[talanum1 (OP)]

For a transition, for example, an electron in an atom: the quantum mechanical wisdom is that a single photon is emitted, that has energy the energy difference of the two energy levels.

I wonder if the same transition can be described by the emittance of two photons at the same time. One to accelerate the electron and one to decelerate it again. Then the overall effect is one photon in which the frequency of the two photons sums together. In this case, there must be negative frequency.

[Bored chemist]

No
A photon has angular momentum.
The transitions that happen are only possible when there's also a change in angular momentum of the atom or its electrons.

If you had two photons the momentum wouldn't be conserved.
https://en.wikipedia.org/wiki/Selection_rule#Angular_momentum
Having said that, there are two photon transitions; but they are much less probable and the probability of absorption is proportional to the square of the intensity of the light.
https://en.wikipedia.org/wiki/Two-photon_absorption