Time-dependent Wave Packet Calculations Research Articles

QUANTUM DYNAMICS OF THE He + Li2 INELASTIC SCATTERING

In this paper, we report the results of three dimensional time dependent quantum wave packet calculations carried out for He+Li2 inelastic reaction in the collision energy range 0.43–1.18 eV. A three dimensional potential energy surface (PES) computed by Varandas was used for the dynamical calculations.1 The state to state and state to all transition probabilities for total angular momentum J = 0 have been calculated in a broad range of collision energies. Integral cross-sections and rate constants have been calculated from the wave packet transition probabilities by means of J-shifting approximation based on a capture model and a uniform J-shifting method for J > 0.

Three-dimensional wave packet dynamics of H 2 + D 2 reaction

Initial state selected time-dependent wave packet calculations were carried out for the H 2( v 1 = high) + D 2( v 2 = low) reaction within a three degrees of freedom model. The probabilities for different competitive processes were studied on two realistic global potential energy surfaces (PESs) – BMKP and ASP. The orientation of the cold diatom did not greatly affect the reaction processes, while the orientation of the hot diatom had a significant effect. The BMKP surface generally gave lower energy thresholds than the ASP surface, except for the collision induced dissociation (CID) within the T II geometry where the hot diatom comes in head-on perpendicular to the cold diatom. Isotopic substitution effects were studied on the recent BMKP PES. The H 2 + D 2 reaction was more effective for CID and showed more structured probability curves for single exchange reaction (SE) and three-body complex formation (3BC) than the H 2 + H 2 reaction.

Quantum and classical study of surface characterization by three-dimensional helium atom scattering

Exact time-dependent wavepacket calculations of helium atom scattering from model symmetric, chiral, and hexagonal surfaces are presented and compared with their classical counterparts. Analysis of the momentum distribution of the scattered wavepacket provides a convenient method to obtain the resulting energy and angle resolved scattering distributions. The classical distributions are characterized by standard rainbow scattering from corrugated surfaces. It is shown that the classical results are closely related to their quantum counterparts and capture the qualitative features appearing therein. Both the quantum and classical distributions are capable of distinguishing between the structures of the three surfaces.

Time Dependent Wave Packet Study of the H<sup>-</sup>+ H<sub>2</sub> Nonreactive Scattering

Time dependent wave packet calculations have been performed for the H-+ H2nonreactive scattering, summed of elastic and inelastic probabilities, on the recent reported potential energy surface of the systems. The total probabilities for total angular momentum J up to 35 have been calculated to get the converged integral cross sections over collision energy range of 0.20 - 1.42 eV. Integral cross-sections and rate constants have been calculated from the wave packet transition probabilities for the initial states (υ = 0, j = 0) by means of J-shifting method and uniform J-shifting method for J > 0.

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

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

Nonadiabatic quantum reactive scattering of the OH(A Σ2+)+D2

The seams of conical intersection exist between the ground (1 (2)A(')) and the first-excited (2 (2)A(')) electronic potential energy surfaces (PESs) of OH(A (2)Σ(+),X (2)Π) + H(2) system. This intersection induces the nonadiabatic quenching of OH(A (2)Σ(+)) by D(2). We present nonadiabatic quantum dynamics study for OH(A (2)Σ(+)) + D(2) on new five-dimensional coplanar PESs. The ab initio calculations of PESs are based on multireference configuration interaction (MRCI)/aug-cc-pVQZ level. A back-propagation neural network is utilized to fit the PESs and nonadiabatic coupling. High degrees of rotational excitation of quenched OH(X (2)Π) products are found in nonreactive quenching channel, and the quenched D(2) products are vibrationally excited up to quantum number v(2) (')=8. The theoretical results of nonadiabatic time-dependent wave-packet calculation are in good agreement with the existing experimental data.

The reaction between HO and (H2O) n (n = 1, 3) clusters: reaction mechanisms and tunneling effects

The reaction between the HO radical and (H2O)n (n = 1, 3) clusters has been investigated employing high-level quantum mechanical calculations using DFT-BH&HLYP, QCISD, and CCSD(T) theoretical approaches in connection with the 6-311 + G(2df,2p), aug-cc-pVTZ, and aug-cc-pVQZ basis sets. The rate constants have also been calculated and the tunneling effects have been studied by means of time–dependent wavepacket calculations, performed using the Quantum–Reaction Path Hamiltonian method. According to the findings of previously reported theoretical works, the reaction between HO and H2O begins with the formation of a pre-reactive complex that is formed before the transition state, the formation of a post-reactive complex, and the release of the products. The reaction between HO and (H2O)2 also begins with the formation of a pre-reactive complex, which dissociates into H2O…HO + H2O. The reaction between HO and (H2O)3 is much more complex. The hydroxyl radical adds to the water trimer, and then it occurs a geometrical rearrangement in the pre-reactive hydrogen-bonded complex region, before the transition state. The reaction between hydroxyl radical and water trimer is computed to be much faster than the reaction between hydroxyl radical and a single water molecule, and, in both cases, the tunneling effects are very important mainly at low temperatures. A prediction of the atmospheric concentration of the hydrogen-bonded complexes studied in this work is also reported.

