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Highly accurate potential energy surfaces are critically important for chemical reaction dynamics. The large number of degrees of freedom and the intricate symmetry adaption pose a big challenge to accurately representing potential energy surfaces (PESs) for polyatomic reactions. Recently, our group has made substantial progress in this direction by developing the fundamental invariant-neural network (FI-NN) approach. Here, we review these advances, demonstrating that the FI-NN approach can represent highly accurate, global, full-dimensional PESs for reactive systems with even more than 10 atoms. These multi-channel reactions typically involve many intermediates, transition states, and products. The complexity and ruggedness of this potential energy landscape present even greater challenges for full-dimensional PES representation. These PESs exhibit a high level of complexity, molecular size, and accuracy of fit. Dynamics simulations based on these PESs have unveiled intriguing and novel reaction mechanisms, providing deep insights into the intricate dynamics involved in combustion, atmospheric, and organic chemistry. [ABSTRACT FROM AUTHOR]

We present a comprehensive investigation into the dissociative chemisorption of HOD on a rigid Ni(100) surface using an approximate full-dimensional (9D) quantum dynamics approach, which was based on the time-dependent wave-packet calculations on a full-dimensional potential energy surface obtained through neural network fitting to density functional theory energy points. The approximate-9D probabilities were computed by averaging the seven-dimensional (7D) site-specific dissociation probabilities across six impact sites with appropriate relative weights. Our results uncover a distinctive bond-selective effect, demonstrating that the vibrational excitation of a specific bond substantially enhances the cleavage of that excited bond. The product branching ratios are substantially influenced by which bond undergoes excitation, exhibiting a clear preference for the product formed through the cleavage of the excited bond over the alternative product. [ABSTRACT FROM AUTHOR]

We present a new approach to incorporate the geometric phase in the time-dependent wave packet calculations based on the analytic diabatic potential energy matrices for two-state systems connecting via a conical intersection. The approach only requires information on the location of the conical intersection and the adiabatic potential energy surface of the ground electronic state and merely takes the same computational cost as a diabatic calculation. Demonstrations of the benchmark H + H2/HD reactions show that the new approach can accurately include the geometric phase in dynamics calculation and can be easily extended to the cold regime where the GP effects become more pronounced. Due to its simplicity and numerical efficiency, the new approach has the potential to extend the dynamics study of the geometric effects to a wide range of reaction systems. [ABSTRACT FROM AUTHOR]

The mode-specific dynamics for the dissociative chemisorption of H2O on rigid Ni(100) is investigated by approximate nine-dimensional (9D) quantum dynamics calculations. The vibrational state-specific 9D dissociation probabilities are obtained by site-averaging the site-specific seven-dimensional results based on an accurate full-dimensional potential energy surface newly developed by neural network fitting to density functional theory energy points with the revised version of the Perdew, Burke, and Ernzerhof functional. The mode specificity of H2O/Ni(100) is very different from that of H2O/Ni(111) or H2O/Cu(111) whose reactivity enhancement by vibrational excitations is quite efficient. For H2O/Ni(100), it is found that the excitation in the symmetric stretching mode is more efficacious than increasing the translational energy in promoting the reaction, while the excitations in the asymmetric stretching mode and bending mode are less efficacious than the translational energy at low collision energies. These interesting observations can be attributed to the near central-barrier reaction for H2O/Ni(100), as well as large discrepancies between the site-specific mode specificities at different impact sites. The mode-specific dynamics obtained in this study is different from that obtained with the reaction path Hamiltonian approach, indicating the importance of full-dimensional quantum dynamics for gas–surface reactions. [ABSTRACT FROM AUTHOR]

We employ the initial state-selected time-dependent wave packet approach to an atom-triatom reaction to study the H + HOD → OH + HD/OD + H2 reaction without the centrifugal sudden approximation, based on an accurate potential energy surface which was recently developed by neural network fitting to high level ab initio energy points. The total reaction probabilities and integral cross sections, which are the exact coupled-channel results, are calculated for the HOD reactant initially in the ground and several vibrationally excited states, including the bending excited state, OD stretching excited states, OH stretching excited states, and combined excitations of them. The reactivity enhancements from different initial states of HOD are presented, which feature strong bond-selective effects of the reaction dynamics. The current results for the product branching ratios, reactivity enhancements, and relative cross sections are largely improved over the previous calculations, in quantitatively good agreement with experiment. The thermal rate constant for the title reaction and the contributions from individual vibrational states of HOD are also obtained. [ABSTRACT FROM AUTHOR]

This study presents a parallel algorithm for high-dimensional quantum dynamics simulations in poly atomic reactions, integrating distributed- and shared-memory models. The distributions of the wave function and potential energy matrix across message passing interface processes are based on bundled radial and angular dimensions, with implementations featuring either two- or one-sided communication schemes. Using realistic parameters for the H + NH3 reaction, performance assessment reveals linear scalability, exceeding 90% efficiency with up to 600 processors. In addition, owing to the universal and concise structure, the algorithm demonstrates remarkable extensibility to diverse reaction systems, as demonstrated by successes with six-atom and four-atom reactions. This work establishes a robust foundation for high-dimensional dynamics studies, showcasing the algorithm's efficiency, scalability, and adaptability. The algorithm's potential as a valuable tool for unraveling quantum dynamics complexities is underscored, paving the way for future advancements in the field. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A framework for quantum state-to-state integral and differential cross sections of triatomic reactive scattering using the Multi-Configuration Time-Dependent Hartree (MCTDH) method is introduced, where a modified version of the Heidelberg MCTDH package is applied. Parity of the system is adopted using only non-negative helicity quantum numbers, which reduces the basis set size of the single particle functions in angular degree of freedom almost by half. The initial wave packet is constructed in the space-fixed frame, which can accurately account for the centrifugal potential. By using the reactant-coordinate-based method, the product state-resolved information can be accurately extracted. Test calculations are presented for the H + H2 reactive scattering. This work demonstrates the capability of the MCTDH method for extracting accurate state-to-state integral and differential cross sections. As an efficient scheme for high-dimensional problems, the MCTDH method may be promising for the study of product state-resolved cross sections for polyatomic reactive systems. [ABSTRACT FROM AUTHOR]

