Hybrid quantum/classical molecular dynamics for a proton transfer reaction coupled to a dissipative bath

A hybrid quantum/classical molecular dynamics approach is applied to a proton transfer reaction represented by a symmetric double well system coupled to a dissipative bath. In this approach, the proton is treated quantum mechanically and all bath modes are treated classically. The transition state theory rate constant is obtained from the potential of mean force, which is generated along a collective reaction coordinate with umbrella sampling techniques. The transmission coefficient, which accounts for dynamical recrossings of the dividing surface, is calculated with a reactive flux approach combined with the molecular dynamics with quantum transitions surface hopping method. The hybrid quantum/classical results agree well with numerically exact results in the spatial-diffusion-controlled regime, which is most relevant for proton transfer in proteins. This hybrid quantum/classical approach has already been shown to be computationally practical for studying proton transfer in large biological systems. These results have important implications for future applications to hydrogen transfer reactions in solution and proteins.     

Quantum/classical studies of vibrationally mediated photodissociation of Ar x H2O

Results of multiple configuration quantum/classical simulations of the dynamics of Ar x H2O photodissociation are reported. In agreement with experimental studies of Nesbitt and co-workers [J. Chem. Phys. 2000, 112, 7449], we find that the OH products emerge rotationally excited, compared to the dissociation of bare H2O. The wavelength dependence of the total cross section and the energy transfer to the argon atom are also investigated. The trends are interpreted in terms of features in the Ar x H2O A state potential surface.     

Classical and quantum studies of the photodissociation of a HX (X=Cl,F) molecule adsorbed on ice

The photodissociation dynamics of a HX (X = Cl,F) molecule adsorbed on a hexagonal ice surface at T = 0 K is studied using time-dependent quantum wave packets and quasiclassical trajectories. The relevant potential energy surfaces are calculated using high-level ab initio methods. We present here two dimensional calculations for the dynamics of the hydrogen photofragment for both HCl and HF molecules. The purpose of this paper is to compare the photodissociation dynamics of the two molecules which are adsorbed on the ice surface with different equilibrium geometries. The total photodissociation cross section and the angular distribution are calculated. The comparison with classical trajectory calculations provides evidence for typical quantum effects and reveals rainbow structures.     

Optimal laser control of ultrafast photodissociation of I2- in water: mixed quantum/classical molecular dynamics simulation

A linearized optimal control method in combination with mixed quantum/classical molecular dynamics simulation is used for numerically investigating the possibility of controlling photodissociation wave packets of I(2)(-) in water. Optimal pulses are designed using an ensemble of photodissociation samples, aiming at the creation of localized dissociation wave packets. Numerical results clearly show the effectiveness of the control although the control achievement is reduced with an increase in the internuclear distance associated with a target region. We introduce effective optimal pulses that are designed using a statistically averaged effective dissociation potential, and show that they semiquantitatively reproduce the control achievements calculated by using optimal pulses. The control mechanisms are interpreted from the time- and frequency-resolved spectra of the effective optimal pulses.     

Probing state-to-state reaction dynamics using H-atom Rydberg tagging time-of-flight spectroscopy

In the last decade or so, the H-atom Rydberg tagging time-of-flight (HRTOF) technique has made a significant impact in the study of state-to-state reaction dynamics, and especially in the study of transition state dynamics of elementary chemical reactions and quantum state resolved dynamics of molecular photodissociation of important molecules. In this perspective, we will discuss mainly the state-to-state dynamics of three important elementary reactions: H + H(2), O((1)D) + H(2) and F + H(2) that have been studied in our laboratory in recent years using the HRTOF method. In addition, we will also mention briefly the experimental results of other reactive systems. In the end, we will also present a brief research outlook in the study of molecular reaction dynamics using this powerful experimental method.     

小分子光解动力学的理论研究

光解过程是化学中的核心问题之一。量子态分辨的光解动力学可以使人们在原子与分子的层次上深刻理解光解反应的机制。态-态水平的光解动力学在过去四十年中取得了长足的进步,实验和理论的相互结合极大地促进了我们对光解反应本质的认识。本文综述了小分子态-态光解动力学的理论研究进展,总结了H2O和CH3I这两个最具代表性体系的态-态光解动力学研究成果,并提出了该领域未来面临的挑战。     

Quantum wave packet ab initio molecular dynamics: an approach to study quantum dynamics in large systems