Photochemistry of the water dimer: Time-dependent quantum wave-packet description of the dynamics at the S1-S conical intersection

The photoinduced electron-driven proton-transfer dynamics of the water-dimer system has been investigated by time-dependent quantum wave-packet calculations. The main nuclear degrees of freedom driving the system from the Frank-Condon region to the S(0)-S(1) conical intersection are the distance between the oxygen atoms and the displacement of the hydrogen atom from the oxygen-oxygen bond center. Two important coupling modes have been investigated: Rotation of the H-donating water dangling proton and asymmetric stretching of the H-accepting water dangling protons' O(a)H bonds. Potential energy surfaces of the ground and lowest excited electronic states have been constructed on the basis of ab initio calculations. The time-dependent quantum wave-packet propagation has been employed within the (2 + 1)-dimensional systems for the description of the nonadiabatic dynamics of water dimer. The effects of the initial vibrational state of the system on the electronic population transfer and dissociation dynamics are presented. To approximate the photochemical behavior of water dimer in bulk water, we add a boundary condition into the (2 + 1)-dimensional systems to simulate the existence of water bulk. The results provide insight into the mechanisms of excited state deactivation of the water-dimer system in gas phase and in bulk water through the electron-driven proton-transfer process.

Time-dependent wave packet calculation of the LiH + H reactive scattering on a new potential energy surface

A new potential energy surface is proposed for the ground electronic state of LiH 2 and the quantum wave packet calculation for LiH + H reaction is performed. The full configuration interaction method and an aug-cc-pVQZ basis set are employed to calculate the potential energy for a set of criteriously selected geometries. The many-body expansion procedure is used to describe the analytical PES function. The new PES leads to a very different wave packet dynamics for both exothermic ( Li + H 2 ) and thermoneutral ( H + LiH ) reactions when compared with the previous ones.

Time-dependent quantum dynamics of the He + H+He reaction

Time-dependent quantum-mechanical wave packet calculations have been carried out to calculate the reaction probabilities and cross sections for the proton transfer reaction, He + H+He → HeH+ + He, in a collision energy range 0.0–0.5 eV. A global analytical potential energy surface developed by Panda and Sathyamurthy (2003 J. Phys. Chem. A 107 7125) has been used for the purpose. The probability curves are characterized by numerous oscillatory structures attributed to the presence of resonances. The calculated reaction probabilities are found to be weakly dependent on vibrational and rotational excitations of the diatom for total angular momentum (J) = 0. For higher J values, rotational excitation results in a decline in probability values for j = 1 followed by enhancements for j = 2 and 3. The oscillations seen in reaction probabilities are not fully washed out in the integral cross sections. The dependence of cross section on initial orientations of the reactants is also studied.

Modified potential energy surface and time-dependent wave packet dynamics study for Cl + CH 4 → HCl + CH 3 reaction

Based on the ab initio results of reactants, products and saddle point at the CCSD(T)/aug-cc-pvtz level, a modified analytical potential energy surface (PES) for Cl + CH 4 → HCl + CH 3 reaction is calibrated. In this process, the geometries and vibrational frequencies of the reactants, the products and the saddle point are adjusted, and the experimental rate constants are also emphasized. Then discussions are involved concerning some characters of the present PES. To test its dynamical properties, reduced-dimensional time-dependent wave packet calculations are performed. Both the static and dynamical properties of the present PES are analyzed and compared with the experimental and other theoretical results available at present.

Quantum Dynamics of Br + HD Reaction

In this article we report the results of three-dimensional time-dependent quantum wavepacket calculations carried out for the Br + HD( v = 0, j = 0) reaction in the collision energy range 0.0-1.2 eV. An accurate potential energy surface computed by Kurosaki was used for the dynamical calculations. Both reactive channels, BrH + D and BrD + H, show vibrational enhancement of the reaction cross sections. For the three initial vibrational states considered, the production of BrD channel dominates over that of BrH for the considered collision energy range. The two arrangement channels exhibit different initial rotational state dependence. The cross section for the formation of BrD is almost independent of j whereas the same for the formation of BrH increases with increase in j. A comparison with the results on an e-LEPS surface shows that the two surfaces behave very differently with respect to the cross section for the initial rotational states.

