenic one-electron ions (H-Kr35+) and demonstrate with self-consistent calculations that state-of-the-art DFAs indeed exhibit large errors for the 2p and 3d excited states. We consider 56 functionals at the local density approximation (LDA), generalized gradient approximation (GGA) as well as meta-GGA levels, and several hybrid functionals such as the recently proposed machine-learned DM21 local hybrid functional. The best non-hybrid functional for the 1s ground state is revTPSS. As predicted by Sun et al., the 2p and 3d excited states are more difficult for DFAs, and LDA functionals turn out to yield the most systematic accuracy for these states among non-hybrid functionals. The best performance for the three states overall is observed with the BHandH global hybrid GGA functional, which contains 50% Hartree-Fock exchange and 50% LDA exchange. The performance of DM21 is found to be inconsistent, yielding good accuracy for some states and systems and poor accuracy for others. Based on these results, we recommend including a variety of one-electron cations in future training of machine-learned density functionals.

Critical screening parameters of one-electron systems with screened Coulomb potentials: high Rydberg limit

We develop an efficient numerical method to directly calculate the critical screening parameters for one-electron systems with Hulthén and Debye–Hückel screened Coulomb potentials (SCPs). Compared to indirect methods, which locate the critical screening parameters via searching the potential parameters with near-zero energy, the method developed in this work directly calculates the critical screening parameters as eigenvalues of a generalized eigenvalue problem. This feature allows us to simultaneously determine the critical parameters for bound states from low-lying excitation to high-lying Rydberg limit with high accuracy. The method is applied to SCPs to investigate the asymptotic behavior of critical screening parameters as the principal quantum number n approaches infinity. It has been shown that the critical screening parameters in Hulthén and Debye–Hückel potentials follow the 2n −2 and 4n −2/π asymptotic laws, respectively, and that the orbital angular momentum affects the higher-order coefficients linearly.

Spin-Photon Coupling for Atomic Qubit Devices in Silicon

Electrically addressing spin systems is predicted to be a key component in developing scalable semiconductor-based quantum processing architectures, to enable fast spin qubit manipulation and long-distance entanglement via microwave photons. However, single spins have no electric dipole, and therefore a spin-orbit mechanism must be integrated in the qubit design. Here, we propose to couple microwave photons to atomically precise donor spin qubit devices in silicon using the hyperfine interaction intrinsic to donor systems and an electrically-induced spin-orbit coupling. We characterise a one-electron system bound to a tunnel-coupled donor pair (1P-1P) using the tight-binding method, and then estimate the spin-photon coupling achievable under realistic assumptions. We address the recent experiments on double quantum dots (DQDs) in silicon and indicate the differences between DQD and 1P-1P systems. Our analysis shows that it is possible to achieve strong spin-photon coupling in 1P-1P systems in realistic device conditions without the need for an external magnetic field gradient.

Reply to “Comment on ‘Origin of symmetry-forbidden high-order harmonic generation in the time-dependent Kohn-Sham formulation’”

In reply to the Comment by O. Neufeld et al. [Phys. Rev. A 105, 047101 (2022)], we argue that the conclusions of Phys. Rev. A 103, 043106 (2021) remain valid. We disprove the claim that the unphysical even-order harmonics originate from convergence issues related to reflections at the boundary of the simulation box. By additional calculations, we show that such reflections perturb the high-order harmonic generation spectra by oscillations with periods much smaller than the distance between the harmonics. We also demonstrate that the convergence argument of the Comment, in contrast to our multielectron excitations argument, cannot explain why there are no unphysical even-order harmonics in one-electron systems. Moreover, we show that the argument put forward in the Comment to conclude that the time-dependent Kohn-Sham equations are superior to the time-dependent natural Kohn-Sham equations is not valid.

Optimal Tuning Perspective of Range-Separated Double Hybrid Functionals.

