State-resolved Reaction Research Articles

Reactant coordinate based state-to-state reactive scattering dynamics implemented on graphical processing units.

A parallel code for state-to-state quantum dynamics with propagation of time-dependent wavepacket in reactant coordinates has been developed on graphical processing units (GPUs). The propagation of wavepacket and the transformation of wavepacket from reactant to product Jacobi coordinates are entirely calculated on GPUs. A new interpolation procedure is introduced for coordinate transformation to decrease the five-loop computation to two four-loop computations. This procedure has a negligible consumption of extra GPU memory in comparison with that of the wavepacket and produces a considerable acceleration of the computational speed of the transformation. The code is tested to get differential cross sections of H+HD reaction and state-resolved reaction probabilities of O+HD for total angular momenta J = 0, 10, 20, and 30. The average speedups are 57.0 and 83.5 for the parallel computations on two C2070 and K20m GPUs relative to serial computation on Intel E5620 CPU, respectively.

Quantum state-resolved gas/surface reaction dynamics probed by reflection absorption infrared spectroscopy

We report the design and characterization of a new molecular-beam/surface-science apparatus for quantum state-resolved studies of gas/surface reaction dynamics combining optical state-specific reactant preparation in a molecular beam by rapid adiabatic passage with detection of surface-bound reaction products by reflection absorption infrared spectroscopy (RAIRS). RAIRS is a non-invasive infrared spectroscopic detection technique that enables online monitoring of the buildup of reaction products on the target surface during reactant deposition by a molecular beam. The product uptake rate obtained by calibrated RAIRS detection yields the coverage dependent state-resolved reaction probability S(θ). Furthermore, the infrared absorption spectra of the adsorbed products obtained by the RAIRS technique provide structural information, which help to identify nascent reaction products, investigate reaction pathways, and determine branching ratios for different pathways of a chemisorption reaction. Measurements of the dissociative chemisorption of methane on Pt(111) with this new apparatus are presented to illustrate the utility of RAIRS detection for highly detailed studies of chemical reactions at the gas/surface interface.

A quantum time-dependent wave-packet study of intersystem crossing effects in the O(3P0, 1, 2) + D2(v = 0, j = 0) reaction

We investigated spin-orbit-induced intersystem crossing effects in the title reaction by the time-dependent wave-packet method combined with an extended split operator scheme. We performed non-adiabatic calculations of the fine-structure-resolved cross section and adiabatic calculations of integral cross section. The calculations are based on the potential energy surfaces of (3)A(') and the two degenerate (3)A('') states [S. Rogers, D. Wang, A. Kuppermann, and S. Walch, J. Phys. Chem. A 104, 2308 (2000)], together with the spin-orbit coupling matrix [B. Maiti and G. C. Schatz, J. Chem. Phys. 119, 12360 (2003)] and singlet (1)A(') potential energy surface [J. Dobbyn and P. J. Knowles, Faraday Discuss. 110, 247 (1998)]. The results of the O((3)P) + D2 are similar to those of the O((3)P) + H2 reaction. The product spin state-resolved reaction cross section and the total reaction cross section both show that the adiabatic channel is dominant in all cases, and the non-adiabatic channels have cross sections of several orders of magnitude smaller than the adiabatic channels at high collision energy. Although the cross sections caused by the intersystem crossing effects in the O((3)P) + D2 reaction are larger than those in the O((3)P) + H2 reaction, the differences in non-adiabaticity between these two reaction systems are quite modest. Based on the results of the O((3)P) + H2 reaction, we can predict that the influence of spin-orbit on the total reaction cross sections of the O((3)P) + D2 reaction is also insignificant. However, these non-adiabatic effects can be reflected in the presence of some forward-scattering in the angular distribution for the OD product.