The initial state-selected time-dependent wave packet approach to an atom-triatom reaction is employed to study the H + H2O → H2 + OH reaction without the centrifugal sudden approximation. The total reaction probabilities and integral cross sections, which are the exact coupled-channel results, are calculated for the H2O reactant initially in the ground and several vibrationally excited states, including bending excited states, first and second stretching excited states, and simultaneous excitations of both bending and stretching modes. The reactivity enhancements from different initial states of the H2O reagent are presented and discussed in detail. The thermal rate constant for the title reaction and the contributions to this coefficient from individual vibrational states of H2O are also obtained and compared with the previous theoretical and experimental data. [ABSTRACT FROM AUTHOR]

In this work, the permutation invariant polynomial neural network (PIP-NN) approach is employed to construct a quasi-diabatic Hamiltonian for system with non-Abelian symmetries. It provides a flexible and compact NN-based diabatic ansatz from the related approach of Williams, Eisfeld, and co-workers. The example of H 3 + is studied, which is an (E + A) × (e + a) Jahn–Teller and Pseudo-Jahn–Teller system. The PIP-NN diabatic ansatz is based on the symmetric polynomial expansion of Viel and Eisfeld, the coefficients of which are expressed with neural network functions that take permutation-invariant polynomials as input. This PIP-NN-based diabatic ansatz not only preserves the correct symmetry but also provides functional flexibility to accurately reproduce ab initio electronic structure data, thus resulting in excellent fits. The adiabatic energies, energy gradients, and derivative couplings are well reproduced. A good description of the local topology of the conical intersection seam is also achieved. Therefore, this diabatic ansatz completes the PIP-NN based representation of DPEM with correct symmetries and will enable us to diabatize even more complicated systems with complex symmetries. [ABSTRACT FROM AUTHOR]

The exchange processes of D + H2O and D + HOD reactions are studied using initial state-selected time-dependent wave packet approach in full dimension. The total reaction probabilities for different partial waves, together with the integral cross sections, are obtained both by the centrifugal sudden (CS) approximation and exact coupled-channel (CC) calculations, for the H2O(HOD) reactant initially in the ground rovibrational state. In the CC calculations, small resonance peaks in the reaction probabilities and quick diminishing of the resonance peaks with the increase of total angular momenta J do not lead to clear step-like features just above the threshold in the cross sections for the title reactions, which are different in other isotopically substituted reactions where the hydrogen atom was included as the reactant instead of the deuterium atom [B. Fu, Y. Zhou, and D. H. Zhang, Chem. Sci. 3, 270 (2012); B. Fu and D. H. Zhang, J. Phys. Chem. A 116, 820 (2012)]. It is interesting that the shape resonance-induced features resulting from the reaction tunneling are significantly diminished accordingly in the reactions of the deuterium atom and H2O or HOD, owing to the weaker tunneling capability of the reagent deuterium atom in the title reactions than the reagent hydrogen atom in other reactions. In the CS calculations, the resonance peaks persist in many partial waves but cannot survive the partial-wave summations. The cross sections for the D′ + H2O → D′OH + H and D′ + HOD → D′OD + H reactions are substantially larger than those for the D′ + HOD → HOD′ + D reaction, indicating that the D′/H exchange reactions are much more favored than the D′/D exchange. [ABSTRACT FROM AUTHOR]

We describe a time-dependent wavepacket based method for the calculation of the state-to-state cross sections for the Cl+H2 reaction including all couplings arising from the nonzero spin and electronic orbital angular momenta of the Cl atom. Reactant-product decoupling allows us to use a physically correct basis in both the reactant and the product arrangements. Our calculated results agree well with the experimental results of Yang and co-workers. We also describe a model with two coupled potential energy surfaces, which includes the spin-orbit coupling, which is responsible for the largest non-Born–Oppenheimer effects in the Cl+H2 reaction but neglects the off-diagonal electronically diabatic coupling and all Coriolis couplings due to the electronic spin and orbital angular momenta. The comparison of the results of the full six-state and two-state models with an electronically adiabatic (one-state) description reveals that the latter describes well the reaction out of the ground spin-orbit state, while the two-state model, which is computationally much faster than the full six-state model, describes well the reaction from both the ground and excited spin-orbit states. [ABSTRACT FROM AUTHOR]

Thawed Gaussian wavepackets have been used in recent years to compute approximations to the thermal density matrix. From a numerical point of view, it is cheaper to employ frozen Gaussian wavepackets. In this paper, we provide the formalism for the computation of thermal densities using frozen Gaussian wavepackets. We show that the exact density may be given in terms of a series, in which the zeroth order term is the frozen Gaussian. A numerical test of the methodology is presented for deep tunneling in the quartic double well potential. In all cases, the series is observed to converge. The convergence of the diagonal density matrix element is much faster than that of the antidiagonal one, suggesting that the methodology should be especially useful for the computation of partition functions. As a by product of this study, we find that the density matrix in configuration space can have more than two saddle points at low temperatures. This has implications for the use of the quantum instanton theory. [ABSTRACT FROM AUTHOR]