We study the optimal tuning of the free parameters in range-separated double hybrid functionals, based on enforcing the exact conditions of piecewise linearity and spin constancy. We find that introducing the range separation in both the exchange and the correlation terms allows for the minimization of both fractional charge and fractional spin errors for singlet atoms. The optimal set of parameters is system specific, underlining the importance of the tuning procedure. We test the performance of the resulting optimally tuned functionals for the dissociation curves of diatomic molecules. We find that they recover the correct dissociation curve for the one-electron system, H2+, and improve the dissociation curves of many-electron molecules such as H2 and Li2, but they also yield a nonphysical maximum and only converge to the correct dissociation limit at very large distances.

High Harmonic Generation from Oriented Asymmetric Molecules in the Presence of Static Electric Field

Abstract We investigate the high harmonic generation during the interaction of the femtosecond laser field with oriented asymmetric diatomic molecules in the presence of an external static electric field. Based on the numerical solution of the time-dependent Schrödinger equation for the model one-electron system, we calculate the high harmonic generation spectrum for a wide range of static-field strengths. The possibilities for visualizing low-frequency (terahertz and mid-infrared) radiation using time-delay measurements of even high harmonics intensities are discussed.

Transition Metal Complexes Derived From 1H-Imidazole Ligand: Synthesis, Characterization, Cyclic Voltammetric Studies and In Vitro Antibacterial Evaluation

Metal complexes consist of metal ions chelated by a group of oppositely charged ions or neutral ligands. These compounds have various applications in stereochemistry, spectroscopy, catalysis, electrochemistry, agriculture, and the medical field; all play some significant roles. This work reports the complexes of Cr3+, Co2+, and Zn2+ metal ions derived from a 1H-imidazole ligand system. The complexes were characterized using EA, conductivity measurement, UV-Vis, FTIR, TGA, PXRD, HRMS, SEM-EDX, and 1H and 13C{H}NMR for the Zn2+ complex. Based on these characterizations, the ligand was found to act as a monodentate and formed a complex with the metal ions via a nitrogen atom. An octahedral geometry was obtained for Cr3+ and Co2+, with composition as [Cr(IM)4(H2O)2](NO3)3 and [Co(IM)6]Cl2, and tetrahedral geometry for Zn2+ as [Zn(IM)2(H2O)2]. Redox conduct of the free chelate and the complexes was studied using cyclic voltammetry (CV). The result showed that Cr3+ and Co2+ compounds displayed a reductive wave of a one-electron irreversible system for Cr3+ to Cr2+ and Co2+ to Co+ . The ligand shows a comparable electrochemical response to Cr3+ and Co2+ complexes with a reduction peak denoting a reduction involving one-electron transfer, while the Zn2+ complex shows neither oxidative nor reductive waves. The free ligand and the complexes were evaluated for antimicrobial activity against Gram-positive: (Staphylococcus aureus and Streptococcus pyogenes) and Gram-negative: (Escherichia coli and Klebsiella pneumoniae). From the result obtained, the complexes demonstrated enhanced activity compared to the ligand. The order of the activities among complexes on the organisms can be arranged as follows: Co2+ &gt; Cr3+ &gt; Zn2+

Effective one-electron approach to proton collisions with molecular hydrogen

The two-centre wave-packet convergent close-coupling approach to ion–atom collisions is extended to study proton collisions with molecular hydrogen including electron-capture channels. We use a model potential to represent the molecular target as an effective one-electron spherically symmetric system. This greatly simplifies the target structure, allowing us to use already existing code developed for ion collisions with single-electron targets. Calculated total cross sections for electron capture, single ionisation, and excitation processes generally agree well with experimental data and other theoretical calculations where available. However, the total electron capture cross section is found to overestimate the experimental data at low energies, while the total ionisation cross section is slightly underestimated. Additionally, we present state-resolved cross sections for capture into the 1s, 2ell , and 3ell states of the projectile where deviation between various previous calculations is substantial. Our results lead to overall improvement over previous theoretical studies although discrepancies with experiment are observed for 3p and 3d capture. We conclude that treating molecular hydrogen as an effective one-electron system within the two-centre coupled-channel approach to one-electron targets can give reasonably accurate total cross sections at intermediate and high energies, without the need for a complex and computationally demanding two-electron target representation.