A methodology to efficiently conduct simultaneous dynamics of electrons and nuclei is presented. The approach involves quantum wave packet dynamics using an accurate banded, sparse and Toeplitz representation for the discrete free propagator, in conjunction with ab initio molecular dynamics treatment of the electronic and classical nuclear degree of freedom. The latter may be achieved either by using atom-centered density-matrix propagation or by using Born-Oppenheimer dynamics. The two components of the methodology, namely, quantum dynamics and ab initio molecular dynamics, are harnessed together using a time-dependent self-consistent field-like coupling procedure. The quantum wave packet dynamics is made computationally robust by using adaptive grids to achieve optimized sampling. One notable feature of the approach is that important quantum dynamical effects including zero-point effects, tunneling, as well as over-barrier reflections are treated accurately. The electronic degrees of freedom are simultaneously handled at accurate levels of density functional theory, including hybrid or gradient corrected approximations. Benchmark calculations are provided for proton transfer systems and the dynamics results are compared with exact calculations to determine the accuracy of the approach.     

Hybrid quantum/classical studies of photodissociation and recombination of I2 (A) in rare gas matrices: A linear chain model

A hybrid quantum/classical model is developed for the photodissociation and recombination dynamics of an I₂ molecule in low-temperature rare-gas (Rg) matrices. The simplified model consists of an I₂ molecule embedded in a linear chain of Rg atoms. The aggregate is partitioned into a quantum system and a classical bath, which are self-consistently coupled. Two partitioning schemes are used. The first treats the I-I coordinate quantum mechanically and the Rg coordinates classically. The second and more reliable scheme includes in the quantum system both the I-I mode and the symmetric motion of the two nearest Rg atoms. Both models show substantial energy transfer from the dissociating I₂ to the solvent, followed by coherent vibrational motion of the recombined I₂. It is found that the one-dimensional quantum/classical scheme is consistent with its higher dimensional counterpart, although the latter shows much faster dephasing. © 1996 John Wiley & Sons, Inc.     

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.     

Mixed quantum/classical investigation of the photodissociation of NH3(A) and a practical method for maintaining zero-point energy in classical trajectories

The photodissociation dynamics of ammonia upon excitation of the out-of-plane bending mode (mode nu(2) with n(2)=0,[ellipsis (horizontal)],6 quanta of vibration) in the A electronic state is investigated by means of several mixed quantum/classical methods, and the calculated final-state properties are compared to experiments. Five mixed quantum/classical methods are tested: one mean-field approach (the coherent switching with decay of mixing method), two surface-hopping methods [the fewest switches with time uncertainty (FSTU) and FSTU with stochastic decay (FSTU/SD) methods], and two surface-hopping methods with zero-point energy (ZPE) maintenance [the FSTUSD+trajectory projection onto ZPE orbit (TRAPZ) and FSTUSD+minimal TRAPZ (mTRAPZ) methods]. We found a qualitative difference between final NH(2) internal energy distributions obtained for n(2)=0 and n(2)>1, as observed in experiments. Distributions obtained for n(2)=1 present an intermediate behavior between distributions obtained for smaller and larger n(2) values. The dynamics is found to be highly electronically nonadiabatic with all these methods. NH(2) internal energy distributions may have a negative energy tail when the ZPE is not maintained throughout the dynamics. The original TRAPZ method was designed to maintain ZPE in classical trajectories, but we find that it leads to unphysically high internal vibrational energies. The mTRAPZ method, which is new in this work and provides a general method for maintaining ZPE in either single-surface or multisurface trajectories, does not lead to unphysical results and is much less time consuming. The effect of maintaining ZPE in mixed quantum/classical dynamics is discussed in terms of agreement with experimental findings. The dynamics for n(2)=0 and n(2)=6 are also analyzed to reveal details not available from experiment, in particular, the time required for quenching of electronic excitation and the adiabatic energy gap and geometry at the time of quenching.     

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.     

Including quantum effects in the dynamics of complex (i.e., large) molecular systems

The development in the 1950s and 1960s of crossed molecular beam methods for studying chemical reactions at the single-collision molecular level stimulated the need and desire for theoretical methods to describe these and other dynamical processes in molecular systems. Chemical dynamics theory has made great strides in the ensuing decades, so that methods are now available for treating the quantum dynamics of small molecular systems essentially completely. For the large molecular systems that are of so much interest nowadays (e.g., chemical reactions in solution, in clusters, in nanostructures, in biological systems, etc.), however, the only generally available theoretical approach is classical molecular dynamics (MD) simulations. Much effort is currently being devoted to the development of approaches for describing the quantum dynamics of these complex systems. This paper reviews some of these approaches, especially the use of semiclassical approximations for adding quantum effects to classical MD simulations, also showing some new versions that should make these semiclassical approaches even more practical and accurate.     

