I am a researcher in condensed-matter physics, and I recently started a research project with another professor, for which I hired a student for a six-month undergraduate internship. The student was under my supervision. During the internship she showed good motivation, but did not make any actual contribution to the progress of the project.
Finally, she started a Ph.D. with someone else. I personally took over the project, taking care of both technical and conceptual parts, which requires a lot of time and work.
I kindly invited her multiple times to double check some of my work, but she had not done anything on the project since the end of the internship.
In the past few months she started having an attitude that I find disturbing. She replies to emails once in a while, proposing new conceptual points to explore, as if I were the student and she was the supervisor. On top of that, she ignores the invitations to double check my calculations, which would require actual work on her side.
Given that she did not make any actual contribution to the project, I am inclined to not include her as an author of any eventual publication. I think that it would be definitely fair to include her in the acknowledgments, but unfair to include her as an author.
What do you think about this? How would you inform her of this decision?