question: Why is fluorine the best nucleophile in polar aprotic solutions, when electronegative atoms are supposed to be weak nucleophiles?
comment: (I’m going to assume you mean in terms of halogens since there are stronger nucleophiles than F-) It has to do with reaction rates. In an aprotic solvent there is no protons (hence the name). HF is a weak acid, so it’s conjugate base is very strong [F-]. Acid base reactions usually happen the fastest, which is called the kinetic product. An acid, by definition, would be protic. A proton is small, and removing it from a protic solution does not require rearrangements, so it has a low energy requirement and can happen quick. F- and HA react to form HF and A- Nucleophilic attack requires backside attacking, which causes rearrangement of the electrophile, and is usually between larger molecules. This has a higher energy requirement to react. Since F- is unstable compared to other halogens, it’s going to so the easier thing first, and pluck a proton from the protic environment. If there are no protons around to quickly grab, the nucleophile will have the time to overcome the energy barrier of rearranging / nucleophilic attack. The reason F- is so reactive is because its higher electron / proton ratio. Compare F- to Br- F- has 10/9 which is 1.111 Br- has 36/35 which is 1.029 The Br- is closer to 1 than F-, showing that the negative electron has less of an effect in a larger molecule. The electron in F- is less stable and therefore more reactive. Also, Bromine and iodine (and chlorine to a degree) have the ability to polarize themselves. They have very large orbitals, meaning they have an easier time distributing electrons. Since they have so much room for activity, the electrons can kind of chill and are harder to organize for an attack. It’s important to remember nucleophilicity and electronegativity are similar but different concepts. Electronegativity represents the affinity to pull electrons in a bond. Nucleophilicity represents the affinity of a negative source to attack the electrophile.
passages: Pentacoordinated compounds should theoretically be less electrophilic than tetracoordinated analogues due to steric hindrance and greater electron density from the ligands, yet experimentally show greater reactivity with nucleophiles than their tetracoordinated analogues. Advanced ab initio calculations were performed on series of tetracoordinated and pentacoordinated species to further understand this reactivity phenomenon. Each series varied by degree of fluorination. Bond lengths and charge densities are shown as functions of how many hydride ligands are on the central atoms. For every new hydride, there is one less fluoride.
   Historically, only three atomic fluorine sources were available for radical fluorination: Fluorine (F), hypofluorites (O—F based reagents) and XeF. Their high reactivity, and the difficult handling of F and the hypofluorites, limited the development of radical fluorination compared to electrophilic and nucleophilic methods. The uncovering of the ability of electrophilic N—F fluorinating agents to act as atomic fluorine source led to a renaissance in radical fluorination.
   Monofluorinated (MOFO) and difluorinated (DIFO) cyclooctynes were created to increase the rate through the addition of electron-withdrawing fluorine substituents at the propargylic position. Fluorine is a good electron-withdrawing group in terms of synthetic accessibility and biological inertness. In particular, it cannot form an electrophilic Michael acceptor that may side-react with biological nucleophiles.
   Although the use of molecular fluorine as an electrophilic fluorine source is often the cheapest and most direct method, F often forms radicals and reacts with C-H bonds without selectivity. Proton sources or Lewis acids are required to suppress radical formation, and even when these reagents are present, only certain substrates react with high selectivity. Handling toxic, gaseous F requires special apparatus and great care to avoid contact with air or water.
   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.
  
  Section::::Edwards equations.
  
  The first generation of the Edwards equation was
   Section::::E2 competition.
  
  A common side reaction taking place with S2 reactions is E2 elimination: the incoming anion can act as a base rather than as a nucleophile, abstracting a proton and leading to formation of the alkene. This pathway is favored with sterically hindered nucleophiles. Elimination reactions are usually favoured at elevated temperatures because of increased entropy. This effect can be demonstrated in the gas-phase reaction between a sulfonate and a simple alkyl bromide taking place inside a mass spectrometer:
   In molecules whose vibrational mode involves a rotational or pseudorotational mechanism (such as the Berry mechanism or the Bartell mechanism), van der Waals strain can cause significant differences in potential energy, even between molecules with identical geometry. PF, for example, has significantly lower potential energy than PCl. Despite their identical trigonal bipyramidal molecular geometry, the higher electron count of chlorine as compared to fluorine causes a potential energy spike as the molecule enters its intermediate in the mechanism and the substituents draw nearer to each other.
   Electrophilic fluorination rely on sources of "F". Often such reagents feature N-F bonds, for example F-TEDA-BF. Asymmetric fluorination, whereby only one of two possible enantiomeric products are generated from a prochiral substrate, rely on electrophilic fluorination reagents. Illustrative of this approach is the preparation of a precursor to anti-inflammatory agents:
  
