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Midtdal, John

doi:10.1103/physrev.138.a1010

Cited by 145 publications

(23 citation statements)

References 5 publications

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“…Updated theoretical ionization energies and Lamb shis for one-electron [7] and twoelectron [8] atomic ions have been published more recently and are generally accepted as very accurate. ese recent results differ very little from the earlier computed values of Garcia and Mack [5] or Midtdal and Aashamar [6].…”

Section: Introductioncontrasting

confidence: 54%

“…As shown in Table 3, the Lamb shi values calculated using this simple equation agree well with those computed by Johnson and Soff [7] for the one-electron system. For the two-electron system, the values calculated by (11) are higher than those computed by Midtdal and Aashamar [6], but they compare well with those computed by Drake [8], which are more recent and probably more accurate.…”

Section: The Lamb Shiftmentioning

confidence: 44%

“…e size of hydride ion (negative hydrogen ion) is different from the hydrogen atom, and obviously the sizes of the negative helium, lithium, and beryllium ions are as well. We have not applied any corrections to negative ions for the twoto �ve-electron systems, because the size of the hydride ion [7] and Garcia and Mack [5] for oneelectron and Midtdal and Aashamar [6] and Drake [8] for two-electron ions.…”

Section: Discussionmentioning

confidence: 99%

“…Column 2 of Table 2 shows the nonrelativistic kinetic energy ((1/2) 0 2 ), for the purpose of comparison, column 3 shows the relativistic correction calculated by (5), column 4 shows the relativistic correction calculated by (9), column 5 shows the Lamb shi correction, column 6 shows the ionization energy calculated by expression (6), and column 7 shows the ionization energy calculated by expression (16) (which is equivalent to (10)).…”

Section: Ionization Energy Of One-electron Atomsmentioning

confidence: 99%

“…General availability of powerful computers allowed highly complicated theoretical calculations of the energy levels and ionization energies of hydrogen [5] and heliumlike ions [6] to be performed. ese sophisticated equations for one-and two-electron atomic ions, which need complex computer routines to compute, include corrections for the variation of mass with velocity, reduced mass, mass polarization, and Lamb shi, and for two-electron ions, corrections for interactions between the two electrons.…”

Section: Introductionmentioning

confidence: 99%

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Relativistic Corrections for Calculating Ionization Energies of One- to Five-Electron Isoelectronic Atomic Ions

Lang

Smith

2013

ISRN Inorganic Chemistry

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We have previously proposed a simple empirical equation to reproduce the literature values of the ionization energies of oneelectron to four-electron atomic ions with very good agreement. However, we used a potential energy approach in our equation, which has no theoretical basis. is paper discusses an alternative kinetic energy expression for one to �ve electrons with simple corrections for relativistic and Lamb shi effects and for two-to-�ve electron ions additional effects including electron relaxation and residual interactions. For calculated values of one-electron (hydrogen-like) and two electron (helium like) atomic ions, the difference with the literature values is typically 0.001% or less. Agreement with the literature values for three-, four-, and �ve-electron ions is 99% or better. First electron affinities calculated by our expression also agree fairly well with generally recommended values. ese results show that there is strong evidence that our methodology can be developed to reliably predict, with fairly good accuracy, ionization energies of multielectron atomic ions that have not been measured.

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Section: Introductioncontrasting

confidence: 54%

Section: The Lamb Shiftmentioning

confidence: 44%

Section: Discussionmentioning

confidence: 99%

Section: Ionization Energy Of One-electron Atomsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Relativistic Corrections for Calculating Ionization Energies of One- to Five-Electron Isoelectronic Atomic Ions

Lang

Smith

2013

ISRN Inorganic Chemistry

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Exploiting the analyticity of Schrödinger operators: Theory and the computation of partial cross sections

Reinhardt

Han

1996

Int. J. Quantum Chem.

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The idea of dilation, or dilatation, analyticity with respect to complex scaling of the interparticle distances for nonrelativistic atomic or molecular electronic Hamiltonians is now over 20 years old and the first major reviews are just over 10. The method continues to be a fruitful source of new theoretical and computational results. Under the scale transformation r = re", the usual "spectrum" of bound states is exactly preserved, and scattering continua are "rotated" off the real axis by an angle of -2Re(e) about their respective thresholds. Useful features of this transformation are (1) that resonances are exposed, and, thus, (complex) resonance eigenvalues are easily calculated as the wave functions are L2, and standard results of Kato-type perturbation theory can thus be applied to them; (2) that utilization of this technique to study atoms in ac and dc fields was an early, and still evolving extension of the original theory; and (3) the fact that the "continua" are rotated off the real energy axis allows scattering information to be extracted from computations carried out entirely L2 in bases as the usual resolvents of scattering theory are no longer singular on the real axis. After a brief survey of the technique and its applications, these ideas are illustrated by discussion of positive energy-bound states and resonances, the extension of the theory to include the dc Stark effect, and a review of the resolution of the initially perplexing problem of atomic and molecular bound states in continua. These theoretical results are followed by a discussion of some very recent computational results, allowing computation of atomic partial photoionization cross sections with no specific coordinate space enforcement of boundary conditions, a highly advantageous situation for calculation of the partial cross section for three-body breakup, as in the process ho + He * He2++ e-+ e-. 0

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New Sandwich‐Type Phthalocyaninato–Metal Quintuple‐Decker Complexes

Wang

Kobayashi

Jiang

2011

Chemistry A European J

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Linked and fused arrays, as well as stacked multidecker complexes, with basic tetrapyrrole units as important p-conjugated systems, are of significant interests for advanced molecular materials with potential applications in the field of organic field transistors (OFETs), [1] nonlinear optics (NLO), [2] and solar cells. [3] Efforts towards extended tetrapyrrole motifs have led to new synthetic methodologies that have resulted in new tetrapyrrole systems with one-, [4] two-, [5] and even three-dimensional conjugated structures. [6, 7] Threedimensional, conjugated, sandwich-type, tetrapyrrole-metal, double-and triple-decker complexes, which have been fabricated by incorporating large metal centers into stacked tetrapyrrole (with two-dimensional conjugation) multidecker systems, [7] have been intensively studied due to the intriguing spectroscopic, [7b,c, 8] electrochemical, [9] and magnetic properties, [10] as well as potential applications in molecular mechanical devices.[11] However, stacked tetrapyrrole-metal complexes with sandwich-type structures have not exceeded three tetrapyrroles until the very recent reports on the tetrakis(tetrapyrrole)-rare-earth-cadmium compounds with a quadruple-decker molecular configuration. [10e, 12] The lack of these type of structures is associated with the limitations in the selection of an appropriate metal ion with suitable coordination number, geometry, charge, and hard/soft-acid/base behavior to match the coordination algorithm of tetrapyrroles. Herein we describe the facile synthesis, spectroscopic characterization, and electrochemical properties of new, sandwich-type, homoleptic, pentakis(phthalocyaninato), quintuple-decker complexes composed of two bis(phthalocyaninato)-lanthanideA C H T U N G T R E N N U N G (III) subunits bridged by two cadmium(II) ions and one phthalocyanine ligand (Scheme 1).A simple one-pot synthetic pathway, which starts from neutral unprotonated bis(2,3,9,10,16,17,23,24-octa- The sandwich-type nature of the quintuple-decker molecular structure of 1-3 was clearly revealed by MALDI-TOF MS and NMR spectroscopy. The MALDI-TOF mass spectra of these three compounds showed intense signals for the protonated molecular ion [M + H] + ( Figure S1 and Table S1 in the Supporting Information), which indicated the composition of two trivalent lanthanide cations, two divalent cadmium cations, and five divalent phthalocyanine anions. Satisfactory NMR spectra were obtained for the three sandwichtype, pentakis(phthalocyaninato), heterometal, quintupledecker complexes 1-3. A C H T U N G T R E N N U N G (butyloxy)phthalocyaninato) (H 2 PcA C H T U N G T R E N N U N G (OC

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Perturbation-Theory Expansions Through 21st Order of the Nonrelativistic Energies of the Two-Electron Systems(2p)2 P

Cited by 145 publications

References 5 publications

Relativistic Corrections for Calculating Ionization Energies of One- to Five-Electron Isoelectronic Atomic Ions

Relativistic Corrections for Calculating Ionization Energies of One- to Five-Electron Isoelectronic Atomic Ions

Exploiting the analyticity of Schrödinger operators: Theory and the computation of partial cross sections

New Sandwich‐Type Phthalocyaninato–Metal Quintuple‐Decker Complexes

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