  We theoretically demonstrate a strong dependence of the annihilation rate
between (singlet) excitons on the sign of dipole-dipole couplings between
molecules. For molecular H-aggregates, where this sign is positive, the phase
relation of the delocalized two-exciton wavefunctions causes a destructive
interference in the annihilation probability. For J-aggregates, where this sign
is negative, the interference is constructive instead, as a result of which no
such coherent suppression of the annihilation rate occurs. As a consequence,
room temperature annihilation rates of typical H- and J-aggregates differ by a
factor of ~3, while an order of magnitude difference is found for
low-temperature aggregates with a low degree of disorder. These findings, which
explain experimental observations, reveal a fundamental principle underlying
exciton-exciton annihilation, with major implications for technological devices
and experimental studies involving high excitation densities.
