Time-dependent Quantum Dynamics Research Articles

Converged quantum dynamics with modified Shepard interpolation and Gaussian wave packets

A new hybrid method is presented in which modified Shepard interpolation of a potential energy surface is combined with time-dependent quantum dynamics calculations. The propagation of a wave packet composed of fixed-width Gaussian functions allows a one-to-one mapping between the quantum dynamics results and a small number of quantum trajectories, allowing electronic structure theory calculations to be performed preferentially in dynamically-important regions. The method is designed for demonstrable convergence of the quantum dynamics results from ab initio calculations. The photodissociation of NOCl is used as a test case.

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.

Time-Dependent Quantum Dynamics Study of the Ne + H2+ (v = 0−9) and D2+ (v = 0−12) Proton Transfer Reactions at Thermal Collision Energies

The Ne + H2+ and D2+ proton transfer reactions were studied (reaction probabilities (P) and cross sections (sigma)) using the time-dependent real wave packet quantum dynamics method at the centrifugal sudden level (CS-RWP method). This was made considering the influence of vibrational excitation of H2+ and D2+ on the dynamics ((v = 0-9, j = 0) and (v = 0-12, j = 0) vibrorotational states, respectively) at thermal collision energies (Ecol = 0.010 to 0.14 eV). The CS-RWP relative cross sections at thermal collision energy (300 K) for Ne + H2+ and Ne + D2+ are in good agreement with the experimental data. The present results suggest the adequacy of the approach used here in describing these and related systems at thermal collision energies and from low to high vibrational excitation of reactants.

Design of laser pulses for selective vibrational excitation of the N6-H bond of adenine and adenine-thymine base pair using optimal control theory

Time dependent quantum dynamics and optimal control theory are used for selective vibrational excitation of the N6-H (amino N-H) bond in free adenine and in the adenine-thymine (A-T) base pair. For the N6-H bond in free adenine we have used a one dimensional model while for the hydrogen bond, N6-H(A)...O4(T), present in the A-T base pair, a two mathematical dimensional model is employed. The conjugate gradient method is used for the optimization of the field dependent cost functional. Optimal laser fields are obtained for selective population transfer in both the model systems, which give virtually 100% excitation probability to preselected vibrational levels. The effect of the optimized laser field on the other hydrogen bond, N1(A)...H-N3(T), present in A-T base pair is also investigated.

An eight-degree-of-freedom quantum dynamics study of the isotopic effect on the reaction: HD+C2H

An eight-dimensional time-dependent quantum dynamics calculation is reported to study the isotopic reaction, HD+C(2)H, on a new modified potential energy surface. Initial-state-selected reaction probability, integral cross section, and rate constants are presented in this isotopic reaction study. Initial-state-selected reaction probability is obtained by summing over all the possible product's arrangements in this isotopic reaction study. This study shows that vibrational excitations of HD enhance the reactivity, whereas stretching excitations of C(2)H only have a small effect on the reactivity. Furthermore, the bending excitations of C(2)H, compared to the ground-state reaction probability, hinder the reactivity. The present results are consistent with those obtained for the H(2)+C(2)H reaction. The comparison of these two reactions also shows the isotopic effect in the initial-state-selected reaction probability, integral cross section, and rate constants. The rate constant comparison shows that the HD+C(2)H reaction has a smaller reactivity than the H(2)+C(2)H reaction.

Time dependent quantum dynamics study of the Ne+H2+(v=–4)→NeH++H proton transfer reaction

The Ne + H2+-->NeH+ + H proton transfer reaction was studied using the time dependent real wave packet quantum dynamics method at the helicity decoupling level, considering the H2+ molecular ion in the (v=0-4, j=0) vibrorotational states and a wide collision energy interval. The calculated reaction probabilities and reaction cross sections were in a rather good agreement with reanalyzed previous exact quantum dynamics results, where a much smaller collision energy interval was considered. Also, a quite good agreement with experimental data was found. These results suggested the adequacy of the approach used here to describe this and related systems.

