Quantum Wave Packet Calculations Research Articles

Fractional revivals in the rovibrational motion of I2

Motivated by pump-probe experiments of I(2) in a room-temperature sample, the detection of fractional revivals is investigated using full-dimensional quantum wave packet calculations. It is shown that the structures observed in the pump-probe signal depend sensitively on the probe parameters employed and that the observed signal reflects a particular phase effect between fractional revivals.

Quantum scattering calculation of the O(1D)+HBr reaction.

Three-dimensional time-dependent quantum wave packet calculation for the O((1)D)+HBr reaction has been carried out using an accurate ab initio global potential energy surface [K. A. Peterson, J. Chem. Phys. 113, 4598 (2000)]. The calculations show that the initial state-selected reaction probabilities are dominated by resonance structures, and the lifetime of the resonance is generally in the subpicosecond time scale. The energy dependence of the reaction cross section is computed, which manifests still resonance structures, and is a decreasing function of the translational energy. The thermal rate constants are also computed, which are nearly independent on the temperature. The calculation results are discussed and compared to similar reaction with deep well.

New results for the OH (nu = 0,j = 0) + CO (nu = 0,j = 0) --> H + CO2 reaction: Five- and full-dimensional quantum dynamical study on several potential energy surfaces.

Full- [six-dimensional (6-D)] and reduced-dimensional [five-dimensional (5-D)] quantum wave packet calculations have been performed for the title reaction to obtain reaction probabilities deriving from the ground rovibrational states of OH and CO with total angular momentum J = 0. Three potential energy surfaces (PES) are studied, namely, those of Bradley and Schatz (BS), Yu, Muckerman, and Sears (YMS), and Lakin, Troya, Schatz, and Harding (LTSH). 6-D calculations are performed only for the BS PES, while 5-D results are reported for all three PES'. The 6-D results obtained in the present work improve on those previously reported, since a larger vibrational basis and a better representation of the OH and CO bonds has been introduced. In particular, we now employ a generalized Lanczos-Morse discrete variable representation for both the OH and CO vibrations. In a further improvement, the generalized discrete variable representation of the CO vibration is based on different CO intramolecular potentials for the asymptotic and product grids employed in our projection formalism. This new treatment of the vibrational bases allows for a large reduction in computation time with respect to our previous implementation of the wave packet method, for a given level of accuracy. As a result, we have been able to extend the range of collision energies for which we can obtain converged 6-D results to a higher energy (0.8 eV) than was possible before (0.5 eV). The comparison of the new 6-D and previous 5-D results for the BS PES shows good agreement of the general trend in the reaction probabilities over all collision energies considered (0.1-0.8 eV), while our previous 6-D calculation showed reaction probabilities that differed from the 5-D results by up to 10% between 0.5 and 0.8 eV. The 5-D reaction probabilities reveal interesting trends for the different PES'. In particular, at low energies (< 0.2 eV) the LTSH PES gives rise to much larger reactivity than the other PES', while at high energies (> 0.3 eV) its reaction probability decreases with respect to the BS and YMS PES', being more than a factor of 2 smaller at 0.8 eV. A 5-D calculation on a modified version of the LTSH surface shows that the van der Waals interaction in the entrance channel, which is not correctly described in the other PES' is largely responsible for its larger reactivity at low energies. The large difference between the 5-D reaction probabilities for the YMS and LTSH PES' serves to emphasize the importance of the van der Waals interaction for the reactivity at low energies, because most of the stationary point energies on the YMS and LTSH PES are rather similar, being in line with high-level ab initio information.

Time-dependent quantum wave packet calculation for nonadiabatic F(2P3/2,2P1/2)+H2 reaction

In this paper we present a time-dependent quantum wave packet calculation for the reaction of F(2P3/2,2P1/2)+H2 on the Alexander–Stark–Werner potential energy surface. The reaction probabilities and the integral cross sections for the reaction of F(2P3/2,2P1/2)+H2 (v=j=0) are computed using time-dependent quantum methods with the centrifugal sudden approximate. The results are compared with recent time-independent quantum calculations. The two-surface reaction probability for the initial ground spin–orbit state of J=0.5 is similar to the time-independent result obtained by Alexander et al. [J. Chem. Phys. 113, 11084 (2000)]. Our calculation also shows that electronic coupling has a relatively minor effect on the reactivity from the P3/22 state but a non-negligible one from the P1/22 state. By comparison with exact time-independent calculations, it is found that the Coriolis coupling plays a relatively minor role. In addition, most of the reactivity of the excited state of fluorine atom results from the spin–orbit coupling.

