A Precise Description of the Electronic Structures and Spin-Allowed Transition Properties of PF and Its Cation:All-Electron Configuration-Interaction Investigations Including Relativistic Effect

The electronic structures of PF and PF＋ are calculated with the high-level configuration interaction method. To improve the precision of calculations, the spin-orbit coupling effect, the scalar relativistic effect, and the Davidson correction（q-Q） are also considered. The spectroscopic parameters of bound states are derived by the electronic structures of PF and PF＋, which are in good accordance with the measurements. The transition dipole moments of spin-allowed transitions are evaluated, and the radiative lifetimes of several A S states of PF and PF＋ are obtained.

Understanding of the activity difference between nanogold and bulk gold by relativistic effects

It is a challenge to thoroughly understand the astonishing difference in catalytic activity between nanogold and bulk gold for some oxidation reactions. In this work,the Au–O interactions in various surroundings were investigated by DFT calculations and compared with the Ag–O interactions. We have found the three points.First,only Au–O bond can be significantly strengthened by the linear O–Au–O structure. Second,the Au–O bond is always stronger than the Ag–O bond when the bonds are embedded in common surroundings. Third,the Au–O bond becomes weaker than the Ag–O bond when the number of neighboring Au atoms becomes large,because the Au–O interactions are suppressed by the presence of neighboring gold atoms. The origin of these three points can be attributed to wider spatial extension of d orbitals of gold,induced by strong relativistic effects. The strong relativistic effects make nanogold with smaller coordinate numbers highly active due to the ease in forming strong Au–O bonds,especially for the O–Au–O bond,whereas gold atoms in bulk with larger coordination numbers chemically inert due to the strong suppression by neighboring gold atoms destabilizing the O–Au–O bond.

RELATIVISTIC EFFECTS IN THE CdF SYSTEM

In this paper,the monrelativistic and relativistic pseudo- potentials(i.e.HF-MEFIT-PP and WB-MEFIT-PP)for Cd were used to cal- cutate the potential curves of the six Low-Lying states of CdF system. Furthermore,we carried out their spectroscopic constants(R.,Do,T.,and ω.).Based on the above results,the relativistic effects on the spectroscopic constants were discussed.

Relativistic effect on synergy of electron cyclotron and lower hybrid waves on EAST

In recent experiments on EAST,the electron temperature at the center can be raised to 9.7 ke V by injecting electron cyclotron(EC)and lower hybrid(LH)waves simultaneously.With such strong core electron heating,the relativistic effect could play an important role in the interactions between the plasma and waves.In order to explore the relativistic effect on synergy between the EC and LH waves on EAST,ray-tracing/Fokker-Planck simulations are conducted to investigate electron heating for a typical discharge with a center electron temperature of 9.7 ke V.It is found that the relativistic effect can cause the EC wave to deposit its power deeper in the plasma core,where the synergy between the EC and LH waves occurs and enhances the absorption of the LH waves.As a result,a high center electron temperature can be achieved.

Decoherence of macroscopic objects from relativistic effect

We study how the decoherence of macroscopic objects originates intrinsically from the relativistic effect. With the degree of freedom of the center of mass（CM） characterizing the collective quantum state of a macroscopic object（MO）,it is found that an MO consisting of N particles can decohere with a time scale of no more than p （√N）^-1. Here, the special relativity can induce the coupling of the collective motion mode and the relative motion modes in an order of 1/c^2, which intrinsically results in the above minimum decoherence.

Relativistic effects on the back-to-back correlation functions of boson-antiboson pairs in high energy heavy ion collisions

We calculate the back-to-back correlation （BBC） functions of relativistic boson-antiboson pairs in high energy heavy ion collisions using the Monte Carlo method. The relativistic effects on the BBC functions of ФФ and K＋K pairs are investigated. The investigations indicate that the relativistic effects on the BBC functions of K＋K- pairs with large momenta are significant, and the effect is sensitive to the particle freeze-out temperature.

