Quantum effect induced kinetic molecular sieving of hydrogen and deuterium in microporous materials

We report here our investigations using Monte Carlo and molecular dynamics (MD) simulations, as well as quasi-elastic neutron scattering experiments, to study the adsorption and diffusion of H₂ and D₂ in zeolite Rho. In the simulations, quantum effects are incorporated via the Feynman-Hibbs variational approach. At low temperatures, we observe a reversal of kinetic molecular sieving in which D₂ diffuses faster than H₂. Based on fits of bulk data, we suggest new set of potential parameters for hydrogen, with the Feynman-Hibbs variational approach used for quantum corrections. The transport properties obtained from MD simulations are in excellent agreement with the experimental results, with both showing significant quantum effects on the transport at low temperature. The MD simulation results on two different structures of zeolite Rho clearly demonstrate that the quantum effect is very sensitive to pore size. High transport flux selectivity is noted at low temperatures, suggesting feasibility of kinetic isotope separation.     

Comment on "A centroid molecular dynamics study of liquid para hydrogen and ortho deuterium" [J. Chem. Phys. 121, 6412 (2004)

We show that the two phase points considered in the recent simulations of liquid para hydrogen by Hone and Voth lie in the liquid-vapor coexistence region of a purely classical molecular dynamics simulation. By contrast, their phase point for ortho deuterium was in the one-phase liquid region for both classical and quantum simulations. These observations are used to account for their report that quantum mechanical effects enhance the diffusion in liquid para hydrogen and decrease it in ortho deuterium.(c) 2005 American Institute of Physics.     

On the direct calculation of the free energy of quantization for molecular systems in the condensed phase

Using the path integral formalism or the Feynman-Hibbs approach, various expressions for the free energy of quantization for a molecular system in the condensed phase can be derived. These lead to alternative methods to directly compute quantization free energies from molecular dynamics computer simulations, which were investigated with an eye to their practical use. For a test system of liquid neon, two methods are shown to be most efficient for a direct evaluation of the excess free energy of quantization. One of them makes use of path integral simulations in combination with a single-step free energy perturbation approach and was previously reported in the literature. The other method employs a Feynman-Hibbs effective Hamiltonian together with the thermodynamic integration formalism. However, both methods are found to give less accurate results for the excess free energy of quantization than the estimate obtained from explicit path integral calculations on the excess free energy of the neon liquid in the classical and quantum mechanical limit. Suggestions are made to make both methods more accurate.     

Quantum effects on hydrogen isotope adsorption on single-wall carbon nanohorns

H(2) and D(2) adsorption on single-wall carbon nanohorns (SWNHs) have been measured at 77 K, and the experimental data were compared with grand canonical Monte Carlo simulations for adsorption of these hydrogen isotopes on a model SWNH. Quantum effects were included in the simulations through the Feynman-Hibbs effective potential. The simulation predictions show good agreement with the experimental results and suggest that the hydrogen isotope adsorption at 77 K can be successfully explained with the use of the effective potential. According to the simulations, the hydrogen isotopes are preferentially adsorbed in the cone part of the SWNH with a strong potential field, and quantum effects cause the density of adsorbed H(2) inside the SWNH to be 8-26% smaller than that of D(2). The difference between H(2) and D(2) adsorption increases as pressure decreases because the quantum spreading of H(2), which is wider than that of D(2), is fairly effective at the narrow conical part of the SWNH model. These facts indicate that quantum effects on hydrogen adsorption depend on pore structures and are very important even at 77 K.     

Nuclear quantum and H/D isotope effects on three-centered bonding diborane: Path integral molecular dynamics simulations

Nuclear quantum and H/D isotope effects of bridging and terminal hydrogen atoms of diborane (B₂H₆) molecules were systematically studied by classical ab initio molecular dynamics (CLMD) and ab initio path integral molecular dynamics (PIMD) simulations with BHandHLYP/6-31++G** level of theory at room temperature (298.15 K). Calculated results clearly show that H/D isotope effect appears in the distribution of hydrogen (deuterium) of B₂H₆ (B₂D₆). Geometry of B₂H₆ also plays a significant role in the nuclear quantum effect proved by PIMD simulations, but slightly deviated from its equilibrium structure when simulated via CLMD simulation. The bond lengths between boron atoms R (B1 … B2) and the bridging hydrogen atoms R_HH (H_B1 … H_B2) of the B₂H₆ molecule obtained from PIMD simulations are slightly longer than those of the deuterated form of the diborane (B₂D₆) molecule. The principal component analysis (PCA) was also employed to distinguish the important modes of bridging hydrogen as related to the nuclear quantum and H/D isotope effects. The highest level of contribution obtained from PCA of PIMD simulations is bending, while various mixed vibrations with less contribution were also found. Therefore, the nuclear quantum and H/D isotope effects need to be taken into account for a better understanding of diborane geometry.     

