The word "diverged' is one of the most important words that Frost uses to communicate the mood of the poem.
In a question like this, much of the answer is going to be dependent on how individuals look at word choice. Different readers will have various reactions to the impact such diction has on the reader. However, I think that "diverged" is essential to conveying the poem's atmosphere. The conditions of choice are brought out in being "diverged." "Diverged" reflects a separation. The implication is that individual choice plays a vital role in defining one's identity. It communicates the idea that only one path can be chosen. In emphasizing this incommensurability, the reader is reminded about how choices can be realities that make "all the difference."
"Diverged" is an important word in establishing vastness, as well. When the speaker comes upon the two roads and invokes the idea of how they diverge, it helps to emphasize how we cannot see past the choices we don't understand. The speaker is unable to see the end results of both roads. One is confronted with the immensity of decision in life. This is why they "diverged" and not merely "parted." When they "diverged" in the woods, there is a depth within the choices that we are forced to make. This helps to communicate feelings within the reader that contribute to the poem's undercurrent.