Semiempirical quantum chemical calculations have been performed using
cluster models for the acid sides of zeolite ZSM-5. The effects of lat
tice relaxation and oxygen protonation at T sites where Al has been su
bstituted for Si have been treated using 12 clusters containing about
100 atoms to represent the 12 distinct T sites. The calculations show
a wide range (1.2 eV) in the (Al,H)/Si substitution energies, but near
ly every site gives rise to at least one acid site whose energy is les
s than 0.2 eV from that of the lowest-energy T9 site. The calculations
also show that there exists a direct correlation between the substitu
tion energy and the proton affinity of a given site-those sites that e
xhibit the largest proton affinity are the ones for which the aluminum
is most stable. From comparing the most favorable location for a prot
on at each of the 12 T sites in ZSM-5, the proton affinities are found
to vary by 0.3 eV (29/kJ/mol). In addition, both the (Al,H)/Si substi
tution energy and the proton affinity depend on the geometric paramete
rs, such as bond lengths and angles, of the optimum configurations for
the acid sites. The most stable sites for protons correspond to ''por
e'' sites where the proton is oriented into the major pores of the zeo
lite lattice. The most important conclusion from this study is that th
ere is a direct relationship between the experimental T-O-T angle and
the proton affinity. This suggests that the T-O-T angle can be used as
a measure of the acidity of the site. This conclusion, although obtai
ned for the 48 sites of zeolite ZSM-5, would be expected to be transfe
rable to other zeolites.