Wave Packet Propagation Method Research Articles

Dynamical Study on Resonance by Using a Wave Packet Propagation Method: Electron Capture in Collision of N5+ Ions with H Atoms

To establish the dynamical aspects of shape resonance, we investigate the electron capture processes N5+ + H → N4+(4s, 4p) + H+ by using a wave packet propagation method that can treat non-adiabatic collision processes. It is found that the incident wave packet is trapped into quasi-bound potentials when the collision energy coincides with that of the rovibrational state of the quasi-molecule. The wave packet component trapped in the N5+ + H effective potential transfers to electron capture channels rather than returns to the initial channel by tunneling again.

State-to-State Reactive Scattering via Real L2 Wave Packet Propagation for Reduced Dimensionality AB + CD Reactions

We present a computational method for the calculation of quantum state-to-state reactive probabilities for reduced dimensionality, three degree-of-freedom, AB + CD ↔ A + BCD reactions. Our approach is based on the recently developed wave packet propagation method in real L2 eigenstates [Skokov, S.; Bowman, J. M. Phys. Chem. Chem. Phys. 2000, 2, 495]. Here we show how the real L2 approach can be used for the calculation of state-to-state probabilities. The “coordinate transformation problem” is relatively easily solved in the L2-eigenstate formulation because the eigenstates used for propagation are analytical functions of the coordinates. The method is tested for the H2 + CN ↔ H + HCN reaction for zero total angular momentum, J, using a previous potential energy surface of Sun and Bowman, who reported reduced dimensionality, time-independent calculations of state-to-state reaction probabilities. New calculations for J > 0 are presented using the adiabatic rotation approximation. In this approximation the L2-eigenstates are obtained efficiently by expanding them in the basis of J = 0 eigenstates. Finally a test of J-shifting is done.

Laser control of molecular photodissociation with use of the complete reflection phenomenon

A new idea of controlling molecular photodissociation branching by a stationary laser field is proposed by utilizing the unusual intriguing quantum-mechanical phenomenon of complete reflection. By introducing the Floquet (or dressed) state formalism, we can artificially create potential curve crossings, which can be used to control molecular processes. Our control scheme presented here is summarized as follows. First, we prepare an appropriate vibrationally excited state in the ground electronic state, and at the same time by applying a stationary laser field of the frequency ω we create two nonadiabatic tunneling (NT) type curve crossings between the ground electronic bound state shifted up by one photon energy ℏω and the excited electronic state with two dissociative channels. In the NT-type of curve crossing where the two diabatic potential curves cross with opposite signs of slopes, it is known that the complete reflection phenomenon occurs at certain discrete energies. By adjusting the laser frequency to satisfy the complete reflection condition at the NT type curve crossing in one channel, the complete dissociation into the other channel can be realized. By taking one- and two-dimensional models which mimic the HOD molecule and using a wave packet propagation method, it is numerically demonstrated that a molecule can be dissociated into any desired channel selectively. Selective dissociation can be realized even into such a channel that cannot be achieved in the ordinary photodissociation because of a potential barrier in the excited electronic state.

Quantum dynamics of model proton-coupled electron transfer reactions

We present detailed studies of the quantum dynamics of model proton-coupled electron transfer (PCET) reactions in solution. We compared the full quantum mechanical calculations with the mean field approaches for the solvent. A multiple time-scale wavepacket propagation method is used for simulating the combined electron/proton/solvent dynamics. The dynamics of the model PCET reactions are found to exhibit extensive mixing of the proton/electron adiabatic states. Such nonadiabatic couplings between adiabatic states are not properly described in mean field calculations except for at short times. The time-scale differences arising from the mass disparities of the different degrees of freedom can affect the detailed dynamics of the model PCET reactions, as illustrated by subtle differences in the sequential PT→ET and ET→PT mechanisms.

Time dependent characteristics of electron tunnelling processes in H−, O− and F− formation on Ag(1 1 1)

Results of a study of electron transfer processes in the interaction of hydrogen, oxygen and fluorine with Ag(111) are reported for a wide range of interaction times. We observe that for long interaction times, the yield of H−, resulting from resonant electron exchange, is much larger than what would be expected for a jellium like metal surface with a similar work function. For short interaction times on the other hand, the yields follow the trend for jellium like surfaces. These results confirm the predictions of the theoretical work using a wave packet propagation method (Phys. Rev. Lett. 80 (1998) 1996) on electron transfer on surfaces with L band gap. In the case of O− and F− significant effects were not observed.

