Mark E. Tuckerman

Reversible multiple time scale molecular dynamics

The Trotter factorization of the Liouville propagator is used to generate new reversible molecular dynamics integrators. This strategy is applied to derive reversible reference system propagator algorithms (RESPA) that greatly accelerate simulations of systems with a separation of time scales or with long range forces. The new algorithms have all of the advantages of previous RESPA integrators but are reversible, and more stable than those methods. These methods are applied to a set of paradigmatic systems and are shown to be superior to earlier methods. It is shown how the new RESPA methods are related to predictor–corrector integrators. Finally, we show how these methods can be used to accelerate the integration of the equations of motion of systems with Nose thermostats.

Nosé–Hoover chains: The canonical ensemble via continuous dynamics

Nose has derived a set of dynamical equations that can be shown to give canonically distributed positions and momenta provided the phase space average can be taken into the trajectory average, i.e., the system is ergodic [S. Nose, J. Chem. Phys. 81, 511 (1984), W. G. Hoover, Phys. Rev. A 31, 1695 (1985)]. Unfortunately, the Nose–Hoover dynamics is not ergodic for small or stiff systems. Here a modification of the dynamics is proposed which includes not a single thermostat variable but a chain of variables, Nose–Hoover chains. The ‘‘new’’ dynamics gives the canonical distribution where the simple formalism fails. In addition, the new method is easier to use than an extension [D. Kusnezov, A. Bulgac, and W. Bauer, Ann. Phys. 204, 155 (1990)] which also gives the canonical distribution for stiff cases.

The nature of the hydrated excess proton in water

Explanations for the anomalously high mobility of protons in liquid water began with Grotthusss idea, of ‘structural diffusion’ nearly two centuries ago. Subsequent explanations have refined this concept by invoking thermal hopping, , proton tunnelling, or solvation effects. More recently, two main structural models have emerged for the hydrated proton. Eigen, proposed the formation of an H9O4+ complex in which an H3O+ core is strongly hydrogen-bonded to three H2O molecules. Zundel, , meanwhile, supported the notion of an H5O2+ complex in which the proton isshared between two H2O molecules. Here we use ab initio path integral simulations to address this question. These simulations include time-independent equilibrium thermal and quantum fluctuations of all nuclei, and determine interatomic interactions from the electronic structure. We find that the hydrated proton forms a fluxional defect in the hydrogen-bonded network, with both H9O4+ and H5O2+ occurring only in thesense of ‘limiting’ or ‘ideal’ structures. The defect can become delocalized over several hydrogen bonds owing to quantum fluctuations. Solvent polarization induces a small barrier to proton transfer, which is washed out by zero-point motion. The proton can consequently be considered part of a ‘low-barrier hydrogen bond’, , in which tunnelling is negligible and the simplest concepts of transition-state theory do not apply. The rate of proton diffusion is determined by thermally induced hydrogen-bond breaking in the second solvation shell.

Explicit reversible integrators for extended systems dynamics

Explicit reversible integrators, suitable for use in large-scale computer simulations, are derived for extended systems generating the canonical and isothermal-isobaric ensembles. The new methods are compared with the standard implicit (iterative) integrators on some illustrative example problems. In addition, modification of the proposed algorithms for multiple time step integration is outlined.

The nature and transport mechanism of hydrated hydroxide ions in aqueous solution

Compared to other ions, protons (H+) and hydroxide ions (OH-) exhibit anomalously high mobilities in aqueous solutions. On a qualitative level, this behaviour has long been explained by ‘structural diffusion’—the continuous interconversion between hydration complexes driven by fluctuations in the solvation shell of the hydrated ions. Detailed investigations have led to a clear understanding of the proton transport mechanism at the molecular level. In contrast, hydroxide ion mobility in basic solutions has received far less attention, even though bases and base catalysis play important roles in many organic and biochemical reactions and in the chemical industry. The reason for this may be attributed to the century-old notion that a hydrated OH- can be regarded as a water molecule missing a proton, and that the transport mechanism of such a ‘proton hole’ can be inferred from that of an excess proton by simply reversing hydrogen bond polarities. However, recent studies have identified OH- hydration complexes that bear little structural similarity to proton hydration complexes. Here we report the solution structures and transport mechanisms of hydrated hydroxide, which we obtained from first-principles computer simulations that explicitly treat quantum and thermal fluctuations of all nuclei. We find that the transport mechanism, which differs significantly from the proton hole picture, involves an interplay between the previously identified hydration complexes and is strongly influenced by nuclear quantum effects.

