Density dynamics in some quantum systems

The quantum domain behavior of classical nonintegrable systems is well‐understood by the implementation of quantum fluid dynamics and quantum theory of motion. These approaches properly explain the quantum analogs of the classical Kolmogorov–Arnold–Moser type transitions from regular to chaotic domain in different anharmonic oscillators. Field‐induced tunneling and chaotic ionization in Rydberg atoms are also analyzed with the help of these theories. Quantum fluid density functional theory may be used to understand different time‐dependent processes like ion‐atom/molecule collisions, atom‐field interactions, and so forth. Regioselectivity as well as confined atomic/molecular systems and their reactivity dynamics have also been explained. © 2013 Wiley Periodicals, Inc.     

Coherent polyatomic dynamics studied by femtosecond time-resolved photoelectron spectroscopy: dissociation of vibrationally excited CS2 in the 6s and 4d Rydberg states

The dissociation dynamics of the 6s and 4d Rydberg states of carbon disulfide (CS(2)*) are studied by time-resolved photoelectron spectroscopy. The CS(2) is excited by two photons of 267 nm (pump) to the 6s and 4d Rydberg states and probed by ionization with either 800 or 400 nm. The experiments can distinguish and successfully track the time dynamics of both spin [1/2] (upper) and [3/2] (lower) cores of the excited Rydberg states, which are split by 60 meV, by measuring the outgoing electron kinetic energies. Multiple mode vibrational wave packets are created within the Rydberg states and observed through recurrence interferences in the final ion state. Fourier transformation of the temporal response directly reveals the coherent population of several electronic states and vibrational modes. The composition of the wave packet is varied experimentally by tuning the excitation frequency to particular resonances between 264 and 270 nm. The work presented here shows that the decay time of the spin components exhibits sensitivity to the electronic and vibrational states accessed in the pump step. Population of the bending mode results in an excited state lifetime of as little as 530 fs, as compared to a several picosecond lifetime observed for the electronic origin bands. Experiments that probe the neutral state dynamics with 400 nm reveal a possible vibrationally mediated evolution of the wave packet to a different Franck-Condon window as a consequence of Renner-Teller splitting. Upon bending, symmetry lowering from D(infinityh) to C(2v) enables ionization to the CS(2) (+) (B (2)Pi(u)) final state. The dissociation dynamics observed are highly mode specific, as revealed by the frequency and temporal domain analysis of the photoelectron spectra.     

Solvent triggered change of the electron excitation route of KI in supercritical NH3

The UV-spectroscopic behavior of KI contact ion pairs (CIPs) dissolved in supercritical NH3 was studied combining classical molecular dynamics simulations with electronic structure calculations, and the results show that an abrupt change of the photoexcitation route of KI CIPs occurs at very low solvent densities. Few NH3 solvating molecules are required to hamper the well-known photoinduced intramolecular electron (e-) transfer observed in isolated ion pairs of alkali metal halides in the vapor drawing the e- to solvent cavities leading to a charge-transfer-to-solvent process.     

Dynamics of Rydberg electron transfer to CH3CN: velocity dependent studies

The dynamics of free-ion production through electron transfer in K(np)/CH3CN collisions are examined through measurements using velocity-selected Rydberg atoms. The data show that Rydberg electron transfer leads to the creation of two groups of dipole-bound CH3CN- ions, one long lived (tau>85 micros), the other short lived (tau<1 micros). The velocity dependences associated with the production of both groups of ions are similar, the ion formation rate decreasing markedly with decreasing Rydberg atom velocity, principally as a consequence of postattachment electrostatic interactions between the product ions. The results are in reasonable accord with the predictions of a Monte Carlo collision model that considers the effect of crossings between the diabatic potential curves for the covalent K(np)/CH3CN system and the K+/CH3CN- ion pair. This model also accounts for the relatively small reaction rate constants, approximately 0.5-1.0 x 1.0(-8) cm(3) s(-1), associated with the formation of long-lived CH3CN- ions. No velocity dependence in the lifetime of the CH3CN- ions is observed.     

