An empirical relation between oscillator strengths calculated from the dipole length and dipole velocity formalisms in the optical absorption of conjugated molecules

1978 ◽  
Vol 48 (2) ◽  
pp. 155-163 ◽  
Author(s):  
Toshiaki Kakitani ◽  
Hiroko Kakitani
Keyword(s):  
Optical Absorption ◽  
Empirical Relation ◽  
Oscillator Strengths ◽  
Conjugated Molecules ◽  
Dipole Length

Bond Lengths in Conjugated Molecules: The Present Position

1951 ◽  
Vol 207 (1088) ◽  
pp. 91-100 ◽  
Keyword(s):  
Bond Order ◽  
Empirical Relation ◽  
Simple Theory ◽  
Reliable Estimate ◽  
Present Position ◽  
Conjugated Molecules ◽  
X Ray ◽  
Bond Lengths ◽  
Hydrocarbon Molecules ◽  
Semi Empirical

A survey is given of the present methods for calculating bond lengths in conjugated molecules. Except in simple cases this has to be achieved by combining a calculated bond order with a semi-empirical relation between order and length. There are several definitions of bond order in current use, some of which can be shown to be less valuable than others. Recent accurate X -ray analysis has shown convincingly that the concept of bond order is a valid one, though there are limits to the degree of accuracy that may be claimed. Several possible improvements upon the simple theory are mentioned, most of which indicate alterations in bond lengths calculated from the simple theory, of the order of 0.005 Å. It is concluded that for condensed hydrocarbon molecules, the lengths of individual bonds may be predicted to within about 0.015 Å. For heteromolecules there are still too many additional factors for any reliable estimate to be possible.

ENERGY-GAP VARIATION IN MIXED III–V ALLOYS

1967 ◽  
Vol 45 (2) ◽  
pp. 255-261 ◽  
Author(s):  
A. G. Thompson ◽  
J. C. Woolley
Keyword(s):  
Optical Absorption ◽  
Mole Fraction ◽  
Energy Gap ◽  
Optical Transition ◽  
Empirical Relation ◽  
Energy Gaps ◽  
Direct Optical Transition ◽  
Crystal Type ◽  
The Mean ◽  
Alloy Systems

Values of E0, the lowest direct optical transition, are available for several III-V alloy systems, from measurements of optical absorption, electroreflectance, electroluminescence, etc. It is shown that in all available cases the variation of E0 with composition can be fitted very well to an equation of the form E0 = A + Bx + Cx2, where x is the mole fraction of one component compound. Such a relation is expected from a virtual-crystal type of analysis.If E0m is the mean of the energy gaps of the component compounds of the system, it is found that an empirical relation of the form [Formula: see text] appears to hold where α is approximately 0.3 eV3/2.

Systematic Trends in Atomic Oscillator Strengths: The Helium Isoelectronic Sequence

1972 ◽  
Vol 50 (12) ◽  
pp. 1363-1369 ◽  
Author(s):  
M. Cohen ◽  
R. P. McEachran
Keyword(s):  
Electric Dipole ◽  
Nuclear Charge ◽  
Principal Quantum Number ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Isoelectronic Sequence ◽  
Dipole Oscillator ◽  
Good Agreement ◽  
Comparison Data ◽  
Dipole Length

Electric dipole oscillator strengths (f values) have been calculated for a large number of singlet and triplet S–P, P–D, and D–F transitions in the helium isoelectronic sequence through O+6. The analytical orbital wave functions employed were of frozen-core type, and generally produce very good agreement between length and velocity values of the calculated oscillator strengths. A conspicuous exception occurs in many cases where the principal quantum number remains unchanged in the transition, and the more reliable dipole length values have been adopted for such transitions. The smooth variation of the calculated f values as functions of the inverse of the nuclear charge Z provided a sensitive check on the accuracy of the computations and indicated a considerable number of P–D transitions where the velocity values seemed the more reliable. Wherever comparison data are available, our calculated oscillator strengths are in excellent agreement with the most accurate values; in other cases, the absolute uncertainty in the f values should in no case exceed 5%.

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