6.2.2. Definition of Effective Properties 3064 6.3. Response Properties to Magnetic Fields 3066 6.3.1. Nuclear Shielding 3066 6.3.2. Indirect Spin−Spin Coupling 3067 6.3.3. EPR Parameters 3068 6.4. Properties of Chiral Systems 3069 6.4.1. Electronic Circular Dichroism (ECD) 3069 6.4.2. Optical Rotation (OR) 3069 6.4.3. VCD and VROA 3070 7. Continuum and Discrete Models 3071 7.1. Continuum Methods within MD and MC Simulations 3072

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Quantum mechanical continuum solvation models.

The term ``sensitized luminescence'' in crystalline phosphors refers to the phenomenon whereby an impurity (activator, or emitter) is enabled to luminesce upon the absorption of light in a different type of center (sensitizer, or absorber) and upon the subsequent radiationless transfer of energy from the sensitizer to the activator The resonance theory of Forster, which involves only allowed transitions, is extended to include transfer by means of forbidden transitions which, it is concluded, are responsible for the transfer in all inorganic systems yet investigated The transfer mechanisms of importance are, in order of decreasing strength, the overlapping of the electric dipole fields of the sensitizer and the activator, the overlapping of the dipole field of the sensitizer with the quadrupole field of the activator, and exchange effects These mechanisms will give rise to ``sensitization'' of about 103−104, 102, and 30 lattice sites surrounding each sensitizer in typical systems The dependence of transfer efficiency upon sensitizer and activator concentrations and on temperature are discussed Application is made of the theory to experimental results on inorganic phosphors, and further experiments are suggested

A Theory of Sensitized Luminescence in Solids

Magnetic and electric dipole transitions between levels of the 4fx configuration perturbed by a static crystalline field are treated. The expression obtained for the pure‐electronic electric‐dipole transition probability involves matrix elements of an even‐order unit tensor between the two 4fx states involved in the transition. The contributions to the transition probability from interactions, via the crystalline field, with the nd 94fx−1, 4fx−1 nd, 4fx−1 ng configurations are shown to add linearly, in such a manner as to multiply each odd k crystal‐field parameter Ak q by a constant. If ``J mixing'' in the 4fx configuration is neglected ΔJ between the upper and lower 4fx levels is restricted to six units or less. If ``L mixing'' is neglected then ΔL is also restricted to six units or less. Application is made to the fluorescence spectra of PrCl3 and EuCl3. Many of the missing and weak transitions are explained.

Intensities of Crystal Spectra of Rare‐Earth Ions

The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

Reaction-rate theory: fifty years after Kramers

It is pointed out that one of the main effects of correlation phenomena in d- and f-bands is to give rise to behaviour characteristic of the atomic or Heitler-London model. To investigate this situation a simple, approximate model for the interaction of electrons in narrow energy bands is introduced. The results of applying the Hartree-Fock approximation to this model are examined. Using a Green function technique an approximate solution of the correlation problem for this model is obtained. This solution has the property of reducing to the exact atomic solution in the appropriate limit and to the ordinary uncorrelated band picture in the opposite limit. The condition for ferromagnetism of this solution is discussed. To clarify the physical meaning of the solution a two-electron example is examined.

Electron correlations in narrow energy bands

1. Introduction 2. The quantum mechanical method 3. Angular momentum 4. The theory of radiation 5. One-electron spectra 6. The central-field approximation 7. The Russell-Saunders case: energy levels 8. The Russell-Saunders case: eigenfunctions 9. The Russell-Saunders case: line strengths 10. Coupling 11. Intermediate coupling 12. Transformations in the theory of complex spectra 13. Configurations containing almost closed shells. X-rays 14. Central fields 15. Configuration interaction 16. The Zeeman effect 17. The Stark effect 18. The nucleus in atomic spectra Appendix. Universal constants and natural atomic units.

The Theory of Atomic Spectra

By optical rotatory power is meant the property of a medium to rotate the plane of polarization of linearly polarized light that is transmitted through it. The first effect of this kind was discovered by Arago in 1811. He found that quartz had this property in the direction of the optical axis, the direction along with ordinary double refraction vanishes.

Theories of Optical Rotatory Power

The question of nuclear motions associated with electron transitions is discussed from the standpoint of quantum mechanics. It appears that Heisenberg’s indetermination principle gives the clue to the inexactness of the earlier method based on Franck’s postulate since its strict application calls for a violation of the principle. The existence of an entirely new type of band spectrum due to the wave nature of matter is predicted and the interpretation of Rayleigh’s mercury band at 2476–2482 A.U. as of this type is suggested. Finally it is shown that while Franck’s postulate is also true for electron jumps in atoms, it is of but trivial interest because its inexactness is much greater for the electrons than for heavy nuclei.

Nuclear Motions Associated with Electron Transitions in Diatomic Molecules

A theory of the relative intensity of the various bands in a system of electronic bands is developed by an extension of an idea used by Franck in discussing the dissociation of molecules by light absorption. The theory predicts the existence of two especially favored values of the change in the vibrational quantum numbers, in accord with the empirical facts as discussed by Birge.

Edward U. Condon

Papers

The Theory of Atomic Spectra

The Theory of Atomic Spectra

Theories of Optical Rotatory Power

Nuclear Motions Associated with Electron Transitions in Diatomic Molecules

A Theory of Intensity Distribution in Band Systems