Ab initio molecular dynamics simulation of the solvation and transport of hydronium and hydroxyl ions in water

Charge defects in water created by excess or missing protons appear in the form of solvated hydronium H3O+ and hydroxyl OH− ions. Using the method of ab initio molecular dynamics, we have investigated the structure and proton transfer dynamics of the solvation complexes, which embed the ions in the network of hydrogen bonds in the liquid. In our ab initio molecular dynamics approach, the interatomic forces are calculated each time step from the instantaneous electronic structure using density functional methods. All hydrogen atoms, including the excess proton, are treated as classical particles with the mass of a deuterium atom. For the H3O+ ion we find a dynamic solvation complex, which continuously fluctuates between a (H5O2)+ and a (H9O4)+ structure as a result of proton transfer. The OH− has a predominantly planar fourfold coordination forming a (H9O5)− complex. Occasionally this complex is transformed in a more open tetrahedral (H7O4)− structure. Proton transfer is observed only for the more waterlik...

A reciprocal space based method for treating long range interactions in ab initio and force-field-based calculations in clusters

A new reciprocal space based formalism for treating long range forces in clusters is presented. It will be shown how the new formalism can be incorporated into plane-wave based density function theory calculations, standard Ewald summation calculations, and smooth particle-mesh Ewald calculations to yield accurate and numerically efficient descriptions of long range interactions in cluster systems.

Efficient molecular dynamics and hybrid Monte Carlo algorithms for path integrals

New path integral molecular dynamics (PIMD) and path integral hybrid Monte Carlo (PIHMC) algorithms are developed. It is shown that the use of a simple noncanonical change of variables that naturally divides the quadratic part of the action into long and short wavelength modes and multiple time scale integration techniques results in very efficient algorithms. The PIMD method also employs a constant temperature MD technique that has been shown to give canonical averages even for stiff systems. The new methods are applied to the simple quantum mechanical harmonic oscillator and to electron solvation in fluid helium and xenon. Comparisons are made with PIMC and the more basic PIMD and PIHMC methods.

Aqueous basic solutions: hydroxide solvation, structural diffusion, and comparison to the hydrated proton

Many hydrogen-bonded liquids, molecular solids, and lowdimensional systems support anomalous diffusion mechanisms of topological charge defects created by the addition or removal of protons. The most familiar examples are the “classic” cases of aqueous acidic and basic solutions,1 where the defects appear in the form of hydrated hydronium (H3O) and hydroxide (OH-) ions, denoted as H+(aq) and OH-(aq), respectively.2 While anomalous charge migration has important consequences in chemical,1,3,4 biological,5-8 and technological9,10 applications, Vide infra, providing a molecular-level, mechanistic understanding of the fascinating physical principles underlying the charge transport process is a challenging, yet fundamental, problem in physical chemistry.11

Efficient and general algorithms for path integral Car–Parrinello molecular dynamics

In path integral molecular dynamics, efficient sampling of the phase space is not guaranteed due to the stiff harmonic part of the action arising from the quantum kinetic energy. This problem has been eliminated by incorporating a sufficient number of thermostats into the dynamical scheme and by introducing a transformation of the path ‘‘bead’’ variables. In this paper, an efficient Car–Parrinello path integral molecular dynamics algorithm, sufficiently general to include the use of ultrasoft pseudopotentials is introduced. Difficulties encountered when combining thermostats and transformations of the Cartesian ‘‘bead’’ coordinates with the generalized orthonormality condition are circumvented by employing a constrained nonorthogonal orbital method.