Quantum Mechanical Wave Packet Propagation Research Articles

Resonant Charge-Transfer in Grazing Collisions of H− with Vicinal Nanosurfaces on Cu(111), Au(100) and Pd(111) Substrates: A Comparative Study

We compare the electron dynamics at monocrystalline Cu(111), Au(100) and Pd(111) precursor substrates with vicinal nanosteps. The unoccupied bands of a surface superlattice are populated via the resonant charge transfer (RCT) between the surface and a H − ion that flies by at grazing angles. A quantum mechanical wave packet propagation approach is used to simulate the motion of the active electron, and time-evolved wave packet densities are used to visualize the dynamics through the superlattice. The survived ion fraction in the reflected beam generally exhibits modulations as a function of the vicinal terrace size and shows peaks at those energies that access the image state subband dispersions. Differences in magnitudes of the ion-survival as a function of the particular substrate selection and the ion-surface interaction time, based on the choice of two ion-trajectories, are examined. A square well model, producing standing waves between the steps on the surface, explains the energies of the maxima in the ion survival probability for all the metals considered. This indicates that the primary process of confinement induced subband formation is robust. The work may motivate measurements and applications of shallow-angle ion-scattering spectroscopy to access electronic substructures in periodically nanostructured surfaces.

Ion survival in grazing collisions of H− with vicinal nanosurfaces as a probe for subband electronic structures

We study the electron dynamics at a monocrystalline Pd(111) surface with stepped vicinal nanostructures modeled in a simple Kronig-Penney scheme. The unoccupied bands of the surface are resonantly excited \textit{via} the resonant charge transfer (RCT) interaction of the surface with a hydrogen anion reflected at grazing angles. The interaction dynamics is simulated numerically in a quantum mechanical wave packet propagation approach. Visualization of the wave packet density shows that, when the electron is transferred to the metal, the surface and image subband states are the most likely locations of the electron as it evolves through the superlattice. The survival probability of the interacting ion exhibits strong modulations as a function of the vicinal-terrace size and shows peaks at those energies that access the image state subband dispersions. A simple square well model producing standing waves between the steps on the surface suggests the application of such ion-scattering at shallow angles to map electronic substructures in vicinal surfaces. The work also serves as the first proof-of-principle in the utility of our computational method to address, via RCT, surfaces with nanometric patterns.

Ozone Photodissociation: Isotopic and Electronic Branching Ratios for Symmetric and Asymmetric Isotopologues

We present new calculations of the branching ratios between the various electronic and isotopic photodissociation channels of ozone. Special emphasis is placed on the isotopic/isotopologue differences because the contribution of the ozone photodissociation to the oxygen isotope and ozone isotopologue enrichments or fractionations is important for atmospheric applications. These branching ratios, which depend on photon energy, have been calculated with a full quantum mechanical wavepacket propagation approach: the multiconfiguration time-dependent Hartree (MCTDH) method. Five ozone isotopologues are considered: three symmetric, (16)O(3) (noted 666), (16)O(17)O(16)O (676), and (16)O(18)O(16)O (686); two asymmetric, (16)O(2)(17)O (noted 667) and (16)O(2)(18)O (668). The 668 and 667 asymmetric isotopologues can dissociate into either 66 + 8 or 68 + 6 for 668 and into 66 + 7 or 67 + 6 for 667. In the ranges of the Chappuis and Hartley bands, the dissociation is very fast and electronic and isotopic branching ratios are obtained from the wavepacket fluxes through complex absorbing potentials (CAPs) located perpendicular to the dissociation channels of the potential energy surfaces (PESs) of the A (1)B(1) (Chappuis) and B 3(1)A' (Hartley/Huggins) electronic states. In the range of the Huggins band the dissociation is much slower and the isotopic branching ratios of 667 and 668 asymmetric isotopologues, (e.g; 668 → 66 + 8 or 86 + 6) are obtained from the ratios of two partial absorption cross sections corresponding to the selective excitation of one or the other of the two isomers of C(s) symmetry, which dissociate respectively into 66 + 8 and 86 + 6. We find that the photodissociation of the 668 asymmetric isotopologue favors the 68 + 6 channel with a propensity varying between 52% (Hartley) and 54% (Huggins) as a function of the photon energy. The electronic branching ratios to the singlet channel (O(3) + hυ → O((1)D) + O(2)((1)Δ)) are all close to 90% above ≈32,000 cm(-1). Below this energy, the singlet channel is energetically closed and only the triplet channel (O(3) + hυ → O((3)P) + O(2)((3)Σ)) is open. These branching ratios are required to calculate the photolysis rates of each ozone isotopologue, which in turn contribute to the atomic oxygen and the ozone isotopic enrichments in the atmosphere.

