Chemistry Reference
In-Depth Information
corresponds to a planar slit pore with a spacing of about 70
˚
. The second box
contains a bulk solvent reservoir and the third box a helium vapor phase (used as a
reference phase to deconstruct free energies of transfer into stationary and mobile
phase contributions). These two boxes are cubic and their volumes are allowed to
fluctuate in response to an external pressure bath (whereas the volume of the slit
pore is fixed).
The three simulation boxes are in thermodynamic contact through the exchange
of solvent and analyte molecules via CBMC particle transfer [
3
,
4
] and identity
exchange moves [
5
,
6
] (i.e., this move converts a molecule of type
A
into a molecule
of type
B
in one simulation box and concurrently converts
B
to
A
in another box)
that ensure that the chemical potential of these species is the same in all three boxes.
Exchange of solvent molecules is an extremely important aspect of the simulation
setup because there is no way to know, a priori, the correct amount of solvent
molecules to be placed in the stationary-phase box with its hydrophobic surfaces in
order to represent a given chromatographic condition (composition of the mobile
phase, temperature, and pressure). In addition, these particle transfer and exchange
moves allow for a much more efficient sampling of the spatial distribution of the
solvent and analyte molecules than could be achieved by simple translational
moves that mimic diffusive behavior. Precise information on the spatial distribution
allows for the calculation of distribution coefficients and free energies of transfer
between the mobile and stationary phase (the free energy of retention) from the
ratio of average analyte number densities in each phase:
RT
ln
r
b
D
G
a!b
¼
RT
ln
K
¼
r
a
;
(1)
where
r
i
is the number density of the species in phase
i.
The distribution coefficients
and free energies computed from the simulations can be directly compared with
experimental retention data to validate simulation results.
The coupled-decoupled CBMC method [
3
,
4
,
7
] selects trial configurations for a
stepwise growth of the trial molecule using a biased preselection process to find
favorable regions of phase space and, thereby, greatly increases the acceptance
rates for particle transfer and identity exchange moves. In addition, it allows for the
sampling of the conformational degrees of freedom of articulated molecules via
regrowing a part of the molecule that includes either one or multiple terminal
segments [
3
] or only interior segments [
8
]. The CBMC technique can also be
extended to utilize multiple energy scales. To enhance computational efficiency
for simulations using molecular mechanics force fields, the biased preselection of
configurations first generates a set of growth directions based on the bonded
interactions (e.g., bond stretching and angle bending) for which the cost of the
energy calculation depends only on the trial molecule and is independent of system
size. This is followed by a selection of a specific growth direction based on a less
expensive approximation of the nonbonded interactions (shorter cutoff and only
direct-space part of the Ewald sum), while the final acceptance of the move is based
on the full potential including a correction for the more expensive part of the
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