Adiabatic/Nonadiabatic State-to-State Reactive Scattering Dynamics Implemented on Graphics Processing Units

An efficient graphics processing units (GPUs) version of time-dependent wavepacket code is developed for the atom-diatom state-to-state reactive scattering processes. The propagation of the wavepacket is entirely calculated on GPUs employing the split-operator method after preparation of the initial wavepacket on the central processing unit (CPU). An additional split-operator method is introduced in the rotational part of the Hamiltonian to decrease communication of GPUs without losing accuracy of state-to-state information. The code is tested to calculate the differential cross sections of H + H2 reaction and state-resolved reaction probabilities of nonadiabatic triplet-singlet transitions of O((3)P,(1)D) + H2 for the total angular momentum J = 0. The global speedups of 22.11, 38.80, and 44.80 are found comparing the parallel computation of one GPU, two GPUs by exact rotational operator, and two GPU versions by an approximate rotational operator with serial computation of the CPU, respectively.

Wave packet calculations on nonadiabatic effects for the O(3P)+HF(1Σ+) reaction under hyperthermal conditions

We present wave packet calculations of total and state-to-state reaction probabilities and integral cross sections for the nonadiabatic dynamics of the O((3)P)+HF → F((2)P)+OH((2)Π) reaction at hyperthermal collision energies ranging from 1.2 to 2.4 eV. The validity of the centrifugal sudden approximation is discussed for the title reaction and a comprehensive investigation of the influence of nonadiabatic effects on the dynamics of this reactive system at high (hyperthermal) collision energies is presented. In general, nonadiabatic effects are negligible for averaged observables, such as total reaction probabilities and integral cross sections, but they are clearly observed in detailed observables such as rotationally state-resolved reaction probabilities. A critical discussion of nonadiabatic effects on the dynamics of the title reaction is carried out by comparing with the reverse reaction and the characteristics of the adiabatic and diabatic potential energy surfaces involved.

Static surface temperature effects on the dissociation of H2 and D2 on Cu(111)

A model for taking into account surface temperature effects in molecule-surface reactions is reported and applied to the dissociation of H(2) and D(2) on Cu(111). In contrast to many models developed before, the model constructed here takes into account the effects of static corrugation of the potential energy surface rather than energy exchange between the impinging hydrogen molecule and the surface. Such an approximation is a vibrational sudden approximation. The quality of the model is assessed by comparison to a recent density functional theory study. It is shown that the model gives a reasonable agreement with recently performed ab initio molecular dynamics calculations, in which the surface atoms were allowed to move. The observed broadening of the reaction probability curve with increasing surface temperature is attributed to the displacement of surface atoms, whereas the effect of thermal expansion is found to be primarily a shift of the curve to lower energies. It is also found that the rotational quadrupole alignment parameter is generally lowered at low energies, whereas it remains approximately constant at high energies. Finally, it is shown that the approximation of an ideal static surface works well for low surface temperatures, in particular for the molecular beams for this system (T(s) = 120 K). Nonetheless, for the state-resolved reaction probability at this surface temperature, some broadening is found.

Visualizing Reaction Progress and the Geometry and Instability of the Transition State

Transition state theory (TST), also called activated complex theory, is often discussed in general chemistry and physical chemistry courses when learning kinetics. This demonstration takes the abstract concepts of transition state, activation energy, and reaction progress (reaction coordinate) and makes them more concrete and accessible. The demonstration uses a children’s toy (Hoberman Switch Pitch) to model a chemical reaction that follows a reactant through a transition state before making a product. The reaction progress, activation energy, and specific geometry of the transition state are discussed as part of a question and answer dialogue. The complex, multidimensionality of a reaction coordinate and the inherent instability of a transition state become evident. The demonstration also shows that certain reactions may “go” more readily if the energy of a reactant is in a particular type of internal mode (vibrations or rotations). The preferential partition of a given total energy into internal modes of motion versus translational collision energy may allow a system to access the transition state more easily. The demonstration may also aid in the teaching of isomerization reactions, collision theory, and state-resolved reaction dynamics.

