Degenerate many‐body perturbation theory: Excited states of H2

1975 ◽  
Vol 63 (5) ◽  
pp. 2199-2205 ◽  
Author(s):  
Uzi Kaldor
Keyword(s):  
Perturbation Theory ◽  
Excited States ◽  
Many Body ◽  
Many Body Perturbation Theory

Dielectronic recombination and satellite line spectra of highly charged tungsten ions1This article is part of a Special Issue on the 10th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas.

2011 ◽  
Vol 89 (5) ◽  
pp. 581-589 ◽  
Author(s):  
U.I. Safronova ◽  
A.S. Safronova ◽  
P. Beiersdorfer
Keyword(s):  
Perturbation Theory ◽  
Excited States ◽  
Transition Probabilities ◽  
Dielectronic Recombination ◽  
Rate Coefficients ◽  
Atomic Data ◽  
Correct Identification ◽  
Many Body ◽  
International Colloquium ◽  
Many Body Perturbation Theory

We present our recent progress on theoretical studies that involve auto-ionizing states of highly charged tungsten ions. Such auto-ionizing states have two channels for decay, which requires that both radiative and auto-ionization atomic data be calculated and combined in a detailed study of the dielectronic recombination (DR). Three atomic codes are used to produce relativistic atomic data (energy levels, radiative transition probabilities, and auto-ionization rates). These are the relativistic many-body perturbation theory (RMBPT) code, the multiconfiguration relativistic Hebrew University Lawrence Livermore atomic code (HULLAC), and the Hartree–Fock relativistic (Cowan) code. Branching ratios relative to the first threshold and intensity factors are calculated for satellite lines, and DR rate coefficients are determined for the excited states. The total DR rate coefficient is derived as a function of electron temperature, and it is shown that the contribution of the highly excited states is very important for the calculation of the total DR rates. Synthetic dielectronic satellite spectra are constructed, and the atomic properties specific to the relevant tungsten ions are highlighted. First, we will consider the results for Na-like tungsten (W63+) and Mg-like tungsten (W62+) using all three codes. Then, we move to even higher ionization states and present the results in Li-like W (W71+). For this we use the RMBPT code as well as the quasi-relativistic many-body perturbation theory (MZ) code. The inclusion of the DR process is essential for correct identification of the lines in impurity spectra and for understanding the main contributions to the total radiation losses.

scholarly journals THEORETICAL STUDYING EXCITED STATES SPECTRUM OF THE YTTERBIUM WITHIN THE OPTIMIZED RELATIVISTIC MANY-BODY PERTURBATION THEORY

2021 ◽  
pp. 118-125
Author(s):  
V. Ternovsky ◽  
A. Svinarenko ◽  
Yu. Dubrovskaya
Keyword(s):  
Perturbation Theory ◽  
Excited States ◽  
Theoretical Data ◽  
Zeroth Approximation ◽  
Relativistic Energy ◽  
Many Body ◽  
Hartree Fock ◽  
Ytterbium Atom ◽  
Many Body Perturbation Theory ◽  
Experimental Values

Theoretical studying spectrum of the excited states for the ytterbium atom is carried out within the relativistic many-body perturbation theory with ab initio zeroth approximation and generalized relativistic energy approach.  The zeroth approximation of the relativistic perturbation theory is provided by the optimized Dirac-Kohn-Sham ones. Optimization has been fulfilled by means of introduction of the parameter to the Kohn-Sham exchange potentials and further minimization of the gauge-non-invariant contributions into radiation width of atomic levels with using relativistic orbital set, generated by the corresponding zeroth approximation Hamiltonian. The obtained theoretical data on energies E and widths W of the ytterbium excited states are compared with alternative theoretical results (the Dirac-Fock, relativistic Hartree-Fock, perturbation  theories) and available experimental data. Analysis shows that the theoretical and experimental values ​​of energies are in good agreement with each other, however, the values ​​of widths differ significantly. In our opinion, this fact is explained by insufficiently accurate estimates of the radial integrals, the use of unoptimized bases, and some other approximations of the calculation.