Critical screening parameters and critical behaviors of one-electron systems with screened Coulomb potentials

The critical screening parameters for one-electron systems screened by Hulthén, Debye–Hückel, and exponential cosine screened Coulomb potentials are calculated with an accuracy close to the precision of numerical arithmetic. The results for a H atom with an infinitely heavy nucleus are reported from the ground to high-lying excited states, and those for arbitrary two-body charged systems are derived from the Zm-scaling law. A thorough comparison of the critical screening parameters for the ground and the first p-wave excited states with previous predictions is made to demonstrate the accuracy of our calculations. The critical behaviors of system-bound and pseudo-continuum eigenenergies for s- and non-s-wave states are shown to follow the quadratic and linear laws, respectively. The variation of the corresponding wave functions is analyzed in detail. For systems with non-zero orbital angular momenta, the bound states convert into shape-type resonances when the screening parameter exceeds the critical value. The resonance energy shares the same linear law as the pseudo-continuum state, while the resonance width varies by an l-dependent power law. It is further shown that the different asymptotic behaviors of the resonance energy and width are consistent with the complex analog of the Hellmann–Feynman theorem.

Variations of the Hartree-Fock fractional-spin error for one electron.

Fractional-spin errors are inherent in all current approximate density functionals, including Hartree-Fock theory, and their origin has been related to strong static correlation effects. The conventional way to encode fractional-spin calculations is to construct an ensemble density that scales between the high-spin and low-spin densities. In this article, we explore the variation of the Hartree-Fock fractional-spin (or ghost-interaction) error in one-electron systems using restricted and unrestricted ensemble densities and the exact generalized Hartree-Fock representation. By considering the hydrogen atom and H+ 2 cation, we analyze how the unrestricted and generalized Hartree-Fock schemes minimize this error by localizing the electrons or rotating the spin coordinates. We also reveal a clear similarity between the Coulomb hole of He-like ions and the density depletion near the nucleus induced by the fractional-spin error in the unpolarized hydrogen atom. Finally, we analyze the effect of the fractional-spin error on the Møller-Plesset adiabatic connection, excited states, and functional- and density-driven errors.

Pump-probe photoemission simulated in real time: Revealing many-particle signatures

We simulate the photoemission from an electronically excited system by computing the escape of electron density in real space using time-dependent density functional theory in real time. We show that for a one-electron system, the angular resolved photoemission after an initial excitation can be interpreted as the mapping of a previously unoccupied orbital. For the molecule perylene-3,4,9,10-tetracarboxylic dianhydride, the angular resolved photoemission (ARPES) calculated after a preceding pump pulse reveals signatures of the many-particle character of the first electronic excitation: The photoemission results from more than one time-dependent orbital, and comparing the ARPES pattern to a particle-hole analysis of the first electronic excitation confirms that the excitation does not just correspond to one electron having been moved into a previously empty orbital, but is a superposition of several single-particle excitations.

Rayleigh and Raman Scattering from Alkali Atoms

Two computational methods developed recently [McNamara, Fursa, and Bray, Phys. Rev. A 98, 043435 (2018)] for calculating Rayleigh and Raman scattering cross sections for atomic hydrogen have been extended to quasi one-electron systems. A comprehensive set of cross sections have been obtained for the alkali atoms: lithium, sodium, potassium, rubidium, and cesium. These cross sections are accurate for incident photon energies above and below the ionization threshold, but they are limited to energies below the excitation threshold of core electrons. The effect of spin-orbit interaction, importance of accounting for core polarization, and convergence of the cross sections have been investigated.