Analysis of the CH-chromophore spectra and dynamics in dideutero-methyliodide CHD2I1

We report the infrared spectra of dideutero-methyliodide CHD2I in the range from 500 to 12 000 cm−1. Twenty two vibrational bands were assigned to the coupled CH-stretching and bending vibrations of the CH-chromophore. They were analysed in terms of an effective Hamiltonian including strong anharmonic resonances up to the polyad N = 4 corresponding to a maximum of four quanta of stretching excitation. The ab initio potential hypersurface for the three-dimensional CH-chromophore subspace was calculated at the full MP2 level. This surface was finally scaled to fit experiment with vibrational energy levels being calculated by an adiabatic successive truncation technique. The resulting spectrum was represented by the same effective Hamiltonian as used for the experimental data, the results from both approaches agreeing well. The time-dependent quantum dynamics were obtained from this Hamiltonian adjusted to experiment. It showed very fast but incomplete energy transfer from pure CH-stretching excitation with four or five quanta to partial CH-bending excitation in about 100 fs. These results are discussed in terms of a doorway to further excitation transfer to the lower frequency modes measured before by femtosecond pump–probe experiments in our group. 1Dedicated to Hubert van den Bergh on the occasion of his 65th birthday.

A time-dependent quantum dynamics investigation of the guanine-cytosine system: A six-dimensional model

The dynamics of the guanine-cytosine base pair has been studied in the time-dependent quantum approach. A six-dimensional model involving the nonlinear three hydrogen bridges has been utilized. The modifications induced in the hydrogen transfer from a base to the other by the explicit inclusion of the out-of-plane hydrogen atom position in the three bridges have been evidenced and the consequences on stacking interaction and base pair opening are considered. The relevance of these aspects in biological properties has been suggested.

Accurate ab initio electronic structure calculations of the stable helium complex: HeBeO

A three-dimensional global potential energy surface for the simple helium-containing complex HeBeO is developed at a highly-accurate CASPT2 ab initio level with large basis sets. Both time-dependent and time-independent quantum dynamics calculations have subsequently been performed to obtain wavefunctions of bound vibrational states as well as resonance states on the newly developed potential surface. It has been found that the system has more than 10 bound vibrational states even for zero total angular momentum. Quantum number assignment for the obtained vibrational states is also given.

An eight-degree-of-freedom, time-dependent quantum dynamics study for the H2+C2H reaction on a new modified potential energy surface

An eight-dimensional time-dependent quantum dynamics wave packet approach is performed for the study of the H2+C2H-->H+C2H2 reaction system on a new modified potential energy surface (PES) [L.-P. Ju et al., Chem. Phys. Lett. 409, 249 (2005)]. This new potential energy surface is obtained by modifying Wang and Bowman's old PES [J. Chem. Phys. 101, 8646 (1994)] based on the new ab initio calculation. This new modified PES has a much lower transition state barrier height at 2.29 kcal/mol than Wang and Bowman's old PES at 4.3 kcal/mol. This study shows that the reactivity for this diatom-triatom reaction system is enhanced by vibrational excitations of H2, whereas the vibrational excitations of C2H only have a small effect on the reactivity. Furthermore, the bending excitations of C2H, compared to the ground state reaction probability, hinder the reactivity. The comparison of the rate constant between this calculation and experimental results agrees with each other very well. This comparison indicates that the new modified PES corrects the large barrier height problem in Wang and Bowman's old PES.

Theoretical study of the simplest Xe-containing molecule: HXeH

The simplest metastable Xe-containing compound HXeH has been theoretically investigated using highly-accurate CASPT2-level electronic structure calculations taking the relativistic effects into account. A new three-dimensional global potential energy surface has been developed and time-dependent wave packet quantum dynamics calculations were then performed to obtain vibrational energy levels of the metastable states for the HXeH, HXeD and DXeD systems. It has been found that low-lying vibrational states below and just above the H + Xe + H dissociation limit have extremely long lifetimes in a nanosecond time scale. The present theoretical results suggest that these rare-gas containing molecules can experimentally be detected in the gas phase.

Theoretical study of the H + Br 2 and Mu + Br 2 reactions: A new ab initio potential energy surface and quantum dynamics calculations

A new global potential energy surface for the H + Br 2 → HBr + Br reaction has been developed at the MRCI+Q/aug-cc-pVTZ ab initio level of theory. It has been found that this level calculation gives a negative barrier slightly below the H + Br 2 reactant energy level. Time-dependent and time-independent quantum dynamics calculations have been performed on this potential energy surface. The calculated cumulative reaction probabilities for J = 0 around the reaction threshold energy region show a very similar behavior for both the H + Br 2 and Mu + Br 2 reaction, in qualitative disagreement with experimental measurements, where a positive activation energy was observed for the H + Br 2 reaction while a negative activation energy for the Mu + Br 2 reaction. Variational calculations of vibrational energy levels have also been performed to study dynamical vibrational bonding for the Br–Mu–Br molecule. It has been found that the system has several vibrational bonding states, whose wave functions are localized around the transition-state of the Br + MuBr′ → MuBr + Br′ exchange reaction, below the lowest Br + MuBr asymptotic energy level. This result qualitatively supports the recent experimental finding that a long-lived radical containing a Mu atom is produced in the Mu + Br 2 reaction.