2,2‘-Bithiophene Radical Cation: An Experimental and Computational Study

Electronic absorption and resonance Raman spectra of the radical cation of bithiophene are reported. The bithiophene radical cation was produced by γ-radiolysis in a glassy matrix at 77 K, and the Raman spectrum excited in resonance with the two absorption bands at 425 and 590 nm. The electronic states relevant to the observed electronic transitions were identified and characterized by CASSCF calculations. The optical absorption and resonance Raman spectra were calculated by wave packet propagation methods using the ab initio calculated molecular parameters. The calculated spectra agree well with the experimental ones. The importance of carrying out full wave packet propagation calculations is underlined by the fact that in one case the simple Savin formula gave a completely wrong prediction of the resonance Raman spectrum.

The Radical Cation and Lowest Rydberg States of 1,4-Diaza[2.2.2]bicyclooctane (DABCO)

The radical cation and the two lowest excited singlet Rydberg states of DABCO (1,4-diazabicyclo[2.2.2]octane) are studied. Experimentally, the radical cation of DABCO is generated by either laser flash photolysis in solution at room temperature or by γ-irradiation in a Freon glass at 77 K, and its electronic absorption and resonance Raman spectra in these two media are reported. The present resonance Raman spectra differ substantially from previous reports given in the literature, and it is concluded that a number of bands attributed previously to the DABCO radical cation are due to other species. Theoretically, the absorption and resonance Raman spectra are interpreted on the basis of density functional theory (DFT; B3LYP/6-31G(d)) calculations and wave packet propagation methods. The same DFT calculations are used to interpret excitation and multiphoton ionization spectra of the two lowest singlet Rydberg states, making use of the close similarity between a Rydberg state and its ionic core. From the combined results it is concluded that DFT calculations with a relatively modest basis set provide a valuable framework to predict potential energy surfaces of radical cations and Rydberg states in terms of minima and Hessians.

Quantum dynamics of laser‐ and field‐induced desorption of molecules from metal surfaces

The desorption of adspecies from surfaces by laser radiation or static electric fields is an important subject for the microstructuring of materials and a challenge to theory: Not only the excitation mechanism, but also the subsequent, ultrafast dynamics in a dissipative environment, needs to be properly described. After a brief review on previous work, in this work a few new issues concerning the laser- or field-induced desorption of molecules from metal surfaces [NO from Pt(111), and NH3 from Cu(111)] will be addressed with the help of open-system density matrix theory and wave packet propagation methods. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 210–219, 2000

Quantum dynamics of laser- and field-induced desorption of molecules from metal surfaces

The desorption of adspecies from surfaces by laser radiation or static electric fields is an important subject for the microstructuring of materials and a challenge to theory: Not only the excitation mechanism, but also the subsequent, ultrafast dynamics in a dissipative environment, needs to be properly described. After a brief review on previous work, in this work a few new issues concerning the laser- or field-induced desorption of molecules from metal surfaces [NO from Pt(111), and NH3 from Cu(111)] will be addressed with the help of open-system density matrix theory and wave packet propagation methods. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 210–219, 2000

Wavepacket propagation for reactive scattering using real L2 eigenfunctions with damping

A wavepacket propagation method for reactive scattering using real L2 eigenstates is proposed and tested. The wavepacket propagation is carried out by explicit time evolution of a basis of real L2 eigenstates. The wavepacket is damped at each time step to avoid unphysical reflections at the grid edges and then re-expanded in terms of the real eigenstates. Most of the computational effort is associated with the calculation of eigenstates, while the propagation in the real L2 basis and analysis are relatively inexpensive. In addition, once the L2 basis is available the wavepacket propagation for any initial state can be done very efficiently. Propagation by complex L2 eigenstates is also briefly reviewed. In this approach no explicit time propagation is required since the time-to-energy wavepacket transformation is analytical for any given potential. Applications of both methods for a one-dimensional Eckart potential show excellent agreement with exact results for the energy dependence of the reaction probability. The real L2 approach is also applied to three-dimensional D+H2 for zero total angular momentum. Reaction probabilities for H2(v=0, j=0–5), summed over final DH states, as well as the cumulative reaction probability are presented over a wide energy range and compared to previous accurate results.

