Neruda uses night and day as a major symbolic elements in "Tonight I Can Write."
As the poem progresses, the night becomes increasingly associated with the period of time when the narrator feels he loved a woman - the woman he writes about in the poem. (We might point out that the woman seems to be nearly symbolic herself and may represent an aspect of life or youth.)
We might take the night to symbolize love or the emotional coherence of the narrator's love. It is this that has been "shattered" and which feels "still more immense without her" as the narrator reflects on the scope of the love he once had for the woman.
Having lost the woman, the poet writes the lines of the poem and the "verse falls to the soul like dew to the pasture," suggesting that his sadness is connected to morning dew, daybreak or the night's end.
The poem's retrospection points to an idea that perhaps more than love has been lost by the narrator. Perhaps a way of being for the narrator has been lost as well.
The same night whitening the same trees.
We, of that time, are no longer the same.
Where the narrator once was able to love the woman while she only sometimes loved him, as he narrates the poem he feels that now he no longer loves her as he once did. His former fervor and dedication have turned to diffidence.
He now may love her, but not with certainty or clarity. The night has passed where that love lived/existed fully.