Comparison between different reactions of group IV hydride with H

The four-dimensional time-dependent quantum dynamics calculations for reactions of group IV hydride with H are carried out by employing the semirigid vibrating rotor target model and the time-dependent wave packet method. The reaction possibility, cross section and rate constants for reactions (H+SiH 4 and H+GeH 4 ) in different initial vibrational and rotational states are obtained. The common feature for such kind of reaction process is summarized. The theoretical result is consistent with available measurement, which indicates the credibility of this theory and the potential energy surface.

Dynamical pruning of static localized basis sets in time-dependent quantum dynamics

We investigate the viability of dynamical pruning of localized basis sets in time-dependent quantum wave packet methods. Basis functions that have a very small population at any given time are removed from the active set. The basis functions themselves are time independent, but the set of active functions changes in time. Two different types of localized basis functions are tested: discrete variable representation (DVR) functions, which are localized in position space, and phase-space localized (PSL) functions, which are localized in both position and momentum. The number of functions active at each point in time can be as much as an order of magnitude less for dynamical pruning than for static pruning, in reactive scattering calculations of H2 on the Pt(211) stepped surface. Scaling of the dynamically pruned PSL (DP-PSL) bases with dimension is considerably more favorable than for either the primitive (direct product) or DVR bases, and the DP-PSL basis set is predicted to be three orders of magnitude smaller than the primitive basis set in the current state-of-the-art six-dimensional reactive scattering calculations.

A full dimensional, nine-degree-of-freedom, time-dependent quantum dynamics study for the H2+C2H reaction

A full dimensional, nine-degree-of-freedom (9DOF), time-dependent quantum dynamics wave packet approach is presented for the study of the H2+C2H-->H+C2H2 reaction system. This is the first full dimensional quantum dynamics study for a diatom-triatom reaction system. The effects of the initial vibrational and rotational excitations of the reactants on the reactivity of this reaction are investigated. This study shows that vibrational excitations of H2 enhance the reactivity; whereas, the vibrational excitations of C2H only have a small effect on the reaction probability. In addition, the bending excitations of C2H, compared to the ground state reaction probability, hinder the reactivity. Comparison of the ground state reaction probabilities of the 9DOF and 8DOF shows the reaction probability from the full dimensional calculation is larger, with more prominent resonance features.

Two-photon excitation dynamics in bound two-body Coulomb systems including ac Stark shift and ionization

One of the dominant systematic effects that shift resonance lines in high-precision measurements of two-photon transitions is the dynamic (ac) Stark shift. For suitable laser frequencies, the ac Stark shift acquires an imaginary part which corresponds to the rate of resonant one-photon ionization of electrons into a continuum state. At the current level of spectroscopic accuracy, the underlying time-dependent quantum dynamics governing the atomic two-photon excitation process must be well understood, and related considerations are the subject of the present paper. In order to illustrate the basic mechanisms in the transient regime, we investigate an analytically solvable model scenario for the population dynamics in the density matrix formalism and describe in detail how to generalize the corresponding equations of motion for individual experimental use. We also calculate the dynamic Stark shift for two-photon $S\text{\ensuremath{-}}S$ and $S\text{\ensuremath{-}}D$ transitions in bound two-body Coulomb systems and the corresponding two-photon transition matrix elements. In particular, we investigate transitions for which the $1S$ ground state or alternatively the metastable $2S$ state acts as the lower-energy state, and for which states with $n\ensuremath{\leqslant}20$ represent the upper states. Relativistic and radiative corrections to the excitation dynamics, and the corresponding limitations to the accuracy of the measurements, are briefly discussed. Our considerations suggest the general feasibility of a detection mechanism, offering high quantum efficiency, based on two-step three-photon resonant ionization spectroscopy, for large classes of experimentally relevant two-photon transitions in two-body Coulomb systems.

Time-Dependent Quantum Wave Packet Calculations of Three-Dimensional He - O2 Inelastic Scattering.

We have studied a three-dimensional time-dependent quantum dynamics of He - O2 inelastic scattering by using a recently published ab initio potential energy surface. The state-to-state transition probabilities at zero total angular momentum have been calculated in the energy range of 0.12-0.59 eV, and the product rotational distributions are extracted. J-shifting approximation is used to estimate the probabilities for J > 0. The integral cross sections and thermal rate constants are then calculated.