Extracting continuum information fromΨ(t)in time-dependent wave-packet calculations

The theory of measurement projection operators in grid-based time-dependent wave-packet calculations involving electronic continua in atoms and molecules is discussed. A hierarchy of projection operators relevant in their individual restricted configuration spaces is presented. At asymptotically large distances from the scattering or interaction center the projection operators involve plane waves only. To reach this asymptotic regime, however, large propagation times and large boxes may be required. At somewhat smaller distances from the scattering center, the projection operators are expressed in terms of analytical single-center Coulomb scattering waves with incoming wave boundary conditions. If propagation of the wave packet to these asymptotic regimes is impeded, the projection operators involve the exact scattering states which are not readily available in the wave-packet calculation and hence must be supplied by an additional, typically very demanding, calculation. The present approach suggests an exact way of analyzing the timely problem of the one-electron continuum in nonperturbative calculations. A key feature is that the propagated wave packet includes every interaction of the full Hamiltonian. The practicality of the proposed method is illustrated by the nontrivial example of strong-field ionization of the molecular hydrogen ion. Finally, the extension of the presented ideas to single and double ionization of two-electron systems is discussed.

R-matrix calculation of antiproton capture by helium ions

Rigorous treatment is presented for antiproton capture by helium ions, i.e., $\overline{p}+{\text{He}}^{+}\ensuremath{\rightarrow}{(\overline{p}{\text{He}}^{+})}^{\ensuremath{\ast}\ensuremath{\ast}}\ensuremath{\rightarrow}\overline{p}{\text{He}}^{2+}+e$, by using $R$-matrix theory. The present work applies the $R$-matrix method to an exotic collision system containing an antiproton, a nucleus, and an electron. The eigenvalue problem in the $R$-matrix method is solved by the discrete-variable-representation algorithm without use of any decoupling approximation. The probability of antiproton capture is calculated for the total angular momentum $J=30$. A huge number of the overlapping resonances are found to be prominent everywhere over a wide range of energies. As suggested in a time-dependent wave-packet propagation calculation [K. Sakimoto, Phys. Rev. A 74, 022709 (2006)], the resonances make a dominant contribution to the antiproton capture. It is found that the nonadiabatic coupling is always weak in off-resonance collisions, but can be very strong in resonance collisions.

A Time-Dependent Quantum Dynamical Study of the H + HBr Reaction

Time-dependent wave packet calculations were carried out to study the exchange and abstraction processes in the title reaction on the Kurosaki-Takayanagi potential energy surface (Kurosaki, Y.; Takayanagi, T. J. Chem. Phys. 2003, 119, 7838). Total reaction probabilities and integral cross sections were calculated for the reactant HBr initially in the ground state, first rotationally excited state, and first vibrationally excited state for both the exchange and abstraction reactions. At low collision energy, only the abstraction reaction occurs because of its low barrier height. Once the collision energy exceeds the barrier height of the exchange reaction, the exchange process quickly becomes the dominant process presumably due to its larger acceptance cone. It is found that initial vibrational excitation of HBr enhances both processes, while initial rotational excitation of HBr from j(0) = 0 to 1 has essentially no effect on both processes. For the abstraction reaction, the theoretical cross section at E(c) = 1.6 eV is 1.06 A(2), which is smaller than the experimental result of 3 +/- 1 A(2) by a factor of 2-3. On the other hand, the theoretical rate constant is larger than the experimental results by about a factor of 2 in the temperature region between 220 and 550 K. It is also found that the present quantum rate constant is larger than the TST result by a factor of 2 at 200 K. However, the agreement between the present quantum rate constant and the TST result improves as the temperature increases.

Accurate quantum wave packet study of the N( 2D) + D 2 reaction

Accurate time-dependent wave packet calculations have been performed for the isotopic N( 2D) + D 2 reaction on the recent reported 1 2A″ DMBE (double many body expansion) potential energy surface of the NH 2 system. The total reaction probabilities for total angular momentum J up to 75 have been calculated to get the converged integral cross-section over a collision energy range of 0.0–1.0 eV. Then, the ground-state thermal rate constant has been derived from the integral cross-section and the intermolecular isotope effect is further discussed.

