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A Lewis acid (named for the American physical chemist Gilbert N. Lewis) is a chemical species that contains an empty orbital which is capable of accepting an electron pair from a Lewis base to form a Lewis adduct. A Lewis base, then, is any species that has a filled orbital containing an electron pair which is not involved in bonding but may form a dative bond with a Lewis acid to form a Lewis adduct. For example, NH3 is a Lewis base, because it can donate its lone pair of electrons. Trimethylborane (Me3B) is a Lewis acid as it is capable of accepting a lone pair. In a Lewis adduct, the Lewis acid and base share an electron pair furnished by the Lewis base, forming a dative bond. In the context of a specific chemical reaction between NH3 and Me3B, a lone pair from NH3 will form a dative bond with the empty orbital of Me3B to form an adduct NH3•BMe3. The terminology refers to the contributions of Gilbert N. Lewis. The terms nucleophile and electrophile are more or less interchangeable with Lewis base and Lewis acid, respectively. However, these terms, especially their abstract noun forms nucleophilicity and electrophilicity, emphasize the kinetic aspect of reactivity, while the Lewis basicity and Lewis acidity emphasize the thermodynamic aspect of Lewis adduct formation. In many cases, the interaction between the Lewis base and Lewis acid in a complex is indicated by an arrow indicating the Lewis base donating electrons toward the Lewis acid using the notation of a dative bond — for example, ←. Some sources indicate the Lewis base with a pair of dots (the explicit electrons being donated), which allows consistent representation of the transition from the base itself to the complex with the acid: A center dot may also be used to represent a Lewis adduct, such as . Another example is boron trifluoride diethyl etherate, . In a slightly different usage, the center dot is also used to represent hydrate coordination in various crystals, as in for hydrated magnesium sulfate, irrespective of whether the water forms a dative bond with the metal.
[2]Paolo Prandoni, [3]LCAV, EPFL
The concept of "basis" for a vector space is one of the most profound
and fruitful ideas in linear algebra. Basis vectors are the "building
blocks" that all other vectors are built from; by "disassembling" a
vector into a linear combination of basis elements we are able to "look
inside" the vector and highlight many of its relevant features.
A vector space has an infinite number o