Simulation of tunneling in enzyme catalysis by combining a biased propagation approach and the quantum classical path method: application to lipoxygenase

The ability of using wave function propagation approaches to simulate isotope effects in enzymes is explored, focusing on the large H/D kinetic isotope effect of soybean lipoxygenase-1 (SLO-1). The H/D kinetic isotope effect (KIE) is calculated as the ratio of the rate constants for hydrogen and deuterium transfer. The rate constants are calculated from the time course of the H and D nuclear wave functions. The propagations are done using one-dimensional proton potentials generated as sections from the full multidimensional surface of the reacting system in the protein. The sections are obtained during a classical empirical valence bond (EVB) molecular dynamics simulation of SLO-1. Since the propagations require an extremely long time for treating realistic activation barriers, it is essential to use an effective biasing approach. Thus, we develop here an approach that uses the classical quantum path (QCP) method to evaluate the quantum free energy change associated with the biasing potential. This approach provides an interesting alternative to full QCP simulations and to other current approaches for simulating isotope effects in proteins. In particular, this approach can be used to evaluate the quantum mechanical transmission factor or other dynamical effects, while still obtaining reliable quantized activation free energies due to the QCP correction.     

An accurate and simple quantum model for liquid water

The path-integral molecular dynamics and centroid molecular dynamics methods have been applied to investigate the behavior of liquid water at ambient conditions starting from a recently developed simple point charge/flexible (SPC/Fw) model. Several quantum structural, thermodynamic, and dynamical properties have been computed and compared to the corresponding classical values, as well as to the available experimental data. The path-integral molecular dynamics simulations show that the inclusion of quantum effects results in a less structured liquid with a reduced amount of hydrogen bonding in comparison to its classical analog. The nuclear quantization also leads to a smaller dielectric constant and a larger diffusion coefficient relative to the corresponding classical values. Collective and single molecule time correlation functions show a faster decay than their classical counterparts. Good agreement with the experimental measurements in the low-frequency region is obtained for the quantum infrared spectrum, which also shows a higher intensity and a redshift relative to its classical analog. A modification of the original parametrization of the SPC/Fw model is suggested and tested in order to construct an accurate quantum model, called q-SPC/Fw, for liquid water. The quantum results for several thermodynamic and dynamical properties computed with the new model are shown to be in a significantly better agreement with the experimental data. Finally, a force-matching approach was applied to the q-SPC/Fw model to derive an effective quantum force field for liquid water in which the effects due to the nuclear quantization are explicitly distinguished from those due to the underlying molecular interactions. Thermodynamic and dynamical properties computed using standard classical simulations with this effective quantum potential are found in excellent agreement with those obtained from significantly more computationally demanding full centroid molecular dynamics simulations. The present results suggest that the inclusion of nuclear quantum effects into an empirical model for water enhances the ability of such model to faithfully represent experimental data, presumably through an increased ability of the model itself to capture realistic physical effects.     

Hydride transfer in liver alcohol dehydrogenase: quantum dynamics, kinetic isotope effects, and role of enzyme motion.

The quantum dynamics of the hydride transfer reaction catalyzed by liver alcohol dehydrogenase (LADH) are studied with real-time dynamical simulations including the motion of the entire solvated enzyme. The electronic quantum effects are incorporated with an empirical valence bond potential, and the nuclear quantum effects of the transferring hydrogen are incorporated with a mixed quantum/classical molecular dynamics method in which the transferring hydrogen nucleus is represented by a three-dimensional vibrational wave function. The equilibrium transition state theory rate constants are determined from the adiabatic quantum free energy profiles, which include the free energy of the zero point motion for the transferring nucleus. The nonequilibrium dynamical effects are determined by calculating the transmission coefficients with a reactive flux scheme based on real-time molecular dynamics with quantum transitions (MDQT) surface hopping trajectories. The values of nearly unity for these transmission coefficients imply that nonequilibrium dynamical effects such as barrier recrossings are not dominant for this reaction. The calculated deuterium and tritium kinetic isotope effects for the overall rate agree with experimental results. These simulations elucidate the fundamental nature of the nuclear quantum effects and provide evidence of hydrogen tunneling in the direction along the donor-acceptor axis. An analysis of the geometrical parameters during the equilibrium and nonequilibrium simulations provides insight into the relation between specific enzyme motions and enzyme activity. The donor-acceptor distance, the catalytic zinc-substrate oxygen distance, and the coenzyme (NAD(+)/NADH) ring angles are found to strongly impact the activation free energy barrier, while the donor-acceptor distance and one of the coenzyme ring angles are found to be correlated to the degree of barrier recrossing. The distance between VAL-203 and the reactive center is found to significantly impact the activation free energy but not the degree of barrier recrossing. This result indicates that the experimentally observed effect of mutating VAL-203 on the enzyme activity is due to the alteration of the equilibrium free energy difference between the transition state and the reactant rather than nonequilibrium dynamical factors. The promoting motion of VAL-203 is characterized in terms of steric interactions involving THR-178 and the coenzyme.     