Chebyshev high-dimensional model representation (Chebyshev-HDMR) potentials: application to reactive scattering of H2 from Pt(111) and Cu(111) surfaces

Gas phase and surface reactions involving polyatomic molecules are of central importance to chemical physics, and require accurately fit potential energy surfaces describing the interaction in their systems. Here, we propose a method for generating a High Dimensional Model Representation (HDMR) of a multidimensional potential energy surface (PES) and apply it to reactive molecule-surface scattering problems. In the HDMR treatment, all N degrees of freedom (DOF) of an N-dimensional PES are represented but only n < N are explicitly coupled. The HDMR is obtained from Chebyshev polynomial expansions for each degree of freedom, where expansion coefficients are efficiently evaluated using discrete cosine transform (DCT) algorithms and properties of Chebyshev polynomials. HDMR surfaces constructed for the reactive scattering of H2 from Pt(111) and Cu(111) are used in quantum dynamics simulations; the resultant state-resolved reaction and scattering probabilities are compared to those from simulations using full (6D) PESs and n-mode PESs from previous work. The results are encouraging, and suggest that this method may be applicable to "late barrier" reactive systems for which the previously-used n-mode representation fails.

The investigation of nonadiabatic effects for the N + ND → N2 + D reaction

Nonadiabatic quantum dynamical calculations have been carried out on the two coupled potential energy surfaces (12A' and 22A') (Mota et al., J Theor Comput Chem 2009, 8, 849) for the title reaction. Initial state-resolved reaction probabilities and cross sections for ground and excited states for collision energies of 0.0051.0 eV are determined, respectively. Nonadiabatic transition is enhanced about four times by isotopic substitution of N + NH by N + ND reaction. It turns out that the nonadiabatic effects exert no significant contribution in the N + ND ? N2 + D reaction. (c) 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Alignment dependent chemisorption of vibrationally excited CH4(ν3) on Ni(100), Ni(110), and Ni(111)

We present a stereodynamics study of the dissociative chemisorption of vibrationally excited methane on the (100), (110), and (111) planes of a nickel single crystal surface. Using linearly polarized infrared excitation of the antisymmetric C-H stretch normal mode vibration (ν(3)), we aligned the angular momentum and C-H stretch amplitude of CH(4)(ν(3)) in the laboratory frame and measured the alignment dependence of state-resolved reactivity of CH(4) for the ν(3) = 1, J = 0-3 quantum states over a range of incident translational energies. For all three surfaces studied, in-plane alignment of the C-H stretch results in the highest dissociation probability and alignment along the surface normal in the lowest reactivity. The largest alignment contrast between the maximum and minimum reactivity is observed for Ni(110), which has its surface atoms arranged in close-packed rows separated by one layer deep troughs. For Ni(110), we also probed for alignment effects relative to the direction of the Ni rows. In-plane C-H stretch alignment perpendicular to the surface rows results in higher reactivity than parallel to the surface rows. The alignment effects on Ni(110) and Ni(100) are independent of incident translational energy between 10 and 50 kJ/mol. Quantum state-resolved reaction probabilities are reported for CH(4)(ν(3)) on Ni(110) for translational energies between 10 and 50 kJ/mol.

Quantum Mechanics Rate Constant for the N+ND Reaction

We present nonadiabatic quantum dynamical calculations on the two coupled potential energy surfaces (12A′ and 22A′) [J. Theor. Comput. Chem. 8, 849 (2009)] for the reaction. Initial state-resolved reaction probabilities and cross sections for the N+ND→N2+D reaction and N′+ND→N+N′D reaction for collision energies of 5 meV to 1.0 eV are determined, respectively. It is found that the N+ND→N2+D reaction is dominated in the N+ND reaction. In addition, we obtained the rate constants for the N+ND→N2+D reaction which demand further experimental investigations.