  Section::::Methods for preparation of C–F bonds.:Electrophilic fluorination.:Electrosynthetic methods.
   Many schemes attempting to quantify relative nucleophilic strength have been devised. The following empirical data have been obtained by measuring reaction rates for a large number of reactions involving a large number of nucleophiles and electrophiles. Nucleophiles displaying the so-called alpha effect are usually omitted in this type of treatment.
  
  Section::::Properties.:Nucleophilicity.:Swain-Scott equation.
  
  The first such attempt is found in the Swain–Scott equation derived in 1953:
   For example, iodoperfluoroalkanes are well-designed for XB crystal engineering. In addition, this is also why F can act as a strong XB donor, but fluorocarbons are weak XB donors because the alkyl group connected to the fluorine is not electronegative. In addition, the Lewis base (XB acceptor) tends to be electronegative as well and anions are better XB acceptors than neutral molecules.
   Triplet fluorenylidene reacts with olefins in a stepwise fashion to produce a racemic mixture, provided that the rate of spin inversion (intersystem crossing) is not significantly faster than rates of intermediate bond rotation.
  
  Section::::Singlet Fluorenylidene Reactivity.
   BULLET::::4. FL equilibrates with the ground state triplet FL by intersystem crossing.
  
  Section::::Reaction of Fluorenylidene in Solution.
  
  Fluorenylidene reacts with olefins as predicted by the Skell-Woodworth rules. The stereochemistry of cycloaddition products depends on the relative rates of cyclopropanation (or other reactions) and intersystem crossing. Stabilization of specific spin states, and, by extension, increased stereospecificity can be achieved by using solvents of different polarities .
  
  Section::::Triplet Fluorenylidene Reactivity.
   Like S2 reactions, there are quite a few factors that affect the reaction rate of S1 reactions. Instead of having two concentrations that affect the reaction rate, there is only one, substrate. The rate equation for this would be Rate=k[Sub]. Since the rate of a reaction is only determined by its slowest step, the rate at which the leaving group "leaves" determines the speed of the reaction. This means that the better the leaving group, the faster the reaction rate. A general rule for what makes a good leaving group is the weaker the conjugate base, the better the leaving group. In this case, halogens are going to be the best leaving groups, while compounds such as amines, hydrogen, and alkanes are going to be quite poor leaving groups. As S2 reactions were affected by sterics, S1 reactions are determined by bulky groups attached to the carbocation. Since there is an intermediate that actually contains a positive charge, bulky groups attached are going to help stabilize the charge on the carbocation through resonance and distribution of charge. In this case, tertiary carbocation will react faster than a secondary which will react much faster than a primary. It is also due to this carbocation intermediate that the product does not have to have inversion. The nucleophile can attack from the top or the bottom and therefore create a racemic product. It is important to use a protic solvent, water and alcohols, since an aprotic solvent could attack the intermediate and cause unwanted product. It does not matter if the hydrogens from the protic solvent react with the nucleophile since the nucleophile is not involved in the rate determining step.
   Section::::Factors affecting the rate of the reaction.:Nucleophile.
   This free-energy relationship relates the pseudo first order reaction rate constant (in water at 25 °C), "k", of a reaction, normalized to the reaction rate, "k", of a standard reaction with water as the nucleophile, 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).
   In this case the attack will occur on the carbon with both R groups attached to it since that is the more substituted position.
  
  Section::::Effects of large pi ligands.
  
  When large pi ligands are present they can undergo different kinds of nucleophilic attacks. In the following figure the nucleophilic attack can occur from either the top or bottom and reduce the double bond and add the nucleophile.
  
  This nucleophilic attack can occur at either the top or bottom also and add the nucelophile.
  
