Re: At the molecular (quantum) level, how does water evaporation occur?

Liquid water has a very complex structure and along with that structure
many modes of energy storage and exchange between those modes.  The 0.7 X
10^-19J that one gets by dividing the heat of vaporization by the number of
molecules present represents an average value for the energy needed to free
a single molecule from this web of interactions (primarily hydrogen bonding
in this case) and put it into the vapor state.  It does not represent some
kind of limiting value like the ionization potential for electron removal
from an atom however.  At a given instant a particular water molecule might
require more or less than this amount to free it from whatever
entanglements it has.  While it is possible a single photon could free a
molecule if absorbed on the surface layer it is much more probable that the
absorbed energy will be rapidly redistributed to the vibration, rotation,
and finally kinetic energy of the molecules.  Raising the kinetic energy is
of course what raises the temperature and gives a greater number of
molecules at the upper end of the Maxwell-Boltzman distribution having
enough energy to escape from the surface layer.  Note too that this energy
does not have to be absorbed at the surface to free the molecule but can be
absorbed anywhere in the body of water.  This rapid redistribution of
absorbed photon energy to other modes is exploited in the microwave oven. 
Microwave photons on the order of 10^-24J are readily absorbed because they
match the rotational excitation energy spacing.  This energy is quickly
transferred to kinetic energy as the molecules interact with one another. 
Similar transfers happen with the absorption of infrared light which tends
to excite vibration modes.  Our 0.7 X 10^-19J photon falls into the
infrared part of the electromagnetic spectrum.  Visible light, like the
green photon, typically excites electronic levels.  It turns out water is
pretty good at the radiationless transfer of this electronic excitation
energy to vibration, rotation and kinetic forms as well. So in short while
it is conceivable that photons with energy in excess of 0.7 X 10^-19J could
directly free a molecule if absorbed at the surface the molecule would have
to do so by somehow converting all this electrical excitation directly to
kinetic energy by interacting with neighboring molecules and this is
nowhere nearly as likely as having the energy absorbed into the bulk of the
sample.  We should also note that water evaporates in the dark as well as
in the light so light absorption at the surface is apparently not a major
factor.