We show that it is possible to control the dissociation energies of mo
lecules with an external magnetic field. We focus our interest on the
lowest dissociation channel for which the two atomic and/or molecular
products are formed in their ground state. The crucial requirement is
the paramagnetic character of at least one of the two dissociation pro
ducts. Then, an external magnetic field lowers the energy of the param
agnetic species in its lowest Zeeman component and, possibly, the corr
esponding energy of dissociation of the parent molecule. This it true
for diatomic molecules when at least one of the atoms has an odd numbe
r of electrons. This is also true for oxygen and phosphorus atoms whic
h have a P-3(2) ground state. The Zeeman energy shift of paramagnetic
species is always of the order of 1 cm(-1) per tesla. The main theoret
ical difficulty is to determine the correlation diagram existing betwe
en the bound states of the parent molecule and the states of the produ
cts, or equivalently, how the energy evolves as a function of the inte
rnuclear distance corresponding to the dissociation coordinate. Little
is known about this evolution, except for diatomic molecules, because
the large internuclear distances are difficult to observe experimenta
lly. The main part of the information come from ab initio calculations
. For diatomic molecules, the dissociation coordinate is also the uniq
ue internuclear distance while for polyatomic molecules, the potential
energy surface has 3N-6 coordinates and multidimensional effects shou
ld be considered. In any case, the singlet-triplet-quintet, etc... (or
doublet-quartet, etc...) interactions should play an important role i
n the correlation diagram because crossings are expected between singl
et and triplet potential energy curves (from short to long internuclea
r distances) and these interactions transform the crossings into antic
rossings. The specific examples of alkali diatomic molecules (Li-2, Na
-2, etc...), of NO2 and of (O-2)(2) are analyzed in details. (C) 1997
John Wiley & Sons, Inc.