The effects of relativistic broadening and frequency down-shift on electron-cyclotron emission measurements in EAST

This paper presents a theoretical calculation of the effects of relativistic broadening and frequency down-shift on the electron cyclotron emission measurements for a wide range of plasma parameters in the Experimental Advanced Superconducting Tokamak （EAST）. The calculation is based on the radiation transfer equation, with the reabsorption and reemission processes taken into account. The broadening effect contributes to the radial resolution of the measurement, and the calculation results indicate that it is -2 cm in the case of the central electron temperature 10 keV. A pseudo radial displacement of the obtained electron temperature profile occurs if the relativistic frequency down-shift effect is not taken into account in the determination of the emission layer position. The shift could be a few centimeters as the electron temperature increases, and this effect should be taken into account.

Relativistic and distorted wave effects on Xe 4d electron momentum distributions

The relativistic and distorted wave effects are investigated for the electron momentum distributions of Xe 4d electrons.The theoretical results show good agreements with the experimental data measured previously with electron momentum spectroscopy. The distorted wave effect and the relativistic effect are found to play important roles in the low and high momentum regions, respectively.

Ab initio studies on the electronic structure of the complexes containing Mo——S bond using relativistic effective core potentials

An ab initio calculation was performed on the electronic structures of MoS,MoS_4^(2-) and Mo_2S_2 using relativistic effective core potential(RECP)for molybdenum,and non-relativistic ECP for sulfur.We predicted that the equilibrium bond length and the dissociation energy of MoS in ground state are 3.89 a.u.and 4.67 eV,respectively,and that the bond is a triple-bond.The ground state of MoS_4^(2-) in Td symmetry is ~1A_1 and π-bonding dominates σ-donation in the molybdenum- sulfur interaction.The Mo_2S_2 is a model contracted from bi-nuclear sulfur-bridged clusters,and the bonding orbitals 1 b_(1u),1b_1g and 1b_2g make the dominant contribution to the stabilization of sulfur- bridged species.

Revisiting the Electron Radius in Light of Length Contraction

In previous work, the electron radius was identified as the “actual electron radius.” However, this is more accurately described as the electron radius at rest. This study reexamines the electron with an emphasis on the electron radius under motion, incorporating the effects of length contraction. The findings suggest that the radius is subject to Lorentz contraction, which has interesting implications for relativistic effects at the subatomic level.

Relativistic thermodynamic properties of a weakly interacting Fermi gas in a weak magnetic field

This paper derives the analytical expression of free energy for a weakly interacting Fermi gas in a weak magnetic field, by using the methods of quantum statistics as well as considering the relativistic effect. Based on the derived expression, the thermodynamic properties of the system at both high and low temperatures are given and the relativistic effect on the properties of the system is discussed. It shows that, in comparison with a nonrelativistic situation, the relativistic effect changes the influence of temperature on the thermodynamic properties of the system at high temperatures, and changes the influence of particle-number density on them at extremely low temperature. But the relativistic effect does not change the influence of the magnetic field and inter-particle interactions on the thermodynamic properties of the system at both high and extremely low temperatures.

Benchmark Calculations on the Atomization Enthalpy,Geometry and Vibrational Frequencies of UF_6 with Relativistic DFT Methods

Benchmark calculations on the molar atomization enthalpy, geometry, and vibrational frequencies of uranium hexafluoride （UF6） have been performed by using relativistic density functional theory （DFT） with various levels of relativistic effects, different types of basis sets, and exchange-correlation functionals. Scalar relativistic effects are shown to be critical for the structural properties. The spin-orbit coupling effects are important for the calculated energies, but are much less important for other calculated ground-state properties of closed-shell UF6. We conclude through systematic investigations that ZORA- and RECP-based relativistic DPT methods are both appropriate for incorporating relativistic effects. Comparisons of different types of basis sets （Slater, Gaussian, and plane-wave types） and various levels of theoretical approximation of the exchange-correlation functionals were also made.

