What is the purpose of Macbeth's letter to his wife? (Act 1, scene v)

In Shakespeare's Macbeth, there is a
clear purpose to the letter our "hero" sends to his
wife.

Macbeth, first and foremost, has wondrous news to
tell Lady Macbeth. First, he met witches who offered him predictions. One has already
come true, which means they will have more lands, money and honor in the King's court;
the other promises that he will be King, and she will be Queen one day—it seems obvious
he believes the old women after the first prediction came to be. In learning how excited
he is about being Scotland's sovereign, we get the briefest glimpse of his "vaulting
ambition"—his desire to become King that will eclipse everything else of value in his
life.

We learn that Macbeth and his wife are very close.
Not only because of how he addresses her, but also because he shares his news
immediately rather than letting her wait until he returns
home.

The third and perhaps most important purpose of the
letter is to see how Lady Macbeth reacts to this news. We come to see how hard and
calculating she is, and find that she worries that her husband is too kind to do what
must be done if they are to secure the throne for themselves: which means murdering the
King, for she sees no other way in which the crown can come to
Macbeth.

Then she wishes Macbeth home quickly so that she
can tell him what he needs to hear in order to do what he
must:

Hie thee
hither, that I may pour my spirits in thine ear. (I, v,
20-21)

It almost sounds as if
she is casting her own spell: come quickly so I can pour my evil intentions
("spirits") into your ear, so you won't hesitate to follow
through.

It could logically be argued that without Lady
Macbeth's encouragement, Macbeth might have been satisfied with the rewards he had been
given, and not kill the King: he says as much to his wife when he returns. In essence,
this letter galvanizes the plot forward at the hands of Lady Macbeth's
machinations.