  The parity-violating energy difference (PVED) between two enantiomers of a
chiral molecule is caused by the weak interaction. Because of the smallness of
the PVED, nonzero PVED is yet to be discovered in experimental searches. To
detect the PVED, the search for molecules with large PVED values is important.
Previously, one of the authors proposed that the PVED may be significantly
enhanced in ionized or excited states. The significant enhancement of the PVED
in some electronic excited states is proven in this study using H$_2$X$_2$
(X=O, S, Se, Te) molecules as examples. The maximum enhancement was an about
360-fold increase for H$_2$Se$_2$. For the PVED calculation, we employ the
finite-field perturbation theory (FFPT) within the equation-of-motion
coupled-cluster theory based on the exact two-component molecular-mean field
Hamiltonian. The relation between the enhancement of the PVED and the
contribution to the PVED from the highest occupied molecular orbital is also
examined. The effects of computational elements, such as parameters related to
the electron correlation and FFPT on PVED values in excited states of
H$_2$X$_2$ molecules are studied.
