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Clar's rule states that for a benzenoid polycyclic aromatic hydrocarbon (i.e. one with only hexagonal rings), the resonance structure with the largest number of disjoint aromatic π-sextets is the most important to characterize its chemical and physical properties. Such a resonance structure is called a Clar structure. In other words, a ...
Pushing a person in a swing is a common example of resonance. The loaded swing, a pendulum, has a natural frequency of oscillation, its resonant frequency, and resists being pushed at a faster or slower rate. A familiar example is a playground swing, which acts as a pendulum. Pushing a person in a swing in time with the natural interval of the ...
In nonlinear systems a resonant interaction is the interaction of three or more waves, usually but not always of small amplitude.Resonant interactions occur when a simple set of criteria coupling wave vectors and the dispersion equation are met.
Examples include the coupled oscillation of Christiaan Huygens' pendulums, fireflies, neurons, the London Millennium Bridge resonance, and large arrays of Josephson junctions. [ 59 ] Moreover, from the theoretical physics standpoint, dynamical chaos itself, in its most general manifestation, is a spontaneous order.
Perturbation theory is applicable if the problem at hand cannot be solved exactly, but can be formulated by adding a "small" term to the mathematical description of the exactly solvable problem. For example, by adding a perturbative electric potential to the quantum mechanical model of the hydrogen atom, tiny shifts in the spectral lines of ...
Below is an example of how NRT may generate a list of resonance structures. (1) Given an input wavefunction, NRT creates a list of reference Lewis structures. The LEWIS option tests each structure and rejects those that do not conform to the Lewis bonding theory (i.e., those that do not fulfill the octet rule , pose unreasonable formal charges ...
In Mathematics, a structure on a set (or on some sets) refers to providing it (or them) with certain additional features (e.g. an operation, relation, metric, or topology). Τhe additional features are attached or related to the set (or to the sets), so as to provide it (or them) with some additional meaning or significance.
In another case, the stereoelectronic effect can result in an increased contribution of one resonance structure over another, which leads to further consequences in reactivity. For 1,4- benzoquinone monoxime, there are significant differences in the physical properties and reactivities between C2-C3 double bond and C5-C6 double bond.