How is temperature related to quantum vibrational states of molecules? When a molecule of greenhouse gas absorbs a photon of long wave infrared radiation it is boosted to the next allowed vibrational state. The vibrational state, as I understand it, involves deformations of the chemical bonds between the atoms. Does that higher quantum vibrational state represent a temperature change? Does the absorption of IR directly warm the atmosphere? In a response on this forum Floris wrote:

"However, there are also absorption bands in the near-IR, at 1.4, 1.9, 2.0 and 2.1 µm (see Carbon Dioxide Absorption in the Near Infrared. These bands will absorb energy of the sun "on the way down", and result in atmospheric heating."

That implies that absorption of some radiation directly warms the atmosphere. Is that true?
Part of the problem is that I don't understand how different materials/media are warmed by electromagnetic radiation. I understand the concept of greenhouse gas molecules only being excited by photons that match the energy gap between allowed quantum states of the molecule. I also, somewhat, understand collisional broadening of absorption bands in that it must happen somewhat in conjunction with the collision and take advantage of the fact that collisional energy (kinetic energy) isn't quantized. But I'm not finding basic explanations of how different parts of the Sun's spectrum excites the different media of the Earth's surface to cause heating.
That's more background, however, although I'd like to eventually gain more understanding of what happens at the atomic and molecular level in that process. My main question is the stated one, does molecular absorption of radiation directly warm the atmosphere?
 A: As indicated by the link that rob posted in the comments to your question, by a strict definition of temperature rotational/vibrational energy of excited gas molecules do count as much as the translational energy of their movement. So yes, the temperature of the air will rise by definition simply by the act of absorbing IR radiation.
But let us consider what happens in a bit more detail: A single CO2 molecule will absorb a photon and then, after a certain time span reemit it. In a gas consisting of many CO2 molecules a single molecule will collide with other molecules; the average time between these collisions is, at least under the conditions of the lower atmosphere, much shorter than the average time between absorption and reemittance. When an excited molecule hits another one, this may lead to a conversion of the rotational/vibrational energy into translatorial energy and the molecule will move faster, i.e. thermalization occurs and the gas will get warmer (If we define temperature solely by the translational movements). This of course happens in the other direction too, i.e. a molecule may get excited when hit by another one, so very soon after the start of IR absorption the gas will settle into an equilibrium where there will be the same level of emission as there is of absorption according to Kirchhoffs law. The addition of non-greenhouse gases like N2 will result in the shifting of energy from the CO2 to the N2 gas component, which frees the CO2 molecules to increase absorption. 
So, in a nutshell, yes, the air will be warmed by the absorbed IR radiation but this does not lead to less emissions. 19th. century scientist John Tyndall compared the atmospheric greenhouse effect with a river that was dammed at a certain point; once the dammed lake was full and the water overflowing over the dam (e.g. equilibrium reached) the outflow of the water would be identical to the inflow, but neverteless the lake would be deeper and contain more water than other parts of the river. In the same way air can be warmer because of absorption of IR radiation but still emit as much radiation as it absorbs.
This answer helped me much to clarify my thinking about this issue: https://physics.stackexchange.com/a/67578/157769
You might also be interested in a closely related question of mine: Is there a difference in the infrared absorption spectrum of a greenhouse gas when pure and when mixed with non-greenhouse gases?
