Quasiclassical Simulations Research Articles

Direct chemical dynamics simulations: coupling of classical and quasiclassical trajectories with electronic structure theory

AbstractIn classical and quasiclassical trajectory chemical dynamics simulations, the atomistic dynamics of collisions, chemical reactions, and energy transfer are studied by solving the classical equations of motion. These equations require the potential energy and its gradient for the chemical system under study, and they may be obtained directly from an electronic structure theory. This article reviews such direct dynamics simulations. The accuracy of classical chemical dynamics is considered, with simulations highlighted for the F− + CH3OOH reaction and of energy transfer in collisions of CO2 with a perfluorinated self‐assembled monolayer (F‐SAM) surface. Procedures for interfacing chemical dynamics and electronic structure theory computer codes are discussed. A Hessian‐based predictor–corrector algorithm and high‐accuracy Hessian updating algorithm, for enhancing the efficiency of direct dynamics simulations, are described. In these simulations, an ensemble of trajectories is calculated which represents the experimental and chemical system under study. Algorithms are described for selecting the appropriate initial conditions for bimolecular and unimolecular reactions, gas‐surface collisions, and initializing trajectories at transition states and conical intersections. Illustrative direct dynamics simulations are presented for the Cl− + CH3I SN2 reaction, unimolecular decomposition of the epoxy resin constituent CH3NHCHCHCH3 versus temperature, collisions and reactions of N‐protonated diglycine with a F‐SAM surface that has a reactive head group, and the product energy partitioning for the post‐transition state dynamics of C2H5F → HF + C2H4 dissociation. © 2012 John Wiley & Sons, Ltd.This article is categorized under: Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics

Electron rescattering at metal nanotips induced by ultrashort laser pulses

We investigate plateau and cutoff structures in photoelectron spectra from nanoscale metal tips interacting with few-cycle near-infrared laser pulses. These hallmarks of electron rescattering, well-known from atom-laser interaction in the strong-field regime, appear at remarkably low laser intensities with nominal Keldysh parameters of the order of $\ensuremath{\gtrsim}\phantom{\rule{-0.16em}{0ex}}\phantom{\rule{-0.16em}{0ex}}10$. Quantum and quasiclassical simulations reveal that a large field enhancement near the tip and the increased backscattering probability at a solid-state target play a key role. Plateau electrons are by an order of magnitude more abundant than in comparable atomic spectra, reflecting the high density of target atoms at the surface. The position of the cutoff serves as an in situ probe for the locally enhanced electric field at the tip apex.

Molecular Dynamics Investigations of Ozone on an Ab Initio Potential Energy Surface with the Utilization of Pattern-Recognition Neural Network for Accurate Determination of Product Formation

The singlet-triplet transformation and molecular dissociation of ozone (O(3)) gas is investigated by performing quasi-classical molecular dynamics (MD) simulations on an ab initio potential energy surface (PES) with visible and near-infrared excitations. MP4(SDQ) level of theory with the 6-311g(2d,2p) basis set is executed for three different electronic spin states (singlet, triplet, and quintet). In order to simplify the potential energy function, an approximation is adopted by ignoring the spin-orbit coupling and allowing the molecule to switch favorably and instantaneously to the spin state that is more energetically stable (lowest in energy among the three spin states). This assumption has previously been utilized to study the SiO(2) system as reported by Agrawal et al. (J. Chem. Phys. 2006, 124 (13), 134306). The use of such assumption in this study probably makes the upper limits of computed rate coefficients the true rate coefficients. The global PES for ozone is constructed by fitting 5906 ab initio data points using a 60-neuron two-layer feed-forward neural network. The mean-absolute error and root-mean-squared error of this fit are 0.0446 eV (1.03 kcal/mol) and 0.0756 eV (1.74 kcal/mol), respectively, which reveal very good fitting accuracy. The parameter coefficients of the global PES are reported in this paper. In order to identify the spin state with high confidence, we propose the use of a pattern-recognition neural network, which is trained to predict the spin state of a given configuration (with a prediction accuracy being 95.6% on a set of testing data points). To enhance the prediction effectiveness, a buffer series of five points are validated to confirm the spin state during the MD process to gain better confidence. Quasi-classical MD simulations from 1.2 to 2.4 eV of total internal energy (including zero-point energy) result in rate coefficients of singlet-triplet transformation in the range of 0.027 ps(-1) to 1.21 ps(-1). Also, we find very low dissociation probability up to 2.4 eV of internal energy during the investigating period (5 ps), which suggests that dissociation does not occur directly from the singlet ground-state, but it involves the excited triplet-state as an intermediate step and requires more reaction time to occur.

