In chemistry, π-effects or π-interactions are a type of non-covalent interaction that involves π systems. Just like in an electrostatic interaction where...

participation in π bonding and their presence necessarily terminates a π system or separates two π systems. A basis p orbital that takes part in a π system can contribute...

Cation–π interaction is a noncovalent molecular interaction between the face of an electron-rich π system (e.g. benzene, ethylene, acetylene) and an adjacent...

In mathematics, a π-system (or pi-system) on a set Ω {\displaystyle \Omega } is a collection P {\displaystyle P} of certain subsets of Ω , {\displaystyle...

applications in measure theory and probability. A major application of 𝜆-systems is the π-𝜆 theorem, see below. Let Ω {\displaystyle \Omega } be a nonempty...

A_{3},\ldots \right\}} has the finite intersection property (and is even a π–system). If the inclusions A 1 ⊇ A 2 ⊇ A 3 ⋯ {\displaystyle A_{1}\supseteq A_{2}\supseteq...

disjoint subsets. Dynkin's π-λ theorem says, if P {\displaystyle P} is a π-system and D {\displaystyle D} is a Dynkin system that contains P , {\displaystyle...

polar-π interactions. In general, π-effects are associated with the interactions of molecules with the π-systems of arenes. π–π interactions are associated...

conjugated π system via resonance (mesomerism) or inductive effects (or induction)—called +M or +I effects, respectively—thus making the π system more nucleophilic...

a substituent moves from one part of a π-system to another part with simultaneous rearrangement of the π-system. True sigmatropic reactions are usually...

on opposite faces of the system and this can only be achieved in a conrotatory process. In open systems containing (4n + 2) π electrons, terminal bonding...

The number π (/paɪ/ ; spelled out as pi) is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to...

{\mathcal {B}}\right\}.} A π-system is a prefilter if and only if it is proper. Every filter is a proper π-system and every proper π-system is a prefilter but...

In theoretical computer science, the π-calculus (or pi-calculus) is a process calculus. The π-calculus allows channel names to be communicated along the...

cyclic molecule with a π electron system that has higher energy, i.e., it is less stable due to the presence of 4n delocalised (π or lone pair) electrons...

covalently bound atoms with specific characteristics: A delocalized conjugated π system, most commonly an arrangement of alternating single and double bonds. Coplanar...

{\mathcal {B}}\right\}.} A π–system is a prefilter if and only if it is proper. Every filter is a proper π–system and every proper π–system is a prefilter but...

Pi (/ˈpaɪ/ ; Ancient Greek /piː/ or /peî/, uppercase Π, lowercase π, cursive ϖ; Greek: πι) is the sixteenth letter of the Greek alphabet, representing...

organic chemistry, the di-π-methane rearrangement is the photochemical rearrangement of a molecule that contains two π-systems separated by a saturated...

coordinate systems used in mathematics normally use radians rather than degrees; (note 90 degrees equals π⁄2 radians). And these systems of the mathematics...

diarylethenes are prone to oxidation, leading to a re-aromatization of the π-system. The most common example is (E)-stilbene, which upon irradiation undergoes...

Polar coordinate system. Many modern programming languages provide a function that will compute the correct azimuth φ, in the range (−π, π), given x and...

or pi meson, denoted with the Greek letter pi (π), is any of three subatomic particles: π0 , π+ , and π− . Each pion consists of a quark and an antiquark...

and conditions may be chemically meaningful. Molecules with an extended π system such as linear polyenes and polyaromatic compounds are well described by...

element from some index set λ-system (Dynkin system) – Family closed under complements and countable disjoint unions π-system – Family of sets closed under...

symbol ω), a conjugated system (π) or even a sigma bond (σ). The relationship is antarafacial when opposite faces of the π system or isolated orbital are...

depending on how many π-electrons are in the system. Shown below is a diagram of a two-electron fragment approaching a four-electron π-system using frontier...

products and new materials. The underlying concept has also been applied to π-systems involving heteroatoms, such as carbonyls and imines, which furnish the...

follows: π ε ϱ ι φ ε ϱ ε ι ω ~ ν ε υ ' ϑ ε ι ω ~ ν ε ‘ ξ η κ o σ τ ω ~ ν π δ ∠ ′ π ε π ε ∠ ′ π ϛ π ϛ ∠ ′ π ζ π μ α γ π α δ ι ε π α κ ζ κ β π α ν κ δ π β ι...

four-atom π-system and a three-atom π-system to form a seven-membered ring. Allyl or oxyallyl cations (propenylium-2-olate) are commonly used three-atom π-systems...