Recent development of self-interaction-free time-dependent density-functional theory for nonperturbative treatment of atomic and molecular multiphoton processes in intense laser fields

In this paper, we present a short account of some recent developments of self-interaction-free density-functional theory (DFT) and time-dependent density-functional theory (TDDFT) for accurate and efficient treatment of the electronic structure, and time-dependent quantum dynamics of many-electron atomic and molecular systems. The conventional DFT calculations using approximate and explicit exchange-correlation energy functional contain spurious self-interaction energy and improper long-range asymptotic potential, preventing reliable treatment of the excited, resonance, and continuum states. We survey some recent developments of DFT/TDDFT with optimized effective potential (OEP) and self-interaction correction (SIC) for both atomic and molecular systems for overcoming some of the above mentioned difficulties. These DFT (TDDFT)/OEP-SIC approaches allow the use of orbital-independent single-particle local potential which is self-interaction free. In addition we discuss several numerical techniques recently developed for efficient and high-precision treatment of the self-interaction-free DFT/TDDFT equations. The usefulness of these procedures is illustrated by a few case studies of atomic, molecular, and condensed matter processes of current interests, including (a) autoionizing resonances, (b) relativistic OEP-SIC treatment of atomic structure (Z=2-106), (c) shell-filling electronic structure in quantum dots, (d) atomic and molecular processes in intense laser fields, including multiphoton ionization, and very-high-order harmonic generation, etc. For the time-dependent processes, an alternative Floquet formulation of TDDFT is introduced for time-independent treatment of multiphoton processes in intense periodic or quasiperiodic fields. We conclude this paper with some open questions and perspectives of TDDFT.

Theory of the photodissociation of ozone in the Hartley continuum: Potential energy surfaces, conical intersections, and photodissociation dynamics

Ab initio potential energy and transition dipole moment surfaces are presented for the five lowest singlet even symmetry electronic states of ozone. The surfaces are calculated using the complete active space self consistent field method followed by contracted multireference configuration interaction (MRCI) calculations. A slightly reduced augmented correlation consistent valence triple-zeta orbital basis set is used. The ground and excited state energies of the molecule have been computed at 9282 separate nuclear geometries. Cuts through the potential energy surfaces, which pass through the geometry of the minimum of the ground electronic state, show several closely avoided crossings. Close examination, and higher level calculations, very strongly suggests that some of these seemingly avoided crossings are in fact associated with non-symmetry related conical intersections. Diabatic potential energy and transition dipole moment surfaces are created from the computed ab initio adiabatic MRCI energies and transition dipole moments. The transition dipole moment connecting the ground electronic state to the diabatic B state surface is by far the strongest. Vibrational-rotational wavefunctions and energies are computed using the ground electronic state. The energy level separations compare well with experimentally determined values. The ground vibrational state wavefunction is then used, together with the diabatic B<--X transition dipole moment surface, to form an initial wavepacket. The analysis of the time-dependent quantum dynamics of this wavepacket provides the total and partial photodissociation cross sections for the system. Both the total absorption cross section and the predicted product quantum state distributions compare well with experimental observations. A discussion is also given as to how the observed alternation in product diatom rotational state populations might be explained.

SIX-DIMENSIONAL DYNAMICS OF DISSOCIATIVE CHEMISORPTION OFH2ON METAL SURFACES

The theory of time-dependent quantum dynamics of dissociative chemisorption of hydrogen on metal surfaces is reviewed, in the framework of electronically adiabatic scattering from static surfaces. Four implementations of the time-dependent wave packet (TDWP) method are discussed. In the direct product pseudo-spectral and the spherical harmonics pseudo-spectral methods, no use is made of the symmetry associated with the surface unit cell. This symmetry is exploited by the symmetry adapted wave packet and the symmetry adapted pseudo-spectral (SAPS) method, which are efficient for scattering at normal incidence. The SAPS method can be employed for potential energy surfaces of general form.Comparison to experiment shows that the TDWP method yields good, but not yet excellent, quantitative accuracy for dissociation of (ν = 0, j = 0) H2if the calculations are based on accurately fitted density functional theory calculations that are performed using the generalized gradient approximation. The influence of the molecule's vibration (rotation) is well (reasonably well) described. The theory does not yet yield quantitatively accurate results for rovibrationally inelastic scattering. The theory has helped with the interpretation of existing experimental results, for instance, by solving a parodox regarding the corrugation of Pt(111) as seen by reacting and scattering H2. The theory has also provided some exciting new predictions, for instance, concerning where on the surface of Cu(100) H2reacts depending on its vibrational state. Future theoretical studies of H2reacting on metal surfaces will likely be aimed at validating GGAs for molecule-surface interactions, and understanding trends in collisions of H2with complex metal surfaces.