Gun free zones historically are actually Safety Zones for criminals, terrorists, and the like where they can do whatever damage they intend to do without the threat of being impeded by anyone until law enforcement responds to a call for help.  The response time is typically 10 minutes or more before law enforcement can arrive to address the situation.  In the meantime, state employees and law abiding citizens are unprotected targets.
This proposed regulation flies in the face of the 2nd Amendment to the U.S. Constitution, the Virginia Constitution, and just as importantly in the face of common sense.
Governor, if you would, kindly explain exactly what event at what state executive facility precipitated your coming to the conclusion that this proposed regulation is justifiably necessary for the safety of the public.
I seriously doubt that you can do this, which leads to the conclusion that your motivation is strictly political. The citizens of the Commonwealth deserve better.