The ultraviolet spectrum of OCS from first principles: Electronic transitions, vibrational structure and temperature dependence

Global three dimensional potential energy surfaces and transition dipole moment functions are calculated for the lowest singlet and triplet states of carbonyl sulfide at the multireference configuration interaction level of theory. The first ultraviolet absorption band is then studied by means of quantum mechanical wave packet propagation. Excitation of the repulsive 2 (1)A' state gives the main contribution to the cross section. Excitation of the repulsive 1 (1)A" state is about a factor of 20 weaker at the absorption peak (E(ph) ≈ 45,000 cm(-1)) but becomes comparable to the 2 (1)A' state absorption with decreasing energy (35,000 cm(-1)) and eventually exceeds it. Direct excitation of the repulsive triplet states is negligible except at photon energies E(ph) < 38,000 cm(-1). The main structure observed in the cross section is caused by excitation of the bound 2 (3)A" state, which is nearly degenerate with the 2 (1)A' state in the Franck-Condon region. The structure observed in the low energy tail of the spectrum is caused by excitation of quasi-bound bending vibrational states of the 2 (1)A' and 1 (1)A" electronic states. The absorption cross sections agree well with experimental data and the temperature dependence of the cross section is well reproduced.

Quantum-mechanical wavepacket propagation in a sparse, adaptive basis of interpolating Gaussians with collocation

We present an extension of our earlier work on adaptive quantum wavepacket dynamics [B. Hartke, Phys. Chem. Chem. Phys., 2006, 8, 3627]. In this dynamically pruned basis representation the wavepacket is only stored at places where it has non-negligible contributions. Here we enhance the former 1D proof-of-principle implementation to higher dimensions and optimize it by a new basis set, interpolating Gaussians with collocation. As a further improvement the Tnum approach from Lauvergnat and Nauts [J. Chem. Phys., 2002, 116, 8560] was implemented, which in combination with our adaptive representation offers the possibility of calculating the whole Hamiltonian on-the-fly. For a two-dimensional artificial benchmark and a three-dimensional real-life test case, we show that a sparse matrix implementation of this approach saves memory compared to traditional basis representations and comes even close to the efficiency of the fast Fourier transform method. Thus we arrive at a quantum wavepacket dynamics implementation featuring several important black-box characteristics: it can treat arbitrary systems without code changes, it calculates the kinetic and potential part of the Hamiltonian on-the-fly, and it employs a basis that is automatically optimized for the ongoing wavepacket dynamics.

Semiclassical wave packet study of ozone forming reaction

We have applied the semiclassical wave packet method (SWP) to calculate energies and lifetimes of the metastable states (scattering resonances) in a simplified model of the ozone forming reaction. All values of the total angular momentum up to J=50 were analyzed. The results are compared with numerically exact quantum mechanical wave packet propagation and with results of the time-independent WKB method. The wave functions for the metastable states in the region over the well are reproduced very accurately by the SWP; in the classically forbidden region and outside of the centrifugal barrier, the SWP wave functions are qualitatively correct. Prony's method was used to extract energies and lifetimes from the autocorrelation functions. Energies of the metastable states obtained using the SWP method are accurate to within 0.1 and 2 cm(-1) for under-the-barrier and over-the-barrier states, respectively. The SWP lifetimes in the range of 0.5<tau(n)<100 ps are accurate to within 10%. A three-level model was used to investigate accuracies of different approximations for the reaction rate constant. It was shown that the majority of the metastable states in this system are either long lived (narrow resonances) which can be treated as stable, or short lived (broad resonances) which can be treated without the knowledge of their lifetimes. Only a few metastable states fall into the intermediate range where both energies and lifetimes are needed to model the kinetics. The recombination rate constant calculated with the SWP method at room temperature and pressure is in good agreement with available experimental data.

First-principle dynamical electronic characteristics of Al electromigration in the bulk, surface, and grain boundary

Formulas for the driving force of electromigration have been presented using concepts of the tension density, the external force density, and the effective charge tensor density. The ``dynamic'' wind charge tensor density $Z{\ensuremath{\downdownarrows}}_{a\mathrm{dynamic}\mathrm{}\mathrm{wind}}(\mathbf{r})$ has been revealed over and above the conventional ``static'' wind charge tensor density $Z{\ensuremath{\downdownarrows}}_{a\mathrm{static}\mathrm{}\mathrm{wind}}(\mathbf{r}).$ We have demonstrated the application of the concepts to electromigration reliability problems of ultralarge-scale integration devices where extremely high current densities should be maintained through ultrathin film interconnects. Quantum mechanical wave-packet propagation of an Al atom has been examined in some models of thin Al lines which contain atomic defects, using the first-principle electronic structure calculations under the periodic boundary condition. The dynamical electronic properties by our simulation have demonstrated the characteristic features of the $Z{\ensuremath{\downdownarrows}}_{a\mathrm{dynamic}\mathrm{}\mathrm{wind}}(\mathbf{r})$ in the course of the Al electromigration in the bulk, surface, and grain boundary.

Intramolecular vibrational energy re-distribution of water molecule induced by local-mode excitation

Intramolecular vibrational energy re-distribution (IVR) from local-mode excited states of water molecule is investigated on the basis of exact quantum mechanical wave packet propagation. The energy spectrum is calculated by Fourier transform of auto-correlation function. Progressions of local-mode exicted states are found in the energy range upto 5.5 eV. Wave functions of feature states of the local-mode character are obtained by use of the energy-filtration technique. Time evolution of those wave functions indicates that the vibrational energy of one bond-stretching is transmitted to the bending motion in several tens femtoseconds. The energy transfer to the other bond-stretching takes more than 1 ps.

