Wave Packet Propagation Calculations Research Articles

Intersystem crossing pathways in [5]-, [7]-, and [9]cycloparaphenylenes.

We analyze the energetics and internal conversion dynamics of singlet and triplet manifolds to identify the possible intersystem crossing pathways in odd-numbered [n]cycloparaphenylenes ([n]CPPs, n = 5, 7, and 9). Quantum wavepacket propagation calculations within the linear vibronic coupling framework suggest that both [5]- and [7]CPPs rapidly relax to S2 upon populating "bright" higher singlet excited states. The S2-S1 energy decreases with the increase in CPP size, and hence, [9]CPP exhibits a faster S2 → S1 internal conversion decay. Higher triplet states act as receiver states for the intersystem crossing happening either via S1 or S2. The wavepacket evolving on the receiver triplet state would decay to lower states via multiple conical intersections and reach T1. The estimated size-dependent fluorescence and emission energies are in good accord with the experiment.

Ionization of Rydberg H atoms at band-gap metal surfaces via surface and image states

Wavepacket propagation calculations are reported for the interaction of a Rydberg hydrogen atom with Cu(111) and Cu(100) surfaces (represented by a Chulkov potential), in comparison with a Jellium surface. Both copper surfaces have a projected band gap at the surface in the energy range degenerate with some or all of the Rydberg energies. The charge transfer of the Rydberg electron to the surface is found to be enhanced for n values at which there is a near-degeneracy between the Rydberg energy level and an image state or a surface state of the surface. The enhancement is facilitated by the strong overlap of the surface image-state orbital lying outside the surface and the orbital of the incoming Rydberg atom. These calculations point to the possibility of using Rydberg-surface collisions as a probe of surface electronic structure.

When fast atom diffraction turns 3D

Fast atom diffraction at surfaces (FAD) in grazing incidence geometry is characterized by the slow motion in the direction perpendicular to the surface and fast motion parallel to the surface plane along a low index direction. It is established experimentally that for the typical surfaces the FAD reveals the 2D diffraction patterns associated with exchange of the reciprocal lattice vector perpendicular to the direction of fast motion. The reciprocal lattice vector exchange along the direction of fast motion is negligible. The usual approximation made in the description of the experimental data is then to assume that the effective potential leading to the diffraction results from the averaging of the 3D surface potential along the atomic strings forming the axial channel. In this work we use full quantum wave packet propagation calculations to study theoretically the possibility to observe the 3D diffraction in FAD experiments. We show that for the surfaces with large unit cell, such as can be the case for reconstructed or vicinal surfaces, the 3D diffraction can be observed. The reciprocal lattice vector exchange along the direction of fast motion leads to several Laue circles in the diffraction pattern.

Quantum-well states with image state character for Pb overlayers on Cu(111)

We study theoretically the quantum well states (QWSs) localized in Pb overlayers on Cu(111) surface. Particular emphasis is given to the states with energies close to the vacuum level. Inclusion of the long-range image potential tail into the model potential description of the system allows us to show the effect of hybridization between QWSs and image potential states (ISs). The particle-in-a-box energy sequence characteristic for QWSs evolves into the Rydberg series converging towards the vacuum level. The electron density of the corresponding states is partially moved from inside the metal overlayer into the vacuum. The decay rates due to the inelastic electron-electron scattering decrease with increasing energy, opposite to ``conventional'' QWSs and similar to the ISs. Many-body and wave packet propagation calculations of the inelastic decay rates are supplemented by simple analysis based on the phase accumulation model and wave-function penetration approximation. This allows an analytical description of the dependence of the QWS/ISs hybridization on different parameters and, in particular, on the overlayer thickness.

Electron Localization in Molecular Fragmentation ofH2by Carrier-Envelope Phase Stabilized Laser Pulses

Fully differential data for H2 dissociation in ultrashort (6 fs, 760 nm), linearly polarized, intense (0.44 PW/cm{2}) laser pulses with a stabilized carrier-envelope phase (CEP) were recorded with a reaction microscope. Depending on the CEP, the molecular orientation, and the kinetic energy release (KER), we find asymmetric proton emission at low KERs (0-3 eV), basically predicted by Roudnev and Esry, and much stronger than reported by Kling et al. Wave packet propagation calculations reproduce the salient features and discard, together with the observed KER-independent electron asymmetry, the first ionization step to be the reason for the asymmetric proton emission.

πResonance of Chemisorbed Alkali Atoms on Noble Metals

We have performed a joint experimental and theoretical study of the unoccupied electronic structure of alkali adsorbates on the (111) surfaces of Cu and Ag. Combining angle- and time-resolved two-photon photoemission spectroscopy with wave packet propagation calculations we show that, along with the well known sigma resonance oriented along the surface normal, there exist long-lived alkali-localized resonances oriented parallel to the surface (pi symmetry). These new resonances are stabilized by the projected band gap of the substrate and emerge primarily from the mixing of the p and d Rydberg orbitals of the free alkali atom modified by the interaction with the surface.

