The correct answer is D. no article.
A, B, and C are incorrect because they are all definite articles. A definite article is used to refer to a specific person, place, thing, or idea that is already known to the reader or listener. In this case, the doctor is not a specific doctor that the reader or listener is already familiar with, so a definite article would not be appropriate.
The answer is no article because the doctor's smile is not a specific smile that the reader or listener is already familiar with. It is simply a friendly smile that the doctor has.
