The "unintentional" form is more accurately, "unintentional/unexpected." It covers accidents and surprises, particularly (though not necessarily) unpleasant surprises.
The "attempted" form implies that the action is either unseccessful or of undetermined success. It can be used to express either failure or uncertainty.
For example, when would you use each form with a verb like meli (to love)?
Let's say you meet a girl. She's pretty, she's got a great sense of humor, she shares some of your interests, and you fall in love with her. You would use the neutral/intentional form, because while you weren't intentionally trying to fall in love, it's not a surprising or unwelcome event.
Now, if you were to fall in love with your best friend's girlfriend, you would use the unintentional/unexpected form, because it's something you don't want to happen and may even be actively trying to prevent.
On the other hand if you were to meet someone who you did not consider your type, but end up falling for them anyway, you might still use the unintentional/unexpected form, because it's a surprise, albeit a pleasant one.
The attempted form would be appropriate to use, for example, with regards to a cantankerous or ne'er-do-well family member or friend who makes it very difficult to love them.
I previously described the neutral form of verbs as, "intentional," but they should really be called, "neutral/intentional/expected." This mood covers actions done on purpose, as well as unsurprising events with no intentionality one way or another, or who's intentionality is unimportant.