Classical dynamics of 3D Hydrogen molecular ion in intense laser fields

The classical trajectory method is used to study the dynamics of 3D Hydrogen molecular ion interacting with intense laser fields. In the 3D classical model, a three-body Hamiltonian with one-dimensional nuclear motion restricted to the direction of the laser field is considered. The motion of electron and nucleus is described by the classical Hamiltonian canonical equations. The probabilities of ionization, dissociation and Coulomb explosion as functions of time are calculated and the average distances from electron to the mass-center for various laser parameters are implemented by symplectic method. The dynamics of in two-color laser fields are also investigated. We compare our results with the corresponding quantum-mechanical calculations and find they produce similar qualitative features in many cases.     

Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions

An ab initio electronic wave-packet dynamics coupled with the simultaneous classical dynamics of nuclear motions in a molecule is studied. We first survey the dynamical equations of motion for the individual components. Reflecting the nonadiabatic dynamics that electrons can respond to nuclear motions only with a finite speed, the equations of motion for nuclei include a force arising from the kinematic (nuclear momentum) coupling from electron cloud. To materialize these quantum effects in the actual ab initio calculations, we study practical implementation of relevant electronic matrix elements that are related to the derivatives with respect to the nuclear coordinates. Applications of the present scheme are performed in terms of the configuration state functions (CSF) using the canonical molecular orbitals as basis functions without transformation to particular diabatic basis. In the CSF representation, the nonadiabatic interaction due to the kinematic coupling is anticipated to be rather small, and instead it should be well taken into account through the off-diagonal elements of the electronic Hamiltonian matrix. Therefore it is expected that the nonadiabatic dynamics based on this CSF basis neglecting the kinematic coupling may work. To verify this anticipation and to quantify the actual effects of the kinematic coupling, we compare the dynamics with and without the kinematic-coupling terms using the same CSF set. Applications up to the fifth electronically excited states in a nonadiabatic collision between H(2) and B(+) shows that the overall behaviors of these two calculations are surprisingly similar to each other in an average sense except for a fast fluctuation reflecting the electronic time scale. However, at the same time, qualitative differences in the collision events are sometimes observed. Therefore it turns out after all that the kinematic-coupling terms cannot be neglected in the CSF-basis representation. The present applications also demonstrate that the nonadiabatic electronic wave-packet dynamics within ab initio quantum chemical calculation is feasible.     

Properties of nearly one-electron molecules. I. An iterative Green function approach to calculating the reaction matrix

An ab initio R-matrix method for determining the molecular reaction matrix of scattering theory is introduced. The method makes use of a principal-value Green function to compute the collision channel wave functions for the scattered electron, in combination with the Kohn variational scheme for the evaluation of R-matrix eigenvalues on a spherical boundary surface at short range. This technique permits the size of the bounded volume in the variational calculation to be reduced, making the computations fast and efficient. The reaction matrix is determined in a form that minimizes its energy dependence. Thus the procedure does not require modification or an increase in the computational effort to study the electronic structure and dynamics in Rydberg molecules with extremely polar ion cores. The analysis is specialized to examine the bound-state and free-electron scattering properties of nearly one-electron molecular systems, which are characterized by a Rydberg/scattering electron incident on a closed-shell ion core. However, it is shown that the treatment is compatible with all-electron/ab initio representations of open-shell and nonlinear polyatomic ion cores, emphasizing its generality. The introduced approach is used to calculate the electronic spectrum of the calcium monofluoride molecule, which has the extremely polar (Ca+2F-)+e- closed-shell ion-core configuration. The calculation utilizes an effective single-electron potential determined by M. Arif, C. Jungen, and A. L. Roche [J. Chem. Phys. 106, 4102 (1997)] previously. Close agreement with experimental data is obtained. The results demonstrate the practical utility of this method as a viable alternative to the standard variational approaches.     

