  Use of harmonic guiding potentials is the most common method for implementing
steered molecular dynamics (SMD) simulations, performed to obtain potentials of
mean force (PMFs) of molecular systems using non-equilibrium work (NEW)
theorems. Harmonic guiding potentials are also the natural choice in single
molecule force spectroscopy experiments. The stiff spring approximation (SSA)
of Schulten and coworkers enables to use the work performed along SMD
trajectories to obtain the PMF.
  We discuss and demonstrate how a high spring constant, k, required for the
validity of the SSA can violate another requirement of this theory, i.e., the
validity of Brownian dynamics of the system. Violation of the Brownian
condition results in the introduction of kinetic energy contributions to the
external work, performed during SMD simulations. These inertial effects result
in skewed work distributions, rather than the Gaussian distributions predicted
by SSA. The inertial effects also result in broader work distributions, which
worsen the effect of the skewness when calculating work averages. Remarkably,
our results strongly suggest that the skew and width of work distributions are
independent of the average drift velocity and physical asymmetries.
  The skew and broadening of work distributions result in biased estimation of
the PMF. The bias manifests itself in the form of a systematic error that
increases with simulation time. We discuss the proper upper limit for k, such
that the inertial effects are avoided. This limit, used together with the
relation for the lower limit of k, enables to conduct accurate steering while
satisfying the Brownian dynamics. Furthermore, we argue and demonstrate that
using the peak-value (rather than the statistical mean) of the work
distributions vastly reduces the bias in the calculated PMFs and improves the
accuracy.
