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Recently, usefulness of the noninteger principal quantum numbers for Bessel type orbitals was discussed by Weniger in (Adv Quant Chem 83:209–237, 2021). In this study, we analyzed the applicability and numerical accuracy of basis sets of noninteger Bessel type orbitals to electronic structure calculations. Both numerical and analytical approaches are applied to two-electron atomic systems. The results of the numerical test demonstrated the potential of the noninteger values of principal quantum number for the improving of Bessel type functions approach in use of LCAO methods. Nevertheless, the analytical approach is still not suitable and in development and needs to be investigated further.The performance of the presented basis functions is also compared to the numerical Hartree–Fock results. [ABSTRACT FROM AUTHOR]

At the beginning of 2021, the sensational discovery was made in nuclear physics in the theory of hydrogen-like atoms and ions (having one electron in their outer shells). The essence of the discovery is that taking into account the quantum defect (the Rydberg corrections), the effective principal quantum numbers of the outer electrons can be expressed, along with integers, in terms of common fractions of the form N1/N2 with a significant limitation on the denominator value. Quite expectedly, the results of research caused increased interest because they addressed the foundations of modern physics – the atomic theory. Therefore, in this work we have continued this topic and present some results of statistical analysis of a large array of hydrogen-like states of atoms and ions. Both the ground and excited states of a wide variety of hydrogen-like atoms and ions, including lithium, potassium, sodium, cesium, argentum, and rubidium atoms are considered. Statistical analysis has allowed the correctness of the discovered regularity to be proved and the experimental data array to be transformed into new knowledge on the hydrogen-like states. [ABSTRACT FROM AUTHOR]

An efficient method to study highly excited states at the ab initio level has been introduced and applied to ultralong Rydberg CsNe molecules. Vibrational properties of Rydberg CsNe molecules are investigated on corresponding potential energy curves obtained by perturbation theory. The Rydberg CsNe molecules are associated with a Rydberg Cs(ns/np) atom (n = 20-60) and a ground state Ne(1S0) atom. The starting point for the perturbation treatment of corresponding Rydberg molecular potential energy curves is to generate accurate atomic Rydberg states from realistic ab initio effective core potential. According to the authors' knowledge this is a good reference for ultralong range molecules (order of 1000 Bohr radii) to be studied at the ab initio level. [ABSTRACT FROM AUTHOR]

The possibility that the chemi-ionization processes in atom–Rydberg atom collisions, as well as the corresponding chemi-recombination processes, may be useful for the diagnostics, modelling, and confirmation of existence or non-existence of very dense weakly ionized domains in clouds in broad-line region of active galactic nuclei, has been considered. The obtained results demonstrate the fact that the considered chemi-ionization/recombination processes, which influence on the ionization level and atom excited-state populations, must have a very significant influence on the optical properties of the weakly ionized regions where the neutral hydrogen densities are larger than |$10^{12}\, \rm {cm}^{-3}$| since in such conditions they dominate over the relevant concurrent electron–atom collision processes. This can be used as a diagnostic method to find out if the domains with such densities exist or not. Additionally, our previous results obtained for principal quantum number 2 ≤  n  ≤ 8 and |$4000 \, \textrm{K} \le T \le 10\, 000 \, \textrm{K}$| are extended for principal quantum number 9 ≤  n  ≤ 20 and |$10\, 000 \, \textrm{K} {\lt} T \le 20\, 000 \, \textrm{K}$| and also for low-temperature region (T < 4000 K) for 2 ≤  n  ≤ 20. [ABSTRACT FROM AUTHOR]

Abstract Relativistic spinless rotational-vibrational energy eigenvalue relation has been obtained by solving the Klein-Gordon equation in the presence of General Molecular potential (GMP). The relativistic energy eigenvalue relation has been reduced to the non-relativistic one in the non-relativistic limit. Relativistic and non-relativistic vibrational energies have been computed for the 5 1 Δ g state of Na 2 molecule and compared with Rydberg-Klein-Rees (RKR) data. It has been concluded that depending on relation between scalar and vector potentials, relativistic effect can cause a slight decrease in the vibrational energies or can lead to an increase. In addition, thermodynamic properties such as vibrational mean energy U, vibrational specific heat C, vibrational free energy F and vibrational entropy S for Na 2 (5 1 Δ g) molecule have been examined with respect to temperature and the values of principal quantum number. [ABSTRACT FROM AUTHOR]

The alkaline earth metals calcium (Ca), strontium (Sr), and barium (Ba) typically engage in chemical bonding as classical main-group elements through their ns and np valence orbitals, where n is the principal quantum number. Here we report the isolation and spectroscopic characterization of eight-coordinate carbonyl complexes M(CO)8 (where M = Ca, Sr, or Ba) in a low-temperature neon matrix. Analysis of the electronic structure of these cubic Oh-symmetric complexes reveals that the metal–carbon monoxide (CO) bonds arise mainly from [M(dp)] → (CO)8 p backdonation, which explains the strong observed red shift of the C-O stretching frequencies. The corresponding radical cation complexes were also prepared in gas phase and characterized by mass-selected infrared photodissociation spectroscopy, confirming adherence to the 18-electron rule more conventionally associated with transition metal chemistry. [ABSTRACT FROM AUTHOR]

The Galactic diffuse X-ray emission (GDXE) in the Milky Way Galaxy is spatially and spectrally decomposed into the Galactic center X-ray emission (GCXE), the Galactic ridge X-ray emission (GRXE), and the Galactic bulge X-ray emission (GBXE). The X-ray spectra of the GDXE are characterized by the strong K-shell lines of the highly ionized atoms, and the brightest lines are the K-shell transition (principal quantum number transition of n = 2 → 1) of neutral iron (Fe I-Kα), He-like iron (Fe XXV-Heα), and He-like sulfur (S XVHeα). Accordingly, the GDXE is composed of a high-temperature plasma of ~7 keV (HTP) and a low-temperature plasma of ~1 keV, which emit the Fe XXV-Heα and S XV-Heα lines, respectively. The Fe I-Kα line is emitted from nearly neutral irons, and hence the third component of the GDXE is a cool gas (CG). The Fe I-Kα distribution in the GCXE region is clumpy (Fe I-Kα clump), associated with giant molecular cloud (MC) complexes (Sagittarius A, B, C, D, and E) in the central molecular zone. The origin of the Fe I-Kα clumps is the fluorescence and Thomson scattering from the MCs irradiated by past big flares of the supermassive black hole Sagittarius A*. The scale heights and equivalent widths of the Fe I-Kα, FeXXV-Heα, and FeXXVI-Lyα (n = 2 → 1 transition of H-like iron) lines are different among the GCXE, GBXE, and GRXE. Therefore, their structures and origins are separately examined. This paper gives an overview of the research history and the present understandings of the GDXE, while in particular focusing on the origin of the HTP and CG in the GCXE. [ABSTRACT FROM AUTHOR]