Effective potential, Bohm’s potential plus classical potential, analysis of quantum transmission

The influence of spreading, in wavepacket transmission across a potential barrier has been analyzed, by considering several collisions between a wavepacket and a potential barrier, in which the initial distance between the packet and the barrier—the launching distance, is changed. An effective total potential (Bohm’s quantum potential plus classical potential), has been used, to show that, for suitable classical barrier widths and heights, light masses, as well as mean collision energies, one should expect an increase of the quantum transmission factor as the initial wavepacket—barrier distance is decreased. Numerically converged time-dependent wavepacket propagation calculations confirm that trend, leading to an increase as high as 20% per A, in thin square and Eckart barrier problems. Possibilities of experimentally measuring this effect are also analyzed.

Photoionization-induced dynamics of ammonia: Ab initio potential energy surfaces and time-dependent wave packet calculations for the ammonia cation

An analytical anharmonic six-dimensional three-sheeted potential energy surface for the ground and first excited states of the ammonia cation has been developed which is tailored to model the ultrafast photoinduced dynamics. Selected ab initio cuts, obtained by multireference configuration interaction calculations, have been used to determine the parameters of a diabatic representation for this Jahn-Teller and pseudo-Jahn-Teller system. The model includes higher-order coupling terms both for the Jahn-Teller and for the pseudo-Jahn-Teller matrix elements. The relaxation to the ground state is possible via dynamical pseudo-Jahn-Teller couplings involving the asymmetric bending and stretching coordinates. The photoelectron spectrum of NH3 and the internal conversion dynamics of NH3+ have been determined by wave packet propagation calculations employing the multiconfigurational time-dependent Hartree method. Three different time scales are found in the dynamics calculations for the second absorption band. The ultrafast Jahn-Teller dynamics of the two excited states occurs on a 5 fs time scale. The major part of the internal conversion to the ground state takes place within a short time scale of 20 fs. This fast internal conversion is, however, incomplete and the remaining excited state population does not decay completely even within 100 fs.

Preference for breaking the O–H bond over the O–D bond following HDO ionization by fast ions

Measurements of the fragmentation of deuterium tagged water molecules, namely HDO, by fast proton and F7+ impact exhibit a very strong isotopic preference for cleavage of the OH bond over the OD bond. Explicitly, the former is about five times more likely than the latter for HDO2+ dissociation. HDO+ exhibits similar behaviour, though the asymmetry is smaller at about a factor of 2. Wave-packet propagation calculations are in good agreement with the measured branching ratio for HDO2+ dissociation.

Optimal reflection-free complex absorbing potentials for quantum propagation of wave packets

The conditions for optimal reflection-free complex-absorbing potentials (CAPs) are discussed. It is shown that the CAPs as derived from the smooth-exterior-scaling transformation of the Hamiltonian,[J. Phys. B. 31, 1431 (1998)], serve as optimal reflection-free CAPs (RF-CAPs) in wave-packet propagation calculations of open systems. The initial wave packet, can be located in the interaction region (as in half collision experiments) where the CAPs have vanished or in the asymptote where the absorbing potential non zero. As we show the optimal CAPs can be introduced also in the region where the physical potential has not vanished. The un-avoided reflections due to the use of finite number of grid points (or basis functions) are discussed. A simple way to reduce the "edge grid" reflection effect is described.

Analysis of the population of continuum states in wave packet propagation calculations

We present a ‘virtual detector’ method which allows the extraction of the momentum distributions in continuum states from time-dependent wave packet propagation studies with explicitly time-dependent Hamiltonians. It is based on the approach developed by Balint-Kurti et al (1990 J. Chem. Soc. Faraday Trans. 86 1741) for quantum chemistry applications and consists in measuring a signal in the asymptotic region. In that sense, it is close to the semiclassical method proposed recently in this journal (Feuerstein and Thumm 2003 J. Phys. B: At. Mol. Opt. Phys. 36 707). The advantage of the present approach is that it is based on a rigorous quantum mechanical treatment, robust, easy to handle and requires a much smaller grid size. The method is illustrated with the 3D example of electron detachment from the H− ion colliding with a free-electron metal surface.

Fragmentation ofH2+in strong 800-nm laser pulses: Initial-vibrational-state dependence

The fragmentation of the ${\mathrm{H}}_{2}^{+}$ molecular ion in 25-fs, 800-nm laser pulses in the intensity range 0.05--0.5 P ${\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}$ is investigated by means of wave-packet propagation calculations. We use a collinear reduced-dimensionality model that represents both the nuclear and electronic motion by one degree of freedom including non-Born-Oppenheimer couplings. In order to reproduce accurately the properties of the ``real'' three-dimensional molecule, we introduce a modified ``soft-core'' Coulomb potential with a softening function that depends on the internuclear distance. The analysis of the calculated flux of the outgoing wave packets allows us to obtain fragmentation probabilities and kinetic-energy spectra. Our results show that the relative probabilities for dissociation and Coulomb explosion depend critically on the initial vibrational state of the molecular ion.

