I haven't been able to find my spouse for more than 3 years now. Can I run an Ad in the local paper here in TN in order to get a divorce. No children, no property. Just want to get a divorce.

What does the court/your lawyer say? Some states allow this, but some have very specific requirements for this type of divorce.

Some states also have laws regarding abandonment. Have you contacted an attorney to see what your options are?