Wave packet simulation of nonadiabatic dynamics in highly excited 1,3-dibromopropane

We have conducted wave packet simulations of excited-state dynamics of 1,3-dibromopropane (DBP) with the aim of reproducing the experimental results of the gas-phase pump-probe experiment by Kotting et al. [ Kotting, C. ; Diau, E. W.-G. ; S?lling, T. I. ; Zewail, A. H. J. Phys. Chem. A 2002, 106, 7530 ]. In the experiment, DBP is excited to a Rydberg state 8 eV above the ground state. The interpretation of the results is that a torsional motion of the bromomethylene groups with a vibrational period of 680 fs is activated upon excitation. The Rydberg state decays to a valence state, causing a dissociation of one of the carbon bromine bonds on a time scale of 2.5 ps. Building the theoretical framework for the wave packet propagation around this model of the reaction dynamics, the simulations reproduce, to a good extent, the time scales observed in the experiment. Furthermore, the simulations provide insight into how the torsion motion influences the bond breakage, and we can conclude that the mechanism that delays the dissociation is solely the electronic transition from the Rydberg state to the valence state and does not involve, for example, intramolecular vibrational energy redistribution (IVR).     

Dissociative ionization of Na2 via repulsive Rydberg states: elucidating femtosecond dynamics with nanosecond lasers

We have studied the dissociative ionization behavior of Na2 molecules using two-color, three photon optical-optical double resonance enhanced excitation via the A(1)Sigma(u)(+) and the 2(1)Pi(g) states. Excess energy ranges from about 150 to about 1500 cm(-1) above threshold for dissociative ionization into ground-state Na and Na(+). Slow atomic Na(+) fragments and Na2(+) molecular ions are detected using a linear time-of-flight spectrometer operated in low field extraction, core sampling mode. To explain the observed energy dependence of the Na(+)/Na2(+) branching ratio, we introduce a semiclassical model for the underlying decay dynamics. Franck-Condon overlap densities for bound-free transitions starting in 2(1)Pi(g) vibrational levels indicate that atomic Na(+) fragments are primarily produced via Rydberg states, with principal quantum number n between 5 and 12, converging to the repulsive 1(2)Sigma(u)(+) first excited-state potential of Na2(+). Dynamics along these Rydberg curves involves competition between electronic (autoionizing) and nuclear (dissociative) degrees of freedom. Within the model, the autoionization lifetime tau auto is the only one free parameter available to fit calculated Na(+)/Na2(+) branching ratios as a function of excess energy to the observed values. The lifetime is assumed to be the same multiple c of the Bohr period of each Rydberg potential. A chi(2)-minimization procedure yields, for the range of principal quantum numbers involved, a most likely value of c = 1.5 +/- 0.3, implying that on average the Rydberg electron completes only 1 to 2 orbits before interaction with the excited core electron leads to autoionization.     

On the inverse Born–Oppenheimer separation for high Rydberg states of molecules

The separation of radial electronic and nuclear motions is discussed with special reference to high Rydberg states of molecules. An inverse separation is obtained when the rapid nuclear motion instantaneously adjusts itself to the position of the Rydberg electron. The electron moves in the potential averaged over the position of the nuclei (and their valence electrons). This inverse separation is useful when ωn³ > 1, where ω is the spacing of nuclear energy states (in au) and n is the principal quantum number of the Rydberg electron whose orbital period increases as n³. The inverse Born–Oppenheimer separation can break down owing to the finite kinetic energy of the Rydberg electron. Like the Born–Oppenheimer separation, its inverse can also be formulated in an adiabatic or a diabatic basis. The diabatic inverse Born–Oppenheimer is practical both for interpretation of zero electron kinetic energy (ZEKE) spectra and for computations. Explicit results are given for a model system of an electron orbiting a vibrating dipole, identifying the relevant coupling constants. The discussion emphasizes the radial motion and the limits discussed here are not quite equivalent to the four (or, actually, five) Hund's coupling cases relevant to angular momentum coupling schemes. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 85–100, 1998     

Radiative relaxation and fragmentation dynamics of S 2p-excited hydrogen sulfide

Radiative relaxation of S 2p-excited hydrogen sulfide (H(2)S) is investigated by dispersed ultraviolet and visible fluorescence spectroscopies. We observe distinct changes in the fluorescence spectra as a function of excitation energy. Excitation to Rydberg states below the S 2p ionization threshold yields intense fluorescence from neutral and ionic atomic fragments (H, S(+), and S(2+)). In addition to the atomic emission, fluorescence of the molecular fragment ion HS(+) is preferably found after excitation of the S 2p electron into the unoccupied 6a(1) and 3b(2) orbitals with sigma(*) character. This is interpreted as evidence for ultrafast dissociation of the core-excited molecule prior to electronic relaxation. The rotationally resolved fluorescence spectra of the A (3)Pi-->X (3)Sigma(-) transition are analyzed in terms of the fragmentation dynamics leading to the formation of the excited molecular fragment ion, where changes in bond angle are discussed in terms of the rotational population.     

