Adjacent Sums

Place the numbers 1 thru 9 in a 3x3 grid such that every adjacent pair
(excluding diagonals) has a different sum.

Your first solution will not use three possible sums. Repeat #1, using
these sums.

What is the largest possible difference between two adjacent numbers
in the grid? Can you find solutions with this difference
to satisfy #1 and #2 above?
Source: Original.
Solution
Mail to Ken