Supplementary Material
Local orientational entropy S  in terms of density
We show that Eq 3 for the local orientational entropy,
S  (r ) 
k B
g sw ( | r ) ln g sw ( | r )d
8 2 
can be written in terms of the orientational probability density, r (w | r) , instead of
the orientational distribution, g(w | r). Since the relationship between g(w | r) and
the orientational density r (w | r) is:
gsw (w | r) º r(w | r) / rwo ,
where 1/ (8p 2 ) = rwo is the orientational density of a uniform orientational
distribution, we can rewrite S  in term of r (w | r) as:
S  (r )  k B   ( | r ) ln 8 2  ( | r ) d
  k B   ( | r ) ln   ( | r ) d  k B   ( | r ) ln 8 2 d
  k B   ( | r ) ln   ( | r ) d  k B ln  8 2    ( | r )d
However, r (w | r) is normalized, so its integral
( ò r(w | r)dw ) equals unity. Hence,
S  is simply
S  (r )  k B   ( | r ) ln   ( | r )d  k B ln  8 2 
where the second term on the right signifies the orientational entropy of the
uniform orientational distribution of a water molecule in the bulk:
-kB ò r wo ln( r wo )dw =
kB
kB ln(8p 2 )
2
ln(8
p
)
d
w
=
dw =kB ln(8p 2 ) .
2 ò
2
ò
8p
8p
Hence,
S  (r )  k B   ( | r ) ln   ( | r) d  k B  o lno d .
Definition of water Euler angles
Figure S1. Definition of water Euler angles. The lab coordinate frame is shown in black, and the water frame in
red. The water oxygen is at the origin.
We use the x-convention77 to define the Euler angles of a water molecule’s internal
coordinate frame relative to the grid’s coordinate frame (see Figure). A water
molecule’s X-axis is defined as the vector from its oxygen atom to one of its
hydrogen atoms. Its Z-axis is then defined as perpendicular to the X-axis and the HO-H plane, and its Y-axis is perpendicular to the X- and Z-axes. The line of nodes
(vector N in Figure S1), is the line where the XY planes of the rotating and fixed
frames of reference meet, and it is perpendicular to the Z-axes of both frames. The
angle q is the angle between the two Z-axes, while f and y are the angles between
the line of nodes and the fixed-frame X-axis and the water-frame X axis, respectively.
Molecular dynamics methods
Force-field parameters of the synthetic host molecule cucurbit[7]uril (CB7) (Error!
Reference source not found.) were generated as follows. Partial charges were
computed with the program RESP78, part of AMBER 1164, based on electronic
structure calculations at the 6-31G* level with the program Gaussian 2003. The
remaining parameters were assigned from the GAFF79 force field, with the
AmberTools program Leap. The circular host molecule, which is about 13Å in
diameter, was then computationally immersed in a 36Å x 39Å x 38Å box of preequilibrated TIP4PEW water molecules, using the program Leap. The resulting
system consisted of 126 solute atoms and 1699 water molecules. This initial system
was relaxed with 1500 cycles of steepest descent followed by 500 cycles of
conjugate gradient energy-minimization. The minimized system was then heated to
300K in steps of 50K, each lasting 20ps. The system was then equilibrated for 5ns at
300K. For the equilibration simulations, constant 1 atm pressure was maintained
with isotropic positional scaling and a relaxation time of 0.5 ps to ensure that the
system density remained appropriate. A 400ns NVT production run was then
carried out and trajectory frames for analysis were saved at 0.5 ps intervals. All
simulations were carried out with a pre-release graphical processor unit-enabled
version of the Amber 12 program PMEMD64,80,81 using Langevin dynamics82 at 300K
with a collision frequency of 2 ps-1, periodic boundary conditions, a nonbonded
cutoff distance of 8.0 Å coupled with Particle-Mesh Ewald long-ranged
electrostatics83, a time step of 2fs, and SHAKE84 for covalent bonds to hydrogen
atoms. Center-of-mass translation of the host was removed every 1000 steps to
keep the system centered.
Additional Figures
Figure S2. Number of water molecules within the CB7 cavity as a function of simulation time. Only 50 ns of the
longer simulation are plotted, so that transitions may be discerned.
Figure S3. Probability density functions of Euler angles for waters in various voxels. Left: a low orientational
entropy voxel near the carbonyl oxygens. Middle: a highly occupied voxel in the torus region for regular CB7.
Right: a highly occupied voxel in the toroidal region of for nonpolar CB7. Note that, for one angle, the x-axis
corresponds to cos(θ) instead of θ. All three distributions are flat for bulk water.
Figure S4. Convergence with simulation time of normalized water properties, as labeled, for the four regions
defined in text: Torus, Cavity, Torus Surface and Cavity Surface.