Equilibrium mercury and lead isotope fractionation caused by nuclear volume effects in crystals

To investigate equilibrium mercury(Hg)and lead(Pb)isotope fractionation caused by the nuclear volume effect(NVE)in crystals,the electron densities at nuclei(i.e.,|Ψ(0)|2)for Hg-or Pb-bearing crystalline compounds were investigated by using the relativistic spin orbit zeroth-order regular approximation(ZORA)method with a three-dimensional periodic boundary condition based on the density functional theory(DFT).Many isotope fractionation factors of crystalline compounds are provided for the first time.Our results show,even at1000℃,NVE-driven Hg and Pb isotope fractionation are meaningfully large,i.e.,range from 0.12‰to 0.49‰(202Hg/^(198)Hg),from-0.20‰to 0.17‰(208Pb/^(206)Pb)and from-0.08‰to 0.06‰(207Pb/^(206) Pb)relative to Hg0 vapor and Pb0 vapor,respectively.Specifically,the fractionations range from-0.06‰to-0.20‰(208Pb/^(206)Pb)and from-0.02‰to-0.08‰(207Pb/^(206)Pb)for Pb2+-bearing species,from 0.10‰to 0.17‰(208Pb/^(206)Pb)and from 0.04‰to 0.06‰(207Pb/^(206)Pb)for Pb4+-bearing species in crystals.All calculated Hg-bearing species in crystals will enrich heavier isotope(202Hg)relative to Hg0 vapor.Meanwhile,Pb4+-bearing species enrich heavier Pb isotopes(208Pb and 207Pb)than Pb^(2+)-bearing species in crystals,which the enrichment can be up to 0.37‰(208-Pb/^(206)Pb)and 0.14‰(207Pb/^(206)Pb)at 1000℃,due to their NVEs are in opposite directions.The NVE-driven MIFs of Hg isotopes,which are compared to the Hg202-Hg198baseline,are up to-0.158‰(ΔNV199Hg),-0.024‰(ΔNV200Hg)and-0.094‰(ΔNV201Hg)relative to Hg0 vapor at5000 C.For all studied Hg-bearing species in crystals,the MIFs of two odd-mass isotopes(i.e.,ΔNV199Hg andΔNV201Hg)will be changed proportionally and their ratio(i.e.,ΔNV199Hg/ΔNV201Hg)will be a constant 1.67.The NVE can also cause mass-independent fractionations for 207Pb and 204 Pb compared to the baseline of 208Pb and 206Pb.The largest NVEdriven MIFs are 0.043‰(ΔNV207Pb)and-0.040‰(ΔNV204Pb)among all the studied species relative to Pb0 vapor at 5000 C.The magnitudes of odd-mass isotope MIF(ΔNV207Pb)and even-mass isotope MIF(ΔNV204Pb)are almost the same but with opposite signs,leading to the MIF ratio of them(i.e.,ΔNV207Pb/ΔNV204Pb)is-1.08.

Nonplanar Shock Excitations in a Four Component Degenerate Quantum Plasma:the Effects of Various Charge States of Heavy Ions

A theoretical study on the nonlinear propagation of nonplanar （cylindrical and spherical） electrostatic modified ion-acoustic （mIA） shock structures has been carried out in an unmagnetized, collisionless four component degenerate plasma system （containing degenerate electron fluids, inertial positively as well as negatively charged light ions, and positively charged static heavy ions）. This investigation is valid for both non-relativistic and ultra-relativistic limits. The modified Burgers （mB） equation has been derived by employing the reductive perturbation method, and used to numerically analyze the basic features of shock structures. It has been found that the effects of degenerate pressure and number density of electron and inertial positively as well as negatively charged light ion fluids, and various charging state of positively charged static heavy ions significantly modify the basic features of mIA shock structures. The implications of our results to dense plasmas in astrophysical compact objects （e.g., non-rotating white dwarfs, neutron stars, etc.） are briefly discussed.

Nonlinear ion-acoustic solitary waves in an electron-positron-ion plasma with relativistic positron beam

The propagation characteristics of nonlinear ion–acoustic（IA） solitary waves（SWs） are studied in thermal electron–positron–ion plasma considering the effect of relativistic positron beam. Starting from a set of fluid equations and using the reductive perturbation technique, we derive a Korteweg–de Vries（KdV） equation which governs the evolution of weakly nonlinear IA SWs in relativistic beam driven plasmas. The properties of the IA soliton are studied, and it is shown that the presence of relativistic positron beam significantly modifies the characteristics of IA solitons.

