I tried communicationally, but the Free Dictionary doesn’t find it to be a word.
What I am trying to express is that someone is communicationally challenged, basically meaning they can’t communicate very well.
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Just because a term does not appear in this or that dictionary does not make it “not a word”. For one thing, the “Free Dictionary” falls short of being an accepted standard in the English language.
But for another, productive affixes like un- and -ly can be applied to virtually any word from the target class to produce a perfectly viable new word. So even if you were using a little dictionary that happened to be missing an headword for something like unceremoniously, no one would ever question it if you used it.
So with your particular case of
- communicate > communication
- communication > communicational
- communicational > communicationally
you certainly you could do so. However, whether you should be creating such septasyllabic monsters is something else again; you might well want to use a longer phrase here instead.
You could just say they don’t communicate well, or that they’re poor communicators. All those, and many others, seem an improvement over the ponderous communicationally challenged.
The most recent citation for communicationally
adv. as regards communication; in respect of communications
…in my copy of the OED is in the context of communicationally challenged:
2004 Daily Tel. (Sydney) (Nexis) 14 June 19 : Mind you, if men weren't so communicationally challenged we women might not be driven to such drastic measures.
This is probably no coincidence, since it is a snug fit with the snowclone pattern:
[problem area]-ly challenged
Depending on the context, though, you may also have the choice of using the word communicatively:
adv. In a communicative manner; by means of communication; as regards communication
Notice that there is quite a bit of overlap in the definitions of the two words, and this form is 16 times more common than communicationally in the COCA. Ngrams shows a similar disparity: