Initial Vibrational Level Research Articles

Quasiclassical trajectory theoretical study on the chemical stereodynamics of the O(1D) + H2 → OH + H reaction and its isotopic variants (HD, D2)

The quasiclassical trajectory (QCT) method is used to study stereodynamic information about the reaction O (1D) + H2 → OH + H on the DK (Dobbyn and Knowles) (11A′) ab initio potential energy surface (PES). A wide scale of collision energy (Ec) from 0.05 eV to 0.5 eV is considered in the dynamic calculations. To reveal the rovibrational excitation effect, calculations at a collision energy of 0.52 eV are carried out for the v = 0 ∼ 5, j = 0 and v = 0, j = 0 ∼ 15 initial states. The two popularly used polarization-dependent differential cross sections (PDDCSs), dσ00/dωt (0, 0) and dσ20/dωt(2, 0), and two angular distributions, P(θr) and P(φr) are calculated to obtain an insight into the alignment and the orientation of the product molecules. From the calculations, we can obtain that the alignment of the OH product is weaker at high collision energy and becomes stronger with the increase of initial vibrational level, and it is almost insensitive to the initially rotational excitation. Influences of the mass values of isotopes (HD, D2) on the stereodynamics are also shown and discussed. Comparisons between available theoretical results and experimental results are made and discussed.

Ultracold collisions of O(1D) and H2: The effects of H2 vibrational excitation on the production of vibrationally and rotationally excited OH

A quantum dynamics study of the O((1)D) + H2(v = 0 - 2, j = 0) system has been carried out using the potential energy surfaces of Dobbyn and Knowles [Mol. Phys. 91, 1107 (1997)]. A time-independent quantum mechanical method based on hyperspherical coordinates is adopted for the dynamics calculations. Energy dependent cross section, probability, and rate coefficients are computed for the elastic, inelastic, and reactive channels over collision energies ranging from the ultracold to thermal regimes and for total angular momentum quantum number J = 0. The effect of initial vibrational excitation of the H2 molecule on vibrational and rotational populations of the OH product is investigated as a function of the collision energy. Comparison of results for vibrational levels v = 0 - 2 of H2 demonstrates that the vibrational excitation of H2 and its non-reactive relaxation pathway play a minor role in the overall collisional outcome of O((1)D) and H2. It is also found that while the state-resolved product vibrational distributions are sensitive to the initial collision energy and H2 vibrational level, the product rotational distribution depicts an inverted population that is largely insensitive to initial conditions. Rate coefficients evaluated using a J-shifting approximation show reasonable agreement with available theoretical and experimental results suggesting that the J-shifting approximation may be used to evaluate the rate coefficients for O((1)D) + H2 reaction.

High harmonic generation in $\textbf{H}_{{2}}^{{+}} $ and HD + by intense femtosecond laser pulses: A wave packet approach with nonadiabatic interaction in HD +

We have theoretically investigated the high harmonic generation (HHG) spectra of \(\textrm{H}_2^+ \) and HD + using a time-dependent wave packet approach for the nuclear motion with pulsed lasers of peak intensities (I0) of 3.5 ×1014 and 4.5 ×1014 W/cm2, wavelengths (λL) of 800 and 1064 nm, and pulse durations (T) of 40 and 50 fs, for initial vibrational levels v0 = 0 and 1. We have argued that for these conditions the harmonic generation due to the transitions in the electronic continuum by tunnelling or multiphoton ionization will not be important. Thus, the characteristic features of HHG spectra in our model arise only due to the nuclear motions on the two lowest field-coupled electronic states between which both interelectronic and intraelectronic (due to intrinsic dipole moments, for HD + ) radiative transitions can take place. For HD + , the effect of nonadiabatic (NA) interaction between the two lowest Born–Oppenheimer (BO) electronic states has been taken into account and comparison has been made with the HHG spectra of HD + obtained in the BO approximation. Even harmonics and a second plateau in the HHG spectra of HD + with the NA interaction and hyper-Raman lines in the spectra of both \(\textrm{H}_2^+ \) and HD + for v0 = 1 have been observed for higher value of I0 or λL. Our calculations indicate reasonable efficiencies of harmonic generation even without involving the electronic continuum.

Zero-Energy Resonances of Hydrogen Diatom Isotopologs: Tuning Quasiresonant Transitions in Vibration Space

Highly efficient and specific energy transfer mechanisms that involve rotation-rotation, vibration-vibration, and vibration-rotation exchange in diatomic molecules are examined theoretically in ultracold H(2), D(2), and HD self-collisions as a function of initial vibrational level v. The three quasiresonant mechanisms are found to operate for all vibrational levels and yield complex scattering lengths which vary smoothly with v. Exceptions to this trend occur at select high values of v where the scattering lengths are modulated by orders of magnitude corresponding to the location of an s-wave zero-energy resonance in "vibration space." The quasiresonant mechanisms, which are not very sensitive to the details of the interaction potential, generally control the final distribution of molecular states for any given initial distribution. The zero-energy resonances are more sensitive to the potential and may be used to vibrationally "tune" the interaction strength, similar to methods which vary applied external fields.

Observation of ultrafast NH3 (Ã) state relaxation dynamics using a combination of time-resolved photoelectron spectroscopy and photoproduct detection

The ultrafast excited state relaxation of ammonia is investigated by resonantly exciting specific vibrational modes of the electronically excited NH(3) (Ã) state using three complementary femtosecond (fs) pump-probe techniques: time-resolved photoelectron, ion-yield and photofragment translational spectroscopy. Ammonia can be seen as a prototypical system for studying non-adiabatic dynamics and therefore offers a benchmark species for demonstrating the advantages of combining the aforementioned techniques to probe excited state dynamics, whilst simultaneously illuminating new aspects of ammonia's photochemistry. Time-resolved photoelectron spectroscopy (TRPES) provides direct spectroscopic evidence of σ* mediated relaxation of the NH(3) (Ã) state which manifests itself as coupling of the umbrella (ν(2)) and symmetric N-H stretch (ν(1)) modes in the photoelectron spectra. Time-resolved ion yield (TRIY) and time-resolved photofragment translation spectroscopy (TRPTS) grant a measure of the dissociation dynamics through analysis of the H and NH(2) photodissociation co-fragments. Initial vibrational level dependent TRIY measurements reveal photoproduct formation times of between 190 and 230 fs. Measurement of H-atom photoproduct kinetic energies enables investigation into the competition between adiabatic and non-adiabatic dissociation channels at the NH(3) (Ã)/NH(3) (X̃) conical intersection and has shown that upon non-adiabatic dissociation into NH(2) (X̃) + H, the NH(2) (X[combining tilde]) fragment is predominantly generated with significant fractions of internal vibrational energy.

Dissociative electron attachment to vibrationally excited H2 molecules involving the [formula omitted] resonant Rydberg electronic state

Dissociative electron attachment cross sections (DEA) on vibrationally excited H2 molecule taking place via the 2Σg+ Rydberg-excited resonant state are studied using the local complex potential (LCP) model for resonant collisions. The cross sections are calculated for all initial vibrational levels (vi=0–14) of the neutral molecule. In contrast to the previously noted dramatic increase in the DEA cross sections with increasing vi, when the process proceeds via the X 2Σu+ shape resonance of H2, for the 2Σg+ Rydberg resonance the cross sections increase only gradually up to vi=3 and then decrease. Moreover, the cross sections for vi⩾6 exhibit pronounced oscillatory structures. A discussion of the origin of the observed behavior of calculated cross sections is given. The DEA rate coefficients for all vi levels are also calculated in the 0.5–1000eV temperature range.

Theoretical study of the photodissociation of Li2+ in one-color intense laser fields

A theoretical treatment of the photodissociation of the molecular ion Li(2) (+) in one-color intense laser fields, using the time-dependent wave packet approach in a Floquet Born-Oppenheimer representation, is presented. Six electronic states 1,2 (2)Σ(g)(+), 1,2 (2)Σ(u)(+), 1 (2)Π(g), and 1 (2)Π(u) are of relevance in this simulation and have been included. The dependences of the fragmental dissociation probabilities and kinetic energy release (KER) spectra on pulse width, peak intensity, polarization angle, wavelength, and initial vibrational level are analyzed to interpret the influence of control parameters of the external field. Three main dissociation channels, 1 (2)Σ(g)(+) (m = -1), 2 (2)Σ(g)(+) (m = -2), and 2 (2)Σ(u)(+) (m = -3), are seen to dominate the dissociation processes under a wide variety of laser conditions and give rise to well separated groups of KER features. Different dissociation mechanisms for the involved Floquet channels are discussed.

Dissociation of H+2 ions by collisions with electrons

We have studied the electron impact dissociation of vibrationally excited H+2. A distribution of initial vibrational states given by the overlap factors between the vibrational ground state of H2 and different vibrational levels of H+2 has been considered. It was found that the relative contributions of the initial vibrational levels to the dissociative excitation cross section mimic the vibrational distribution of the H+2 molecular ion for electron energies larger than the energy difference between the energy of the repulsive state 2Σ+u and that of the lowest vibrational level of the ground state X2Σ+g at the outer classical turning point.

On the relation between the activation energy for electron attachment reactions and the size of their thermal rate coefficients

Rate coefficients k(T) for dissociative electron attachment (DEA) to molecules in many cases exhibit a more or less strong rise with increasing temperature T (the electron temperature T(e) and the molecular temperature T(G) are assumed to be in thermal equilibrium, i.e., T = T(e) = T(G)). This rise is frequently modeled by the Arrhenius equation k(T) = k(A) exp[-E(a)∕(k(B)T)], and an activation energy E(a) is deduced from fits to the experimental data k(T). This behavior reflects the presence of an energy barrier for the anion on its path to the dissociated products. In a recent paper [J. Kopyra, J. Wnorowska, M. Foryś, and I. Szamrej, Int. J. Mass Spectrom. 268, 60 (2007)] it was suggested that the size of the rate coefficients for DEA reactions at room temperature exhibits an exponential dependence on the activation energy, i.e., k(E(a); T ≈ 300 K) = k(1) exp[-E(a)∕E(0)]. More recent experimental data for molecules with high barriers [T. M. Miller, J. F. Friedman, L. C. Schaffer, and A. A. Viggiano, J. Chem. Phys. 131, 084302 (2009)] are compatible with such a correlation. We investigate the validity and the possible origin of this dependence by analyzing the results of R-matrix calculations for temperature-dependent rate coefficients of exothermic DEA processes with intermediate barrier toward dissociation. These include results for model systems with systematically varied barrier height as well as results of molecule-specific calculations for CH(3)Cl, CH(3)Br, CF(3)Cl, and CH(2)Cl(2) (activation energies above 0.2 eV) involving appropriate molecular parameters. A comparison of the experimental and theoretical results for the considered class of molecules (halogenated alkanes) supports the idea that the exponential dependence of k(T = 300 K) on the activation energy reflects a general phenomenon associated with Franck-Condon factors for getting from the initial neutral vibrational levels to the dissociating final anion state in a direct DEA process. Cases are discussed for which the proposed relation does not apply.

Dynamic and spectral mixing in nanosystems

In the framework of simple spin-boson Hamiltonian we study an interplay between dynamic and spectral roots to stochastic-like behavior. The Hamiltonian describes an initial vibrational state coupled to discrete dense spectrum reservoir. The reservoir states are formed by three sequences with rationally independent periodicities typical for vibrational states in many nanosize systems. We show that quantum evolution of the system is determined by a dimensionless parameter which is characteristic number of the reservoir states relevant for the initial vibrational level dynamics. Our semi-quantitative analytic results are confirmed by numerical solution of the equation of motion. We anticipate that predicted in the paper both kinds of stochastic-like behavior (namely, due to spectral mixing and recurrence cycle dynamic mixing) can be observed by femtosecond spectroscopy methods in nanosystems.

Competition between reaction channels in electron collisions of vibrationally excited

The competing processes taking place in the reactive collisions of vibrationally hot with electrons, namely dissociative recombination, dissociative excitation, vibrational excitation, elastic scattering and vibrational de-excitation have been studied using a theoretical approach based on the multichannel quantum defect theory. The energy range considered is 0.1–12 eV. The high sensitivity of these processes to the initial vibrational state of is illustrated. In the case of a Franck–Condon distribution of initial vibrational levels, the comparison with the recent experimental results is performed.

Quantum dynamics of the H+O2→O+OH reaction

Quantum scattering calculations of the H+O(2)-->O+OH reaction are presented using two different representations of the electronically adiabatic potential energy surface of the HO(2) system. The calculations have been performed using a three-dimensional time-independent quantum reactive scattering program based on hyperspherical coordinates. The effect of vibrational and rotational excitations of the O(2) molecule on the reactivity is investigated by carrying out calculations for vibrational quantum numbers v=0-8 and rotational quantum numbers j=1-9 for both potential surfaces. While the energy threshold for the reaction is lowered with increase in vibrational or rotational excitation of the molecule the overall energy dependence of the reaction probability remained largely unaffected with rovibrational excitations. Vibrational excitation was found to wash out resonances in the reaction probabilities. The sensitivity of the rate coefficients to the initial vibrational level of the O(2) molecule is investigated and it is found that the rate coefficient is a strong function of the vibrational quantum number of the O(2) molecule. The effect is more pronounced at low temperatures with the rate coefficient at 400 K increasing by about eight orders of magnitude when the vibrational level of O(2) is increased from 0 to 6. Thermal rate coefficients of the reaction calculated using cumulative reaction probabilities within a J-shifting approximation have been found to be in reasonable agreement with experimental results. Results show that vibrational excitation of the O(2) molecule needs to be considered in evaluating thermal rate coefficients of the reaction.

Low-Energy Electron Attachment to the Dichlorodifluoromethane (CCl2F2) Molecule

Results from a joint experimental study of electron attachment to dichlorodifluoromethane (CCl(2)F(2)) molecules in the gas phase are reported. In a high resolution electron beam experiment involving two versions of the laser photoelectron attachment method, the relative cross section for formation of the dominant anion Cl(-) was measured over the energy range 0.001-1.8 eV at the gas temperature T(G) = 300 K. It exhibits cusp structure at thresholds for vibrational excitation of the nu(3)(a(1)) mode due to interaction with the attachment channels. With reference to the thermal attachment rate coefficient k(T = 300 K) = 2.2(8) x 10(-9) cm(3) s(-1) (fitted average from several data), a new highly resolved absolute attachment cross section for T(G) = 300 K was determined. Partial cross sections for formation of the anions Cl(-), Cl(2)(-), F(-), ClF(-), and CCl(2)F(-) were measured over the range 0-12 eV, using three different electron beam experiments of medium energy resolution. The dependence of the attachment rate coefficient k(T(e);T(G) = 300 K) on electron temperature T(e) was calculated over the range 50-15 000 K, based on a newly constructed total cross section for anion formation at T(G) = 300 K. R-matrix calculations for Cl(-) production have been carried out for comparison with the experimental data. The R-matrix results are in line with the main experimental observations and predict the dependence of the DEA cross section on the initial vibrational level nu(3)() and on the vibrational temperature. Furthermore, the cross section for vibrational excitation of the nu(3) mode has been computed.

Above-Threshold Dissociation of HD+ in Femtosecond Laser Field

The above-threshold dissociation (ATD) of the HD+ molecular ion in femtosecond laser field is investigated theoretically The energy-dependent distribution of the dissociated fragments is calculated using an asymptotic-flow expression in the momentum space. The calculations show that the ATD of HD+ is sensitive to the initial vibrational level of ground electronic state. Multiphoton ATDs can be observed in the dissociation processes. The dynamics phenomena are interpreted by using the concept of light-dressed potential.

Low-energy electron attachment to chloroform (CHCl3) molecules: A joint experimental and theoretical study

Results from a joint experimental and theoretical study of electron attachment to chloroform (CHCl3) molecules in the gas phase are reported. In an electron swarm study involving a pulsed Townsend technique with equal gas and electron temperatures, accurate attachment rate coefficients were determined over the temperature range 295–373K; they show an Arrhenius-type rise with increasing temperature, corresponding to an activation energy of 0.11(1)eV. In a high resolution electron beam experiment involving two versions of the laser photoelectron attachment method, the relative cross section for Cl− formation from CHCl3 over the energy range 0.001–1.25eV at the gas temperature TG=300K was measured. It exhibits clear downward cusp structure at the threshold for excitation of one quantum of the vibrational symmetric deformation mode ν3, indicating that this mode is active in the primary attachment process. With reference to our thermal attachment rate coefficient k(T=300K)=3.9(2)×10−9cm3s−1, a new highly resolved absolute attachment cross section for TG=300K was determined. This cross section is extended to higher energies by measurements, carried out with a pulsed electron beam apparatus which also provided new data for the distinctly weaker fragment anions HCl2− and CCl2−. The resulting total absolute cross section for anion formation is used to calculate the dependence of the attachment rate coefficient k(Te;TG) on electron temperature Te over the range 50–15000K at the fixed gas temperature TG=300K. In addition, we report the dependence of the relative cross section for Cl− formation on gas temperature (TG=310–435K). For comparison with the experimental data, R-matrix calculations have been carried out for the dominant anion channel Cl−. The results recover the main experimental observations and predict the dependence of the DEA cross section on the initial vibrational level ν3 and on the vibrational temperature. Our results are compared with those of previous electron beam and electron swarm experiments.

Collisional quenching at ultralow energies: Controlling efficiency with internal state selection

Calculations have been carried out for the vibrational quenching of excited H(2) molecules which collide with Li(+) ions at ultralow energies. The dynamics has been treated exactly using the well-known quantum coupled-channel expansions over different initial vibrational levels. The overall interaction potential has been obtained from the calculations carried out earlier by our group using highly correlated ab initio methods. The results indicate that specific features of the scattering observables, e.g., the appearance of Ramsauer-Townsend minima in elastic channel cross sections and the marked increase of the cooling rates from specific initial states, can be linked to potential properties at vanishing energies (sign and size of scattering lengths) and to the presence of either virtual states or bound states. The suggestion is made such that by selecting the initial state preparation of the molecular partners, the ionic interactions would be amenable to controlling quenching efficiency at ultralow energies.

Low-energy electron collisions with CH3Br: the dependence of elastic scattering, vibrational excitation, and dissociative attachment on the initial vibrational energy

Using the laser photoelectron attachment (LPA) method at an energy width of 1–2 meV, the Br− yield due to dissociative electron attachment to the molecule CH3Br has been measured over the energy range 1–180 meV at a gas temperature of 600 K. The data clearly exhibit the vibrational Feshbach resonance predicted by Wilde et al (2000 J. Phys. B: At. Mol. Opt. Phys. 33 5479) and associated with the v3 = 4 vibrational level of the C–Br stretch mode in the neutral molecule. We also report the dependence of the rate coefficient for Rydberg electron attachment (measured at high principal quantum numbers n ≈ 150) on gas temperature and find an Arrhenius-type behaviour compatible with the results of R-matrix calculations and with earlier findings of electron swarm experiments. With the aim to stimulate experiments, we report absolute cross sections for elastic scattering and vibrationally inelastic scattering involving the C–Br stretch mode v3 of CH3Br for several initial vibrational levels in the range v3 = 0–4; they were obtained with R-matrix calculations based on the same potential input as that involved in the computations of the cross sections for dissociative attachment.

Comparison of ADK ionization rates as a diagnostic for selective vibrational level population measurement

We have used a wavefunction-modified Ammosov–Delone–Krainov (ADK) method to calculate the ionization rates of H2, N2 and CO2 as a function of initial vibrational level of the molecules. A strong increase in the ionization rate, with vibrational level, is found for H2, while N2 and CO2 show a lesser increase. We have also compared the enhancement ratios between the ground and excited vibrational levels obtained from (1) a focal-volume averaged ADK procedure and (2) simple over-the-barrier calculations, and found dramatic differences in ionization dependence on vibrational levels for the different molecules.

Quasiclassical Trajectory Simulations of OH(v) + NO2 → HONO2* → OH(v‘) + NO2: Capture and Vibrational Deactivation Rate Constants

Quasiclassical trajectory calculations are used to investigate the dynamics of the OH(v) + NO(2) --> HONO(2) --> OH(v') + NO(2) recombination/dissociation reaction on an analytic potential energy surface (PES) that gives good agreement with the known structure and vibrational frequencies of nitric acid. The calculated recombination rate constants depend only weakly on temperature and on the initial vibrational energy level of OH(v). The magnitude of the recombination rate constant is sensitive to the potential function describing the newly formed bond and to the switching functions in the PES that attenuate inter-mode interactions at long range. The lifetime of the nascent excited HONO(2) depends strongly not only on its internal energy but also on the identity of the initial state, in disagreement with statistical theory. This disagreement is probably due to the effects of slow intramolecular vibrational energy redistribution (IVR) from the initially excited OH stretching mode. The vibrational energy distribution of product OH(v') radicals is different from statistical distributions, a result consistent with the effects of slow IVR. Nonetheless, the trajectory results predict that vibrational deactivation of OH(v) via the HONO(2) transient complex is approximately 90% efficient, almost independent of initial OH(v) vibrational level, in qualitative agreement with recent experiments. Tests are also carried out using the HONO(2) PES, but assuming the weaker O-O bond strength found in HOONO (peroxynitrous acid). In this case, the predicted vibrational deactivation efficiencies are significantly lower and depend strongly on the initial vibrational state of OH(v), in disagreement with experiments. This disagreement suggests that the actual HOONO PES may contain more inter-mode coupling than found in the present model PES, which is based on HONO(2). For nitric acid, the measured vibrational deactivation rate constant is a useful proxy for the recombination rate, but IVR randomization of energy is not complete, suggesting that the efficacy of the proxy method must be evaluated on a case-by-case basis.

Reactive collisions between electrons and NO+ ions: rate coefficient computations and relevance for the air plasma kinetics

Extensive calculations of the rate coefficients for dissociative recombination (DR), elastic collisions, inelastic collisions (ICs) and superelastic collisions of NO+ ions on initial vibrational levels, , with electrons of energy between 10−5 and 10 eV have been performed, with a method based on multichannel quantum defect theory. Comparisons of the DR rate coefficients with the plasma experimental results give a good agreement, confirming that the vibrationally excited NO+ ions recombine more slowly than those in the ground state. Also, our ground state IC rate coefficients are very similar to previously computed R-matrix data. The rate coefficients have been fitted to a modified Arrhenius law, and the corresponding parameters are given, in order to facilitate the use of the reaction data in kinetical plasma modelling.