The time-dependent wave packet method was extended to calculate the state-to-state differential cross section for the title four-atom abstraction reaction with H2O in the ground rovibrational state. One spectator OH bond length was fixed in the study, but the remaining five degrees of freedom were treated exactly. It was found that (a) the differential cross section changes from being strongly backward peaked at low collision energy to sideward scattering at E=1.4 eV, and (b) the rotational state-resolved differential cross section for H2 differs substantially from that for OH. [ABSTRACT FROM AUTHOR]

A new continuous configuration time-dependent self-consistent field method has been developed to study polyatomic dynamical problems by using the discrete variable representation for the reaction system, and applied to a reaction system coupled to a bath. The method is very efficient because the equations involved are as simple as those in the traditional single configuration approach, and can account for the correlations between the reaction system and bath modes rather well. [ABSTRACT FROM AUTHOR]

The initial state selected time-dependent wave packet method has been extended to calculate the total reaction probability for atom-triatom reactions with total angular momentum J > 0 by treating both bonds in the triatom reagent reactively. The total exchange and abstraction reaction probabilities for the title reaction with J = 15 calculated with 2 K-blocks (the projection of the total angular momentum on the body-fixed axis) show that one has to treat both OH bonds in the H[SUB2]O reagent reactively for the exchange reaction, but for the abstraction reaction one can treat one OH bond as a spectator bond to get accurate results. This is in accord with what had been found for the total reaction probabilities for J=0 [Phys. Rev. Lett. 89, 103201 (2002)]. The J= 15 reaction probabilities also show that the CS (centrifugal sudden) approximation is inadequate for the title reaction, in particular for the abstraction reaction. The integral cross sections for the abstraction reaction, calculated without the CS approximation but by freezing one OH bond in the H[SUB2]O reagent for the ground and first vibrationally excited states, are found to be substantially larger than the corresponding CS integral cross sections. However, the integral cross section for the ground vibrational state is still much smaller than the existing experimental result. Since the treatment of freezing OH bond is not expected to introduce any noticeable error, it is conceivable that the experiments overestimated the integral cross section for the abstraction reaction. [ABSTRACT FROM AUTHOR]

The initial state selected time-dependent wave packet method has been developed to study the H+ CH[sub 4] reaction in seven dimensions by employing the model developed by Palma and Clary [J. Chem. Phys. 112, 1859 (2000)]. The latter eight-dimensional model only assumes that the nonreacting CH[sub 3] group keeps a C[sub 3V] symmetry in reaction. The CH bond lengths in the nonreacting CH[sub 3] group were fixed in the study to reduce the number of degrees of freedom to seven. Our calculations reveal that it is very important to accurately deal with the umbrella motion of the CH[sub 3] group while studying this reaction. We investigated the effects of the fundamental vibrational excitations of CH[sub 4] on the reaction. Finally, we compare our rate constant for the ground rovibrational initial state with available experimental and other theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents fully converged integral cross sections for the D[sub 2](j[sub 1]=0,2,4)+OH(j[sub 2]=0,2,4)→HOD+D reaction on the YZCL2 potential energy surface. It is found that the influence of reagent rotation excitation on reactivity is relatively mild compared with that of the D[sub 2] vibration excitation, but is fairly important to the thermal rate constant at low temperature. In general, the OH rotation excitation tends to hinder the reaction, and the D[sub 2] rotation excitation tends to enhance the reactivity. The simultaneous reagent rotation has some correlated effect, with the influence of the D[sub 2] rotation excitation considerably dependent on the OH rotation excitation. It is also found that the reaction is strongly dependent on j[sub 12] (the coupled angular momentum between j[sub 1] and j[sub 2]), K[sub 0] (the projection of the reagent rotation on the body fixed axis), and the parity of the system, in particular for either the OH or D[sub 2] rotationally excited initial states, but this dependence becomes relatively weaker as the collision energy increases. Excellent agreement achieved between theory and experiment on the thermal rate coefficients for temperatures up to 400 K clearly shows that the YZCL2 potential energy surface is capable of producing “quantitatively” accurate results for the title reaction. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We report dynamics on two interpolated global potential energy surfaces (PES) for the H[sub 2]+OH reaction. The first PES is based on both QCISD(T)/6-311++G(3df,2pd) and MRCI/aug-cc-pVTZ ab initio calculations. In the second version, the energies at the interpolation data points are improved to the UCCSD(T)/aug-cc-pVQZ level. Fully converged integral cross sections were calculated on these two PESs for the title reaction for the ground rovibrational and two rotationally excited initial states. Good agreement between theory and experiment for rate coefficients for temperatures up to 1050 K are only achieved on the second PES. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Examines the effects of rotational excitation of reagents on the dynamics of the H2+OH reaction. Purpose of the extension of time-dependent wave packet method; Ways to obtain the thermal rate constant; Theoretical methodology of the initial state selected wave packet approach to diatom-diatom reactions.

Discusses the accuracy of an interpolation approach to molecular potential energy surfaces for quantum reactive scattering by comparison of the quantum reaction probability for a model surface and its interpolated approximation. Effective convergence of an ab initio surface with the size of the interpolation data set.

Studies the diffusion dynamics of a hydrogen atom on a copper surface in the uncorrelated hopping regime using the transition state wave packet approach to the thermal rate constant. Efficiency of the approach; Zero-point-energy effect of the copper modes on the flux-flux autocorrelation function; Calculation of the approximate quantum correction to the transition state theory.