Reactive resonances in the F + CHD3 reaction—a quantum dynamics study

We present quantum dynamical investigations into the F + CHD(3) reaction. In our reduced dimensionality study we treat the two most important degrees of freedom, which describe the bond making and bond breaking explicitly, while treating the remaining spectator modes adiabatically. Cumulative as well as final state resolved reaction probabilities and cross sections are calculated for the two isotopic channels F + CHD(3) → FH + CD(3) and F + CHD(3) → FD + CHD(2). Our theoretical results are compared to the experimental findings of Liu and co-workers [Zhou et al., Mol. Phys., 2010, 108, 957]. Potential resonance states in the low collision energy regime are analyzed in detail employing Smith's lifetime matrix and bound state calculations.

Reaction dynamics of Br + HD: quantum wave packet on three potential energy surfaces

The initial state-resolved reaction probabilities, reaction cross-sections, and rate constants of the reaction Br + HD are computed on 3 potential energy surfaces (denoted as e-LEPS, MB2, and MB3, respectively) by carrying out quantum time-dependent wave packet calculations. The results show that the reactivity of Br + HD on MB3 is much stronger than that on e-LEPS and somewhat weaker than that on MB2. Both of the vibrational and the rotational excitation of reagent HD enhance the reaction, which depends on the PESs and the strongest enhancement effects are on e-LEPS.

Mode-specific reactivity ofCH4onPt(110)−(1×2): The concerted role of stretch and bend excitation

The state-resolved reaction probability of CH4 on Pt(110)−(1×2) was measured as a function of CH4 translational energy for four vibrational eigenstates comprising different amounts of C-H stretch and bend excitation. Mode-specific reactivity is observed both between states from different polyads and between isoenergetic states belonging to the same polyad of CH4. For the stretch/bend combination states, the vibrational efficacy of reaction activation is observed to be higher than for either pure C-H stretching or pure bending states, demonstrating a concerted role of stretch and bend excitation in C-H bond scission. This concerted role, reflected by the nonadditivity of the vibrational efficacies, is consistent with transition state structures found by ab initio calculations and indicates that current dynamical models of CH4 chemisorption neglect an important degree of freedom by including only C-H stretching motion.

Effect of collision energy on cross sections and product alignments for the C(1D) + H2 (v = 0, j = 0) insertion reactions

Quasi-classical trajectory (QCT) calculations of total reaction probabilities and vibrationally state-resolved reaction probabilities at total angular momentum J = 0 as a function of collision energy for the C(1D) + H2 (v = 0, j = 0) reactions have been performed on an ab initio potential-energy surface [ J. Chem. Phys. 2001, 115, 10701]. In addition, the integral cross sections as a function of collision energy have been carried out for the same reaction. The product rotational alignments have also been calculated, which are almost invariant with respect to collision energies.

State-resolved reactivity of CH4 on Pt(110)-(1×2): The role of surface orientation and impact site

The reactivity of methane (CH(4)) on Pt(110)-(1 x 2) has been studied by quantum state-resolved surface reactivity measurements. Ground state reaction probabilities, S(0)(v=0) congruent with S(0)(laser-off), as well as state-resolved reaction probabilities S(0)(2nu(3)), for CH(4) excited to the first overtone of the antisymmetric C-H stretch (2nu(3)) have been measured at incident translational energies in the range of 4-64 kJ/mol. We observe S(0)(2nu(3)) to be up to three orders of magnitude higher than S(0)(v=0), demonstrating significant vibrational activation of CH(4) dissociation on Pt(110)-(1 x 2) by 2nu(3) excitation. Furthermore, we explored the azimuthal and polar incident angle dependence of S(0)(2nu(3)) and S(0)(v=0) for a fixed incident translational energy E(t)=32 kJ/mol. For incidence perpendicular to the missing row direction on Pt(110)-(1 x 2) and polar angles theta>40 degrees, shadowing effects prevent the incident CH(4) molecules from impinging into the trough sites. Comparison of this polar angle dependence with reactivity data for incidence parallel to the missing rows yields state-resolved site specific reactivity information consistent with a Pt(110)-(1 x 2) reactivity that is dominated by top layer Pt atoms located at the ridge sites. A comparison of S(0)(v=0) measured on Pt(110)-(1 x 2) and Pt(111) yields a lower average barrier for Pt(110)-(1 x 2) by 13.7+/-2.0 kJ/mol.