Cage motions induced by electronic and vibrational excitations: Cl2 in Ar

Femtosecond dynamics of molecular vibrations as well as cage motions in the B<--X transition of Cl2 in solid Ar have been investigated. We observed molecular vibrational wave-packet motion in experimental pump-probe spectra and an additional oscillation with a 500 fs period which is assigned to the zone-boundary phonon of the Ar crystal. The cage motion is impulsively driven by the B<--X transition due to the expansion of the electronic cloud of the chromophore. To clarify the underlying mechanism, we performed simulations based on the diatomics-in-molecules method which takes into account the different shapes of the Cl2 electronic wave function in the B and X states as well as the anisotropic interaction with the matrix. The simulation results show that Ar atom motion in the (100) plane is initiated by the electronic transition and that only those Ar atoms oscillate coherently with an approximately 500 fs period which are essentially decoupled from the molecular vibration. Their phase and time evolution are in good agreement with the experimentally observed oscillation, supporting the assignment as a displacive excitation of coherent phonons.     

Femtosecond time-resolved molecular multiphoton ionization and fragmentation of Na2: experiment and quantum mechanical calculations

We present a comparison between experimental and theoretical results for pump/probe multiphoton ionizing transitions of the sodium dimer, initiated by femtosecond laser pulses. It is shown that the motion of vibrational wave packets in two electronic states is probed simultaneously and their dynamics is reflected in the total Na ₂ ⁺ ion signal which is recorded as a function of the time delay between pump and probe pulse. The time dependent quantum calculations demonstrate that two ionization pathways leading to the same final states of the molecular ion exist: one gives an oscillating contribution to the ion signal, the other yields a constant background. From additional measurements of the Na⁺-transient photofragmentation spectrum it is deduced that another ionization process leading to different final ionic states exists. The process includes the excitation of a doubly excited bound Rydberg state. This conclusion is supported by the theoretical simulation.     

Chemical reaction dynamics of Rydberg atoms with neutral molecules: a comparison of molecular-beam and classical trajectory results for the H(n)+D2-->HD+D(n') reaction

Recent molecular-beam experiments have probed the dynamics of the Rydberg-atom reaction, H(n)+D2-->HD+D(n) at low collision energies. It was discovered that the rotationally resolved product distribution was remarkably similar to a much more limited data set obtained at a single scattering angle for the ion-molecule reaction H++D2-->D++HD. The equivalence of these two problems would be consistent with the Fermi-independent-collider model (electron acting as a spectator) and would provide an important new avenue for the study of ion-molecule reactions. In this work, we employ a classical trajectory calculation on the ion-molecule reaction to facilitate a more extensive comparison between the two systems. The trajectory simulations tend to confirm the equivalence of the ion+molecule dynamics to that for the Rydberg-atom+molecule system. The theory reproduces the close relationship of the two experimental observations made previously. However, some differences between the Rydberg-atom experiments and the trajectory simulations are seen when comparisons are made to a broader data set. In particular, the angular distribution of the differential cross section exhibits more asymmetry in the experiment than in the theory. The potential breakdown of the classical model is discussed. The role of the "spectator" Rydberg electron is addressed and several crucial issues for future theoretical work are brought out.     

Communication: Heavy Rydberg states: the H+H- system

Heavy Rydberg states are analogs of electronic Rydberg states, but with the electron replaced by a much heavier ion. We calculate ab initio the extremely long-range vibrational H(+)H(-) heavy Rydberg states in H(2), and compare these to recent experiments. The calculated resonance positions and widths agree well with experiment, but we predict additional sharp interloper resonances corresponding to vibrational states trapped inside the barrier on potential energy curve 7 (1)Σ(g)(+).     