Dimensionality effects on transition state resonances for [formula omitted] and [formula omitted] reactive collisions

The transition state resonances of the title reactions have been studied on the accurate double many-body expansion (DMBE) potential energy surface for H3 using two-dimensional (2D) and three-dimensional (3D) time-dependent wave packet propagation methods. It is shown that the resonance energies are strongly associated with the vibrational threshold states of the molecular fragment obtained upon dissociation, both in the 2D and 3D calculations. However, although the two systems have the same threshold states, the resonance widths for the 2D D+HD collisions are found to be considerably narrower than for the 3D ones, while no such phenomenon is observed for H+DH. As a result, we have concluded that there is an apparent dimensional effect on the resonance widths of the heavy–light–heavy (HLH) reaction.

Semiclassical Wave Packet Dynamics with Electronic Structure Computed on the Fly: Application to Photophysics of Electronic Excited States in Condensed Phase

Many semiclassical wave packet propagation methods require only local potential energy surface information in order to update a Gaussian wave packet over a short time interval. These data, which include the evaluation of the potential energy at the instantaneous configuration space center of the wave packet, plus the gradient vector and Hessian (second derivative) matrix at the same configuration, can be generated efficiently by extant electronic structure packages. This leads to an algorithm for propagating semiclassical Gaussian wave packets using electronic structure data computed “on the fly” in the course of the propagation. The feasibility of such a strategy for condensed phase systems is demonstrated by using it (with an appropriate approximate level of electronic structure theory) to calculate Franck−Condon absorption and emission spectra of all-trans 1,3,5,7-octatetraene in the gas phase, and in both chloroform and methanol solvents. Good agreement with the corresponding experimentally measured s...

Wave-packet propagation approach in the theory of charge transfer in projectile–metal surface interactions

A brief review of the results obtained recently with the wave packet propagation method in the problem of resonant charge transfer (RCT) in collisions of atomic particles with metal surfaces is given. This method can be equally applied to the case of free-electron metal targets and to metal surfaces with a projected band gap. It provides a very transparent understanding of the one-electron processes occuring in such collisions. The new features of the RCT process due to the presence of a projected band gap for the electron motion along the normal to the surface are described for Li and H − projectiles colliding with a Cu(1 1 1) surface. It is shown that the decay of the resonance states located inside the band gap is strongly dominated by the 2D surface state continuum, while the decay into bulk Cu is strongly reduced. The resonance widths obtained for the metal with the projected band gap are, as a rule, significantly smaller than the widths in the corresponding jellium metal problem. These results provide new opportunities for theoretical investigations of the resonant charge transfer.

Stabilisation of alkali-adsorbate-induced states on Cu(111) surfaces

The Li and Cs alkali-adsorbate-induced states on a model Cu(111) surface are studied theoretically using the coupled angular mode and the wave packet propagation methods. Their energy position and their decay rate via one-electron transfer into the metal are calculated. An unoccupied alkali-induced state is found with a rather long lifetime, much longer than those found in the case of free-electron metal surfaces. This is attributed to the combined effect of the hybridisation of the alkali levels and of the Cu(111) projected band gap along the normal to the surface that blocks the electron transfer between the adsorbate and the metal. This qualitatively explains the experimental finding of a long-lived state by Bauer et al. [Phys. Rev. B 55 (1997) 10 040] and Ogawa et al. [Phys. Rev. Lett. 82 (1999) 1931].

Resonant charge transfer in ion–metal surface collisions: Effect of a projected band gap in theH−−Cu(111)system

A wave-packet propagation method is applied to the treatment of the resonant charge transfer (RCT) process in the interaction between an ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ ion and a Cu(111) surface. Using a model description of the Cu(111) electronic structure, it is shown that the RCT efficiency is deeply influenced by the presence of the Cu(111) projected band gap, that partially blocks the electron transfer in the direction normal to the surface. The differences between the RCT process on a free electron metal surface and on a Cu(111) surface are discussed. The two cases are associated with very different pictures of the electron transfer. In particular, the importance of the Cu(111) surface state for the decay of the ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ ion is demonstrated. The effect of the band gap is also shown to strongly depend on the interaction time. For short interaction times (large collision velocities), the electron wave packet does not have enough time to probe the metal band structure and the RCT on a Cu(111) surface is very similar to that on a free electron surface. For long interaction times (low collision velocities), the RCT efficiency is drastically reduced by the presence of the band gap. The wave-packet propagation method is also used to discuss the validity of the rate equation approach in the case of a free electron metal target.