Reactivity of the Ground and Excited Spin−Orbit States for the Reaction of the F(2P3/2,2P1/2) with D2

In this paper, we present a time-dependent quantum wave packet calculation based on the Alexander−Stark−Werner (ASW) potential energy surfaces (PESs) to study the reactivity of the ground and excited spin−orbit states for the reaction of F(2P3/2,2P1/2) with D2 (v = j = 0). The reaction probabilities and the integral cross sections are calculated. Furthermore, the multistate cross sections are compared with the single-state calculation. The multistate cross section is smaller than the single-state calculation at higher collision energy. The effect of the nonadiabatic coupling becomes more and more obvious as the collision energy increases. The overall reactivity of the excited state of F is, at most, 25% of that of the ground spin−orbit states. The threshold energy of the F(2P3/2) + D2 reaction is ∼0.10 kcal/mol. The contributions of the excited state of F are 0.9% and 3.1% of the total average rate constant, at 200 and 500 K, respectively. The effect of the excited spin−orbit state rate constant to the average rate constant is very small but grows slowly as the temperature increases.

Quantum Scattering with Energy-Filtered Plane Wave Packets: Visualizing the F + HD “Ridge” Mechanism

We develop a very simple, previously neglected, idea for enhancing the power of quantum wave packet calculations to interpret chemical reactions. This is that, once the energy-domain wave function is calculated, an infinite variety of time-dependent wave packets may be recovered from it, simply by multiplying by an energy filter and taking the Fourier transform. Each packet corresponds to a different initial wave packet along the scattering coordinate. We show that, when incorporated into the plane wave packet method [J. Chem. Phys. 2002, 117, 4623], the filters can isolate features in the differential cross section and generate separate wave packets visualizing the dynamics of each feature. The filters also enable one to focus the wave packets, so as to minimize artifacts caused by spreading. We demonstrate these ideas on the F + HD reaction, by isolating the low energy ridge from the differential cross section and generating a focused plane wave packet that visualizes its dynamics. We find that the ridge is produced by a “Catherine wheel” rotation and decay of the FHD complex through about 180°.

Quantum Dynamics Study of Torsional Excitation of Glycine in Collision with Hydrogen Atom on ab Initio Potential Energy Surface

Quantum mechanical study has been carried out to investigate C−C torsional excitation in glycine via collisional energy transfer with hydrogen atom. In this study, ab initio calculation is carried out to generate potential energies on a two-dimensional grid (torsional angle and radial coordinate) for given fixed orientational angle (θ, φ). These discrete energies are fitted with a local linear least-squares method to generate potential energies at any given point in two-dimensional space for dynamics calculation. Time-dependent quantum wave packet calculation is employed to study energy transfer to the C−C torsional mode of glycine, and state-to-state transition probabilities are obtained for different initial angles of collision. Strong angle-dependent energy transfer is observed from the calculation. Although the total energy transferred to the torsional mode is small, collision from certain angles can result in relatively large conformational change in torsion by as much as 30° degrees.

Accurate quantum mechanical calculation for the N+OH reaction

Accurate three-dimensional time-dependent quantum wave packet calculations for the N+OH reaction on the A″3 potential energy surface [Guadagnini, Schatz, and Walch, J. Chem. Phys. 102, 774 (1995)] have been carried out. The calculations show for the first time that the initial state-selected reaction probabilities are dominated by resonance structures, and the lifetime of the resonance is generally in the subpicosecond time scale. The calculated reaction cross sections indicate that they are a decreasing function of the translational energy, which is in agreement qualitatively with the quasiclassical trajectory calculations. The rate constants obtained from the quantum mechanical calculations are consistent with the quasiclassical trajectory results and the experimental measurements.

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.

Nonadiabatic Dynamics: A Comparison of Surface Hopping Direct Dynamics with Quantum Wavepacket Calculations

A semiclassical direct dynamics method for nonadiabatic systems is tested by comparing with quantum wave packet dynamics, looking at the molecular dynamics of the butatriene molecule after formation of the radical cation in the first excited, A, state. There is a conical intersection coupling this state to the cationic ground state, X, and this plays a major role in the system evolution. The direct dynamics study consists of 80 trajectories, with the potential energy surfaces calculated on-the-fly using a complete active space (CASSCF) electronic wave function. The quantum dynamics used a model Hamiltonian and the multiconfigurational time-dependent Hartree (MCTDH) method to solve the time evolution of the nuclear wave packet. The results show that the methods give a similar description of the initial part of the dynamics, with a similar time scale for the interstate crossing. A qualitatively different behavior is, however, seen after crossing to the lower adiabatic surface, with a recurrence in the quan...