Zero-point energy constrained quasiclassical, classical, and exact quantum simulations of isomerizations and radial distribution functions of the water trimer using an ab initio potential energy surface

A recently suggested constrained quasiclassical trajectory (c-QCT) method for avoiding the zero-point leak in the water dimer [11] is applied to the water trimer, employing an ab initio full-dimensional potential energy surface. We demonstrate the failure of the standard/unconstrained QCT method for (H 2O) 3 and show the utility of c-QCT dynamics. In addition, standard classical molecular dynamics and c-QCT dynamics are contrasted for the time-dependence of isomerizations between the multiple global and local minima as well as radial distribution functions are obtained at low temperature and at 300 K. Results from these calculations are compared with rigorous quantum path integral Monte Carlo calculations.

Erratum: “Comparisons of classical and Wigner sampling of transition state energy levels for quasiclassical trajectory chemical dynamics simulations” [J. Chem. Phys. 133, 044313 (2010)

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Comparisons of classical and Wigner sampling of transition state energy levels for quasiclassical trajectory chemical dynamics simulations

Quasiclassical trajectory calculations are compared, with classical and Wigner sampling of transition state (TS) energy levels, for C(2)H(5)F( not equal)-->HF+C(2)H(4) product energy partitioning and [Cl...CH(3)...Cl](-) central barrier dynamics. The calculations with Wigner sampling are reported here for comparison with the previously reported calculations with classical sampling [Y. J. Cho et al., J. Chem. Phys. 96, 8275 (1992); L. Sun and W. L. Hase, J. Chem. Phys. 121, 8831 (2004)]. The C(2)H(5)F( not equal) calculations were performed with direct dynamics at the MP2/6-31G( *) level of theory. Classical and Wigner sampling give post-transition state dynamics, for these two chemical systems, which are the same within statistical uncertainties. This is a result of important equivalences in these two sampling methods for selecting initial conditions at a TS. In contrast, classical and Wigner sampling often give different photodissociation dynamics [R. Schinke, J. Phys. Chem. 92, 3195 (1988)]. Here the sampling is performed for a vibrational state of the ground electronic state potential energy surface (PES), which is then projected onto the excited electronic state's PES. Differences between the ground and the excited PESs may give rise to substantially different excitations of the vibrational and dissociative coordinates on the excited state PES by classical and Wigner sampling, resulting in different photodissociation dynamics.

Differential Cross Sections and Product Rotational Polarization in A + BC Reactions Using Wave Packet Methods: H+ + D2 and Li + HF Examples

The state-to-state differential cross sections for some atom + diatom reactions have been calculated using a new wave packet code, MAD-WAVE3, which is described in some detail and uses either reactant or product Jacobi coordinates along the propagation. In order to show the accuracy and efficiency of the coordinate transformation required when using reactant Jacobi coordinates, as recently proposed [ J. Chem. Phys. 2006 , 125 , 054102 ], the method is first applied to the H + D(2) reaction as a benchmark, for which exact time-independent calculations are also performed. It is found that the use of reactant coordinates yields accurate results, with a computational effort slightly lower than that when using product coordinates. The H(+) + D(2) reaction, with the same masses but a much deeper insertion well, is also studied and exhibits a completely different mechanism, a complex-forming one which can be treated by statistical methods. Due to the longer range of the potential, product Jacobi coordinates are more efficient in this case. Differential cross sections for individual final rotational states of the products are obtained based on exact dynamical calculations for some selected total angular momenta, combined with the random phase approximation to save the high computational time required to calculate all partial waves with very long propagations. The results obtained are in excellent agreement with available exact time-independent calculations. Finally, the method is applied to the Li + HF system for which reactant coordinates are very well suited, and quantum differential cross sections are not available. The results are compared with recent quasiclassical simulations and experimental results [J. Chem. Phys. 2005, 122, 244304]. Furthermore, the polarization of the product angular momenta is also analyzed as a function of the scattering angle.

Theoretical study of hydrogen dissociative adsorption on strained pseudomorphic monolayers of Cu and Pd deposited onto a Ru(0001) substrate

We present an extensive study based on the density functional theory (DFT) of the hydrogen dissociative adsorption on strained pseudomorphic monolayers of Cu or Pd deposited onto a Ru(0001) substrate. First, the full six-dimensional potential energy surfaces (PESs) are obtained by interpolation of the DFT ab initio calculations using the corrugation reducing procedure. The accuracy of these PESs is analyzed in detail. Then, the dissociative adsorption probability has been determined by means of six-dimensional (6D) quasi-classical dynamics simulations for both normal and off-normal incidence. Although H(2) dissociation is known to be non activated on Pd(111) and strongly activated on Cu(111), we have found that it is activated on both Pd/Ru(0001) and Cu/Ru(0001). Surprisingly, the minimum activation energy for H(2) dissociation is very similar on both pseudomorphic monolayers, approximately 100 meV. In both cases, H(2) dissociation occurs after the first encounter between the molecule and the surface (direct process) and, as expected, the adsorption probabilities follow, to a good approximation, normal energy scaling.

