With a simple Acknowledgement of Application letter such as this, there's no need to keep viable applicants in suspense.
Stop letting the best qualified candidates get away!
They've taken the time to fill out that long, arduous application along with a detailed previous employment history, and signed copies of letter of recommendation.
The least you can do is acknowledge that you've received all necessary information to proceed to the next step in the hiring process.
Affirm their interest with your company and your interest in them by using this letter.
It's both effective and expedient.
Here's the template.
To: ___ [Applicant]___
We appreciate your interest in being employed by our firm.
We regret to inform you, however, that the available position[s] has been filled, and we cannot give your application further consideration at the present time.
Your application will be kept on file for future reference should an opening arise.