Halliday & Matthiessen (2014: 586-7):
Table 8-7 includes some verbal group nexuses with adjectival forms serving as the Event of the projecting verbal group: (i) desideration: be willing/keen/eager/anxious to do; (ii) fear: be afraid/scared to do. The forms afraid and scared are verbal in origin, but they function as adjectives now, as can be seen by the form taken by intensification (very rather than much): be very afraid/scared to do. Since these forms are adjectival, they are obviously anomalous as verbal groups. But they fit in systemically: they are agnate with verbal forms, and all the forms of the desiderative set are agnate expressions of modulation. We could try to push the analysis even further to include patterns with nominal forms such as (i) desideration: have a mind to do, and (ii) intention: make up one’s mind to do. But here we are really going beyond what can be accommodated within the verbal group since these constructions involve grammatical metaphor of the ideational kind.