Path-integral dynamics of water using curvilinear centroids

Abstract

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 onthe-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.

Which quantum statistics–classical dynamics method is best for water?

“…When used to compute the IR spectrum of water, CMD gives redshifts and broadening in the stretch band, [40][41][42] and RPMD gives spurious resonances; 43 TPRMD damps out these resonances, but gives artificially broadened spectral lineshapes. 30 Recently, we developed a ring-polymer method, called quasi-centroid molecular dynamics (QCMD), 44 which appears to avoid most of these errors, by making a better mean-field approximation to Matsubara dynamics than CMD, without artificially damping the dynamics as in TRPMD. The QCMD method is expensive, but not prohibitively so, and has recently yielded IR spectra for liquid water and ice described by the simple q-TIP4P/F potential energy surface.…”

“…The QCMD spectra for gas-phase water are close to the exact quantum results, suggesting that the QCMD condensed phase spectra are of comparable quality. 44 Given these new developments, it is timely to ask which is better at describing the dynamics of liquid water and ice (and related systems): LSC-IVR, or ring-polymer methods such as QCMD? We present here new LSC-IVR spectra, computed for liquid water at 300 K and ice at 150 K, which are compared with recently calculated CMD, TRPMD and QCMD results from ref.…”

Inexpensive modeling of quantum dynamics using path integral generalized Langevin equation thermostats

“…Condensed phase systems can be studied [13] either by an exact treatment of the quantum dynamics of a subset of the nuclear degrees of freedom [14], or through classical dynamics on the quantum free energy surface of the nuclei [15,16]. Among the methods in the latter class, several of the most popular ones are based on the imaginary time path integral framework -such as (thermostatted) ring polymer molecular dynamics [17,18] ((T)RPMD), centroid molec- * venkat.kapil@epfl.ch ular dynamics [19,20] (CMD) and the recently developed quasi-centroid molecular dynamics [21] (QCMD). These methods ignore real time coherence but include effects arising from equilibrium quantum fluctuations and have been validated on several model systems and small molecules for which exact or highly accurate results are available [15,18,20,22].…”

“…Finally, we test the approach on condensed-phase systems. We begin by studying the IR spectrum of hexagonal ice at 150 K and liquid water at 300 K using the q-TIP4P/f water model [40] and a linear dipole moment surface, as used in a number of prior investigations [21,41,42]. The IR spectrum Cμμ(ω) is calculated using the autocorrelation of the time derivative of the instantaneous dipole moment of the system µ(t) and is normalized to integrate to unity.…”

“…We instead present results from QCMD simulations taken from Ref. [21]. As shown in the top and middle panels of Fig.…”