Computation of the properties of liquid neon, methane, and gas helium at low temperature by the Feynman-Hibbs approach

The properties of liquid methane, liquid neon, and gas helium are calculated at low temperatures over a large range of pressure from the classical molecular-dynamics simulations. The molecular interactions are represented by the Lennard-Jones pair potentials supplemented by quantum corrections following the Feynman-Hibbs approach. The equations of state, diffusion, and shear viscosity coefficients are determined for neon at 45 K, helium at 80 K, and methane at 110 K. A comparison is made with the existing experimental data and for thermodynamical quantities, with results computed from quantum numerical simulations when they are available. The theoretical variation of the viscosity coefficient with pressure is in good agreement with the experimental data when the quantum corrections are taken into account, thus reducing considerably the 60% discrepancy between the simulations and experiments in the absence of these corrections.     

Accelerating the convergence of path integral dynamics with a generalized Langevin equation

The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.     

Hydrogen Bonding and Vaporization Thermodynamics in Hexafluoroisopropanol-Acetone and -Methanol Mixtures. A Joined Cluster Analysis and Molecular Dynamic Study

Binary mixtures of hexafluoroisopropanol with either methanol or acetone are analyzed via classical molecular dynamics simulations and quantum cluster equilibrium calculations. In particular, their populations and thermodynamic properties are investigated with the binary quantum cluster equilibrium method, using our in-house code Peacemaker 2.8, upgraded with temperature-dependent parameters. A novel approach, where the final density from classical molecular dynamics, has been used to generate the necessary reference isobars. The hydrogen bond network in both type of mixtures at molar fraction of hexafluoroisopropanol of 0.2, 0.5, and 0.8 respectively is investigated via the molecular dynamics trajectories and the cluster results. In particular, the populations show that mixed clusters are preferred in both systems even at 0.2 molar fractions of hexafluoroisopropanol. Enthalpies and entropies of vaporization are calculated for the neat and mixed systems and found to be in good agreement with experimental values.     

Proton-coupled electron transfer in soybean lipoxygenase: dynamical behavior and temperature dependence of kinetic isotope effects

The dynamical behavior and the temperature dependence of the kinetic isotope effects (KIEs) are examined for the proton-coupled electron transfer reaction catalyzed by the enzyme soybean lipoxygenase. The calculations are based on a vibronically nonadiabatic formulation that includes the quantum mechanical effects of the active electrons and the transferring proton, as well as the motions of all atoms in the complete solvated enzyme system. The rate constant is represented by the time integral of a probability flux correlation function that depends on the vibronic coupling and on time correlation functions of the energy gap and the proton donor-acceptor mode, which can be calculated from classical molecular dynamics simulations of the entire system. The dynamical behavior of the probability flux correlation function is dominated by the equilibrium protein and solvent motions and is not significantly influenced by the proton donor-acceptor motion. The magnitude of the overall rate is strongly influenced by the proton donor-acceptor frequency, the vibronic coupling, and the protein/solvent reorganization energy. The calculations reproduce the experimentally observed magnitude and temperature dependence of the KIE for the soybean lipoxygenase reaction without fitting any parameters directly to the experimental kinetic data. The temperature dependence of the KIE is determined predominantly by the proton donor-acceptor frequency and the distance dependence of the vibronic couplings for hydrogen and deuterium. The ratio of the overlaps of the hydrogen and deuterium vibrational wavefunctions strongly impacts the magnitude of the KIE but does not significantly influence its temperature dependence. For this enzyme reaction, the large magnitude of the KIE arises mainly from the dominance of tunneling between the ground vibronic states and the relatively large ratio of the overlaps between the corresponding hydrogen and deuterium vibrational wavefunctions. The weak temperature dependence of the KIE is due in part to the dominance of the local component of the proton donor-acceptor motion.     

Rigid quantum Monte Carlo simulations of condensed molecular matter: water clusters in the n=2-->8 range

The numerical advantage of quantum Monte Carlo simulations of rigid bodies relative to the flexible simulations is investigated for some simple systems. The results show that if high frequency modes in molecular condensed matter are predominantly in the ground state, the convergence of path integral simulations becomes nonuniform. Rigid body quantum parallel tempering simulations are necessary to accurately capture thermodynamic phenomena in the temperature range where the dynamics are influenced by intermolecular degrees of freedom; the stereographic projection path integral adapted for quantum simulations of asymmetric tops is a significantly more efficient strategy compared with Cartesian coordinate simulations for molecular condensed matter under these conditions. The reweighted random series approach for stereographic path integral Monte Carlo is refined and implemented for the quantum simulation of water clusters treated as an assembly of rigid asymmetric tops.     