Quantum mechanism in the photodissociation of NaFH complex: a challenge to semiclassical analysis

The photodissociation of collinear HF⋯Na van der Waals complexes is investigated by quantum mechanical wave packet propagation and by five semiclassical trajectory methods. For this system, with strongly avoided crossing, none of the semiclassical theories is qualitatively correct for either half-lives or the branching ratios. Quantum calculations show a substantial isotope effect.

Ground state of a spinless charged particle in a periodic magnetic field

The ground-state energy of a two-dimensional, spinless, charged particle in a periodic magnetic field is studied by an exact quantum-mechanical wave-packet propagation method. The periodic magnetic-field modulation removes the degeneracy of the lowest Landau level, and a cluster of states appears both above and below \ensuremath{\hbar}${\mathrm{\ensuremath{\omega}}}_{\mathrm{c}}$, the homogeneous field lowest Landau level. With two magnetic flux units threading through each magnetic unit cell, the lowest Landau level splits into two separate subbands, with three magnetic flux units the lowest Landau level splits into three separate subbands, and so forth. When a spin energy term is added to the Hamiltonian of the charged particle in the periodic magnetic field, the lowest Landau level becomes unaffected by the periodic magnetic field modulation, in agreement with Dubrovin and Novikov.

Surface hopping and fully quantum dynamical wavepacket propagation on multiple coupled adiabatic potential surfaces for proton transfer reactions

A general method for fully quantum mechanical wavepacket propagation on multiple adiabatic potential surfaces is developed. An analytical expression is derived for the second-derivative nonadiabatic coupling terms that arise in the adiabatic representation. Both this fully quantum mechanical wavepacket propagation method and the mixed quantum/classical surface hopping method “molecular dynamics with quantum transitions” (MDQT) are applied to a one-dimensional two-state model system for a proton transfer reaction. The remarkable agreement between the wavepacket and the MDQT methods justifies the use of MDQT for simulation of proton transfer reactions in solution.

Application of the frozen Gaussian approximation to the photodissociation of CO 2

The semiclassical frozen Gaussian approximation of Herman and Kluk is compared with exact quantum mechanical wavepacket propagation for the collinear photodissociation of CO 2. The approximation is found to be quantitatively accurate even at long times, and to reproduce all of the dynamical features in the absorption spectrum. However, the statistical errors in the Monte Carlo integration over the initial phase space are found to degrade with time and to demand an increasingly large number of sample points for longer times. The reasons for this numerical difficulty are discussed.

Classical model of femtosecond time-resolved absorption spectra of dissociating molecules

We present a simple classical model for understanding time-resolved absorption spectra of molecules that are in the process of dissociating. The model applies to absorption spectra that are obtained by measuring the spectral power density of an ultrafast, continuum probe pulse after transmission through the sample. We show that the classical model can yield results in good agreement with quantum-mechanical wave packet propagation calculations. In a close analogy with collisional line broadening, the time-resolved absorption spectra are shown to have an impact region near the separated-atom transition frequency and a far-wing region. The impact region is due to radiation emitted after the molecule has separated into atomic fragments, and the far-wing region is due to radiation emitted during the time of strong molecular interaction. The spectrum in the impact region depends upon an effective phase shift for a ‘‘partial’’ collision, which begins at the time that the probe pulse sweeps through the molecular transition frequency. For narrow wave packets, this phase shift can be directly measured, and the molecular transition frequency can be recovered as a function of time along the path of dissociation. For very broad wave packets, the time-resolved absorption spectra approach a statistical limit, in which the absorption line shape becomes an image in frequency space of the probability density in configuration space at the time of excitation by the probe pulse. In all cases, the frequency-integrated absorption is proportional to the net population of molecules that are excited by the probe pulse. In principle, this result can be used to obtain the strength of the transition dipole moment as a function of internuclear separation. We also consider fluorescence induced by a short optical probe pulse, as in the experiments of Zewail and co-workers. Fluorescence measurements are shown to be fundamentally different from measurements of the transmitted spectral power density: fluorescence depends upon the net population excited by the probe pulse, whereas the transmitted spectral power density depends upon interference between the incident probe field and the polarization field. Thus these two experimental techniques are sensitive to different aspects of the dissociation process.

Modifying atomic collision dynamics with intense ultrashort laser pulses.

It has been suggested that ''short'' pulses of intense laser radiation can modify atomic collision dynamics in new and interesting ways. Recent experimental results in sodium-argon vapor with 1.6-psec pulses verify the existence of such an effect, although smaller in magnitude and at somewhat higher field intensities than had been predicted from theoretical arguments. Using quantum-mechanical wave-packet propagation on a realistic potential-energy curve under the parameters of the experiment, we determine that the time between curve crossings, the standard against which pulse durations should be measured, is on the order of 0.8 psec or less. The experimental results can then be understood in the context of having used too long a pulse to have clearly observed short-pulse effects.