What elements in "Rappaccini's Daughter" characterize the romantic movement?
It is worth remembering that Hawthorne was actually known as a Dark Romantic, which means that his fiction focuses on the dark side of Romanticism rather than skylarks and the beauty of nature. Dark Romantics used their fiction to paint a far gloomier picture of the world that sought to expose the psychological complexities of humanity and the evil that is in each and every one of us.
We can see this theme present in this story through the way in which Giovanni identifies evil in Beatrice, who is poisoned by her father with the various plants that he grows. Note the way in which Giovani both sees Beatrice as being "beautiful" and "inexpressibly terrible." He later in the story refers to her as a "poisonous thing" and fears that she has contaminated him, turning him into "as hateful, as ugly, as loathsome and deadly a creature" as he feels she is. It is his drive to attain goodness for her that ironically leads to her death. His hopes of "redeeming" her actually result in the loss of her own life. There are many similarities with this short story and "The Birthmark," another story by Hawthorne, where similarly a woman with a blemish finds that the man in her life wants it removed, only taking her life in the process.
The "poison" in Beatrice suggests that there is good and evil in all of us. Giovanni is unable to accept the presence of evil in humanity, and Beatrice is the human victim of his lack of understanding. This is a key theme of Dark Romanticism.
Within the romantic movement of literature, authors focused on emotion, imagination, and nature.
Throughout the story, Giovanni is caught up in his desire to be closer to Beatrice. He leads with his emotional heart rather than with his rational brain. He knows something is wrong with Beatrice and yet he cannot bring himself to stop seeing her.
Hawthorne makes it necessary for the reader, and Giovanni, to move beyond what is known to be true or what logically can happen. Instead, he requires that the reader accept certain elements of fantasy or imagination to move the story along. If the reader, or Giovanni, stopped to question whether Beatrice can truly possess "poison" the story would not be able to continue as the reader would be thinking concretely rather than imaginatively.
Much of "Rappaccini's Daughter" revolves around the use of nature descriptions to set the tone for the story. The setting surrounds Giovanni with glorious descriptions of the garden in which natural and hybrid plants exist. Hawthorne does not simply state that there is an overgrown garden, he describes every square foot of that garden so that the reader is lost in the vines, perfume, and sounds of the same garden that intrigues Giovanni.
Just as some Romantic writers were interested in portrayals of love and sublimity, some Romantic writers were interested in portrayals of other kinds of intense emotion: darker, rougher, or more evil emotion. Hawthorne, rather than focusing on the parts of humanity that seem to connect us with the divine, preferred to focus on the darker aspects of our nature, the aspects that might horrify or unnerve us to see laid bare.
We see, in Giovanni Guasconti, both an ability to love (or at least to feel something which is the "cunning semblance of love which flourishes in the imagination, but strikes no depth of root into the heart") as well as an ability to despise and destroy. Worse yet, he can despise and ultimately destroy the one he loves. One implication of the story is that this dark side of his nature, of human nature in fact, is the stronger of the two. At the very least, this darkness is bound up with our nature in such a way that we must cease to exist without it; this is why Beatrice cannot survive when she quaffs Professor Baglioni's "antidote" for her poisonousness. In focusing on human emotional intensity, as well as our connection to and with nature, Hawthorne writes a Romantic story.