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The Laporte rule is a rule that explains the intensities of absorption spectra for chemical species. It is a selection rule that rigorously applies to atoms, and to molecules that are centrosymmetric, i.e. with an inversion centre. It states that electronic transitions that conserve parity are forbidden. Thus transitions between two states that ...
The Laporte rule is a selection rule formally stated as follows: In a centrosymmetric environment, transitions between like atomic orbitals such as s-s, p-p, d-d, or f-f, transitions are forbidden. The Laporte rule (law) applies to electric dipole transitions, so the operator has u symmetry (meaning ungerade, odd).
The lattice must also be stable under chemical and photochemical conditions, as these are the environments the conversion will take place within. Finally, this host lattice ought to have low symmetry, allowing for a slight relaxation of the Laporte selection rules. The normally forbidden transitions lead to an increase in the f-f intermixing ...
Otto Laporte (July 23, 1902 – March 28, 1971) was a German-born American physicist who made contributions to quantum mechanics, electromagnetic wave propagation theory, spectroscopy, and fluid dynamics. His name is lent to the Laporte rule in spectroscopy and to the Otto Laporte Award of the American Physical Society. [1]
In spectroscopy, a forbidden mechanism (forbidden transition or forbidden line) is a spectral line associated with absorption or emission of photons by atomic nuclei, atoms, or molecules which undergo a transition that is not allowed by a particular selection rule but is allowed if the approximation associated with that rule is not made. [1]
A training data set is a data set of examples used during the learning process and is used to fit the parameters (e.g., weights) of, for example, a classifier. [9] [10]For classification tasks, a supervised learning algorithm looks at the training data set to determine, or learn, the optimal combinations of variables that will generate a good predictive model. [11]
The use of a sequence of experiments, where the design of each may depend on the results of previous experiments, including the possible decision to stop experimenting, is within the scope of sequential analysis, a field that was pioneered [12] by Abraham Wald in the context of sequential tests of statistical hypotheses. [13]
Randomization is a statistical process in which a random mechanism is employed to select a sample from a population or assign subjects to different groups. [1] [2] [3] The process is crucial in ensuring the random allocation of experimental units or treatment protocols, thereby minimizing selection bias and enhancing the statistical validity. [4]