Quantum Dynamical Methods Research Articles

Mode specific dynamics of the H2 + CH3 → H + CH4 reaction studied using quasi-classical trajectory and eight-dimensional quantum dynamics methods

An eight-dimensional quantum dynamical model is proposed and applied to the title reaction. The reaction probabilities and integral cross sections have been determined for both the ground and excited vibrational states of the two reactants. The results indicate that the H2 stretching and CH3 umbrella modes, along with the translational energy, strongly promote the reactivity, while the CH3 symmetric stretching mode has a negligible effect. The observed mode specificity is confirmed by full-dimensional quasi-classical trajectory calculations. The mode specificity can be interpreted by the recently proposed sudden vector projection model, which attributes the enhancement effects of the reactant modes to their strong couplings with the reaction coordinate at the transition state.

Simulating Excited State Dynamics in Systems with Multiple Avoided Crossings Using Mapping Variable Ring Polymer Molecular Dynamics.

Mapping variable ring polymer molecular dynamics (MV-RPMD) is an approximate quantum dynamics method based on imaginary-time path integrals for simulating electronically nonadiabatic photochemical processes. By employing a mapping protocol to transform from a discrete electronic state basis to continuous Cartesian phase-space variables, the method captures electronic state transitions coupled to nuclear motion using only classical MD trajectories. In this work, we extend the applicability of MV-RPMD to simulations of photoinduced excited electronic state dynamics in nonadiabatic systems with multiple avoided crossings. We achieve this by deriving a new electronic state population estimator in the phase space of electronic variables that is exact at equilibrium and numerically accurate in real time. Further, we introduce an efficient constraint protocol to initialize an MV-RPMD simulation to a particular electronic state. We numerically demonstrate the accuracy of this estimator and constraint technique in describing electronic state dynamics from an initial nonequilibrium state in six model systems, three of which describe photodissociation.

An eight-dimensional quantum dynamics study of the Cl + CH4→ HCl + CH3 reaction.

In this work, the later-barrier reaction Cl + CH4 → HCl + CH3 is investigated with an eight-dimensional quantum dynamics method [R. Liu et al., J. Chem. Phys. 137, 174113 (2012)] on the ab initio potential energy surface of Czakó and Bowman [J. Chem. Phys. 136, 044307 (2012)]. The reaction probabilities with CH4 initially in its ground and vibrationally excited states are calculated with a time-dependent wavepacket method. The theoretical integral cross sections (ICSs) are extensively compared with the available experimental measurements. For the ground state reaction, the theoretical ICSs excellently agree with the experimental ones. The good agreements are also achieved for ratios between ICSs of excited reactions. For ICS ratios between various states, the theoretical values are also consistent with the experimental observations. The rate constants over 200-2000 K are calculated and the non-Arrhenius effect has been observed which is coincident with the previous experimental observations and theoretical calculations.

Should thermostatted ring polymer molecular dynamics be used to calculate thermal reaction rates?

We apply Thermostatted Ring Polymer Molecular Dynamics (TRPMD), a recently proposed approximate quantum dynamics method, to the computation of thermal reaction rates. Its short-time transition-state theory limit is identical to rigorous quantum transition-state theory, and we find that its long-time limit is independent of the location of the dividing surface. TRPMD rate theory is then applied to one-dimensional model systems, the atom-diatom bimolecular reactions H + H2, D + MuH, and F + H2, and the prototypical polyatomic reaction H + CH4. Above the crossover temperature, the TRPMD rate is virtually invariant to the strength of the friction applied to the internal ring-polymer normal modes, and beneath the crossover temperature the TRPMD rate generally decreases with increasing friction, in agreement with the predictions of Kramers theory. We therefore find that TRPMD is approximately equal to, or less accurate than, ring polymer molecular dynamics for symmetric reactions, and for certain asymmetric systems and friction parameters closer to the quantum result, providing a basis for further assessment of the accuracy of this method.