Calculates integral cross sections for diatom-diatom chemical reactions without the centrifugal sudden (CS) approximation by extending the initial state selected time-dependent wave packet method. Description of the converged cross section for the ground rovibrational state of the title reaction; Accuracy of the CS approximation to the reaction.

Evaluates the adequacy of cumulative reaction probability (CRP) calculation using centrifugal sudden approximation. Provision of accurate thermal rate constant by the CRP Boltzmann average; Demonstration of the J-shifting approximation; Comparison between the CS rate constant and the ground rovibrational state of the reagents.

Reports on the calculation of the cumulative reaction probability for the four-atom reaction H[sub 2] + OH ->H + H[sub 2]O using one of the formulations of Miller, Schwartz and Tromp and the transition state wave packet approach of Zhang and Light. Use of transition state normal coordinates.

A time-dependent wave packet method has been employed to calculate the state-to-state reaction probability for the H+H2O(0,0,0)→H2(v1,j1)+OH(v2,j2) reaction for J=0 and initial nonrotating H2O on the modified Schatz–Elgersman potential energy surface in full six dimensions (6D). Starting from a wave packet for an atom–triatom asymptotic state in atom–triatom Jacobi coordinates, we transfer the wave packet to diatom–diatom Jacobi coordinates after the wave packet moves into the interaction region. Propagation is then carried out in the diatom–diatom Jacobi coordinates until the reaction flux measured in the diatom–diatom asymptotic region is converged. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A new time-dependent approach to the cumulative reaction probability, N(E), has been developed based on the famous formulation given by Miller and co-workers [J. Chem. Phys. 79, 4889 (1983)], N(E)=[(2π)2/2] tr[δ(E-H)Fδ(E-H)F]. Taking advantage of the fact that the flux operator has only two nonzero eigenvalues, we evaluate the trace efficiently in a direct product basis of the first flux operator eigenstates and the Hamiltonian eigenstates on the dividing surface (internal states). Because the microcanonical density operator, δ(E-H), will eliminate contributions to N(E) from an internal state with the energy much higher than the total energy E, we can minimize the number of internal states required by choosing a dividing surface with the lowest density of internal states. If the dividing surface is located in an asymptotic region, one just needs to include all the open channels, i.e., with internal energy lower than the total energy. Utilizing the Fourier transform for δ(E-H), we can obtain the information for all the energies desired by propagating these wave packets once. Thus the present approach will be much more efficient than the initial state selected wave packet (ISSWP) approach to N(E) for systems with many rotation degrees of freedom because the density of states in asymptotic region for such systems is much higher than that in the transition state region. With the present method one can also calculate the cumulative reaction probability from an initial state (or to a final state) by locating the second flux operator in the corresponding asymptotic region. This provides an alternative to the ISSWP approach which may be more efficient if the reaction probabilities from a large number of initial states are desired. The method is applied to the 3D H + H2 (even rotation) reaction for J=0 by locating the first dividing surface in the transition state region. The demonstration also shows an aspect less than ideal; the contribution... [ABSTRACT FROM AUTHOR]