Representing and Selecting Vibrational Angular Momentum States for Quasiclassical Trajectory Chemical Dynamics Simulations

Linear molecules with degenerate bending modes have states, which may be represented by the quantum numbers N and L. The former gives the total energy for these modes and the latter identifies their vibrational angular momentum jz. In this work, the classical mechanical analog of the N,L-quantum states is reviewed, and an algorithm is presented for selecting initial conditions for these states in quasiclassical trajectory chemical dynamics simulations. The algorithm is illustrated by choosing initial conditions for the N = 3 and L = 3 and 1 states of CO2. Applications of this algorithm are considered for initial conditions without and with zero-point energy (zpe) included in the vibrational angular momentum states and the C-O stretching modes. The O-atom motions in the x,y-plane are determined for these states from classical trajectories in Cartesian coordinates and are compared with the motion predicted by the normal-mode model. They are only in agreement for the N = L = 3 state without vibrational angular momentum zpe. For the remaining states, the Cartesian O-atom motions are considerably different from the elliptical motion predicted by the normal-mode model. This arises from bend-stretch coupling, including centrifugal distortion, in the Cartesian trajectories, which results in tubular instead of elliptical motion. Including zpe in the C-O stretch modes introduces considerable complexity into the O-atom motions for the vibrational angular momentum states. The short-time O-atom motions for these trajectories are highly irregular and do not appear to have any identifiable characteristics. However, the O-atom motions for trajectories integrated for substantially longer period of times acquire unique properties. With C-O stretch zpe included, the long-time O-atom motion becomes tubular for trajectories integrated to approximately 14 ps for the L = 3 states and to approximately 44 ps for the L = 1 states.

Feynman–Hibbs correction in classical molecular dynamics simulations of solid C60 under a progressively raised pressure and temperature

Feynman–Hibbs corrections in molecular dynamics computer calculations of solid C60 are implemented within the classical effective pair potential approach. The potential model chosen for the site–site interactions is of the Buckingham exp-6 type (Rigby 1986 The Forces Between Molecules (New York: Oxford University Press)), fitted to the Cheng and Klein or the Kitaïgorodsky potential. Structural and thermodynamic properties of the C60 crystal lattice are investigated over a wide range of pressures and temperatures, and data obtained are compared to experimental results and those obtained from a classical approach (Baameur et al 2000 Phys. Status Solidi 220 821). It will be demonstrated that ‘quantum corrections’ applied in a simple quasi-classical simulations have a great influence upon most calculated properties and increase their accuracy when compared to classical approaches. The observed transition pressure with the distorted lattice and cell contraction compares favourably well with experimental data and equation of state calculations. All measured properties are reported together with the phonon density of states at different pressures.

Direct versus resonances mediated F+OH collisions on a new 3A" potential energy surface.

A theoretical study of the F(2P) + OH(2Pi) --> HF(1Sigma+) + O(3P) reactive collisions is carried out on a new global potential energy surface (PES) of the ground 3A" adiabatic electronic state. The ab initio calculations are based on multireference configuration interaction calculations, using the aug-cc-pVTZ extended basis sets of Dunning et al. A functional representation of the PES shows no nominal barrier to reaction, contrary to previous results by others. Wave packet and quasiclassical trajectory calculations have been performed for this PES to study the F + OH(v = 0,j) reactive collision. The comparison was performed at fixed and constant values of the total angular momentum from 0 to 110 and relative translational energy up to 0.8 eV. The reaction presents a dynamical barrier, essentially due to the zero-point energy for the bending vibration near the saddle point. This determines two different reaction mechanisms. At energies higher than approximately 0.125 eV the reaction is direct, while below that value it is indirect and mediated by heavy-light-heavy resonances. Such resonances, also found in the simulations of the photodetachment spectrum of the triatomic anion, manifest themselves in the quasiclassical simulations, too, where they are associated to periodic orbits.

Classical treatments of quantum mechanical effects in collisions of weakly bound complexes

Abstract Classical and quantum simulations of Ne + Ar2 collision dynamics are performed in order to investigate where quantum mechanical effects are most important and where classical simulations provide good descriptions of the dynamics. It is found that when Ar2 is in a low-lying vibrational state, the differences between the results of quantum and quasiclassical simulations are profound. However, excellent agreement between the results of the quantum and classical simulations can be achieved when the initial conditions for the classical trajectories are sampled from the quantum phase space distribution given by the Wigner function. These effects are largest when collisions occur under constrained geometries or when Ar2 is in its ground vibrational state. The results of this work suggest that sampling the initial conditions using the Wigner function provides a straightforward way to incorporate the most important quantum mechanical effects in simulations of collisions involving very cold weakly bound complexes.

