  T.Kishimoto raised the problem to classify all compactifications of
contractible affine 3-folds into smooth Fano 3-folds with second Betti number
two and classified such compactifications whose log canonical divisors are not
nef. In this article, we show that there are 14 deformation equivalence classes
of smooth Fano 3-folds which can admit structures of such compactifications
whose log canonical divisors are trivial. We also construct an example of such
compactifications with trivial log canonical divisors for each of all the 14
classes.