A time-dependent wave packet method has been developed to study atom–triatom ABC+D→AB+CD reactions in full six dimensions (6D). The approach employs a body-fixed coupled angular momentum basis for three angular coordinates, and three 1D bases for three radial coordinates. It permits the calculation of diatom AB vibrational state resolved total reaction probability for an initial rovibrational state of the triatom ABC. The approach is applied to study the H+H2O→H2+OH reaction on the modified Schatz–Elgersman potential energy surface. Initial state-selected total reaction probabilities are presented for initial ground and several vibrationally excited states of H2O for total angular momentum J=0, along with the final OH vibrational state distributions. We also report the cross sections for reaction from the initial ground vibrational and the first bending excited states of H2O. Comparisons are made between our results and those from other theoretical calculations and experiments. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The determination of potential energy surfaces (PES) from values calculated ab initio at a set of points or from spectral data (vibration–rotation energy level information and rotation constants) are important and often difficult problems. The former is a ‘‘potential interpolation’’ problem, the latter a ‘‘potential inversion’’ problem. These are indeterminate problems in which the known data is insufficient to yield a unique solution. We present here a new constrained variational approach to the direct solution of these problems. The constraints are the known exact values of the potential or the exact perturbation corrections desired. The variational functional is chosen to provide control of the magnitude and smoothness of the correction function or potential. The method is very simple, very fast computationally, and yields exact solutions to the perturbation or interpolation equations in a single application. The potential inversion is completed by iteration to converge the perturbation solutions for a given set of assigned levels, and then by repeating with additional levels assigned in sequence to the data set to yield a physically acceptable PES very quickly. This procedure yields a smooth PES from which the energy levels in the dataset are calculated exactly. Information on rotational constants may also be used. Both interpolation and inversion procedures are applied to the the two dimensional (R,θ) PES for ArOH(A 2Σ+). A combined application of these two procedures is also presented in the paper, where we first interpolate a PES from ab initio points and then correct the ab initio fitted surfaces using spectral data. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A time-dependent (TD) quantum wavepacket calculation of reaction probabilities is reported for the reaction HO + CO → H + CO2 for total angular momentum J=0. The dynamics calculation employs the potential-averaged five-dimensional model (PA5D) and is made possible by using a normalized angular quadrature scheme to minimize the requirement for computer memory. Reaction probabilities are obtained from the ground state as well as rotationally excited state in either one of the reactant diatoms. Strong resonances are found in the present study and calculated reaction probabilities are dominated by many narrow and overlapping resonances. These features are in qualitative agreement with several lower dimensional quantum dynamics studies. However, quantitative comparison of the present result with previously reported quantum calculations, including a recent planar four-dimensional (4D) calculation of Goldfield et al., shows that our calculated reaction probabilities are much smaller than those found in reduced dimensionality calculations. We also found reaction probability to be more sensitive to the rotational motion of CO than of HO. In addition to reaction probabilities, the bound state calculation for the stable intermediate complex HOCO has also been carried out and energies of several low-lying vibrational states are obtained. The potential energy surface (PES) of Schatz–Fitzcharles–Harding (SFH) is used in all the calculates presented in this paper. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Converged full-dimensional (6D) quantum mechanical calculation of energy levels of intramolecular stretching excited (HF)2(ν1ν2) is presented for (ν1ν2)=(01), (10), (02), (20), and (11). The bound state calculation for the excited HF dimer employs the SQSBDE potential energy surface of Quack and Suhm and is for total angular momentum J=0. This calculation provides the first rigorous theoretical result of energy levels for HF stretching excited HF dimer in full dimensions. The calculated fundamental transition frequencies are ν1=3940.6 cm-1 and ν2=3896.4 cm-1. These values are somewhat larger than the corresponding experimental measurement of 3930.9 cm-1 for ν1 and 3868.3 cm-1 for ν2. The overtone frequencies are calculated to be 2ν1=7713.5 cm-1, 2ν2=7642.5 cm-1, and ν1+ν2=7841.8 cm-1. The theoretical tunneling splittings of the fundamentals ν2 and ν1 are, respectively, a factor of 5.3 and 3.7 smaller than the ground state splitting, compared to a factor of 3 from the experimental measurement. The splittings of the overtone states 2ν2, 2ν1, and ν1+ν2 are smaller than that of the ground state by factors of 9.6, 48, and 1.8, respectively. Some of the calculated energy levels of excited (HF)2 are spectroscopically characterized and assigned. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Accurate time-dependent (TD) quantum wavepacket calculations are reported for the combustion reaction HD+OH. Due to the lack of symmetry, the HD+OH reaction has roughly twice the number of channels of the corresponding H2+OH reaction and produces two distinguishable products–HOH and HOD. In order to make the TD calculation possible on workstations with limited memories, we employed a normalized quadrature scheme in the wavepacket propagation by the split-operator propagator. The normalized quadrature scheme eliminates the need to store large matrices during the wavepacket propagation while preserving the unitarity of the split-operator propagator and producing numerically stable results. This approach made TD dynamics calculations possible on small-memory workstations for the title reaction and for other polyatomic reactions. Reaction probabilities, cross sections, rate constants, and reaction branching ratios are reported in this paper for the title reaction. The observed strong dependence of the reaction probabilities on the reactive HD rotation and the relative weak dependence on the nonreactive OH rotation are explained in terms of a steric effect. The isotope effect in the branching ratio is examined and physical explanation is given for the observed branching ratio at low and high kinetic energies. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Detailed results of the converged full-dimensional 6D quantum calculations of the vibrational levels of (HF)2, (DF)2, and HFDF, for total angular momentum J=0, are presented. The ab initio 6D potential energy surface by Quack and Suhm was employed. This study provides a comprehensive description of the bound state properties of the HF dimer and its isotopomers, including their dissociation energies, frequencies of the intermolecular vibrations, tunneling splittings, and extent of wave function delocalization. Quantum number assignment of the calculated eigenstates by plotting different cuts through the wave functions worked rather well for (HF)2, but proved to be much harder for (DF)2 and HFDF, indicating stronger vibrational mode mixing in these species. The ground-state tunneling splitting for the HF dimer from our exact 6D calculations, 0.44 cm-1, is very close to that from a previous 4D rigid-rotor calculation, 0.48 cm-1 [J. Chem. Phys. 99, 6624 (1993)]. This is in disagreement with the result of a recent 6D bound state calculation for (HF)2 by Necoechea and Truhlar, which gave a ground-state tunneling splitting a factor of 3.7 times larger than the 4D result. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present in this paper a time-dependent approach to the calculation of photofragmentation dynamics using the flux formulation. The method is essentially a time-dependent version of the flux formulation for photodissociation calculation recently pursued by Manolopoulos and Alexander. In the present approach, the partial decay width of photofragmentation is obtained by calculating the flux at a given surface using a time-dependent method. This particular time-dependent approach for photofragmentation has two principal advantages. First, it is superior in computational scaling: CPU time ∝Nα(α<2) vs N3 in standard time-independent propagation method. Second, it is quite straightforward to handle the photofragmentation process involving rearrangement with the application of optical potentials. In addition, no bound state projection is necessary using the time-dependent flux method, which is required using the time-dependent golden rule method. This time-dependent method is applied to the calculation of decay width for vibrational predissociation of hydrogen-bonded HFDF, and the computed lifetime are compared with the recent experimental measurement of Farrell and Nesbitt. We also present the results of the full dimensional (6D) calculation of bound state energies for the HFDF complex. The exact dissociation energies are calculated to be 1057.33 cm-1 for (HF)2, 1166.6 cm-1 for (DF)2, 1142.7 cm-1 for HF–DF, and 1078.4 cm-1 for DF–HF. All theoretical calculations have used the SQSBDE potential energy surface due to Quack and Suhm. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We show in this paper a time-dependent (TD) quantum wave packet calculation for the combustion reaction H+O2 using the DMBE IV (double many-body expansion) potential energy surface which has a deep well and supports long-lived resonances. The reaction probabilities from the initial states of H+O2(3Σ-g) (v=0–3, j=1) for total angular momentum J=0 are obtained for scattering energies from threshold up to 2.5 eV, which show numerous resonance features. Our results show that, by carrying out the wave packet propagation to several picoseconds, one can resolve essentially all the resonance features for this reaction. The present TD results are in good agreement with other time-independent calculations. A particular advantage of the time-dependent approach to this reaction is that resonance structures—strong energy dependence of the reaction probability—can be mapped out in a single wave packet propagation without having to repeat scattering calculations for hundreds of energies. We also report calculations of some low-lying vibrational energies of the hydroperoxyl radical HO2(2A‘) and their spectroscopic assignments. The vibrational frequencies of HO2(2A‘) on the DMBE IV potential energy surface are lower than experimental values, indicating the need to further improve the accuracy of the potential energy surface. [ABSTRACT FROM AUTHOR]

