Real Wave Packet Research Articles

A Quantum Dynamics Study of D2 + OH → DOH + D on the WSLFH Potential Energy Function

The quantum dynamics of the reaction D2 + OH → DOH + D on the Wu−Schatz−Lendvay−Fang−Harding ab initio-based potential energy function is investigated. A recently developed four-atom implementation of the real wave packet method is employed. Extensive six-dimensional calculations for a total angular momentum of J = 0 and, within the helicity-decoupled approximation, numerous J > 0 calculations are performed. Cross sections and rate constants for reaction are estimated using a J-shifting procedure and compared with quasi-classical trajectory, transition state theory, and experimental results. The results are also contrasted with comparable results for H2 + OH. A surprising feature is that our rate constants agree best with zero-curvature transition state theory results, indicating that tunneling may not be as important as expected.

Quantum reactive scattering calculations of cross sections and rate constants for the N(2D)+O2(X 3Σg−)→O(3P)+NO(X 2Π) reaction

Time-dependent quantum wave packet calculations have been performed on the two lowest adiabatic potential energy surfaces (2 2A′ and 1 2A″) for the N(2D)+O2(X 3Σg−)→O(3P)+NO(X 2Π) reaction. The calculations have been carried out, on these recently published potential energy surfaces, using the real wave packet method together with a new dispersion fitted finite difference technique for evaluating the action of the radial kinetic energy operator. Reaction probabilities, corresponding to the O2 reactant in its ground vibrational-rotational state, have been calculated for both surfaces and for many different values of the total angular momentum quantum number (J), within the helicity decoupling approximation. The reaction probabilities associated with all other relevant J values have been interpolated, and to a smaller extent extrapolated, using a capture model, to yield probabilities as a function of energy. The probabilities have in turn been summed to yield energy dependent cross sections and then used to compute rate constants. These rate constants are compared with ones obtained from quasiclassical trajectory (QCT) and variational transition state theory (VTST) calculations performed on the same surfaces. There is a good agreement between the wave packet and QCT cross sections for reaction on both potential energy surfaces considered, with the exception of the near threshold region, where the reaction probability is dominated by tunnelling. Comparison of the predicted rate constants shows that for the 2 2A′ surface, above 300 K, the wave packet, QCT and VTST results are quite similar. For the 1 2A″ surface, however, significant differences occur between the wave packet and the other methods. These differences become smaller with increasing temperature. It is likely that these differences arise, at least in part, from the fact that, when calculating the rate constants, the reactants are restricted to be in their lowest vibrational-rotational state in the wave packet calculations but are selected from a thermally equilibrated population in the other methods.

CHEMICAL REACTION DYNAMICS WITH REAL WAVE PACKETS

An approach to carrying out accurate quantum dynamics simulations of chemical reactions, termed the real wave packet (RWP) method, is outlined. The method focuses on propagation of just the real part of a complex-valued wave packet, halving computational memory and effort requirements in comparison with comparable high accuracy quantum propagation methods. Applications to 3-atom and 4-atom chemical reactions are reviewed. Potential future directions are indicated.

Chebyshev real wave packet propagation: H+O2 (J=0) state-to-state reactive scattering calculations

In this paper we explore the relative performance of two recently developed wave packet methodologies for reactive scattering, namely the real wave packet Chebyshev domain propagation of Gray and Balint-Kurti [J. Chem. Phys. 108, 950 (1998)] and the Lanczos subspace wave packet approach of Smith et al. [J. Chem. Phys. 116, 2354 (2002); Chem. Phys. Lett. 336, 149 (2001)]. In the former method, a modified Schrödinger equation is employed to propagate the real part of the wave packet via the well-known Chebyshev iteration. While the time-dependent wave packet from the modified Schrödinger equation is different from that obtained using the standard Schrödinger equation, time-to-energy Fourier transformation yields wave functions which differ only trivially by normalization. In the Lanczos subspace approach the linear system of equations defining the action of the Green operator may be solved via either time-dependent or time-independent methods, both of which are extremely efficient due to the simple tridiagonal structure of the Hamiltonian in the Lanczos representation. The two different wave packet methods are applied to three dimensional reactive scattering of H+O2 (total J=0). State-to-state reaction probabilities, product state distributions, as well as initial-state-resolved cumulative reaction probabilities are examined.

