Upon still further study, now I'm even more confused.
I'll re-display the picture below for everybody's convenience.
Since two atoms must be added to the top row, and one to the bottom row, and none to any other rows, AND
since two atoms must be added to the first column, and one to the third column, and none to any other columns, it follows that atoms must be added at r1c1, r1c3, and r5c1.
Now, what about the bonds?
The top row needs three new bonds, so that's easy: r1c1-r1c2, r1c2-r1c3, and r1c3-r1c4.
The bottom row needs two new bonds, so that's easy too: r5c1-r5c2, and r5c2-r5c4. But the latter is a non-adjacent bond. That requires me to further modify my original assumptions. Apparently, bonds don't have to be between two adjacent atoms, as long as there are no other atoms between the two in the same row (or column).
That takes care of the horizontal bonds.
Vertically, everything is already OK, except in the leftmost column, which needs two new bonds. These could be r1c1-r2c1 and r4c1-r5c1. But r2c1-r4c1 is also a legal bond, at least if non-adjacent vertical bonds are allowed, in the same way that non-adjacent horizontal bonds are apparently allowed (judging by the previously mentioned r5c2-r5c4).
Thus, the puzzle apparently has multiple solutions, which is a definite NO-NO
in the puzzle business (whether sudoku, kakuro, or any other puzzle).
On top of that, the resulting solution is not connected. The rightmost column is isolated from the rest of the puzzle. That's a peculiar molecule!
And, there are circles (benzene-ring-type configurations) in all the solutions.
It seems to me, it ought to be back to the drawing board for this type of puzzle, or at least for this example. The improved version should also include a clarification of the rules.