Photoassociation of cesium atoms into the double minimum [formula omitted] state

We have observed the transition from the free colliding pair of cesium atoms into the outer well of the double minimum Cs231Σu+ state. This photoassociation process takes place in a cesium vapor consisting predominantly of atoms, in which dimers have been about 85% thermally dissociated. Excellent agreement with quasiclassical simulations was found. We discuss the possibility of using a double minimum Cs231Σu+ state for the formation of ultracold Cs2X1Σg+ molecules.

Local interpolation of ab initio potential energy surfaces for direct dynamics studies of chemical reactions

A `direct' molecular dynamics technique, which calculates the ab initio data points simultaneously within the dynamics simulation is presented. The energies and forces used in quasiclassical trajectory simulations are determined by a least-squares interpolation scheme in rectangular finite elements. The data points are chosen by an automatic selection procedure, which assures that only dynamically relevant parts of the potential energy surface (PES) are interpolated. The energies and gradients at all selected grid points are stored and reused for later trajectories. The efficiency of the method is demonstrated by quasiclassical simulations of scattering experiments on the 3-dimensional PES of the reaction F+H2.

Quantum mechanical and quasiclassical simulations of molecular beam experiments for the F+H2→HF+H reaction on two ab initio potential energy surfaces

Laboratory (LAB) angular distributions (AD) measured in molecular beam experiments by Lee and co-workers in 1985 and very recently by Keil and co-workers for the prototypic F+H2 reaction have been simulated using new quantum mechanical (QM) and quasiclassical trajectory (QCT) state-resolved differential cross sections (DCS) calculated on the ab initio potential energy surfaces (PES) by Stark and Werner (SW) and by Hartke, Stark and Werner (HSW); the latter PES includes spin-orbit coupling corrections added to the entrance channel of the former. The simulations of the 1985 LAB ADs performed using the new QM calculations on the SW PES show a very good agreement with the experimental results for all final vibrational states of the HF product. The inclusion of spin-orbit coupling corrections in the ab initio HSW PES does not seem to improve the agreement between theoretical and experimental results. As for the simulation of the recent experiments of Keil and co-workers, the LAB ADs are very well reproduced by the QM and QCT results on both the SW and HSW PESs with the exception of the negative signal measured at LAB scattering angles of about −8°, arising from HF scattering into the forward hemisphere for the v′=1, j′=5,6,7 states. This peak cannot be accounted for by either of the QM and QCT calculations on any of the two PESs.

Predissociation of the Rg⋯I 2(B) (Rg=Ne, Ar, Kr) complexes: simulations based on the first-order diatomics-in-molecule perturbation theory

Decay dynamics of Rg⋯I 2( B) (rare gas (Rg)=Ne, Ar, Kr) van der Waals complexes via vibrational and electronic predissociation channels is considered using analytical first-order intermolecular diatomics-in-molecule perturbation theory (IDIM-PT1). Symmetry arguments, quantum spectator model, and quasiclassical simulations confirm qualitatively the validity of IDIM-PT1 diabatic potential energy surfaces and electronic coupling matrix elements.

Quasiclassical theory and simulations of strongly coupled plasmas

A survey on the dynamical and thermodynamical properties of plasmas with strong Coulomb interactions in the quasi-classical density–temperature region is given. First the basic theoretical concepts describing non-ideality are discussed. The chemical picture is introduced. It is shown that the non-ideal plasma subsystem of the free charges has a rather large quasi-classical regime, where the quantum effects yield only corrections to the merely classical dynamics. The plasma of free charges may be described by effective potentials which incorporate quantum effects in an approximative way. The simplest effective potentials are only space-dependent, more advanced methods include momentum-dependent interactions. On the basis of these potentials analytical results are derived and simulation methods are developed. It is shown that effective potentials are appropriate for the description of thermodynamical as well as collective properties.

Reply to ‘‘Comment on ‘The conservation of quantum zero-point energies in classical trajectory simulations’ ’’ [J. Chem. Phys. 103, 1989 (1995)

The use of quasiclassical simulations arises from practical considerations: It is not possible to do quantum simulations for most systems. By necessity, only quantum dynamics can reproduce all quantum properties. The use of restricted energy flows by using pseudoholonomic constraints to conserve ‘‘quantum’’ zero-point energy [J. Chem. Phys. 102, 1705 (1995)] is an attempt to reproduce at least one important quantum phenomenon using a (pseudo)classical method. Future applications for the pseudoholonomic-constraint method are discussed.