Extending our previous studies for the H2+OH reaction in five mathematical dimensions (5D) [J. Chem. Phys. 99, 5615 (1993); 100, 2697 (1994)], we present in this paper a full-dimensional (6D) dynamics study for the title reaction. The 6D treatment uses the time-dependent wave-packet approach and employs discrete variable representations for three radial coordinates and coupled angular momentum basis functions for three angular coordinates. The present 6D study employs an energy projection method to extract reaction probabilities for a whole range of energies from a single wave-packet propagation, while previous studies produced only energy-averaged reaction probability from a single wave-packet propagation. The application of the energy-projection method allows us to efficiently map out the energy dependence of the reaction probability on a fine grid which revealed surprisingly sharp resonancelike features at low collision energies on the Schatz–Elgersma potential surface. Our calculation shows that the potential-averaged 5D treatment can produce reaction probabilities essentially indistinguishable from the full-dimensional result. We also report initial state-selected reaction cross sections and rate constants which are in good agreement with our previous calculations. The effect of OH vibration on H2+OH reaction is examined in the present study and our calculation shows that the OH vibration can enhance the rate constant by about a factor of 1.7 in good agreement with the experimental estimate of about 1.5. [ABSTRACT FROM AUTHOR]

A new quantum mechanical study on UV photodissociation of H2O2 at 248 and 266 nm using a 2D fit to the Schinke–Staemmler’s (SS) potential energy surface (PES) [Chem. Phys. Lett. 145, 486 (1988)] is reported. The rotational distributions of the product OH on both the A and B surfaces are found to be considerably hotter than those obtained in a previous quantum study [J. Chem. Phys. 98, 6276 (1993)] using an empirical PES with a very weak dependence on the torsional angle [lowercase_phi_synonym]. The new calculation shows that the rotation distributions in both the A and B states are Gaussianlike with a maximum at j=8 on the A surface and at j=9 on the B surface at 248 nm. Similar distributions are found at 266 nm, but with the maximum shifting lower by approximately one quanta in both the A and B states. The dissociation preferentially produces OH rotations with a high j1∼j2 correlation. These conclusions are in excellent agreement with the classical calculation of Schinke–Staemmler at 193 nm photolysis. Although the j distribution (rotation of OH) is similar on both surfaces, the j12(j[accent:_Right_arrow]12=j[accent:_Right_arrow]1+j[accent:_Right_arrow]2) distribution, which reflects the vector correlation of j[accent:_Right_arrow]1 and j[accent:_Right_arrow]2, is quite different on two surfaces. Our calculation shows that the A surface gives rise to more bending excitation than the B surface, reflected by a hotter j12 distribution on the A surface. The A and B state branching ratio of H2O2 is also evaluated at 248 and 266 nm photolysis. [ABSTRACT FROM AUTHOR]

Following a previous Communication [J. Chem. Phys. 99, 5615 (1993)], which reported several initial state-selected total reaction probabilities for the title reaction for J=0, we present in this paper the methodologies of the previous calculation and show results of new calculations. In particular, the present calculations are extended to all angular momentum J>=0 and obtained reaction cross sections for a range of energies using the centrifugal sudden (CS) approximation. The computed cross sections are used to obtain the state-specific thermal rate constants for both the ground and the excited vibrations of H2. The dynamics calculation, in which the nonreactive OH bond is frozen, includes explicitly five degrees of freedom in the time-dependent quantum dynamics treatment. The comparison of the present accurate cross sections with other approximate theoretical calculations shows discrepancies. The computed rate constants (from the ground rotation state) are larger than experimental measurements at low temperatures, the v=0 rate is larger than the corresponding experimental rate by a factor of 1.8, and the ratio of v=1 to v=0 rate is a factor of 4.8 greater than the experimental ratio at 300 K. The calculated reaction rates are also compared to those of other theoretical calculations and the differences are discussed in the text. [ABSTRACT FROM AUTHOR]

