[Organishe]

Would someone be willing to give a formal definition/explanation of hard vs. soft nucleophiles, and hard and soft acids? The things I know (or think I know) already are that hard nucleophiles tend to do 1,2-addition to a,B-unsaturated ketones, while a soft nucleophile would favor a 1,4-addition, no?  I would guess that an organolithium would be an example of a hard nucleophile, while an organocuprous reagent (R2CuLi), for example, would be a soft nucleophile.

From other threads I've been reading, I get the feeling that it is something to do with what orbital is going to be forming the new bond, perhaps? In a recent thread on SN2 reactions, it was stated that hydrogen sulfide is a softer nucleophile than water, the difference being the 3p orbital involvement, rather than a 2p, I would guess.  

I also know that it has something to do with oxidation and reduction, something to the effect of soft acids are easily oxidized, and soft bases are easily reduced.

Something I am confused on is that I have seen H^- called a soft base, and that seems contradictory to the requirements that I was aware of, such as high polarizability to be soft. Same goes for RLi, I have seen it called a soft base as well.  

Thanks.

[Borek]

These are all approximated concepts, so deon't expect too formal definition.

Then my specialty is pH, not organic chemistry

[kkjc2]

From what I understand:
Hard nucleophiles favour a charge-directed interaction, so they have high charge-density, usually charged or highly polarised and small. Their orbitals do not necessarily overlap that well with the electrophile's accepting orbital, but charge attraction directs them and aids the reaction.

Soft nucleophiles favour an orbital interaction over charge. They are usually not particularly polarised species, but with large and available orbitals for nucleophilic interaction with the electrophile's accepting orbital.

Organolithium are very polarised, (Pauling's electronegativity: C 2.5; Li 1.0)
Charge would dominantly direct the reaction to a more charged centre (ie. the carbonyl carbon (+)C=O(-) in an a,b-unsaturated ketone) therefore yields the 1,2-addition product. The very negative carbon of the R-Li just get attracted to the rather positive carbon of the carbonyl.

Organocopper reagents are not so polarised as the RLi, (Pauling's electronegativity C 2.5; Cu 1.9); so energy wise, it is tending for better orbital interactions. Charge have less effect on this less polarised species.
In the a,b-unsaturated ketone, with the 4 p orbitals in a row system- the 3 pi MO, (which is the LUMO and is the one that interacts with the nucleophile) has a greater contribution from the 1 and 4 atoms - ie, the O and the beta carbon(predicted using the sin wave method); thus best orbital overlap is at the beta carbon not the carbonyl carbon.
Therefore organocopper reagents favours this interaction; giving the 1,4-conjugate addition product.

Thus, RLi are hard; RCu soft.

and in the other thread, H₂:S: has large orbitals, but charge of the lone pair are more spread out - therefore soft. H₂:O: has smaller orbitals, the electron density is high in these orbitals - therefore hard.

I don't know about hard and soft acids...

[Yggdrasil]

One aspect of the answer is that reactions with hard nucleophiles are under kinetic control while reactions with soft nucleophiles are under thermodynamic control.  Hard nucleophiles are fairly reactive species because of high charge density or a formal negative charge, so they will react with the substrate fairly quickly.  In this case, the molecule will simply react with whichever elecrophilic center is more accessible, in the case of an 2,3-unsaturated ketone, the carbonyl carbon.  Since the reaction occurs so quickly and irreversibly, the product is not necessarily the most stable product possible.  Thus, the reaction is dictated by the kinetics of the possible attacks, and not the thermodynamics of the possible products.

Soft nucleophiles, on the other hand, are less reactive so their reactions are less spontaneous and more reversible.  This allows the more thermodynamically stable product to be formed.  In the case of a 2,3-unsaturated ketone, the product of a Michael addition (1,4-addition) is more stable than the product of an attack on the carbonyl (1,2-addition).  Hence, the reaction is controlled by the thermodynamics of the possible product, not the kinetics of the possible attacks.

[FeLiXe]

to add a little bit:
I think hard/soft acid or base refers to the same thing as hard/soft electrophile or nucleophile. You can look at the reaction from a lewis acid/base point of few. Then the nucleophile is the electron pair donor, therefore a base and the electrophile the electron pair acceptor - the acid.