A crossed molecular beams study of the O(3P)+H2 reaction: Comparison of excitation function with accurate quantum reactive scattering calculations

We present the first measurements of the relative excitation function for the O(3P)+H2 reaction, performed with the use of a crossed molecular beams apparatus in conjunction with a high-energy (laser detonation) source of O atoms. The results are in excellent agreement with accurate quantum wave packet calculations.

Calculations of the F + HD reaction on three potential energy surfaces

In this paper, the three-dimensional time-dependent quantum wave packet calculation has been employed to study the non-adiabatic reaction dynamics of F + HD on three, electronically non-adiabatic potential energy surfaces fitted by Alexander, Stark and Werner (J. Chem. Phys., 2000, 113, 11 084; named ASW). The integral cross-sections and branching ratio of the reaction as a function of collision energy are calculated. The integral cross-sections are compared with the experimental measurements and other theoretical results. For the reaction of F in its excited state with HD, the calculated function of integral cross sections as collision energy shows that a steplike feature near 0.9 kcal mol−1 probably arises from the collinear FHD geometry.

Time-resolved photoelectron spectroscopy of molecular dissociation: Classical trajectory versus quantum wave-packet calculations

We present a simulation of ultrafast pump–probe photoelectron spectroscopy based on a classical treatment of the nuclear motion. A comparison with quantum mechanical wave-packet results shows that in the case of the direct dissociation of H2O in its A 1B1 electronic state this method produces extremely accurate results. The energy distribution of the photoelectrons recorded as a function of the pump–probe delay reflects the dissociation process, which takes place within only a few femtoseconds.

Time-dependent quantum wave packet study of H+HCN→H2+CN reaction

Time-dependent quantum wavepacket calculations for the H+HCN reaction are carried out on the ab initio potential energy surface of ter Horst et al. [J. Chem. Phys. 105, 558 (1996)]. The dynamics calculations are performed using both the semirigid vibrating rotor target (SVRT) model [J. Chem. Phys. 111, 3929 (1999)] as well as the pseudo atom–diatom model. Total reaction probabilities from the initial ground state of the reagent are calculated for various values of the total angular momentum quantum number J. Reaction cross sections and rate constants are also calculated. The dynamical result from the SVRT calculation is compared with that from a pseudo atom–diatom calculation in which the HCN is treated as a pseudo diatom. Both the SVRT and pseudo atom–diatom calculations involve three degrees of freedom for the H+HCN reaction due to linearity of the HCN molecule at both reactant and transition states. The results from these two calculations are generally close to each other with some difference at high collision energies. The two models for the current system are essentially the same except that the rotational constant used is different. In particular, the SVRT model uses the correct rotational constant for the linear HCN molecule while the pseudo atom–diatom model produces a rotational constant which is much larger than the correct one.

Converged five-dimensional quantum calculations for OH+CO→H+CO2

We perform five-dimensional quantum wave packet calculations of initial-state-resolved reaction probabilities for the reaction OH+CO→H+CO2, with OH and CO initially in the rovibrational ground state, and total angular momentum J=0. In essence, the dynamics are treated exactly for all molecular degrees of freedom except the CO reactant bond, for which a vibrational-averaging approximation is adopted. Comparison of reaction probabilities to those obtained in an earlier, similar study [D. H. Zhang and J. Z. H. Zhang, J. Chem. Phys. 103, 6512 (1995)] show that the previously obtained results were not well converged, primarily because too few rotational basis functions were used in the calculations. The resonances found in the current study are also more abundant and narrower than in the earlier study. Reaction probabilities from calculations on an updated potential energy surface (PES) [K. S. Bradley and G. C. Schatz, J. Chem. Phys. 106, 8464 (1997)] do not differ significantly from those for the PES used in the rest of the calculations [K. Kudla, G. Schatz, and A. Wagner, J. Chem. Phys. 95, 1635 (1991)], though there is a severe effect on resonance structure.

