Total energy of atomic ions related to low‐order ionization potentials and to diamagnetic susceptibility

1982 ◽  
Vol 76 (12) ◽  
pp. 6091-6094 ◽  
Author(s):  
R. Pucci ◽  
N. H. March
Keyword(s):  
Total Energy ◽  
Diamagnetic Susceptibility ◽  
Ionization Potentials ◽  
Atomic Ions ◽  
Low Order

Ionization Potentials of Higher Atomic Ions

1950 ◽  
Vol 77 (2) ◽  
pp. 304-304 ◽  
Author(s):  
Wolfgang Finkelnburg
Keyword(s):  
Ionization Potentials ◽  
Atomic Ions

Reduced Atmospheric Models Using Dynamically Motivated Basis Functions

2007 ◽  
Vol 64 (10) ◽  
pp. 3452-3474 ◽  
Author(s):  
Frank Kwasniok
Keyword(s):  
Total Energy ◽  
Large Scale ◽  
Empirical Orthogonal Functions ◽  
Basis Functions ◽  
Interaction Patterns ◽  
Order Model ◽  
Dynamical Equations ◽  
Reduced Models ◽  
Mean State ◽  
Low Order

Abstract Nonlinear deterministic reduced models of large-scale atmospheric dynamics are constructed. The dynamical framework is a quasigeostrophic three-level spectral model with realistic mean state and variability as well as Pacific–North America (PNA) and North Atlantic Oscillation (NAO) patterns. The study addresses the problem of finding appropriate basis functions for efficiently capturing the dynamics and a comparison between different choices of basis functions; it focuses on highly truncated models, keeping only 10–15 modes. The reduced model is obtained by a projection of the equations of motion onto a truncated basis spanned by empirically determined modes. The total energy metric is used in the projection; the nonlinear terms of the low-order model then conserve total energy. Apart from retuning the coefficient of horizontal diffusion, no empirical terms are fitted in the dynamical equations of the low-order model in order to properly preserve the physics of the system. Using the methodology of principal interaction patterns (PIPs), a basis is derived that carefully compromises minimizing tendency error with maximizing explained variance in the resolved modes. A new PIP algorithm is introduced that is more compact and robust than earlier PIP algorithms; a top-down approach is adopted, removing modes from the system one by one. The mean state and standard deviation of the streamfunction as well as transient momentum fluxes are well reproduced by a PIP model with only 10 modes. Probability density functions are accurately modeled and autocorrelation functions are captured fairly well using 15 modes. Reduced models based on PIPs are substantially superior to reduced models based on empirical orthogonal functions (EOFs). The leading PIPs have a higher projection onto the PNA and NAO teleconnection patterns than the corresponding EOFs. Both with EOFs and PIPs, the interactions between the resolved modes are predominantly linear and the improvement of PIP models on EOF models stems entirely from better modeling these linear interactions although the full nonlinear tendencies are optimized. There is considerable influence of smaller-scale modes on the large-scale modes due to nonlinear coupling that is not well captured by either EOFs or PIPs. This nonlinear backscattering possibly plays a role in generating the low-frequency variability of the model. The results call for a nonlinear and/or stochastic closure scheme in which PIPs may be suitable basis functions.

Theoretical Chemistry of the 7p series of superheavy elements. I. Atomic Structure studied by multi-configuration Dirac-Fock theory

1981 ◽  
Vol 376 (1766) ◽  
pp. 483-492 ◽  
Keyword(s):  
Total Energy ◽  
Excited States ◽  
Atomic Structure ◽  
Electronic Structures ◽  
Theoretical Chemistry ◽  
Superheavy Elements ◽  
Ionization Potentials ◽  
Heavy Elements ◽  
Neutral Atoms ◽  
Valence States

The multi-configuration Dirac-Fock method is used to estimate the ionization potentials of neutral atoms and ions of the 7p series of super-heavy elements of possible chemical interest. Predictions of the energies of excited states used to construct potentially important valence states are also reported. Electronic structures of these species are studied by partitioning the total energy into core and valence one-electron contributions.

Semiempirical fine-tuning for Hartree–Fock ionization potentials of atomic ions with non-integral atomic number

2013 ◽  
Vol 377 (41) ◽  
pp. 2955-2958 ◽  
Author(s):  
Nicolás A. Cordero ◽  
Norman H. March ◽  
Julio A. Alonso
Keyword(s):  
Atomic Number ◽  
Ionization Potentials ◽  
Fine Tuning ◽  
Atomic Ions ◽  
Hartree Fock

scholarly journals Расчеты релятивистских, корреляционных, ядерных и квантово-электродинамических поправок к энергии и потенциалу ионизации основного состояния гелиеподобных ионов

2020 ◽  
Vol 128 (1) ◽  
pp. 24
Author(s):  
И.И. Тупицын ◽  
С.В. Безбородов ◽  
А.В. Малышев ◽  
Д.В. Миронова ◽  
В.М. Шабаев
Keyword(s):  
Total Energy ◽  
Quantum Electrodynamic ◽  
Ground State ◽  
Finite Size ◽  
Wave Functions ◽  
Ionization Potentials ◽  
Recoil Effect ◽  
Finite Mass ◽  
Variational Calculations ◽  
Field Shift

In this work, nonrelativistic and relativistic variational calculations of the energies and ionization potentials of the ground state of helium-like ions for the nuclear charges in the range Z = 2 − 20 were performed.the leading corrections to the total energy were calculated including the contribution of electronic correlations, relativistic and quantum-electrodynamic (QED) corrections, and the contributions of the finite size ofnucleus (field shift) and the finite mass of the nucleus (recoil effect). Relativistic сalculations of the wave functions were performed using the Dirac-Coulomb-Breit (DCB) Hamiltonian.

Benchmark values of chemical potential and chemical hardness for atoms and atomic ions (including unstable anions) from the energies of isoelectronic series

2016 ◽  
Vol 18 (36) ◽  
pp. 25721-25734 ◽  
Author(s):  
Carlos Cárdenas ◽  
Farnaz Heidar-Zadeh ◽  
Paul W. Ayers
Keyword(s):  
Chemical Potential ◽  
Reference Data ◽  
Ionization Potentials ◽  
Chemical Hardness ◽  
Electron Affinities ◽  
Atomic Ions ◽  
Isoelectronic Series ◽  
Electronic Chemical Potential ◽  
Electronic Chemical

We present benchmark values for the electronic chemical potential and chemical hardness from reference data for ionization potentials and electron affinities.

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