Centroid path integral molecular dynamics simulation of lithium para-hydrogen clusters

Quantum polyamorphism in compressed distinguishable helium-4

We demonstrate that two amorphous solid states can exist in ⁴He consisting of distinguishable Boltzmann atoms under compressed conditions. The isothermal compression of normal or supercritical fluid ⁴He was conducted at 3-25 K using the isobaric-isothermal path integral centroid molecular dynamics simulation. The compression of fluid first produced the low-dispersion amorphous (LDA) state possessing modest extension of atomic necklaces. Further isothermal compression up to the order of 10 kbar to 1 Mbar or an isobaric cooling of LDA induced the transition to the high-dispersion amorphous (HDA) state. The HDA was characterized by long quantum wavelengths of atoms extended over several Angstroms and the promotion of atomic residual diffusion. They were related to the quantum tunneling of atoms bestriding the potential saddle points in this glass. The change in pressure or temperature induced the LDA-HDA transition reversibly with hysteresis, while it resembled the coil-globule transition of classical polymers. The HDA had lower kinetic and higher Gibbs free energies than the LDA at close temperature. The HDA was absent at T ≥ 13 K, while the LDA-HDA transition pressure significantly decreased with lowering temperature. The LDA and HDA correspond to the trapped and tunneling regimes proposed by Markland et al. [J. Chem. Phys. 136, 074511 (2012)], respectively. The same reentrant behavior as they found was observed for the expansion factor of the quantum wavelength as well as for atomic diffusivity.

Another Look at the Mechanisms of Hydride Transfer Enzymes with Quantum and Classical Transition Path Sampling

The mechanisms involved in enzymatic hydride transfer have been studied for years, but questions remain due, in part, to the difficulty of probing the effects of protein motion and hydrogen tunneling. In this study, we use transition path sampling (TPS) with normal mode centroid molecular dynamics (CMD) to calculate the barrier to hydride transfer in yeast alcohol dehydrogenase (YADH) and human heart lactate dehydrogenase (LDH). Calculation of the work applied to the hydride allowed for observation of the change in barrier height upon inclusion of quantum dynamics. Similar calculations were performed using deuterium as the transferring particle in order to approximate kinetic isotope effects (KIEs). The change in barrier height in YADH is indicative of a zero-point energy (ZPE) contribution and is evidence that catalysis occurs via a protein compression that mediates a near-barrierless hydride transfer. Calculation of the KIE using the difference in barrier height between the hydride and deuteride agreed well with experimental results.

Approximate inclusion of quantum effects in transition path sampling

We propose a method for incorporating nuclear quantum effects in transition path sampling studies of systems that consist of a few degrees of freedom that must be treated quantum mechanically, while the rest are classical-like. We used the normal mode centroid method to describe the quantum subsystem, which is a method that is not CPU intensive but still reasonably accurate. We applied this mixed centroid/classical transition path sampling method to a model system that has nontrivial quantum behavior, and showed that it can capture the correct quantum dynamical features.

Nuclear quantum effects on an enzyme-catalyzed reaction with reaction path potential: proton transfer in triosephosphate isomerase

Nuclear quantum mechanical effects have been examined for the proton transfer reaction catalyzed by triosephosphate isomerase, with the normal mode centroid path integral molecular dynamics based on the potential energy surface from the recently developed reaction path potential method. In the simulation, the primary and secondary hydrogens and the C and O atoms involving bond forming and bond breaking were treated quantum mechanically, while all other atoms were dealt classical mechanically. The quantum mechanical activation free energy and the primary kinetic isotope effects were examined. Because of the quantum mechanical effects in the proton transfer, the activation free energy was reduced by 2.3 kcal/mol in comparison with the classical one, which accelerates the rate of proton transfer by a factor of 47.5. The primary kinetic isotope effects of kH/kD and kH/kT were estimated to be 4.65 and 9.97, respectively, which are in agreement with the experimental value of 4+/-0.3 and 9. The corresponding Swain-Schadd exponent was predicted to be 3.01, less than the semiclassical limit value of 3.34, indicating that the quantum mechanical effects mainly arise from quantum vibrational motion rather than tunneling. The reaction path potential, in conjunction with the normal mode centroid molecular dynamics, is shown to be an efficient computational tool for investigating the quantum effects on enzymatic reactions involving proton transfer.

