The ground states of small atoms and molecules, namely those of the hy
drogen, helium, and lithium atoms and the hydrogen molecular ion and h
ydrogen molecule, are studied in the presence of an external magnetic
field. For the one-electron systems the ground state is of the same sy
mmetry for arbitrary field strengths, and the corresponding binding en
ergy shows a monotonic increase with increasing field strength. More i
nteresting, the two- and three-electron systems show ground-state tran
sitions which involve both transitions in the spin multiplicity and sp
atial quantum numbers. An outlook on the expected cascade of transitio
ns in many electron atoms and molecules is provided. (C) 1998 John Wil
ey & Sons, Inc.