  Hybrid particle-field methods are computationally efficient approaches for
modelling soft matter systems. So far applications of these methodologies have
been limited to constant volume conditions. Here, we reformulate particle-field
interactions to represent systems coupled to constant external pressure. First,
we show that the commonly used particle-field energy functional can be modified
to model and parameterize the isotropic contributions to the pressure tensor
without interfering with the microscopic forces on the particles. Second, we
employ a square gradient particle-field interaction term to model non-isotropic
contributions to the pressure tensor, such as in surface tension phenomena.
This formulation is implemented within the hybrid particle-field molecular
dynamics approach and is tested on a series of model systems. Simulations of a
homogeneous water box demonstrate that it is possible to parameterize the
equation of state to reproduce any target density for a given external
pressure. Moreover, the same parameterization is transferable to systems of
similar coarse-grained mapping resolution. Finally, we evaluate the feasibility
of the proposed approach on coarse-grained models of phospholipids, finding
that the term between water and the lipid hydrocarbon tails is alone sufficient
to reproduce the experimental area per lipid in constant-pressure simulations,
and to produce a qualitatively correct lateral pressure profile.