Quantum effect on the internal proton transfer and structural fluctuation in the H+ 5 cluster

The thermal equilibrium state of H+(5) is investigated by means of an ab initio path integral molecular dynamics (PIMD) method, in which degrees of freedom of both nuclei and electrons at finite temperature are quantized within the adiabatic approximation. The second-order Moller-Plesset force field has been employed for the present ab initio PIMD. At 5-200 K, H+(5) is shown to have the structure that the proton is surrounded by the two H(2) units without any exchange of an atom between the central proton and the H(2) unit. At 5 K, the quantum tunneling of the central proton occurs more easily when the distance between the two H(2) units is shortened. At the high temperature of 200 K, the central proton is more delocalized in space between the two H(2) units, with less correlation with the stretching of the distance between the two H(2) units. As for the rotation of the H(2) units around the C(2) axis of H+(5) , the dihedral angle distribution is homogeneous at all temperatures, suggesting that the two H(2) units freely rotate around the C(2) axis, while this quantum effect on the rotation of the H(2) units becomes more weakened with increasing temperature. The influence of the structural fluctuation of H+(5) on molecular orbital energies has been examined to conclude that the highest occupied molecular orbital-lowest unoccupied molecular orbital energy gap is largely reduced with the increase of temperature because of the spatial expansion of the whole cluster.

Inclusion of inversion symmetry in centroid molecular dynamics: a possible avenue to recover quantum coherence

Inversion symmetry is included in the operator formulation of the centroid molecular dynamics (CMD). This work involves the development of a symmetry-adapted CMD (SA-CMD), here particularly for symmetrization and antisymmetrization projections. A symmetry-adapted quasidensity operator, as defined by Blinov and Roy [J. Chem. Phys. 115, 7822 (2001)], is employed to obtain the centroid representation of quantum mechanical operators. Numerical examples are given for a single particle confined to one-dimensional symmetric quartic and symmetric double-well potentials. Two SA-CMD simulations are performed separately for both projections, and centroid position autocorrelation functions are obtained. For each projection, the quality of the approximation as well as the accuracy are similar to those of regular CMD. It is shown that individual trajectories from two separate SA-CMD simulations can be properly combined to recover trajectories for Boltzmann statistics. Position autocorrelation functions are compared to the exact quantum mechanical ones. This explicit account of inversion symmetry provides a qualitative improvement on the conventional CMD approach and allows the recovery of some quantum coherence.

A semiclassical generalized quantum master equation for an arbitrary system-bath coupling

The Nakajima-Zwanzig generalized quantum master equation (GQME) provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a, possibly anharmonic, quantum bath. In this equation, a memory kernel superoperator accounts for the influence of the bath on the dynamics of the system. In a previous paper [Q. Shi and E. Geva, J. Chem. Phys. 119, 12045 (2003)] we proposed a new approach to calculating the memory kernel, in the case of arbitrary system-bath coupling. Within this approach, the memory kernel is obtained by solving a set of two integral equations, which requires a new type of two-time system-dependent bath correlation functions as input. In the present paper, we consider the application of the linearized semiclassical (LSC) approximation for calculating those correlation functions, and subsequently the memory kernel. The new approach is tested on a benchmark spin-boson model. Application of the LSC approximation for calculating the relatively short-lived memory kernel, followed by a numerically exact solution of the GQME, is found to provide an accurate description of the relaxation dynamics. The success of the proposed LSC-GQME methodology is contrasted with the failure of both the direct application of the LSC approximation and the weak coupling treatment to provide an accurate description of the dynamics, for the same model, except at very short times. The feasibility of the new methodology to anharmonic systems is also demonstrated in the case of a two level system coupled to a chain of Lennard-Jones atoms.

