No, you should definitely not write to the reviewers. Direct interaction between the author and the reviewers is not appreciated by journals as it goes against the confidentiality policy of the journal.
Additionally, you will not know the names of the reviewers to who are revieweing your manuscript. Even if a journal asks the authors to name a few preferred reviewers, it does not necessarily mean that the paper will be sent to the same reviewers. The selection of reviewers depends entirely on the editor. In fact, the paper might not have been sent to any of the reviewers whose name you have suggested. So there is no point in writing to the reviewers.
You should, in fact, keep sending emails to the journal every two to three weeks, asking about the status of the manuscript and requesting them to expedite the process.