Many-body perturbation-theory formulas for energy levels of excited states of closed-shell atoms

1992 ◽  
Vol 46 (9) ◽  
pp. 5478-5488 ◽  
Author(s):  
E. Avgoustoglou ◽  
W. R. Johnson ◽  
D. R. Plante ◽  
J. Sapirstein ◽  
S. Sheinerman ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Excited States ◽  
Energy Levels ◽  
Closed Shell ◽  
Many Body ◽  
Many Body Perturbation Theory

Divergence of Many-Body Perturbation Theory for Noncovalent Interactions of Large Molecules

2019 ◽  
Author(s):  
Brian Nguyen ◽  
Guo P Chen ◽  
Matthew M. Agee ◽  
Asbjörn M. Burow ◽  
Matthew Tang ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
System Size ◽  
State Density ◽  
Second Order ◽  
Binding Energies ◽  
Basis Set ◽  
Many Body ◽  
Many Body Perturbation Theory ◽  
Relative Errors ◽  
Ground State Density

Prompted by recent reports of large errors in noncovalent interaction (NI) energies obtained from many-body perturbation theory (MBPT), we compare the performance of second-order Møller–Plesset MBPT (MP2), spin-scaled MP2, dispersion-corrected semilocal density functional approximations (DFA), and the post-Kohn–Sham random phase approximation (RPA) for predicting binding energies of supramolecular complexes contained in the S66, L7, and S30L benchmarks. All binding energies are extrapolated to the basis set limit, corrected for basis set superposition errors, and compared to reference results of the domain-based local pair-natural orbital coupled-cluster (DLPNO-CCSD(T)) or better quality. Our results confirm that MP2 severely overestimates binding energies of large complexes, producing relative errors of over 100% for several benchmark compounds. RPA relative errors consistently range between 5-10%, significantly less than reported previously using smaller basis sets, whereas spin-scaled MP2 methods show limitations similar to MP2, albeit less pronounced, and empirically dispersion-corrected DFAs perform almost as well as RPA. Regression analysis reveals a systematic increase of relative MP2 binding energy errors with the system size at a rate of approximately 1‰ per valence electron, whereas the RPA and dispersion-corrected DFA relative errors are virtually independent of the system size. These observations are corroborated by a comparison of computed rotational constants of organic molecules to gas-phase spectroscopy data contained in the ROT34 benchmark. To analyze these results, an asymptotic adiabatic connection symmetry-adapted perturbation theory (AC-SAPT) is developed which uses monomers at full coupling whose ground-state density is constrained to the ground-state density of the complex. Using the fluctuation–dissipation theorem, we obtain a nonperturbative “screened second-order” expression for the dispersion energy in terms of monomer quantities which is exact for non-overlapping subsystems and free of induction terms; a first-order RPA-like approximation to the Hartree, exchange, and correlation kernel recovers the macroscopic Lifshitz limit. The AC-SAPT expansion of the interaction energy is obtained from Taylor expansion of the coupling strength integrand. Explicit expressions for the convergence radius of the AC-SAPT series are derived within RPA and MBPT and numerically evaluated. Whereas the AC-SAPT expansion is always convergent for nondegenerate monomers when RPA is used, it is found to spuriously diverge for second-order MBPT, except for the smallest and least polarizable monomers. The divergence of the AC-SAPT series within MBPT is numerically confirmed within RPA; prior numerical results on the convergence of the SAPT expansion for MBPT methods are revisited and support this conclusion once sufficiently high orders are included. The cause of the failure of MBPT methods for NIs of large systems is missing or incomplete “electrodynamic” screening of the Coulomb interaction due to induced particle–hole pairs between electrons in different monomers, leaving the effective interaction too strong for AC-SAPT to converge. Hence, MBPT cannot be considered reliable for quantitative predictions of NIs, even in moderately polarizable molecules with a few tens of atoms. The failure to accurately account for electrodynamic polarization makes MBPT qualitatively unsuitable for applications such as NIs of nanostructures, macromolecules, and soft materials; more robust non-perturbative approaches such as RPA or coupled cluster methods should be used instead whenever possible.<br>

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