This is a followup and extension of a previous study [J. Chem. Phys. 98, 5978 (1993)] that reported decay width calculations for vibrational predissociation (VP) of (HF)2 for total angular momentum J=0 using a hybrid potential energy surface. Detailed quantum dynamics calculations of decay widths in (HF)2 are given in the present study for both J=0 and J=1 and results are shown on both the Quack and Suhm surface and the surface of Bunker et al. The lower state of the tunneling doublet in ground vibrational (HF)2 for J=1, K=0 has the - exchange symmetry (tunneling symmetry) in contrast to the + symmetry that the lower state has for J=0. The calculated VP decay widths on two potential energy surfaces (PES) are noticeably different from each other, underscoring the sensitivity of decay widths to details of interaction forces in hydrogen-bonded complexes. The VP dynamics on the PES of Quack and Suhm gives a lifetime differential between ν1 and ν2 excitations that is in close agreement with experiments. The calculations on the PES of Bunker et al. do not exhibit enough sensitivity in lifetime between ν1 and ν2 excitations. In general, theoretical calculations of product rotation distributions are in reasonably good agreement with experimental results. In particular, about 90% of the excess energy in vibrational predissociation of (HF)2 goes into rotations of HF fragments, in good agreement with the recent experimental measurement of Bohac et al. [ABSTRACT FROM AUTHOR]

A time-dependent wave packet method has been employed to compute initial state-specific total reaction probabilities for the benchmark reaction H2+OH→H2O+H on the modified Schatz–Elgersman potential energy surface which is derived from ab initio data. In our quantum treatment, the OH bond length is fixed but the remaining five degrees of freedom are treated exactly in the wave packet calculation. Initial state-specific total reaction probabilities for the title reaction are presented for total angular momentum J=0 and the effects of reagents rotation and H2 vibration on reaction are examined. [ABSTRACT FROM AUTHOR]

Quantum dynamics calculations are carried out to study ultraviolet (UV) photodissociation of H2O2 at a photon energy of 248 nm. The photodissociation process of hydrogen peroxide is simulated by the standard two-surface model using an ab initio ground potential energy surface and a simple empirical excited surface. The time-dependent approach is employed in quantum dynamics calculations due to the short-time nature of the dissociation process. In this calculation, two high-frequency OH stretching modes are kept frozen but the remaining four degrees of freedom are treated fully quantum mechanically. The quantum calculation fully utilizes the symmetry properties of the system and each symmetry block is computed separately. The computed rotational state distribution of the OH fragments is in qualitative agreement with the classical calculation of Bersohn and Shapiro, with most of the excess energy being carried away by the relative translational motion of the OH fragments. The effect of torsional mode on the rotational state distribution is investigated by calculating the Franck–Condon factors of photodissociation using torsionally excited bound state wave function. Our calculated rotational state distribution, averaged over contributions of two parity-splitting states, is found to be in good agreement with that observed in experiment. [ABSTRACT FROM AUTHOR]

Coupled channel golden-rule quantum mechanical calculations of total and partial decay widths are reported for vibrational predissociation of HF dimer. In this calculation, an ab initio potential energy surface is employed in both bound and scattering calculations but the vibrational coupling is given by an electrostatic interaction. The computed lifetime of HF dimer is 4.0 and 4.8 ns for ν2+ and ν2- (‘‘bound-H’’) excitation, and 11 ns for both ν1+ and ν1- (‘‘free-H’’) excitations. These theoretical lifetimes are compared to the experimental values of about 1 ns for the ν2 excitation and about 20 ns for the ν1 excitation. We also present rotational state distributions of HF monomers which are in qualitative agreement with the experimental measurement of Bohac et al. [J. Chem. Phys. 96, 6681 (1992)]. [ABSTRACT FROM AUTHOR]

Calculations of the total and partial decay widths are presented for the vibrational predissociation of H2HF. The calculation is done for the total angular momentum J=0 of the molecule and for the dissociation process H2HF(v=1)→H2(v=0)+HF(v=0). A time-dependent golden rule wave packet method is employed in the numerical calculation for the decay widths. The lifetime of the complex is determined from our calculation to be about 600 ns for para- and 1600 ns for ortho-H2HF. These values are much larger than the experimentally measured value of 27 ns for ortho-H2HF. The large discrepancy in lifetime for H2HF is in sharp contrast to the excellent agreement in lifetime for D2HF between theory and experiment, though the same potential energy surface is used in both calculations. We also present the rotational state distribution of the fragments H2 and HF following the vibrational predissociation of H2HF. It is found that about 58% of the final rotational population is in j=4 states of H2 for para-H2HF and about 48% is in j=5 states of H2 for ortho-H2HF. [ABSTRACT FROM AUTHOR]

Calculations of the total and partial decay widths are presented for the vibrational predissociation of D2HF. The calculation is done for the total angular momentum J=0 of the molecule and for the dissociation process D2HF(v=1)→D2(v=1)+HF(v=0), which is the dominant decaying channel. A time-dependent wave packet approach in the golden rule approximation is employed in the numerical calculation for the decay widths. Our computed total and partial decay widths are in good agreement with those from a time-independent scattering calculation. The time-dependent golden rule wave packet method, which does not solve coupled channel scattering equations, offers an efficient alternative to the time-independent scattering method for computing the decay widths in vibrational predissociation for relatively large molecules. The total time of propagation required in the golden rule wave packet calculation is determined by the duration time of the final state interaction between the fragments on the vibrationally deexcited adiabatic potential surface. This interpretation clearly explains the fact that only a short time is needed in our wave packet propagation, regardless of how long the lifetime of the predissociating state may be. [ABSTRACT FROM AUTHOR]

The time-dependent formulation for vibrational predissociation of weakly bound complexes within the golden rule treatment is presented. The quantum wave packet propagation in this formulation eliminates the difficulty of strenuous long time propagation of the full wave function due to long-lived resonance which occurs in the more exact time-dependent treatment. As a result, the new time-dependent treatment of vibrational predissociation essentially parallels that of direct photodissociation and therefore requires only short time propagation of the wave function. The wave packet propagation is efficiently carried out in the interaction picture and numerical calculations of rotational state distributions and the total decay width are presented for vibrational predissociation of HeCl2. Correct rotational state distribution can be obtained with only a few time propagation steps owing to the use of large step size allowed in the interaction picture. Our approach provides an efficient method for the calculation of vibrational predissociation for more complex systems such as those with more than three atoms. [ABSTRACT FROM AUTHOR]

