  Aromatic B-series were introduced as an extension of standard Butcher-series
for the study of volume-preserving integrators. It was proven with their help
that the only volume-preserving B-series method is the exact flow of the
differential equation. The question was raised whether there exists a
volume-preserving integrator that can be expanded as an aromatic B-series. In
this work, we introduce a new algebraic tool, called the aromatic bicomplex,
similar to the variational bicomplex in variational calculus. We prove the
exactness of this bicomplex and use it to describe explicitly the key object in
the study of volume-preserving integrators: the aromatic forms of vanishing
divergence. The analysis provides us with a handful of new tools to study
aromatic B-series, gives insights on the process of integration by parts of
trees, and allows to describe explicitly the aromatic B-series of a
volume-preserving integrator. In particular, we conclude that an aromatic
Runge-Kutta method cannot preserve volume.