Centroid molecular dynamics approach to the transport properties of liquid para-hydrogen over the wide temperature range

Fundamental transport properties of liquid para-hydrogen (p-H(2)), i.e., diffusion coefficients, thermal conductivity, shear viscosity, and bulk viscosity, have been evaluated by means of the path integral centroid molecular dynamics (CMD) calculations. These transport properties have been obtained over the wide temperature range, 14-32 K. Calculated values of the diffusion coefficients and the shear viscosity are in good agreement with the experimental values at all the investigated temperatures. Although a relatively large deviation is found for the thermal conductivity, the calculated values are less than three times the amount of the experimental values at any temperature. On the other hand, the classical molecular dynamics has led all the transport properties to much larger deviation. For the bulk viscosity of liquid p-H(2), which was never known from experiments, the present CMD has given a clear temperature dependence. In addition, from the comparison based on the principle of corresponding states, it has been shown that the marked deviation of the transport properties of liquid p-H(2) from the feature which is expected from the molecular parameters is due to the quantum effect.

Impurity-stimulated heterogeneous nucleation of supercooled H2 clusters

The sizes and mass spectra of large (N=1900-13,700 molecules) cold (approximately 3.1 K) H2 clusters have been measured after scattering from CO molecules. Cluster-size measurements after between 2 and 8 collisions indicate that 7% of the H2 molecules are evaporated. This loss agrees with calculations for the number of H2 molecules evaporated by the heat released in the transition from an initial liquid state to a final solid state. Even though heterogeneous nucleation is initiated after only a few collisions with CO molecules, the mass spectra show that additional captured CO molecules coagulate to form large CO clusters with up to n=11 molecules, suggesting that the outer layer is sufficiently liquidlike to facilitate mobility of the CO molecules. Since the calculated H2 cluster temperature (approximately 3.1 K) is below the superfluid transition temperature predicted for pH2 with density between 40% and 80% of the triple-point density, a shell-like region of low density near the cluster surface can be expected to be superfluid.

Ab initio centroid path integral molecular dynamics: Application to vibrational dynamics of diatomic molecular systems

An ab initio centroid molecular dynamics (CMD) method is developed by combining the CMD method with the ab initio molecular orbital method. The ab initio CMD method is applied to vibrational dynamics of diatomic molecules, H2 and HF. For the H2 molecule, the temperature dependence of the peak frequency of the vibrational spectral density is investigated. The results are compared with those obtained by the ab initio classical molecular dynamics method and exact quantum mechanical treatment. It is shown that the vibrational frequency obtained from the ab initio CMD approaches the exact first excitation frequency as the temperature lowers. For the HF molecule, the position autocorrelation function is also analyzed in detail. The present CMD method is shown to well reproduce the exact quantum result for the information on the vibrational properties of the system.

Evidence for Superfluidity in Para-Hydrogen Clusters Inside Helium-4 Droplets at 0.15 Kelvin

A linear carbonyl sulfide (OCS) molecule surrounded by 14 to 16 para-hydrogen (pH(2)) molecules, or similar numbers of ortho-deuterium (oD(2)) molecules, within large helium-4 ((4)He) droplets and inside mixed (4)He/(3)He droplets was investigated by infrared spectroscopy. In the pure (4)He droplets (0.38 kelvin), both systems exhibited spectral features that indicate the excitation of angular momentum around the OCS axis. In the colder (4)He/(3)He droplets (0.15 kelvin), these features remained in the oD(2) cluster spectra but disappeared in the pH(2) spectra, indicating that the angular momentum is no longer excited. These results are consistent with the onset of superfluidity, thereby providing the first evidence for superfluidity in a liquid other than helium.

Quantum effects on liquid dynamics as evidenced by the presence of well-defined collective excitations in liquid para-hydrogen

The origin of the well-defined collective excitations found in liquid para-H2 by recent experiments is investigated. The persistence of their relatively long lifetimes down to microscopic scales is well accounted for by calculations carried out by means of path-integral-centroid molecular dynamics. In contrast only overdamped excitations are found in calculations carried within the classical limit. The results provide fully quantitative evidence of quantum effects on the dynamics of a simple liquid.