Aside from the fact that the establishment of "gun free zones" would have absolutely no effect on a person who is intent on criminal violence and merely subjects law-abiding citizens to unreasonable danger, I find that, in order to enact a regulation prohibiting the right of self-defense in public offices, there would have to be some Constitutional and legislative authority for doing so.  I have researched both the Constitution and the Code and can find none.  There is no immediate threat to life, limb, or property, and thus there are no grounds for proceeding on an emergency basis in enacting the proposed regulation.  The fact that the legislature has defined areas in which firearms may or may not be possessed, without having addressed whether or not public offices should be subject to such regulations represents a legislative decision to exclude such offices, and the Executive Branch lacks the authority to enact such regulations unilaterally.  Expressio unius alterius exclusio est.  See in particular, § 2.2-103.  Besides which it would be necessary to pay for armed security to ensure the safety of citizens in public facilities; if you take away the right of self-defense, you become an insurer of the safety of visitors, and will not be able to say the acts of violent criminals was a supervening cause obviating your negligent failure to protect.  Finally, enforcement of such a regulation would in of itself be unlawful.