We develop a path-integral dynamics method for water that resembles centroid
molecular dynamics (CMD), except that the centroids are averages of
curvilinear, rather than cartesian, bead coordinates. The curvilinear
coordinates are used explicitly only when computing the potential of mean
force, the components of which are re-expressed in terms of cartesian
'quasi-centroids' (so-called because they are close to the cartesian
centroids). Cartesian equations of motion are obtained by making small
approximations to the quantum Boltzmann distribution. Simulations of the
infrared spectra of various water models over 150-600 K show these
approximations to be justified: for a two-dimensional OH-bond model, the
quasi-centroid molecular dynamics (QCMD) spectra lie close to the exact quantum
spectra, and almost on top of the Matsubara dynamics spectra; for gas-phase
water, the QCMD spectra are close to the exact quantum spectra; for liquid
water and ice (using the q-TIP4P/F surface), the QCMD spectra are close to the
CMD spectra at 600 K, and line up with the results of thermostatted
ring-polymer molecular dynamics and approximate quantum calculations at 300 and
150 K. The QCMD spectra show no sign of the CMD 'curvature problem' (of
erroneous red shifts and broadening). In the liquid and ice simulations, the
potential of mean force was evaluated on the fly by generalising an adiabatic
CMD algorithm to curvilinear coordinates; the full limit of adiabatic
separation needed to be taken, which made the QCMD calculations 8 times more
expensive than partially adiabatic CMD at 300 K, and 32 times at 150 K (and the
intensities may still not be converged at this temperature). The QCMD method is
probably generalisable to many other systems, provided collective
bead-coordinates can be identified that yield compact mean-field ring-polymer
distributions.Cambridge University Vice Chancellor's award