Quantum State-to-State Vacuum Ultraviolet Photodissociation Dynamics of Small Molecules

The present review focused on selected, recent experimental progress of photodissociation dynamics of small molecules covering the vacuum ultraviolet (VUV) range from 6 eV to20 eV. These advancements come about due to the available laser based VUV light sources along with the developments of advanced experimental techniques, including the velocitymap imaging (VMI), H-atom Rydberg tagging time-of-flight (HRTOF) techniques, as well as the two-color tunable VUV-VUV laser pump-probe detection method. The applications of these experimental techniques have allowed VUV photodissociation studies of many diatomic and triatomic molecules to quantum state-to-state in detail. To highlight the recent accomplishments, we have summarized the results on several important molecular species, including H₂ (D₂, HD), CO, N₂, NO, O₂, H₂O (D₂O, HOD), CO₂, and N₂O. The detailed VUV photodissociation studies of these molecules are of astrochemical and atmospheric relevance. Since molecular photodissociation initiated by VUV excitation is complex and is often governed by multiple electronic potential energy surfaces, the unraveling of the complex dissociation dynamics requires state-to-state cross section measurements. The newly constructed Dalian Coherent Light Source (DCLS), which is capable of generating coherent VUV radiation with unprecedented brightness in the range of 50-150 nm, promises to propel the photodissociation experiment to the next level.     

A semiclassical study of the thermal conductivity of low temperature liquids

The conventional classical energy current auto-correlation function has been extended into a quantum mechanical version and then approximated by the linearized semiclassical initial value representation approach. Comparison of the thermal conductivity to simulation results shows that about 15% quantum correction to the classical molecular dynamics results for liquid neon are quantitatively predicted. For liquid para-hydrogen the quantum effects are sufficiently large that the linearized semiclassical approach is only 20% accurate, while for both liquid He(4) and He(3) the thermal conductivity disagrees by a factor of 2, although exchange effects appear to play a minor role.     

An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. I. Theories

We have reformulated and generalized our recent work [J. Liu and W. H. Miller, J. Chem. Phys. 126, 234110 (2007)] into an approach for generating a family of trajectory-based dynamics methods in the phase space formulation of quantum mechanics. The approach (equilibrium Liouville dynamics) is in the spirit of Liouville's theorem in classical mechanics. The trajectory-based dynamics is able to conserve the quantum canonical distribution for the thermal equilibrium system and approaches classical dynamics in the classical (? → 0), high temperature (β → 0), and harmonic limits. Equilibrium Liouville dynamics provides the framework for the development of novel theoretical∕computational tools for studying quantum dynamical effects in large∕complex molecular systems.     

Classical and quantum mechanical calculations of conformational probability density distributions. Two-rotor molecules

In order to study the dynamical structure of a two-rotor molecule, such as acetone, as a function of temperature, conformational probability density distributions are computed by using three different approaches: the so-called current approach, the classical approach, and the quantum mechanical oscillator approach. It is found that the three procedures yield comparable results, at least at normal temperature (25°C), although the current and, especially, the classical approaches give rise to too sharp distributions when compared with the quantum mechanical results. Owing to its simplicity, the current approach may be used advantageously, and it is easily extendible to many-rotor systems. Finally, it is verified that deuteration does not affect appreciably the conformation.     

Calculation of heat capacities of light and heavy water by path-integral molecular dynamics

As an application of atomistic simulation methods to heat capacities, path-integral molecular dynamics has been used to calculate the constant-volume heat capacities of light and heavy water in the gas, liquid, and solid phases. While the classical simulation based on conventional molecular dynamics has estimated the heat capacities too high, the quantum simulation based on path-integral molecular dynamics has given reasonable results based on the simple point-charge/flexible potential model. The calculated heat capacities (divided by the Boltzmann constant) in the quantum simulation are 3.1 in the vapor H2O at 300 K, 6.9 in the liquid H2O at 300 K, and 4.1 in the ice Ih H2O at 250 K, respectively, which are comparable to the experimental data of 3.04, 8.9, and 4.1, respectively. The quantum simulation also reproduces the isotope effect. The heat capacity in the liquid D2O has been calculated to be 10% higher than that of H2O, while it is 13% higher in the experiment. The results demonstrate that the path-integral simulation is a promising approach to quantitatively evaluate the heat capacities for molecular systems, taking account of quantum-mechanical vibrations as well as strongly anharmonic motions.