Combined QM/MM and path integral simulations of kinetic isotope effects in the proton transfer reaction between nitroethane and acetate ion in water

An integrated Feynman path integral-free energy perturbation and umbrella sampling (PI-FEP/UM) method has been used to investigate the kinetic isotope effects (KIEs) in the proton transfer reaction between nitroethane and acetate ion in water. In the present study, both nuclear and electronic quantum effects are explicitly treated for the reacting system. The nuclear quantum effects are represented by bisection sampling centroid path integral simulations, while the potential energy surface is described by a combined quantum mechanical and molecular mechanical (QM/MM) potential. The accuracy essential for computing KIEs is achieved by a FEP technique that transforms the mass of a light isotope into a heavy one, which is equivalent to the perturbation of the coordinates for the path integral quasiparticle in the bisection sampling scheme. The PI-FEP/UM method is applied to the proton abstraction of nitroethane by acetate ion in water through molecular dynamics simulations. The rule of the geometric mean and the Swain-Schaad exponents for various isotopic substitutions at the primary and secondary sites have been examined. The computed total deuterium KIEs are in accord with experiments. It is found that the mixed isotopic Swain-Schaad exponents are very close to the semiclassical limits, suggesting that tunneling effects do not significantly affect this property for the reaction between nitroethane and acetate ion in aqueous solution.     

A structurally driven spectral transform Lanczos method for mixed quantum—classical canonical simulations (MQCC): the thermodynamics of Kr10–H and the energies of Krn–H, (n:1→9)

We develop and test an approximate approach for canonical simulations of weakly bound atomic or molecular systems for which some degrees of freedom can be treated separately by quantum mechanics. The system chosen for testing is Kr₁₀–H, for which the adiabatic approximation applied to separate the hydrogen degrees of freedom works reasonably well. The hydrogen atom is bound to the Kr clusters at cold temperatures and we calculate several bound states for clusters in the n=1–9 range, in the global minimum configuration. The structural character of the mixed quantum classical simulation is substantially different than the classical simulation for Kr₁₀–H as a result of zero point energy effects. When quantum effects are included, the low temperature dynamics of Kr₁₀–H are dominated by a significant well to well hopping about an incomplete icosahedral krypton core.     

Insights from first principles molecular dynamics studies toward infrared multiple-photon and single-photon action spectroscopy: case study of the proton-bound dimethyl ether dimer

We have used finite temperature ab initio molecular dynamics simulations in conjunction with computation of critical quantum nuclear effects to probe the differences between single-photon argon tagged action spectral results and infrared multiple-photon dissociation experiments for a proton bound molecular ion system. We find that the principal difference between the results in these experimental techniques is essentially that of cluster temperature. The multiple-photon dissociation experiments conducted using room temperature ions reflect a larger degree of conformational freedom compared to the colder single-photon argon tagged action spectral results. Our ab initio molecular dynamics simulation techniques accurately capture the effects of conformational sampling, adequately reproduce both spectra, and can be utilized to assign the dynamically averaged finite temperature spectra.     

Dynamics of the concerted triple proton transfer in cyclic water trimer using the multiconfiguration molecular mechanics algorithm

Cyclic water clusters are important molecular species to understand the nature of hydrogen bonded networks. Theoretical studies for the dynamics of triple proton transfer in the cyclic water trimer were performed. The potential energy surface (PES) of triple proton transfer is generated by the multiconfiguration molecular mechanics (MCMM) algorithm. We have used the MP2/6-31G(d,p) level for high-level ab initio data (energies, gradients, and Hessians), which are used in the Shepard interpolation. Eight high-level reference points were added step by step, including two points for the critical configurations of the large curvature tunneling paths. The more high-level points are used, the better the potential energy surfaces become. The rate constant and kinetic isotope effect (KIE) for the triple proton transfer at 300 K, which have been calculated by the canonical variational transition-state theory with microcanonical optimized multidimensional semiclassical tunneling approximation, are 1.6 x 10(-3) s(-1) and 230, respectively. Tunneling is very important not only for the triple proton transfer but also for the triple deuterium transfer. The MCMM results show good agreement with those from the direct ab initio dynamics calculations.     

Including quantum subsystem character within classical equilibrium simulations

A mixed quantum/classical density matrix approximation is derived. The density matrix makes use of quantum subsystem vibrational wave functions. The diagonal of the density matrix can be used as an equilibrium distribution in Monte Carlo simulations. The approximate distribution compares well with the path integral distribution for a model system. Since it includes quantum subsystem information, it performs much better than the quadratic Feynman-Hibbs distribution. These types of distributions can aid in including quantum vibrational information in otherwise classical simulations.