Intramolecular energy flow and nonadiabaticity in vibrationally mediated chemistry: Wave packet studies of Cl+H2O

Time-dependent and time-independent quantum scattering methods are used to investigate state-to-state inelastic and reactive collision dynamics for a three-dimensional (3D) atom+triatom model of Cl+H2O→HCl+OH. The results elucidate the role of (i) intramolecular vibrational energy transfer and (ii) vibrational nonadiabaticity on the time scale of a reactive encounter in systems with nearly degenerate stretching “local modes.” Adiabatic two-dimensional (2D) vibrational eigenfunctions [ψn(r1,r2,R)] and eigenvalues [En(R)] are first obtained in OH bond coordinates (r1,r2) as a function of Cl–H2O center-of-mass separation (R), which then provides the requisite adiabatic potential energy curves and nonadiabatic coupling matrix elements for full 3D quantum wave packet propagation. Inspection of these 2D vibrational eigenfunctions indicates that near degeneracy between H2O symmetric |01+〉 and antisymmetric |01−〉 states is systematically lifted as R decreases, causing vibrational energy to flow into local-mode OH excitations pointing either toward (“proximal”) or away from (“distal”) the approaching Cl atom, respectively. This suggests a simple yet powerful physical model for mode-specific reactive scattering dynamics, the predictions of which are confirmed by full 3D quantum wave packet calculations over a range of collision velocities.

Time-Dependent Quantum Dynamics Study of the C + CH Reaction on the 2A‘ Surface

Three-dimensional time-dependent quantum wave packet calculation was carried out to study the dynamics of the C + CH reaction on the 2A ' potential energy surface. The energy dependence of the calculated total reaction probabilities exhibits no long-lived resonance despite the presence of a deep well, a feature similar to that on the 1A(2) surface. The effect of initial vibrational and rotational excitation of the reagent on reactivity is investigated, and the reaction rate constants and integral cross sections are calculated and compared with quasiclassical trajectory results. This study shows that results of the quantum calculation are generally in good agreement with the QCT results and the difference is relatively small. The analysis of stereodynamics indicates that the C + CH reaction could occur within a wide range of the attack angle. The C side of the product CH (molecule or radical) is the slight favorite side for the reactive attack.

Theoretical investigation of [formula omitted] vibronic-coupling and ultrafast internal-conversion dynamics in the acetylene cation

The dynamics and spectroscopy of the X 2Π u and A ̃ 2Σ g + states of C 2H 2 + and C 2D 2 + have been investigated in the framework of a vibronic-coupling model. The model includes six of the seven vibrational degrees of freedom and has been constructed on the basis of CASSCF/CASPT2 ab initio electronic-structure calculations. The main feature of the model is a conical intersection of the 2Σ g + state with the 2Π u state. Time-dependent quantum wave-packet calculations have been performed for this model and photoelectron spectra have been obtained by Fourier transformation of the so-called autocorrelation functions. The calculations provide the explanation of the observed extremely short lifetime of the A ̃ 2Σ g + state in terms of an ultrafast internal-conversion process caused by the 2Σ g +– 2Π u conical intersection. The calculated photoelectron spectra and autocorrelation functions are compared with experimental data of Reutt et al. [J. Chem. Phys. 84 (1986) 3022]. The comparison provides evidence that the ultrafast dynamics of the 2Σ g + state is affected by an additional curve crossing involving the 2Π g shake-up state.

Time-dependent quantum wave packet study of the C+CH reaction

The quantum dynamics of the C+CH reaction has been studied by means of time-dependent quantum wave packet calculation on 1A′ potential energy surface. Initial state-specific total reaction probabilities and integral cross section are calculated, and the rate constants obtained are in reasonably good agreement with experimental measurement. Although a deep well is present in the potential surface, no long-lived resonances are found from the dynamics calculation and the reaction proceeds by a direct mechanism, similar to that of O(1D)+H2 reaction. Stereodynamics study of the reaction is carried out by transforming the scattering result to stereodynamics (SD) representation at zero total angular momentum. The SD result shows that the C+CH reaction proceeds from almost all attack angles with a preference for attacking at the C side of CH (molecule or radical) by the carbon atom.

Quantum dynamics calculation of reaction probability for H + Cl2 → HCl + Cl

We present in this paper a time-dependent quantum wave packet calculation of the initial state selected reaction probability for H + Cl2 based on the GHNS potential energy surface with total angular momentumJ = 0. The effects of the translational, vibrational and rotational excitation of Cl2 on the reaction probability have been investigated. In a broad region of the translational energy, the rotational excitation enhances the reaction probability while the vibrational excitation depresses the reaction probability. The theoretical results agree well with the fact that it is an early down-hill reaction.