Classical blended quantum formulation of the parallel TDDVR method to the dynamics on furan

A major portion (∼98%) of the quantum-classical molecular dynamics approach, namely, Time-Dependent Discrete Variable Representation (TDDVR) method, is recently parallelized using shared-memory parallelization scheme with the aim of performing dynamics on relatively large molecular systems. Therefore, we have chosen the furan as a model system for dynamical simulation. Four lowest singlet excited electronic states 1A2(3s), 1B2(V), 1A1(V*), and 1B1(3p) of furan are vibronically coupled through several conical intersections in the vicinity of Frank-Condon region. The major focus of the present paper is to explore the efficiency of our newly implemented parallelized TDDVR algorithm to perform dynamics on large dimensional quantum systems in vibronically coupled electronic manifold. The present version of parallelized TDDVR algorithm show closely linear speed up with increasing number of computing processors. As a significant speed up is achieved by cycling in the correct way over arrays, all dynamical simulations are performed within a reasonable wall clock time. The photoelectron spectra calculated by the TDDVR method show peak by peak correspondence with the experimental spectra. The TDDVR calculated quantum-classical dynamical outcomes, viz., population and photoelectron spectra, etc. show good agreement with the findings of the well-established quantum dynamical method, i.e. Multi Configuration Time-Dependent Hartree (MCTDH) approach.

From ab initio potential energy surfaces to state-resolved reactivities: X + H2O ↔ HX + OH [X = F, Cl, and O((3)P)] reactions.

We survey the recent advances in theoretical understanding of quantum state resolved dynamics, using the title reactions as examples. It is shown that the progress was made possible by major developments in two areas. First, an accurate analytical representation of many high-level ab initio points over a large configuration space can now be made with high fidelity and the necessary permutation symmetry. The resulting full-dimensional global potential energy surfaces enable dynamical calculations using either quasi-classical trajectory or more importantly quantum mechanical methods. The second advance is the development of accurate and efficient quantum dynamical methods, which are necessary for providing a reliable treatment of quantum effects in reaction dynamics such as tunneling, resonances, and zero-point energy. The powerful combination of the two advances has allowed us to achieve a quantitatively accurate characterization of the reaction dynamics, which unveiled rich dynamical features such as steric steering, strong mode specificity, and bond selectivity. The dependence of reactivity on reactant modes can be rationalized by the recently proposed sudden vector projection model, which attributes the mode specificity and bond selectivity to the coupling of reactant modes with the reaction coordinate at the relevant transition state. The deeper insights provided by these theoretical studies have advanced our understanding of reaction dynamics to a new level.

Mode specificity in the HCl + OH → Cl + H2O reaction: Polanyi's rules vs sudden vector projection model.

The dynamics and mode specificity of the HCl + OH → Cl + H2O reaction are investigated using a full-dimensional quantum dynamics method on an accurate global potential energy surface. It is shown that the vibrational excitation of the HCl reactant greatly enhances the reactivity while the OH vibrational excitation has little effect. The surprising HCl vibrational enhancement of this early barrier reaction contradicts a naive extension of Polanyi's rules, but can be explained by the sudden vector projection model, which attributes the promotional effect of the HCl vibration to its strong coupling with the reaction coordinate at the transition state. In addition, it is found that the fundamental and overtone excitations of the HCl reactant change the reaction mechanism from a direct barrier crossing process to a capture-like process.

Clock quantum Monte Carlo technique: An imaginary-time method for real-time quantum dynamics

In quantum information theory, there is an explicit mapping between general unitary dynamics and Hermitian ground state eigenvalue problems known as the Feynman-Kitaev Clock. A prominent family of methods for the study of quantum ground states are quantum Monte Carlo methods, and recently the full configuration interaction quantum Monte Carlo (FCIQMC) method has demonstrated great promise for practical systems. We combine the Feynman-Kitaev Clock with FCIQMC to formulate a new technique for the study of quantum dynamics problems. Numerical examples using quantum circuits are provided as well as a technique to further mitigate the sign problem through time-dependent basis rotations. Moreover, this method allows one to combine the parallelism of Monte Carlo techniques with the locality of time to yield an effective parallel-in-time simulation technique.

Insights into the bond-selective reaction of Cl + HOD(n(OH)) → HCl + OD.