Molecular dynamics of pyrazine after excitation to the S2 electronic state using a realistic 24-mode model Hamiltonian

The molecular dynamics of pyrazine after excitation to the S2 electronic state is investigated using the S2 absorption spectrum as a benchmark. We first present a realistic model Hamiltonian including all 24 vibrational modes of the pyrazine molecule. Using this model, we determined the potential energy surfaces of the lowest two excited states, S1 and S2, which are strongly coupled to each other. We then treated the nuclear motion of all 24 vibrational modes using the multiconfiguration time-dependent Hartree (MCTDH) wave packet propagation method. This method obtains results of good accuracy with acceptable computational effort for such a large system. The calculated spectrum is in good agreement with the experimental one. Furthermore, our results shed light on the role of the 20 modes which are only weakly coupled to the system, and demonstrate that essential physical features, such as symmetries, have to be considered when one wants to treat the molecular dynamics of pyrazine realistically.

Lagrange-distributed approximating-functional approach to wave-packet propagation: Application to the time-independent wave-packet reactant-product decoupling method

A connection is made between a recently introduced Lagrange-distributed approximating-functional and the Paley-Wiener sampling theorem. The Lagrange-distributed approximating-functional sampling is found to provide much superior results to that of Paley-Wiener sampling. The relations between discrete variable representation and Lagrange-distributed approximating functionals are discussed. The latter is used to provide an even spaced, interpolative grid representation of the Hamiltonian, in which the kinetic energy matrix has a banded, Toeplitz structure. In this paper we demonstrate that the Lagrange-distributed approximating-functional representation is an accurate and reliable representation for use in fast-Fourier-transform wave-packet propagation methods and apply it to the time-independent wave-packet reactant-product decoupling method, calculating state-to-state reaction probabilities for the two-dimensional (collinear) and three-dimensional $(J=0)$ ${\mathrm{H}+\mathrm{H}}_{2}$ reactions. The results are in very close agreement with those of previous calculations. We also discuss the connection between the distributed approximating-functional method and the existing mathematical formalism of moving least-squares theory.

An application of distributed approximating functional-wavelets to reactive scattering

A newly developed distributed approximating functional (DAF)-wavelet, the Dirichlet–Gabor DAF-wavelet (DGDW), is applied in a calculation of the state-to-state reaction probabilities for the three-dimensional (3-D) (J=0)H+H2 reaction, using the time-independent wave-packet reactant-product decoupling (TIWRPD) method. The DGDWs are reconstructed from a rigorous mathematical sampling theorem, and are shown to be DAF-wavelet generalizations of both the sine discrete variable representation (sinc-DVR) and the Fourier distributed approximating functionals (DAFs). An important feature of the generalized sinc-DVR representation is that the grid points are distributed at equally spaced intervals and the kinetic energy matrix has a banded, Toeplitz structure. Test calculations show that, in accordance with mathematical sampling theory, the DAF-windowed sinc-DVR converges much more rapidly and to higher accuracy with bandwidth, 2W+1. The results of the H+H2 calculation are in very close agreement with the results of previous TIWRPD calculations, demonstrating that the DGDW representation is an accurate and efficient representation for use in FFT wave-packet propagation methods, and that, more generally, the theory of wavelets and related techniques have great potential for the study of molecular dynamics.

Complex trajectory method in semiclassical propagation of wave packets

We propose a semiclassical wave packet propagation method relying on classical trajectories in a complex phase space. It is based on the Schrödinger wave equation and the usual expansion with respect to ℏ, except that the amplitude of the wave packet is taken into account at the very zeroth order, unlike in the usual WKB method where it is treated as a corrective or first order term. Formally, it amounts to making both the wavelength and the width of the wave packet tend to zero with ℏ. The action and consequently the classical trajectories derived are complex. This method is tested successfully in many cases, analytically or numerically, including the bounce and even the splitting of the wave packet. Our method appears to be much more accurate than the WKB method while less computationally demanding than the Van-Vleck formula. Moreover, it has a particularly interesting property: the singularities (caustics) of the usual semiclassical theories do not appear in this formalism in all cases tested.

Reactant–product decoupling approach to state-to-state dynamics calculation for bimolecular reaction and unimolecular fragmentation

The main purpose of the study is to explore a number of computational methods to be used in the RPD approach to state-to-state quantum dynamics calculation of polyatomic reactions. Specifically, a mixed time-dependent (TD) and energy-dependent (ED) approach to solve the RPD equations is investigated. In the mixed TD and ED approach, the reactant wavefunction is computed by the method of wavepacket propagation while the product wavefunction is calculated by energy-dependent methods. As a result, the reactant–product coordinate transformation only needs to be carried out for the number of energies at which the state-to-state S-matrix elements are needed, which is advantageous if state-to-state information at only a few energies are needed. Similar implementation of the mixed RPD approach is given for calculation of product state distribution in molecular photofragmentation dynamics.