If you've already sent the letter, you should immediately bring both it and your entire separation agreement to an employment lawyer in your area. If you haven't already sent it, why would you want to take on that risk?
Very, very generally, these clauses typically refer to those statements which are untrue or would diminish the company's reputation or ability to do business... but you should not rely on this or take it as permission.
I'm a lawyer, but I'm not your lawyer unless we sign an agreement. While my practice involves a wide array of national and international issues, I am licensed only in Louisiana- where the legal system can be unique. The brief informational response provided here is not a substitute for legal advice, and you may need to act promptly to preserve your rights.
If you are worried that it would be a violation, then why write the letter.
You need to move on with your life.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.
Although you did not specify what your private letter to your former boss would contain, I am going to assume that it will not be complimentary. If the letter will contain negative or disparaging comments, I would avoid sending it. Is whatever you want to say to your former boss worth jeopardizing all or part of the money your former employer paid you? In most instances, that answer is no.