  A theoretical model for the effect of water hydrogen bonding on the
thermodynamics of hydrophobic hydration is proposed as a combination of the
classical density functional theory with the recently developed probabilistic
approach to water hydrogen bonding in the vicinity of a hydrophobic surface.
The former allows one to determine the distribution of water molecules in the
vicinity of a macroscopic hydrophobic particle and calculate the thermodynamic
quantities of hydrophobic hydration as well as their temperature dependence,
whereas the latter allows one to implement the effect of the hydrogen bonding
ability of water molecules on their interaction with the hydrophobic surface
into the DFT formalism. This effect arises because the number and energy of
hydrogen bonds that a water molecule forms near a hydrophobic surface differ
from their bulk values. Such an alteration gives rise to a hydrogen bond
contribution to the external potential field whereto a water molecule is
subjected in that vicinity. This contribution is shown to play a dominant role
in the interaction of a water molecule with the surface. Our approach predicts
that the free energy of hydration of a planar hydrophobic surface in a model
liquid water decreases with increasing temperature in the range from 293 K to
333 K. This result is indirectly supported by the counter-intuitive
experimental observation that under some conditions the hydration of a
molecular hydrophobe is entropically favorable as well as by the molecular
dynamics simulations predicting positive hydration entropy for sufficiently
large (nanoscale) hydrophobes.