Photodissociation of OBrO through the excited 2 2A″(1 2A2) electronic state: Theoretical prediction of the absorption cross-section

Extensive highly correlated multireference configuration interaction calculations were carried out to generate for the first time full three-dimensional (3D) potential energy surfaces of the 1 2 A″(1 2 B 1) ground state and the most important 2 2 A″(1 2 A 2) excited electronic state of OBrO. Because of the bound character of the 2 2 A″ excited state, i.e. a barrier of about 0.75 eV, relative to the 2 2 A″ potential minimum, must be overcome for dissociation into the BrO + O channel, only indirect dissociation is possible and a highly structured absorption spectrum is expected. The other possible dissociation channel of OBrO supplying Br + O 2 should play only a minor role, because a large barrier of about 1.7 eV, relative to the 2 2 A″ potential minimum hinders the dissociation. The calculated 1 2 A″ and 2 2 A″ 3D surfaces were used in three-dimensional (3D) time-dependent wave-packet calculations to obtain a first theoretical estimation of the absorption cross-section for the dissociation through the 2 2 A″ excited state of OBrO. The calculated value of 21.7 × 10 −18 cm 2 is in reasonable agreement with experimental findings (13–20 × 10 −18 cm 2). Despite the close correspondence of theory and experiment, the calculations have shown a sensitive dependence on the potential energy data and the value of the transition dipole moment so that a reliable quantitative theoretical prediction of absorption cross-sections remains a difficult task.

Seven-dimensional quantum dynamics study of the O(P3)+CH4 reaction

The initial state selected time-dependent wave packet calculations have been carried out to study the title reaction with seven degrees of freedom included by restricting the nonreacting CH3 group under C3V symmetry and the CH bond length in the group. Total reaction probabilities as well as integral cross sections were calculated for the ground and four vibrationally excited reagent states. Our calculation shows that the reactivity is very small for the reaction for collision energy up to 1.0eV for all the initial states. Initial vibration excitation of CH4, in particular, the CH stretch excitation, enhances the reactivity, but only part of the excitation energy deposited can be used to reduce the reaction threshold. The rate constant for the ground initial state agrees rather well with that from a recent quasiclassical trajectory study and is larger than that from the semirigid vibrating rotor target calculations, in particular, in the low temperature region. On the other hand, the thermal rate constant calculated from the integral cross sections for these five vibrational states is about a factor of 20 smaller than that from the multiconfiguration time-dependent Hartree study.

Barrier Height Effect on Cl+H2(D2) Reaction

Three-dimensional time-dependent quantum wave packet calculation was performed to study the reaction dynamics of Cl+H2(D2) on two potential energy surfaces (CW PESs). The first CW PES is with spin-orbit correction; the second is without spin-orbit correction. The integral cross-section and reaction probability as a function of collision energy are calculated in the collision energy range of 0.1 eV to 1.4 eV. For reaction of Cl with D2, the reaction section with spin-orbit correction has a shift toward the high energy because the barrier height increases. As for the reaction of Cl with H2 at low collision energy, it is more reactive on the PES with spin-orbit correction than on the low barrier height PES without spin-orbit correction, due to the tunnel effect for the reaction of the Cl with H2. When the collision energy is higher than 0.7 eV, the reactivity on the low barrier height PES is larger than that on the high barrier height PES. It is believed that the barrier height plays a very important role in the reactivity of Cl with (H2, D2). For the Cl+H2 reaction the barrier width is also very important because of the tunneling effect.

Photoinduced multi-mode quantum dynamics of pyrrole at the [formula omitted]– [formula omitted] conical intersections

The photoinduced dynamics of pyrrole at the A 1 2 ( π σ ∗ ) – S 0 and B 1 1 ( π σ ∗ ) – S 0 conical intersections has been investigated by multi-mode time-dependent quantum wave-packet calculations. Diabatic potential-energy surfaces have been constructed for both conical intersection using accurate multi-reference ab initio electronic-structure calculations. In addition to the NH stretching coordinate, the three (four) symmetry-allowed coupling modes of A 2 ( B 1 ) symmetry have been considered for the A 1 2 ( π σ ∗ ) – S 0 ( B 1 ( π σ ∗ ) – S 0 ) conical intersections. Wave-packet dynamics calculations have been performed for three-dimensional models, taking account of the two dominant coupling modes of each conical intersection. The electronic population-transfer processes at the conical intersections, the branching ratio for the dissociation to the ground and excited states of the pyrrolyl radical, and their dependence on the initial preparation of the system have been investigated. It is shown that the excitation of the NH stretching mode strongly enhances the photodissociation rate, while the excitation of the strongest coupling mode has a pronounced effect on the branching ratio of the photodissociation process. Although the inclusion of the second (weaker) coupling mode has little effect on the electronic population dynamics, it leads to interesting changes of the nodal pattern of the wave packet at the conical intersections. The calculations provide insight into the effect of the multiple coupling modes on the process of direct photodissociation through a conical intersection.