Bond-selective reaction dynamics of the title reaction is investigated using full-dimensional quantum dynamical (QD) and quasi-classical trajectory (QCT) methods on a newly constructed ab initio global potential energy surface. Both QD and QCT results indicate that excitation of the local OH vibration in the HOD reactant renders the reaction strongly bond selective, with the OD/OH branching ratio in quantitative agreement with the experiment. In addition, the reactivity is found to be greatly enhanced with the reactant vibrational excitation, thanks to the change of a direct rebound mechanism to a capture mechanism. The QCT calculations also yield product state distributions, which show that the HCl product is vibrationally and rotationally hot while the OD co-product is internally cold. The bond selectivity, vibrational enhancement, and product energy disposal are rationalized by the Sudden Vector Projection model.

Proton-transfer mediated enhancement of nonlocal electronic relaxation processes in X-ray irradiated liquid water.

We have simulated the oxygen 1s Auger-electron spectra of normal and heavy liquid water using ab initio and quantum dynamical methods. The computed spectra are analyzed and compared to recently reported experimental data. The electronic relaxation in liquid water exposed to ionizing X-ray radiation is shown to be far more diverse and complex than anticipated and extremely different than for an isolated water molecule. A core-level ionized water molecule in the liquid phase, in addition to a local Auger process, relaxes through nonlocal energy and charge transfer, such as intermolecular Coulombic decay and electron-transfer mediated decay (ETMD). We evaluate the relative efficiencies for these three classes of relaxation processes. The quantitative estimates for the relative efficiencies of different electronic decay modes help determine yields of various reactive species produced by ionizing X-rays. The ETMD processes which are considered here for the first time in the core-level regime are found to have a surprisingly high efficiency. Importantly, we find that all nonlocal electronic relaxation processes are significantly enhanced by ultrafast proton transfer between the core-ionized water and neighboring molecules.

Multisurface multimode molecular dynamical simulation of naphthalene and anthracene radical cations by using nearly linear scalable time-dependent discrete variable representation method.

The major portion of the algorithm of the time-dependent discrete variable representation (TDDVR) method is recently parallelized using the shared-memory parallelization scheme with the aim of performing dynamics on relatively large molecular systems. Because of the astronomical importance of naphthalene and anthracene, we have investigated their radical cations as models for theoretical simulation of complex photoelectron spectra and nonradiative decay process using the newly implemented parallel TDDVR code. The strong vibronic coupling among the six lowest doublet electronic states makes these polynuclear hydrocarbons dynamically important. The aim of the present investigation is to show the efficiency of our current TDDVR algorithm to perform dynamics on large dimensional quantum systems in vibronically coupled electronic manifold. Both the sequential and the parallelized TDDVR algorithms are almost linear scalable for an increase in number of processors. Because a significant speed-up is achieved by cycling in the correct way over arrays, all of the simulations are performed within a reasonable wall clock time. Our theoretical spectra well reproduce the features of the corresponding experimental analog. The dynamical outcomes, for example, population, photoelectron spectra, and diffused interstellar bands, etc., of our quantum-classical approach show good agreement with the findings of the well-established quantum dynamical method, that is, multi configuration time-dependent Hartree (MCTDH) approach.

Second-quantized surface hopping.

The trajectory surface hopping method for quantum dynamics is reformulated in the space of many-particle states to include entanglement and correlation of trajectories. Used to describe many-body correlation effects in electronic structure theories, second quantization is applied to semiclassical trajectories. The new method allows coupling between individual trajectories via energy flow and common phase evolution. It captures the properties of a wave packet, such as branching, Heisenberg uncertainty, and decoherence. Applied to a superexchange process, the method shows very accurate results, comparable to exact quantum data and improving greatly on the standard approach.

A comparison study of the H + CH4 and H + SiH4 reactions with eight-dimensional quantum dynamics: normal mode versus local mode in the reactant molecule vibration

While molecular vibration of CH4 is well described by the normal-mode paradigm, the local mode picture is more suitable for understanding the SiH4 stretching vibrational motion. To compare the roles of the two types of molecular vibration in reaction dynamics, the H + CH4 → H2 + CH3 and H + SiH4 → H2 + SiH3 reactions have been investigated using an eight-dimensional (8D) quantum dynamics method in which the nonreacting XH3 (X = C, Si) group keeps its C3v symmetry in the reaction. The reaction probabilities, integral cross sections and thermal rate constants in the temperature range of 200–2,000 K were calculated for both reactions. Strong mode specificity was found in both reactions, and the differences were rationalized by the vibrational characteristics of the CH4 and SiH4 reactants.

