Therefore the energy gap has to correspond to the frequency of the incident em waves to set up a resonance and couple in energy.
The appropriate question is why does light of any frequency excite free electrons in a metallic conductor. In this case there is no energy gap and em waves of smaller and smaller frequency still excite the free electrons. Also true as em wave intensity diminishes. Electrons continue to be excited even in the limit that the em wave intensity falls below one photon, so that only one photon at a time could be incident- that is assuming photons actually existed in the em waves.
But photons do not exist in the em waves. The waves can be plane and uniform- no bunching. It's either waves or particles. Where there are waves there are no particles(photons). Particles are how waves of different types interact, like em waves and electron waves in an atom. The solution of Schroedinger's equation for an atom yields electron waves. No sign of a particle whizzing around. The energy level of the waves are descrete. But that is no different from descrete energy levels of em waves in a cavity. But we do not call the descrete em energies in a cavity photons or particles. So we should not think of electrons as particles whizzing around inside the atom. They are also waves and they occupy all the space allotted them at the same time. It's not a probability wave. It is an actual wave.
When em waves encounter electron waves in an atom, we approximate the interaction mathematically and conceptually by thinking that it is the interaction of a photon with an electron. But that is just an approximation. In actuality, the then freed electron immediately goes into a wave again. Only when that electron interacts with another atom in its environment does it take on the properties of a particle, for an instant. For electron flow in a wire this happens so often that the wave never gets a chance to expand and the particle approximation is very accurate. But that is not true in an electron microscope or a double-slit experiment where the electron wave is perserved and interference effects are taken advantage of.
In summary, all particles exist most of the time as waves, not particles. The waves collapse into particles when they interact with other waves. But we do not as yet have a collapse theory that tells us what really happens in those cases. So the particle picture only happens for instants of time probably on the order of a Planck time. Most of the time every thing is waves. Since we can only detect or see particles, the waves are invisible to us. So most of the world is invisible to us. We see photons, but we do not see em waves.
Virtual particles are even less tangible. For example, a static field, electric or magnetic, is said to be composed of virtual particles by physicists. That is so absurd that its amazing that anyone believes it. A field is a field, not a particle, not ever a particle. It can be approximated mathematically as a particle, a zero frequency photon. And if mathematics is all that we can know for sure, then the probability that virtual particles exist is just as high as the probability that fields exist.
But lets use some common sense. I have watched a wire be moved by a field. It makes no sense to think of that process as a bunch of virtual zero-frequency photons hitting the wire. Especially when I can calculate exactly what the field strength is but have no idea how to calculate a virtual particle.
So good physics is simple physics. Fields are simple. The double slit experiment is simply understood as waves passing through both slits at the same time, interferring, and then collapsing into photons that excite electrons at the detector. There is no need for photons in free space. If you think they exist, you are just confusing yourself.