  In this work we revisit the classic problem of homogeneous nucleation of a
liquid droplet in a supersaturated vapor phase. We consider this at different
extents of the driving force, which here is the extent of supersaturation, and
calculate a reaction coordinate (RC) for nucleation as the driving force is
varied. The RC is constructed as a linear combination of three order
parameters, where one accounts for the number of liquid-like atoms, and the
other two for local density fluctuations. The RC is calculated from all-atom
biased and unbiased molecular dynamics (MD) simulations using the spectral gap
optimization approach "SGOOP" [P. Tiwary and B. J. Berne, Proc. Natl. Acad.
Sci. U. S. A. 113, 2839 (2016)]. Our key finding is that as the supersaturation
decreases, the RC ceases to simply be the number of liquid-like atoms, and
instead it becomes important to explicitly consider local density fluctuations
that correlate with shape and density variations in the nucleus. All three
order parameters are found to have similar barriers in their respective
potentials of mean force, however, as the supersaturation decreases the density
fluctuations decorrelate slower and thus carry longer memory. Thus at lower
supersaturations density fluctuations are non-Markovian and can not be simply
ignored from the RC by virtue of being noise. Finally, we use this optimized RC
to calculate nucleation rates in the infrequent metadynamics framework, and
show it leads to more accurate estimate of the nucleation rate with four orders
of magnitude acceleration relative to unbiased MD.
