I'm writing a thank you letter for a technical position after the interview. I'm wondering if it's unprofessional to include additional explanations for a question that was asked in the interview; a question that we ran out of time to do. I know the explanation won't change the interview performance but my thought is that a quick explanation could clarify my thinking process and show dedication.
I don't think it would be unprofessional, but I do think it would be unorthodox and odd. If it were me I'd forego including it in your thank you letter.
I don't think most employers expect you to be perfect and without blemish in an interview. Everyone, including the interviewer, is nervous. If you think you did well with the exception of this one question, then let it go.
As a hiring manager, I would not like it.
It would indicate to me that your thank you email is not really to say thank you. It’s just an excuse to try to re-litigate your interview. I’d file away the email and think 10% worse of you. “Is this guy going to be a high maintenance complainer?” I’d think.
As a hiring manager, I've seen this done. If the answer the candidate includes is concise and complete, this can come across as someone who thought more about the problem given, which shows me they're interested in the position and the problem. I thought it reflected well upon the candidate. If the answer is long, meandering, or incomplete, it reflects worse upon the candidate. I've seen the second more often than the first in these follow-up answers.
However, if you ran out of time to answer the question, it's likely you didn't demonstrate a level of skill that the employer is looking for. I time my interviews such that an excellent candidate will finish with time to spare, a good candidate should get through all the questions, and I expect that an inexperienced candidate probably won't get through them all. It doesn't mean you can't solve the problem, but it means you haven't solved enough problems like that one to meet their level of experience.