Parameterization Schemes in Solid State Physics

Newman, D J

doi:10.1071/ph780489

Cited by 7 publications

(5 citation statements)

References 9 publications

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“…The early work of Hutchings and Ray [24], which explored and indicated the limitations of the point charge model, and more recent work by Faucher et al [25] can be contrasted with attempts of other groups, particularly Newman and coworkers, who have expressed their results in terms of the angular overlap and covalency contributions to the crystal-field parameters [26][27][28].…”

Section: I(c) Crystal-field Calculationsmentioning

confidence: 99%

Spectroscopic Properties of the f-Elements in Compounds and Solutions

Carnall

Beitz

Crosswhite

et al. 1983

Systematics and the Properties of the Lanthanides

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In this systematic examination of some of the spectroscopic properties of the f-elements we deal with both the trivalent lanthanides and actinides. We summarize the present status of our energy level calculations in single crystal matrices and in aqueous solution, and compare the predicted crystal-field structure in certain low-symmetry sites with that observed. Some interesting new structural insights are thereby gained. The state eigenvectors from these calculations are then used in part in reassessing and interpreting the intensities of transitions in aqueous solution via the Judd-Ofelt theory. The parameters of this theory derived from fitting experimental data are compared with those computed from model considerations. Finally, we discuss some recent contributions to the interpretation of excited state relaxation processes in aqueous solution.

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Section: I(c) Crystal-field Calculationsmentioning

confidence: 99%

Spectroscopic Properties of the f-Elements in Compounds and Solutions

Carnall

Beitz

Crosswhite

et al. 1983

Systematics and the Properties of the Lanthanides

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“…With the aid of tensor operators the Coulomb interaction can be expressed as ^coui = E°e a + E \ + E \ + E S- (2) The E 1 In tensor operator notation the crystal-field interaction is written k,q 1=1 k (k) The B s are parameters and the C ^ s are tensor operators which are related to the spherical harmonics.…”

Section: Amentioning

confidence: 99%

Optical Properties of Actinide and Lanthanide Ions

Hessler

Carnall

1980

Lanthanide and Actinide Chemistry and Spectroscopy

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The sharpness of many of the optical absorption and emission lines of the lanthanide ions in ionic crystals has intriguedscientists since 1908. We review some of the recent developments in this area of spectroscopy, emphasizing the optical properties of the tripositive lanthanide and actinide ions.In particular, we shall discuss the single ion properties of line position, intensity, width, and fluorescence lifetime. Such effects as the application of external electric and magnetic fields, hyperfine interactions, and cooperative effects such as long range ordering and energy transfer, although direct extensions of the above properties, must be excluded in such a short review.The optical properties of the lanthanide and actinide ions are due to the unpaired electrons of the ion. The observed sharp transitions have been shown to be intraconfiguration transitions. The most widely studied systems have ground configurations (Xe, 4f n ) and (Rn, 5f n ) for the lanthanide and actinide ions respectively. The number of f-electrons, n, ranges from 1 to 13.The inert rare gas core allows us to discuss the systems in terms of the f-electrons only.Even such a conceptually simple system is complex enough to require a parameterization scheme. The physical significance of such a scheme and its role in developing an understanding of complex systems has been discussed by Newman (1). Our goal is not to uncritically accumulate parameters in some standard scheme which has limited utility, but instead to develop as comprehensive and universal a scheme as possible, one which can be applied to the energy level structure, radiative transition probabilities, temperature-dependent line widths, fluorescent lifetimes, electric and magnetic susceptibilities, hyperfine structure, and cooperative phenomena. In particular, the parameters we deduce should allow us to predict observables in an unmeasured region, be consistent with appropriate ab initio calculations, and be useful as input data into other parameterization schemes. An example of the last point is the analysis 0-8412-0568-X/80/47-131-349$05.00/0

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“…In this work, the mathematical properties of the Laplace transform are used to derive phenomenological expressions for reactive cross sections and microcanonical rates in terms of the parameters used to describe the rate data. These expressions may be viewed as alternate descriptions of the data …”

Section: Introductionmentioning

confidence: 99%

“…These expressions may be viewed as alternate descriptions of the data. 9 As such, they do not contain information that is not in the data; the information is simply presented in a different form. Previously, Menzinger and Wolfgang 10 discussed a number of forms of energy-dependent reactive cross sections and LeRoy 11 discussed the implications of three general forms of the reactive cross section.…”

Section: Introductionmentioning

confidence: 99%

Calculation of Reactive Cross Sections and Microcanonical Rates from Kinetic and Thermochemical Data

Hessler

1998

J. Phys. Chem. A

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In general, kinetic rate data may be represented by van't Hoff's four-parameter equation. When this is true, the mathematical properties of the Laplace transform may be used to derive phenomenological equations that describe the energy-dependent reactive cross sections and microcanonical rates in terms of the same four parameters. Since the macroscopic rate data and microscopic expressions are related by the Laplace transform, these microscopic descriptions do not imply new information; they simply express the information contained in the rate data in another form. The Monte Carlo techniques used to determine confidence envelopes for the rate data may also be used to provide confidence envelopes or “bounds” for the energy-dependent properties. These microscopic expressions may be used to compare and contrast theoretical calculations or as a starting point in RRKM or master equation calculations. Both the forward and reverse H + O2 ↔ OH + O reactions and the associative reaction CH3 + CH3 → C2H6 are used to illustrate the above ideas. In the first example, the cross section for the reverse reaction shows that it is not dominated by the dipole−quadrupole interaction. The cross section for the forward reaction is obtained by fitting rate data from 158 to 5300 K and peaks just above the threshold of 8354 K. In the second example, comparison to recent theoretical calculations highlights the importance of angular momentum and the centrifugal barrier.

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Parameterization Schemes in Solid State Physics

Cited by 7 publications

References 9 publications

Spectroscopic Properties of the f-Elements in Compounds and Solutions

Spectroscopic Properties of the f-Elements in Compounds and Solutions

Optical Properties of Actinide and Lanthanide Ions

Calculation of Reactive Cross Sections and Microcanonical Rates from Kinetic and Thermochemical Data

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