Gothic themes can include horror, terror, the supernatural, spiritual, melancholy, and the imaginary. In "The Haunted Mind," the narrator contemplates a realm between sleep and being awake. He is fascinated with the space/time between dreams and the conscious life. It is magical to him. Likewise, he considers this in strict terms of time (temporal), when it is neither yesterday nor tomorrow. 

You have found an intermediate space, where the business of life does not intrude; where the passing moment lingers, and becomes truly the present a spot where Father Time, when he thinks nobody is watching him, sits down by the way side to take a breath. 

This is supernatural, transcendent, or metaphysical at least since it is a space/time that is out of or above time, a space where/when "mortals live on without growing older!" 

The narrator muses on staying in bed forever, perhaps trying to revel in the afterthoughts of his previous transcendent state. But then he segues from this concealed state in bed to the confinement of a grave. Here is the incursion of horror, another Gothic theme. Now, still in a slightly dreamlike wakefulness, he imagines or sees a funeral procession gliding passed (he says "your" - to the reader) his bed. This train comes with personified feelings of Disappointment, Fatality, and Remorse. 

He wakes out of this half asleep-half awake nightmare and then proceeds to attempt a more pleasant state induced by the soft breathing of someone he might sleep next to. Again, this is a (much more pleasant) state of the fine line between wakefulness and sleep. When he foresees deep sleep, he compares it to a temporary death and supposes the final death will be as calm. 

This story plays mostly with Gothic themes of dreams, appearance vs. reality, but also delves into death and nightmares. 

What are the elements of dark romanticism in Nathaniel Hawthorne's short story The Haunted Mind , mentioning the Gothic and supernatural elements ?

The narrator wakes up but then sinks into the covers and has a chill, not from cold, but from the idea of a frozen world outside. He retreats to the warmth of the bed. But this confinement makes him think of another confined and cold space: the grave. This is where the narrator's thoughts become dark, yet still romantic in that this is the product of his wild imagination. 

The imaginative or perhaps supernatural element occurs when he speculates about a funeral train gliding past the bed, dark thoughts in his mind, becoming visible in reality: "things of the mind become dim spectres to the eye." He notes his (or "your" addressing the reader) mourners. Ghosts, death, mourning, and terror: these are all Gothic elements. 

He considers his faults and regrets, personified, coming to life (or to visible form): "What if Remorse should assume the features of an injured friend?" He adds, "What if he should stand at your bed's foot, in the likeness of a corpse, with a bloody stain upon the shroud?" All of this is like a gloomy weight upon his soul. What began as a pleasant drifting into a dreamy state has turned into a morbid reflection on mortality and regret.