Communication: separable potential energy surfaces from multiplicative artificial neural networks.

We present a potential energy surface fitting scheme based on multiplicative artificial neural networks. It has the sum of products form required for efficient computation of the dynamics of multidimensional quantum systems with the multi configuration time dependent Hartree method. Moreover, it results in analytic potential energy matrix elements when combined with quantum dynamics methods using Gaussian basis functions, eliminating the need for a local harmonic approximation. Scaling behavior with respect to the complexity of the potential as well as the requested accuracy is discussed.

Steric and electrostatic effects on photoisomerization dynamics using QM/MM ab initio multiple spawning

Photoisomerization of conjugated systems is a common pathway for photomechanical energy conversion in biological chromophores. There are many examples where the local environment of the chromophore plays an important role in determining the outcome of photoisomerization. We have investigated the effect of simple steric and electrostatic environments on the excited-state photodynamics of ethylene, a simple model for larger conjugated systems. Ab initio electronic structure methods were combined with molecular mechanical force fields to describe the ground and excited-state potential energy surfaces of ethylene embedded in electrostatic and steric environments. The time evolution of the system following photoabsorption was modeled using the ab initio multiple spawning (AIMS) method for quantum dynamics. We introduce a new method for integration of the equations of motion in AIMS, which detects conical intersections automatically and then decreases the timestep adaptively around them. Neither steric hindrance nor electrostatics have a large effect on the excited-state lifetime, even at effective pressures as large as 2 GPa. However, a nearby point charge creates an electric field that stabilizes one of two symmetry-related conical intersections, biasing the reaction toward a particular photoisomerization pathway. For the larger tetramethylethylene, where steric hindrance is expected to be more pronounced, we also see no effect on the excited-state lifetime. Our results suggest that electrostatic interactions are more effective than steric hindrance in modifying the course of excited-state reactions.

Can the ring polymer molecular dynamics method be interpreted as real time quantum dynamics?

The ring polymer molecular dynamics (RPMD) method has gained popularity in recent years as a simple approximation for calculating real time quantum correlation functions in condensed media. However, the extent to which RPMD captures real dynamical quantum effects and why it fails under certain situations have not been clearly understood. Addressing this issue has been difficult in the absence of a genuine justification for the RPMD algorithm starting from the quantum Liouville equation. To this end, a new and exact path integral formalism for the calculation of real time quantum correlation functions is presented in this work, which can serve as a rigorous foundation for the analysis of the RPMD method as well as providing an alternative derivation of the well established centroid molecular dynamics method. The new formalism utilizes the cyclic symmetry of the imaginary time path integral in the most general sense and enables the expression of Kubo-transformed quantum time correlation functions as that of physical observables pre-averaged over the imaginary time path. Upon filtering with a centroid constraint function, the formulation results in the centroid dynamics formalism. Upon filtering with the position representation of the imaginary time path integral, we obtain an exact quantum dynamics formalism involving the same variables as the RPMD method. The analysis of the RPMD approximation based on this approach clarifies that an explicit quantum dynamical justification does not exist for the use of the ring polymer harmonic potential term (imaginary time kinetic energy) as implemented in the RPMD method. It is analyzed why this can cause substantial errors in nonlinear correlation functions of harmonic oscillators. Such errors can be significant for general correlation functions of anharmonic systems. We also demonstrate that the short time accuracy of the exact path integral limit of RPMD is of lower order than those for finite discretization of path. The present quantum dynamics formulation also serves as the basis for developing new quantum dynamical methods that utilize the cyclic nature of the imaginary time path integral.