Quantum dynamics of the N(4S)+O2 reaction on the X 2A′ and a 4A′ surfaces: Reaction probabilities, cross sections, rate constants, and product distributions

We report real wave packet (WP) calculations of reaction probabilities, cross sections, rate constants, and product distributions of the reaction N(4S)+O2(X 3∑g−)→NO(X 2∏)+O(3P). We propagate initial WPs corresponding to several O2 levels, and employ reactant coordinates and a flux method for calculating initial-state-resolved observables, or product coordinates and an asymptotic analysis for calculating state-to-state quantities. Exact or J-shifting calculations are carried out at total angular momentum J=0 or J>0, respectively. We employ the recent X 2A′ S3 potential energy surface (PES) by Sayós et al. and the earlier a 4A′ PES by Duff et al. In comparing S3 results with the WP ones of a previous X 2A′ S2 PES, we find lower S3 energy thresholds and larger S3 probabilities, despite the higher S3 barrier. This finding is due to the different features of the doublet PESs in the reactant and product channels, at the transition state, and in the NO2 equilibrium region. We analyze the effects of the O2 initial level and show that tunneling through the S3 barrier enhance the room-temperature rate constant by ∼3.7 times with respect to the previous S2 WP rate. The agreement with the room-temperature experimental result is thus notably improved. The NO vibrational distribution is inverted and the rotational ones are strongly oscillating. We explain these nonstatistical results showing that the reaction partners approach each other with a large impact parameter. The WP vibrational distribution is however different from that observed, which is oscillating. WP calculations show that the new S3 PES describes accurately several features of the X 2A′ state, although a lowering of its barrier height by ∼0.56 kcal/mol should bring calculated and observed rate constants in full agreement.

A quantum dynamics study of H2+OH→H2O+H employing the Wu–Schatz–Lendvay–Fang–Harding potential function and a four-atom implementation of the real wave packet method

We carry out numerous six-dimensional wave packet propagations for H2+OH→H2O+H on the ab initio based, Wu–Schatz–Lendvay–Fang–Harding potential energy function. For comparison, some calculations are also carried out on the older but more widely studied potential function of Walch, Dunning, Schatz, and Elgersma. The energy dependence of the total angular momentum J=0 cumulative reaction probability is obtained and J-shifting is used to estimate the bimolecular rate constant as a function of temperature. Some J>0 calculations are also carried out. A novel J-shifting procedure, designed to more accurately describe the effects of angular momentum, is introduced. We compare our results with transition state theory calculations and experiment. An important feature of our work is the development of an efficient, four-atom, parallel implementation of the real wave packet method, augmented with a recently developed finite difference method.

Wave packet dynamics of the N(4S)+O2(X 3Σg−)→NO(X 2Π)+O(3P) reaction on the X 2A′ potential energy surface

We report three-dimensional quantum calculations of total angular momentum J=0 reaction probabilities, J-shifting cross sections, and rate constants of the title reaction. Employing the real wave packet approach, we propagate wave packets corresponding to several O2(v,j) initial levels on the X 2A′ potential surface of Sayós et al. As collision energy increases, the average probabilities first increase monotonically and then become nearly constant, while the cross sections rise in the overall energy range. Numerous probability resonances point out the formation of NOO collision complexes and NO final states. Rotational excitation in O2 decreases the collisional energy thresholds and enhances the state-resolved rate constants, mainly at low temperature. O2 vibrational excitation inhibits the reactivity, although the energy thresholds are still reduced. With respect to previous quasiclassical and mixed quantum-classical studies, we obtain lower thresholds and cross sections but similar rate constants, which are however lower than experimental rates. By inspection of the average properties of the wave packets, we suggest a qualitative reaction mechanism, we propose a modified J-shifting approximation, and we find a possible explanation of the low quantum reactivity on the present potential.

Quantum Mechanical Calculation of Reaction Probabilities and Branching Ratios for the O(1D) + HD → OH(OD) + D(H) Reaction on the X̃A‘ and 11A‘‘ Adiabatic Potential Energy Surfaces

The real wave packet method is used to calculate state-to-state reaction probabilities and branching ratios for the reaction O({sup 1}D) + HD {yields} OH(OD) + D(H) for zero total angular momentum. Calculations are performed on the adiabatic potential energy surfaces corresponding to the {tilde X} {sup 1}A{prime} and 1{sup 1}A{prime} electronic states. Vibrational state-to-state cross sections, product state distributions and branching ratios are estimated using a capture model and J-shifting methods. The results are compared with experiment and with results of quasi-classical trajectory calculations.

Coriolis-Coupled Quantum Dynamics for O(1D) + H2 → OH + H

The O(1D) + H2 → OH + H reaction has been studied with a time-dependent wave packet method for total angular momenta J = 1, 2, 5, 10, 15, 20, and 30. Total reaction probabilities from calculations in which the Coriolis coupling terms (CC) in the Hamiltonian are included are compared with those from calculations in which the Helicity−Conserving (HC) approximation is employed. The calculations were performed combining a real wave packet method with the Coriolis-coupled method on parallel computers. At low values of J, the CC reaction probabilities are somewhat smaller than the HC results; the agreement between the two methods improves, however, as J increases. For this reaction, the HC approximation should yield accurate estimates of the reaction cross section and rate constants. However, because reactive collisions involve a high degree of Coriolis mixing, it is very likely that inclusion of these terms will affect calculation of less averaged quantities such as the differential cross section or OH interna...

