What quotes are there to prove Macbeth is irrational?

Prior to the murder, Macbeth hallucinates a dagger, and he does actually recognize that it is a hallucination.  He calls it "a false creation, / Proceeding from the heat-oppressèd brain" (2.1.39-40).  Even in very stressful moments, it is not normal to hallucinate.  The hallucination, then, makes it seem as though Macbeth is no longer rational.

Then, after the murder, Macbeth flips out.  He feels like he heard a disembodied voice shouting out in his house, "'Glamis hath murdered sleep, and therefore Cawdor / Shall sleep no more. Macbeth shall sleep no more'" (2.2.42-43).  This is an irrational fear, to think that because he murdered someone while they were sleeping that he will no longer be able to sleep.  If anything prevents him from sleeping, it will most likely be guilt. 

Lady Macbeth realizes that Macbeth has brought the murder weapons out of the room with him instead of leaving them with the grooms they plan to frame, but Macbeth refuses to go back into the room with Duncan's body.  He says, "I’ll go no more: / I am afraid to think what I have done; / Look on ’t again I dare not" (2.2.50-53).  It is irrational to be willing to commit a brutal and bloody murder and yet not even be able to look at the body of the victim.  His qualms are seriously misplaced. 

Finally, he fears that if he plunged his hands into the ocean, the quantity of blood on them would turn the green sea red.  He wonders, "Will all great Neptune’s ocean wash this blood / Clean from my hand? No, this my hand will rather / The multitudinous seas incarnadine, / Making the green one red" (2.2.61-64).  Such a thought could simply be an exaggeration that he makes in order to express just how guilty and awful he feels, but even his wife has warned him against dwelling on what has occurred in order to preserve his own mental state.  She says, "These deeds must not be thought / After these ways. So, it will make us mad" (2.2.33-34).  Initially, at least, Macbeth is not able to take this advice, and he seems quite irrational both before and after the murder.