Ion acoustic shock and periodic waves through Burgers equation in weakly and highly relativistic plasmas with nonextensivity

A comparative study is carried out for the nonlinear propagation of ion acoustic shock waves both for the weakly and highly relativistic plasmas consisting of relativistic ions and qdistributed electrons and positions.The Burgers equation is derived to reveal the physical phenomena using the well known reductive perturbation technique.The integration of the Burgers equation is performed by the（G￠/G）-expansion method.The effects of positron concentration,ion–electron temperature ratio,electron–positron temperature ratio,ion viscosity coefficient,relativistic streaming factor and the strength of the electron and positron nonextensivity on the nonlinear propagation of ion acoustic shock and periodic waves are presented graphically and the relevant physical explanations are provided.

Relativistic correction of （v/c）2 to the collective Thomson scattering for high-temperature high-density plasma

Collective Thomson scattering is theoretically investigated with the inclusion of the relativistic correction of （v/c）2. The correction is rather small for the plasma parameters inferred from the spectra of the thermal electron plasma waves in the plasma. Since the full formula of the corrected result is rather complicated, a simplified one is derived for practical use, which is shown to be in good agreement with the un-simplified one.

Optical spectroscopy of CrO and electronic states of the Cr group metal monoxides

All of the experimentally known electronic states of the Cr group metal monoxides(Cr O,Mo O,and WO)have been presented in the paper.The optical spectra of the Cr O molecule have been investigated in the gas phase through a combination of the laser-induced fluorescence(LIF)excitation and single-vibronic-level(SVL)emission spectroscopy in the supersonic expansion.The rotational constants of the vibronic electronic states,including X^(5)Π_(-1)(v=0–3),B^(5)Π_(-1)(v=0–10),and B~5Π_1(v=1,5),and the vibrational constants of the spin–orbit components X^(5)Π_(-1,0,1)have been obtained.The molecular constants of the Mo O and WO molecules have been summarized by reviewing the previous spectroscopic studies,and a comprehensive energy level diagram of the Cr group metal monoxides has been constructed.By comparing the electronic configurations,bond lengths,and vibrational frequencies of all the transition metal monoxides in the ground electronic state,the significance of the relativistic effect in the bonding of the 5d transition metal monoxides has been discussed.The related spectroscopic data of the Cr O molecule are available at https://doi.org/10.57760/sciencedb.j00113.00085.

Spin effects on the relativistic strong EM wave modes in magnetized plasma

Based on the relativistic hydrodynamic model of EM wave-spin plasmas interaction,the spin effects on the relativistic strong EM modes in magnetized plasma are investigated.The dispersion relations of the EM wave propagating parallel and perpendicular to the external magnetic field are obtained.Results show that the strong EM wave modes are affected by the time component of four-spin as well as the increase of electron effective mass.Especially in the case of EM wave propagating parallel to the external magnetic field,the time component of fourspin amplifies the influence of spin effects on the low-frequency modes obviously.

Theoretical investigations on CO oxidation reaction catalyzed by gold nanoparticles

It is crucial to understand the mechanism of low temperature CO oxidation reaction catalyzed by gold nanoparticles so as to find out the origin of the high catalytic reactivity and extend the indus‐trialization applications of nano gold catalysts. In this work, some theoretical works on CO adsorp‐tion, O2 adsorption, atomic oxygen adsorption, formation of surface gold oxide films, reaction mechanisms of CO oxidation involving O2 reaction with CO and O2 dissociation before reacting with CO on gold surfaces and Au/metal oxide were summarized, and the influences of coordination number, charge transfer and relativity of gold on CO oxidation reaction were briefly reviewed. It was found that CO reaction mechanism depended on the systems with or without oxide and the strong relativistic effects might play an important role in CO oxidation reaction on gold catalysts. In particular, the relativistic effects are related to the unique behaviors of CO adsorption, O adsorption, O2 activation on gold surfaces, effects of coordination number and the wide gap between the chem‐ical inertness of bulk gold and high catalytic activity of nano gold. The present work helps us to understand the CO oxidation reaction mechanism on gold catalysts and the influence of relativistic effects on gold catalysis.