On the computation of momentum distributions within wavepacket propagationcalculations

We present a new method to extract momentum distributions from time-dependentwavepacket calculations. In contrast to established Fourier transformation of thespatial wavepacket at a fixed time, the proposed ‘virtual detector’ methodexamines the time dependence of the wavepacket at a fixed position. In firstapplications to the ionization of model atoms and the dissociation of H2+,we find a significant reduction of computing time and are able to extract reliablefragment momentum distributions by using a comparatively small spatialnumerical grid for the time-dependent wavefunction.

Accurate wave packet propagation for large molecular systems: The multiconfiguration time-dependent Hartree (MCTDH) method with selected configurations

The multiconfiguration time-dependent Hartree (MCTDH) method is a general, accurate algorithm for wave packet propagation calculations. Its efficiency is due to the use of an optimally small time-dependent basis set which evolves with the wave packet. The method however suffers from an exponential scaling of the required effort with system size, though with a much lower base than the exponential scaling of the standard propagation scheme. Here, we present a method to reduce the computational resources required for MCTDH calculations on large systems by selecting and propagating only the most important configurations for the representation of the wave function. At the same time the properties of the MCTDH method, such as convergence against numerically exact solutions, are retained.

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.

State resolved reaction rates of the spin-forbidden predissociation of N2O: A quantum dynamics study of the rotational effect

The predissociation of N2O into the 13A′ and 13A″ dissociative states for the total angular momentum J>0 is studied by quantum dynamics calculations. The effective Hamiltonian for describing the predissociation is derived from time-dependent wave packet propagation calculations on the triplet potential energy surfaces. The decay rates of individual rovibrational states in the singlet manifold are obtained by diagonalizing the effective Hamiltonian represented in terms of the singlet rovibrational wave functions. The Fermi golden rule is also applied to test its validity in estimating the decay rate distribution. For J=1 and 2, the rovibrational Hamiltonian is constructed by recoupling the coupled state wave functions obtained by a filter diagonalization. For higher values of J, a random coupling model deduced from the calculations for J=1 and 2 is introduced to estimate the decay rate distributions. In order to compare the calculated decay rate distributions with those by a random matrix/transition state theory (RM/TST), the transition states are defined as the eigenvectors of decay rate matrix whose eigenvalues are used for calculating the RM/TST distributions. It is found that the fluctuation of decay rate distribution decreases with increasing J though the calculated distribution shows significant deviation from the RM/TST prediction even for J=20. A simple model is employed to interpret the origin of the decrease of fluctuation in decay rates with J and the deviation from RM/TST. It is concluded that a sharp decay rate distribution comes from an increase of the absolute number of singlet rovibrational states accessible to the transition state due to the K-mixing, though such a K-mixing is limited. The deviation of calculated distribution from the RM/TST one is thus attributed to incomplete energy randomization in the singlet state N2O.

Resonance Raman spectra of theS3←Stransition of SO2: Electronic, vibrational, and rotational dynamics in solution

Resonance Raman spectra, including absolute scattering cross sections, of sulfur dioxide in the vapor phase and in hexane solution have been obtained at several excitation wavelengths between 235 and 208 nm, on resonance with the strong S3←S0, 1B2←1A1 electronic transition. Due to the narrow rovibronic linewidths in the isolated molecule, the vapor phase spectra are best described as single vibronic level resonance fluorescence and exhibit intensity patterns that depend strongly on excitation wavelength, while the solution phase spectra are only weakly dependent on excitation frequency due to the increased linewidths of the vibronic transitions. The spectra in hexane are dominated by long overtone progressions in the symmetric stretch and its combination bands with the bend. The relative and absolute cross sections are reproduced fairly well through time-dependent wave packet propagation calculations employing an anharmonic S3 state potential previously developed to fit vibronic energy levels of the isolated molecule. The average vibronic homogeneous linewidth in solution is found to be about 560 cm−1 FWHM, implying an electronic dephasing time of approximately 20 fs, and the absence of significant broad fluorescence indicates that the dephasing is dominated by electronic population relaxation. In contrast, the ground state isotropic Raman linewidths are less than 5 cm−1, even for overtones involving up to six stretching quanta, indicating ground state vibrational dephasing times greater than 2 ps. Analysis of the anisotropic band shapes suggests that the rotational motion is not greatly hindered by solvation.

An experimental and theoretical study of the bond selected photodissociation of HOD

Experimental and theoretical studies of the photodissociation of single vibrational states in HOD provide a qualitative and quantitative understanding of the dissociation dynamics and bond selectivity of this process. Vibrationally mediated photodissociation, in which one photon prepares a vibrational state that a second photon dissociates, can selectively cleave the O–H bond in HOD molecules containing four quanta of O–H stretching excitation. Dissociation of HOD(4νOH) with 266 or 239.5-nm photons produces OD fragments in at least a 15 fold excess over OH, but photolysis of the same state with 218.5-nm photons produces comparable amounts of OH and OD. Wave packet propagation calculations on an ab initio potential energy surface reproduce these observations quantitatively. They show that the origin of the selectivity and its energy dependence is the communication of the initial vibrational state with different portions of the outgoing continuum wave function for different photolysis energies.

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.