hard and soft acids and bases

To use the hard-soft principle you first need to know which acids and bases are hard and which are soft — and what 'hard' and 'soft' actually mean physically. The labels are not arbitrary; they describe how polarizable a species is, that is, how easily its electron cloud is distorted by a nearby charge. Hard means a tight, low-polarizability electron cloud; soft means a big, squishy, high-polarizability one. (Pearson built this on Schwarzenbach's older 'class a' and 'class b' metal classification.)

Hard acids are small, highly charged cations with no easily-distorted outer electrons: H+, Li+, Na+, K+, Be2+, Mg2+, Ca2+, Al3+, Cr3+, Fe3+, Co3+, and BF3, plus most s-block and early high-oxidation-state d-block ions. Hard bases are small, electronegative, weakly polarizable donors: F-, Cl-, OH-, O2-, NO3-, CO3 2-, SO4 2-, PO4 3-, H2O, NH3, ROH, and most O- and N-donors. Soft acids are large, low-charge, polarizable cations with filled or nearly-filled d shells: Ag+, Cu+, Au+, Hg2+, Hg2 2+, Cd2+, Pd2+, Pt2+, Tl+, and the metals in low oxidation states (including zero, as in metal carbonyls). Soft bases are large, polarizable, easily-oxidized donors: I-, H-, S2-, R2S, R3P, R3As, CN-, CO, SCN- (through S), and alkenes/arenes that donate pi electrons. Many species sit in between and are called borderline: Fe2+, Co2+, Ni2+, Cu2+, Zn2+, Pb2+ among acids; Br-, NO2-, SO3 2-, N3-, pyridine among bases.

Note the trends that generate the lists. Going down a group, donors and acceptors get softer (F < Cl < Br < I in softness; O < S < Se). Raising the oxidation state of a metal makes it harder (Fe2+ is borderline, Fe3+ is hard; Cu+ is soft, Cu2+ is borderline). This is why classification is not memorization for its own sake: once you see softness as 'large, polarizable, low charge' and hardness as 'small, non-polarizable, high charge,' you can place an unfamiliar ion yourself and then apply hard-with-hard, soft-with-soft to predict its chemistry.