Reaction Dynamics and Vibrational Spectroscopy of CH3D Molecules with Both C−H and C−D Stretches Excited

State-resolved reactions of CH3D molecules containing both C-H and C-D stretching excitation with Cl atoms provide new vibrational spectroscopy and probe the consumption and disposal of vibrational energy in the reactions. The vibrational action spectra have three different components, the combination of the C-H symmetric stretch and the C-D stretch (nu1 + nu2), the combination of the C-D stretch and the C-H antisymmetric stretch (nu2 + nu4), and the combination of the C-D stretch and the first overtone of the CH3 bend (nu2 + 2nu5). The simulation for the previously unanalyzed (nu2 + nu4) state yields a band center of nu0 = 5215.3 cm(-1), rotational constants of A = 5.223 cm(-1) and B = 3.803 cm(-1), and a Coriolis coupling constant of zeta = 0.084. The reaction dynamics largely follow a spectator picture in which the surviving bond retains its initial vibrational excitation. In at least 80% of the reactive encounters of vibrationally excited CH3D with Cl, cleavage of the C-H bond produces CH2D radicals with an excited C-D stretch, and cleavage of the C-D bond produces CH3 radicals with an excited C-H stretch. Deviations from the spectator picture seem to reflect mixing in the initially prepared eigenstates and, possibly, collisional coupling during the reaction.

The effects of the rotational excitation on the Br + H 2 reaction and its dependence on the potential energy surfaces

The initial rotation state-resolved reaction probabilities, reaction cross sections and the rate constants are calculated for the reaction Br + H 2 on three ab initio potential energy surfaces (PES, denoted e-LEPS, MB2 and MB3, respectively) by means of quantum time-dependent wave packet. The results show that on all the three PESs the rotational excitations of H 2 enhance the Br + H 2 reaction remarkably. Such enhancement effects depend on the anisotropy of the PESs and the strongest one is on e-LEPS incorporating its almost collinear feature.

Wave packet and quasiclassical trajectory calculations for the N( 2D) + H 2 reaction and its isotopic variants

The N( 2 D) + H 2( v = 0, j = 0) reaction and its HD and D 2 isotopic variants have been studied by means of quantum mechanical real wave packet and wave packet with split operator and quasiclassical trajectory methodologies on the potential energy surface of Ho et al. [J. Chem. Phys. 119 (2003) 6]. Total initial state-selected and final state-resolved reaction probabilities and product rotational distributions have been calculated for total angular momentum J = 0 in a broad range of collision energies. The real wave packet results are in very good agreement with the corresponding split operator wave packet calculations. A reasonable overall good agreement has been found between the wave packet and quasiclassical trajectory results. Integral cross-sections and thermal rate constants have been calculated from the wave packet reaction probabilities by means of standard J-shifting, refined J-shifting and uniform J-shifting methods in combination with the centrifugal sudden approximation for J > 0. Comparisons with available exact wave packet, quasiclassical trajectory and experimental results are made and discussed.

Theories of reactive scattering

This paper is an overview of the theory of reactive scattering, with emphasis on fully quantum mechanical theories that have been developed to describe simple chemical reactions, especially atom-diatom reactions. We also describe related quasiclassical trajectory applications, and in all of this review the emphasis is on methods and applications concerned with state-resolved reaction dynamics. The review first provides an overview of the development of the theory, including a discussion of computational methods based on coupled channel calculations, variational methods, and wave packet methods. Choices of coordinates, including the use of hyperspherical coordinates are discussed, as are basis set and discrete variational representations. The review also summarizes a number of applications that have been performed, especially the two most comprehensively studied systems, H+H2 and F+H2, along with brief discussions of a large number of other systems, including other hydrogen atom transfer reactions, insertion reactions, electronically nonadiabatic reactions, and reactions involving four or more atoms. For each reaction we describe the method used and important new physical insight extracted from the results.