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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 ...
Near room temperature, these salts are yellow , but these solids become blue when heated to near 70 °C. The bright blue color is characteristic of tetrahedral [NiCl 4] 2−, the intensity being a consequence of the Laporte selection rule. The yellow color results from a polymer consisting of octahedral Ni centers.
Sturges's rule [1] is a method to choose the number of bins for a histogram. Given observations, Sturges's rule suggests using ^ = + bins in the histogram. This rule is widely employed in data analysis software including Python [2] and R, where it is the default bin selection method. [3]
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]
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]
For example, suppose a researcher wishes to estimate the causal effect of smoking (X) on general health (Y). [5] Correlation between smoking and health does not imply that smoking causes poor health because other variables, such as depression, may affect both health and smoking, or because health may affect smoking.