I have read about a different variant of Atomic Chess in the book
'Alternatives Schach' by Lars Döring (german):
After a capture, the capturing piece and all pieces on the squares
orthogonally or diagonally adjacent to it are also removed, but with the
exception of the kings. A king may capture without being removed, and is
not removed when on a square adjacent to the capture.
A move may never put the King of the moving side into attack, neither
before nor after removing of pieces. So a king may never capture a
defended piece, even if the defending piece would also be removed.
In this variant, the initial advantage of white is much smaller.