accidentally
From LSJ
αὐτῇ τῇ ψυχῇ αὐτὴν τὴν ψυχὴν θεωροῦντα ἐξαίφνης ἀποθανόντος ἑκάστου → beholding with very soul the very soul of each immediately upon his death
by chance: P. and V. τύχῃ, P. ἐκ τύχης, κατὰ τύχην.
unintentionally: P. and V. ἀκουσίως; see unintentionally.