Coherent quantum transport in disordered systems: II. Temperature dependence of carrier diffusion coefficients from the time-dependent wavepacket diffusion method

The time-dependent wavepacket diffusion method for carrier quantum dynamics (Zhong and Zhao 2013 J. Chem. Phys. 138 014111), a truncated version of the stochastic Schrödinger equation/wavefunction approach that approximately satisfies the detailed balance principle and scales well with the size of the system, is applied to investigate the carrier transport in one-dimensional systems including both the static and dynamic disorders on site energies. The predicted diffusion coefficients with respect to temperature successfully bridge from band-like to hopping-type transport. As demonstrated in paper I (Moix et al 2013 New J. Phys. 15 085010), the static disorder tends to localize the carrier, whereas the dynamic disorder induces carrier dynamics. For the weak dynamic disorder, the diffusion coefficients are temperature-independent (band-like property) at low temperatures, which is consistent with the prediction from the Redfield equation, and a linear dependence of the coefficient on temperature (hopping-type property) only appears at high temperatures. In the intermediate regime of dynamic disorder, the transition from band-like to hopping-type transport can be easily observed at relatively low temperatures as the static disorder increases. When the dynamic disorder becomes strong, the carrier motion can follow the hopping-type mechanism even without static disorder. Furthermore, it is found that the memory time of dynamic disorder is an important factor in controlling the transition from the band-like to hopping-type motions.

An experimental and theoretical study of nitrogen-broadened acetylene lines

We present experimental nitrogen-broadening coefficients derived from Voigt profiles of isotropic Raman Q-lines measured in the ν2 band of acetylene (C2H2) at 150K and 298K, and compare them to theoretical values obtained through calculations that were carried out specifically for this work. Namely, full classical calculations based on Gordon׳s approach, two kinds of semi-classical calculations based on Robert–Bonamy method as well as full quantum dynamical calculations were performed. All the computations employed exactly the same ab initio potential energy surface for the C2H2–N2 system which is, to our knowledge, the most realistic, accurate and up-to-date one. The resulting calculated collisional half-widths are in good agreement with the experimental ones only for the full classical and quantum dynamical methods. In addition, we have performed similar calculations for IR absorption lines and compared the results to bibliographic values. Results obtained with the full classical method are again in good agreement with the available room temperature experimental data. The quantum dynamical close-coupling calculations are too time consuming to provide a complete set of values and therefore have been performed only for the R(0) line of C2H2. The broadening coefficient obtained for this line at 173K and 297K also compares quite well with the available experimental data. The traditional Robert–Bonamy semi-classical formalism, however, strongly overestimates the values of half-width for both Q- and R-lines. The refined semi-classical Robert–Bonamy method, first proposed for the calculations of pressure broadening coefficients of isotropic Raman lines, is also used for IR lines. By using this improved model that takes into account effects from line coupling, the calculated semi-classical widths are significantly reduced and closer to the measured ones.

Correlation Functions in Open Quantum-Classical Systems

Quantum time correlation functions are often the principal objects of interest in experimental investigations of the dynamics of quantum systems. For instance, transport properties, such as diffusion and reaction rate coefficients, can be obtained by integrating these functions. The evaluation of such correlation functions entails sampling from quantum equilibrium density operators and quantum time evolution of operators. For condensed phase and complex systems, where quantum dynamics is difficult to carry out, approximations must often be made to compute these functions. We present a general scheme for the computation of correlation functions, which preserves the full quantum equilibrium structure of the system and approximates the time evolution with quantum-classical Liouville dynamics. Several aspects of the scheme are discussed, including a practical and general approach to sample the quantum equilibrium density, the properties of the quantum-classical Liouville equation in the context of correlation function computations, simulation schemes for the approximate dynamics and their interpretation and connections to other approximate quantum dynamical methods.

A global ab initio potential energy surface for the X 2A′ ground state of the Si + OH → SiO + H reaction

We report the first global potential energy surface (PES) for the X(2)A' ground electronic state of the Si((3)P) + OH(X(2)Π) → SiO(X(1)Σg(+)) + H((2)S) reaction. The PES is based on a large number of ab initio energies obtained from multireference configuration interaction calculations plus Davidson correction (MRCI+Q) using basis sets of quadruple zeta quality. Corrections were applied to the ab initio energies in the reactant channel allowing a proper description of long-range interactions between Si((3)P) and OH(X(2)Π). An analytical representation of the global PES has been developed by means of the reproducing kernel Hilbert space method. The reaction is found barrierless. Two minima, corresponding to the SiOH and HSiO isomers, and six saddle points, among which the isomerization transition state, have been characterized on the PES. The vibrational spectra of the SiOH/HSiO radicals have been computed from second-order perturbation theory and quantum dynamics methods. The structural, energetic, and spectroscopic properties of the two isomers are in good agreement with experimental data and previous high quality calculations.