We show on very general grounds that for a sufficiently high density o
f states (typically greater than or equal to 100 per cm(-1)) but low e
nough energy (so that chaos does not play a role) most quantum eigenst
ates of moderate sized valence-bonded molecules are likely to be deloc
alized by tunneling interactions between would-be localized states. On
e implication of this is that energy is essentially never trapped in l
ocalized modes or bonds in polyatomic molecules above a threshold ener
gy. Another implication is that spectroscopically prepared zero-order
states, which typically possess some local quality, will bear the impr
int of the tunneling and spawn narrow spectral clusters whose width is
characteristic of the tunneling.