Time-dependent quantum mechanical calculations on H+O2 for total angular momentum J>0. III. Total cross sections

The H+O2→OH+O reaction has been studied with a time-dependent wave packet method for total angular momentum J=15, 20, 25, 35. This work is a continuation of previous studies for J⩽10. The calculations were performed combining a real wave packet method with the Coriolis coupled method on parallel computers. We find that for most energies there is a monotonic decrease of reaction probability with increasing J. Nevertheless, due to the 2J+1 degeneracy, higher angular momentum states contribute significantly to the total reaction cross section. A smoothing/interpolation/extrapolation scheme is employed to compute total reaction cross sections. These cross sections are compared with quasiclassical results on the same potential energy surface, and the most recent experimental cross sections. Comparisons with quasiclassical results show the significance of zero-point energy constraints. The quantum mechanical theoretical cross sections are smaller than the experimental ones everywhere, suggesting that a more accurate potential energy surface is required. There is also some possibility that nonadiabatic effects play a role in this reaction.

Theoretical study of the photodetachment spectroscopy of the IHBr and IDBr anions

The coupled-cluster method with a large basis set with quasi-relativistic effective core potentials on the halogens was utilized to investigate the ground electronic state X 1Σ+ of the IHBr anion. A semi-global, three-dimensional potential energy surface was obtained via spline interpolation of ab initio data. Variational rovibrational calculations were carried out with this potential energy surface, and assignment of fundamentals and low-lying overtones, as well as combination bands, is presented for IH(D)Br anions. Photodetachment spectra for IH(D)Br−+hν→[IH(D)Br]+e− were computed using three-dimensional time-independent real and complex L2 methods and a recently developed real L2 wave packet propagation technique; all methods employed a previous London–Eyring–Polanyi–Sato empirical potential for the neutral system. Well resolved fine structure is found in photodetachment spectra of IHBr−. This structure is assigned to bending excitation based on analysis of the wave functions and the neutral potential energy surface near the Franck–Condon region. This fine structure is largely eliminated in the IDBr− spectrum. The photodetachment spectrum for the first excited asymmetric stretch of IHBr− shows a new feature that is associated with sampling of the transition state region of the neutral surface. Spin-orbit corrected multi-reference configuration interaction calculations indicate that the first excited electronic state is only about 0.06 eV above the ground electronic state of the neutral IHBr system in the Franck–Condon region. The model empirical potential used in the calculations of photodetachment spectra is shown to have roughly the average behavior of these two ab initio potentials.

Quantum mechanical calculation of product state distributions for the O(1D)+H2→OH+H reaction on the ground electronic state surface

The real wave packet method is used to calculate reaction probabilities and product quantum state distributions for the reaction O(1D)+H2→OH+H. The method yields the desired quantities over a wide range of energies from a single wave packet propagation. The calculations are performed on the lowest adiabatic electronic potential energy surface for zero total angular momentum (J=0). A capture model is used to estimate reaction probabilities for J>0 based on our J=0 data, and thus permit the approximate calculation of cross sections. Two different ground state surfaces are used and the results from calculations on the two surfaces are compared with each other and with experiment.

Comparison of Chebyshev, Faber, and Lanczos propagation-based methods for calculating resonances

We compare the numerical performance of three recursive methods for calculating collisional resonances, which are characterized by complex eigenenergies of an optical potential augmented Hamiltonian. The first approach involves a modified Chebyshev propagation of a real wave packet, followed by low-storage filter-diagonalization. A similar filter-diagonalization scheme replaces the Chebyshev propagation with a more general Faber recursion associated with a specific conformal mapping in the complex plane. The complex resonance eigenenergies are also obtained using a complex-symmetric version of the Lanczos algorithm. Numerical tests for a realistic triatomic system (HCO) indicate that the Lanczos method and the low-storage filter-diagonalization based on the Chebyshev propagation are much more efficient than the Faber approach.

A transition state real wave packet approach for obtaining the cumulative reaction probability

We show how the transition state wave packet method of Zhang and Light can be applied within a real wave packet formalism. We also implement random superpositions into the approach, as in the recent work of Matzkies and Manthe, which can significantly reduce the number of propagations at higher temperatures. The net result is a very efficient approach for calculating the cumulative reaction probability, and hence the thermal rate constant, for bimolecular chemical reactions. Full dimensional quantum calculations, including all relevant total angular momenta, of the cumulative reaction probability and thermal rate constant for the D+H2→HD+H are used as illustration.

