Edwards equation

The Edwards equation in organic chemistry is a two-parameter equation for correlating nucleophilic reactivity, as defined by relative rate constants, with the basicity of the nucleophile (relative to protons) and its polarizability. This equation was first developed by John O. Edwards in 1954 and later revised based on additional work in 1956. The general idea is that most nucleophiles are also good bases because the concentration of negatively charged electron density that defines a nucleophile will strongly attract positively charged protons, which is the definition of a base according to Brønsted-Lowry acid-base theory. Additionally, highly polarizable nucleophiles will have greater nucleophilic character than suggested by their basicity because their electron density can be shifted with relative ease to concentrate in one area.

Prior to Edwards developing his equation, other scientists were also working to define nucleophilicity quantitatively. Brønsted and Pederson first discovered the relationship between basicity, with respect to protons, and nucleophilicity in 1924:

where k_b is the rate constant for nitramide decomposition by a base (B) and β_N is a parameter of the equation.

Swain and Scott later tried to define a more specific and quantitative relationship by correlating nucleophilic data with a single-parameter equation derived in 1953:

This equation relates the rate constant k, of a reaction, normalized to that of a standard reaction with water as the nucleophile (k₀), to a nucleophilic constant n for a given nucleophile and a substrate constant s that depends on the sensitivity of a substrate to nucleophilic attack (defined as 1 for methyl bromide). This equation was modeled after the Hammett equation.

However, both the Swain-Scott equation and the Brønsted relationship make the rather inaccurate assumption that all nucleophiles have the same reactivity with respect to a specific reaction site. There are several different categories of nucleophiles with different attacking atoms (e.g. oxygen, carbon, nitrogen) and each of these atoms has different nucleophilic characteristics. The Edwards equation attempts to account for this additional parameter by introducing a polarizability term.

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