A full-dimensional ab initio potential energy surface (PES) and dipole moment surface (DMS) for the ammonia dimer (NH3)2 are reported. The database of the PES consists of 27 736 ab initio energy points and all of these points were calculated at the UCCSD(T)-F12a/AVTZ level. The PES was fitted by using the fundamental invariant neural network (FI-NN) method that satisfies the permutational symmetry of identical atoms, and the root mean square fitting error for the PES is very small as low as 0.562 meV. The geometries for the (NH3)2 DMS are the same as those used for the PES and are calculated at the XYG3/AVTZ level. This PES can describe a variety of internal floppy motions, including all kinds of vibrational modes no matter intermolecular or intramolecular. The CCSD(T)-PES can dissociate correctly to two NH3 monomers, with De = 1135.55 cm−1 (13.58 kJ/mol) which agrees accurately with the 13.5 ± 0.3 kJ/mol predicted by previous work. [ABSTRACT FROM AUTHOR]

Polanyi's rules predict that a late-barrier reaction yields vibrationally cold products; however, experimental studies showed that the H2 product from the late-barrier H + H2O(|04⟩−) and H + HOD(vOH = 4) reactions is vibrationally hot. Here, we report a potential-averaged five-dimensional state-to-state quantum dynamics study for the H + HOD(vOH = 0–4) → H2 + OD reactions on a highly accurate potential energy surface with the total angular momentum J = 0. It is found that with the HOD vibration excitation increasing from vOH = 1 to 4, the product H2 becomes increasingly vibrationally excited and manifests a typical characteristic of an early barrier reaction for vOH = 3 to 4. Analysis of the scattering wave functions revealed that vibrational excitation in the breaking OH bond moves the location of dynamical saddle point from product side to reactant side, transforming the reaction into an early barrier reaction. Interestingly, pronounced oscillatory structures in the total and product vibrational-state-resolved reaction probabilities were observed for the H + HOD(vOH = 3, 4) reactions, in particular at low collision energies, which originate from the Feshbach resonance states trapped in the bending/torsion excited vibrational adiabatic potential wells in the entrance region due to van der Waals interactions. [ABSTRACT FROM AUTHOR]

The 6D time-dependent wave packet calculations were performed to explore H2 dissociation on Ag, Au, and two AgAu alloy surfaces, using four newly fitted potential energy surfaces based on the neural network fitting to density functional theory energy points. The ligand effect resulting from the Ag–Au interaction causes a reduction in the barrier height for H2+Ag/Au(111) compared to H2+Ag(111). However, the scenario is reversed for H2+Au/Ag(111) and H2+Au(111). The 6D dissociation probabilities of H2 on Ag/Au(111) surfaces are significantly higher than those on the pure Ag(111) surface, but the corresponding results for H2 on Au/Ag(111) surfaces are substantially lower than those on the pure Au(111) surface. The reactivity of H2 on Au(111) is larger than that on Ag(111), despite Ag(111) having a slightly lower static barrier height. This can be attributed to the exceptionally small dissociation probabilities at the hcp and fcc regions, which are at least 100 times smaller compared to those at the bridge or top site for H2+Ag(111). Due to the late barrier being more pronounced, the vibrational excitation of H2 on Ag(111) is more effective in promoting the reaction than on Au(111). Moreover, a high degree of alignment dependence is detected for the four reactions, where the H2 dissociation has the highest probability at the helicopter alignment, as opposed to the cartwheel alignment. [ABSTRACT FROM AUTHOR]

A full-dimensional time-dependent wave packet study using mixed polyspherical Jacobi and Radau coordinates for the title reaction has been reported. The non-reactive moiety CH3 has been described using three Radau vectors, whereas two Jacobi vectors have been used for the bond breaking/formation process. A potential-optimized discrete variable representation basis has been employed to describe the vibrational coordinates of the reagent CH4. About one hundred billion basis functions have been necessary to achieve converged results. The reaction probabilities for some initial vibrational states are given. A comparison between the present approach and other methods, including reduced and full-dimensional ones, is also presented. [ABSTRACT FROM AUTHOR]

The dependence of reactivity on different facets of a surface is an interesting subject in dynamics at gas-surface interfaces. Here, we constructed new six-dimensional (6D) potential energy surfaces (PESs) for the dissociative chemisorption of HCl on rigid Ag(100) and Ag(110) surfaces, using the neural network method based on extensive density functional theory (DFT) calculations with the Perdew-Burke-Ernzerhof (PBE) functional, and compared the two PESs with the previously fitted PES of HCl/Ag(111). Time-dependent wave packet calculations show that the new PESs are very well converged with respect to the fitting procedure as well as to the number of DFT data points. The 6D dissociation probabilities for HCl initially in the ground rovibrational state decrease gradually for HCl/Ag(110), HCl/Ag(100), and HCl/Ag(111), consistent with the increasing barrier heights for the three reactions. The validity of the site-averaging approximation for HCl/Ag(110) does not hold well as compared with HCl/Ag(100) and HCl/Ag(111), in particular, at low kinetic energies, due to the strong steering effect this reaction exhibits if it is modeled with the semilocal PBE functional, which results in a low reaction barrier and a deep physisorption well. [ABSTRACT FROM AUTHOR]