Helicity decoupled quantum dynamics and capture model cross sections and rate constants for O(1D)+H2→OH+H

We study, within a helicity decoupled quantum approximation, the total angular momentum J dependence of reaction probabilities for the reaction O(1D)+H2→OH+H. A recently developed real wave packet approach is employed for the quantum calculations. The abinitio based, ground electronic (1A′) potential energy surface of Ho etal. (T-S. Ho, T. Hollebeeck, H. Rabitz, L. B. Harding and G. C. Schatz, J. Chem. Phys., 1996, 105, 10472) is assumed for most of our calculations, although some calculations are also performed with a recent surface due to Dobbyn and Knowles. We find that the low J reaction probabilities tend to be, on average, slightly lower than the high J probabilities. This effect is also found to be reproduced in classical trajectory calculations. A new capture model is proposed that incorporates the available quantum data within an orbital angular momentum or l-shifting approximation to predict total cross sections and rate constants. The results agree well with classical trajectory results and the experimental rate constant at room temperature. However, electronically non-adiabatic effects may become important at higher temperature.

Flux analysis for calculating reaction probabilities with real wave packets

A recent approach to obtain scattering probabilities involves propagating the real part of a wave packet and analysis in the asymptotic product channel. We show that real wave packet propagation can also be used with analysis methods based on flux through a surface. We also show the relation between asymptotic product analysis and flux-based methods. Flux analysis with real wave packets is illustrated with an application to D + H 2→ DH + H in three dimensions.

Quantum dynamics with real wave packets, including application to three-dimensional (J=0)D+H2→HD+H reactive scattering

We show how to extract S matrix elements for reactive scattering from just the real part of an evolving wave packet. A three-term recursion scheme allows the real part of a wave packet to be propagated without reference to its imaginary part, so S matrix elements can be calculated efficiently. Our approach can be applied not only to the usual time-dependent Schrödinger equation, but to a modified form with the Hamiltonian operator Ĥ replaced by f(Ĥ), where f is chosen for convenience. One particular choice for f, a cos−1 mapping, yields the Chebyshev iteration that has proved to be useful in several other recent studies. We show how reactive scattering can be studied by following time-dependent wave packets generated by this mapping. These ideas are illustrated through calculation of collinear H+H2→H2+H and three-dimensional (J=0)D+H2→HD+D reactive scattering probabilities on the Liu–Siegbahn–Truhlar–Horowitz (LSTH) potential energy surface.

Restoration of neutron interferometer contrast by post-interference filtering.

It is argued that the results of a recent neutron interference experiment [Kaiser et al., Phys. Rev. A 45, 31 (1992)], in which contrast lost as a result of difference in effective path lengths is restored by wavelength filtering after recombination, cannot be construed as evidence against the notion that a neutron is a physically real wave packet.

A computational demonstration of the distributed approximating function approach to real time quantum dynamics

The authors report computational applications for the newly developed distributed approximating function (DAF) approach to real time quantal wavepacket propagation for several one-dimensional model problems. The DAF is constructed to fit all wavepackets accurately which can be represented, to the same accuracy, by a polynomial of degree M, or less, within the envelope of the DAF. (This defines the {open_quotes}DAF class{close_quotes} of functions.) By expressing the DAF (and thus the wavepacket to be propagated) in terms of Hermite functions (each a product of a Hermite polynomial and its Gaussian generating function), the DAF approximation to the wavepacket is propagated freely and exactly for a short time {tau}. The Hermite functions are the natural basis states for describing the free evolution of a localized particle and yield a highly banded representation for the free particle propagator. Combining the DAF class free propagation scheme with any of several short time approximations to the full propagator enables one to propagate the wavepacket through a potential. The DAF results for the propagated wavepacket and various scattering amplitudes are shown to be in good agreement with those obtained by more standard methods. 17 refs., 7 figs., 4 tabs.

Damping effects on the coherence term and wave packet reduction

We analyse the damping effects of devices such as an rf-coil and Ge or Bi crystals on the interference fringes in the interference-type experiments. We investigate them in terms of the interaction between the device and the wave packets. We also consider the fluctuations deriving from the macroscopic characteristics of devices, and analyse the damping effects. The visibilities of the interference fringes are calculated and compared with the results of the neutron interference experiment. We get reliable results which indicate the tendency of the results measured by the Missouri-Columbia group and it is certain that our method is more suitable in order to investigate experiments such as those which make use of wave packets. The intensity of the wave packet is also discussed. The difference between the intensity of a beam made up of several single plane waves and the intensity of a real wave packet such as the one describing pulsed neutrons is pointed out.