  Section::::Uses in synthesis.
   Electrophilic fluorination
  
  Electrophilic fluorination is the combination of a carbon-centered nucleophile with an electrophilic source of fluorine to afford organofluorine compounds. Although elemental fluorine and reagents incorporating an oxygen-fluorine bond can be used for this purpose, they have largely been replaced by reagents containing a nitrogen-fluorine bond.
   Fluorine's first ionization energy is third-highest among all elements, behind helium and neon, which complicates the removal of electrons from neutral fluorine atoms. It also has a high electron affinity, second only to chlorine, and tends to capture an electron to become isoelectronic with the noble gas neon; it has the highest electronegativity of any element. Fluorine atoms have a small covalent radius of around 60 picometers, similar to those of its period neighbors oxygen and neon.
  
  Section::::Characteristics.:Reactivity.
   The bond energy of difluorine is much lower than that of either or and similar to the easily cleaved peroxide bond; this, along with high electronegativity, accounts for fluorine's easy dissociation, high reactivity, and strong bonds to non-fluorine atoms. Conversely, bonds to other atoms are very strong because of fluorine's high electronegativity. Unreactive substances like powdered steel, glass fragments, and asbestos fibers react quickly with cold fluorine gas; wood and water spontaneously combust under a fluorine jet.
   The highest oxidation states may be uncommon to everyday life, or even industrial usage. For example, the synthesis of mercury tetrafluoride, the first compound to achieve an oxidation state above +2 for a group 12 element, breaking the filled 5d-shell, again showing the significance of the relativistic effects on the heavy elements, and fueling the debate over whether mercury, cadmium, and zinc are transition metals, occurred at cryogenic temperatures and the compound decomposes at the temperatures of solid nitrogen. More unstable still, the only cobalt(V) species, the cation, has only been observed in gas phase (with no interactions with other atoms, thus no shown stability in any chemical environment). The reason why such unstable species exist is complicated, yet can be summarized as follows on the example of the hypothesized  molecule: According to the modern calculations, five fluorine atoms and one nitrogen atoms can theoretically arrange themselves in different ways, such as and , and , , etc. The + system is of the smallest energy (most stable). However, if a molecule was synthesized, it would have to go through a high-energy transitional state, from which it could decay into two molecules. But since the transitional state is higher in energy than the hexatomic molecule, the energy difference would need to be added to reach the transitional state and thus allow the decay. This energy is called reaction activation barrier. (The second decay mode has an analogical position.) Thus if little energy was added (low temperatures), then the compound could exist; however, the synthesis is a serious problem (not yet solved).
   Due to a stronger resonance effect and inductive effect than the heavier halogens, fluorine is anomalous. The partial rate factor of electrophilic aromatic substitution on fluorobenzene is often larger than one at the "para" position, making it an activating group. Conversely, it is moderately deactivated at the "ortho" and "meta" positions, due to the proximity of these positions to the electronegative fluoro substituent.
  
  Section::::Categories.:Deactivating groups.
   Section::::Organofluorine compounds.
  
  The carbon–fluorine chemical bond of the organofluorine compounds is the strongest bond in organic chemistry. Along with the low polarizability of the molecules, these are the most important factors contributing to the great stability of the organofluorines.
   BULLET::::2. In molecules in which a central atom does not complete the octet rule (has less than the maximum number of electron pairs), then it gives rise to partial double bonding characteristics and thus, making the bonds shorter than 54 pm. For example, the short bond length of BF can be attributed to the delocalization of the fluorine lone pairs.
   Attack occurs at the terminus which will result in the conjugated product shown.
  
  Section::::Internal attack.
  
  Here the ligand that is already attached to the metal acts as the nucleophile and attacks the metal center internally.
  
  Section::::Effects of types of ligands on regiochemistry of attack.
  
  Nucleophilic attack at terminal position of allyl ligands when pi accepting ligand is present.
  
  If sigma donating ligands are present they pump electrons into the ligand and attack occurs at the internal position.
  
  Section::::Effects of asymmetrical ligands.
  
  When asymmetrical allyl ligands are present attack occurs at the more substituted position.
   The most common fluorinating agents used for organic synthesis are "N"-fluoro-"o"-benzenedisulfonimide (NFOBS), "N"-fluorobenzenesulfonimide (NFSI), and Selectfluor.
  
  Section::::Mechanism and stereochemistry.
  
  Section::::Mechanism and stereochemistry.:Prevailing mechanism.
  