Quantum versus classical electron transfer energy as reaction coordinate for the aqueous Ru2+/Ru3+ redox reaction

Applying density functional theory (DFT)-based molecular dynamics simulation methods we investigate the effect of explicit treatment of electronic structure on the solvation free energy of aqueous Ru²⁺ and Ru³⁺.Our approach is based on the Marcus theory of redox half reactions, focussing on the vertical energy gap for reduction or oxidation of a single aqua ion. We compare the fluctuations of the quantum and classical energy gap along the same equilibrium ab initio molecular dynamics trajectory for each oxidation state. The classical gap is evaluated using a standard point charge model for the charge distribution of the solvent molecules (water). The quantum gap is computed from the full DFT electronic ground state energies of reduced and oxidized species, thereby accounting for the delocalization of the electron in the donor orbital and reorganization of the electron cloud after electron transfer (ET). The fluctuations of the quantum ET energy are well approximated by gaussian statistics giving rise to parabolic free energy profiles. The curvature is found to be independent of the oxidation state in agreement with the linear response assumption underlying Marcus theory. By contrast, the diabatic free energy curves evaluated using the classical gap as order parameter, while also quadratic, are asymmetric reflecting the difference in oxidation state. The response of these two order parameters is further analysed by a comparison of the spectral density of the fluctuations and the corresponding reorganization free energies.     

Ab initio molecular dynamics study of formate ion hydration

We perform ab initio molecular dynamics simulations of the aqueous formate ion. The mean number of water molecules in the first solvation shell, or the hydration number, of each formate oxygen is found to be consistent with recent experiments. Our ab initio pair correlation functions, however, differ significantly from many classical force field results and hybrid quantum mechanics/molecular mechanics predictions. They yield roughly one less hydrogen bond between each formate oxygen and water than force field or hybrid methods predict. Both the BLYP and PW91 exchange correlation functionals give qualitatively similar results. The time dependence of the hydration numbers are examined, and Wannier function techniques are used to analyze electronic configurations along the molecular dynamics trajectory.     

Rydberg atom mediated polar molecule interactions: a tool for molecular-state conditional quantum gates and individual addressability

We study the possibility to use interaction between a polar molecule in the ground electronic and vibrational state and a Rydberg atom to construct two-qubit gates between molecular qubits and to coherently control molecular states. A polar molecule within the electron orbit in a Rydberg atom can either shift the Rydberg state, or form a Rydberg molecule. Both the atomic shift and the Rydberg molecule states depend on the initial internal state of the polar molecule, resulting in molecular state dependent van der Waals or dipole-dipole interaction between Rydberg atoms. Rydberg atoms mediated interaction between polar molecules can be enhanced up to 10(3) times. We describe how the coupling between a polar molecule and a Rydberg atom can be applied to coherently control molecular states, and specifically, to individually address molecules in an optical lattice, and to non-destructively readout molecular qubits.     

A quantum defect model for the s, p, d, and f Rydberg series of CaF

We present an improved quantum defect theory model for the "s," "p," "d," and "f" Rydberg series of CaF. The model, which is the result of an exhaustive fit of high-resolution spectroscopic data, parameterizes the electronic structure of the ten ("s"Σ, "p"Σ, "p"Π, "d"Σ, "d"Π, "d"Δ, "f"Σ, "f"Π, "f"Δ, and "f"Φ) Rydberg series of CaF in terms of a set of twenty μ(ll('))(Λ) quantum defect matrix elements and their dependence on both internuclear separation and on the binding energy of the outer electron. Over 1000 rovibronic Rydberg levels belonging to 131 observed electronic states of CaF with n? ≥ 5 are included in the fit. The correctness and physical validity of the fit model are assured both by our intuition-guided combinatorial fit strategy and by comparison with R-matrix calculations based on a one-electron effective potential. The power of this quantum defect model lies in its ability to account for the rovibronic energy level structure and nearly all dynamical processes, including structure and dynamics outside of the range of the current observations. Its completeness places CaF at a level of spectroscopic characterization similar to NO and H(2).