Influence of nuclear exchange on nonadiabatic electron processes in H(+)+H2 collisions

H(+)+H(2) collisions are studied by means of a semiclassical approach that explicitly accounts for nuclear rearrangement channels in nonadiabatic electron processes. A set of classical trajectories is used to describe the nuclear motion, while the electronic degrees of freedom are treated quantum mechanically in terms of a three-state expansion of the collision wavefunction. We describe electron capture and vibrational excitation, which can also involve nuclear exchange and dissociation, in the E = 2-1000 eV impact energy range. We compare dynamical results obtained with two parametrizations of the potential energy surface of H(3)(+) ground electronic state. Total cross sections for E > 10 eV agree with previous results using a vibronic close-coupling expansion, and with experimental data for E < 10 eV. Additionally, some prototypical features of both nuclear and electron dynamics at low E are discussed.     

The effects of collision energy, vibrational mode, and vibrational angular momentum on energy transfer and dissociation in NO2+-rare gas collisions: an experimental and trajectory study

A combined experimental and trajectory study of vibrationally state-selected NO2+ collisions with Ne, Ar, Kr, and Xe is presented. Ne, Ar, and Kr are similar in that only dissociation to the excited singlet oxygen channel is observed; however, the appearance energies vary by approximately 4 eV between the three rare gases, and the variation is nonmonotonic in rare gas mass. Xe behaves quite differently, allowing efficient access to the ground triplet state dissociation channel. For all four rare gases there are strong effects of NO2+ vibrational excitation that extend over the entire collision energy range, implying that vibration influences the efficiency of collision to internal energy conversion. Bending excitation is more efficient than stretching; however, bending angular momentum partially counters the enhancement. Direct dynamics trajectories for NO2+ + Kr reproduce both the collision energy and vibrational state effects observed experimentally and reveal that intracomplex charge transfer is critical for the efficient energy transfer needed to drive dissociation. The strong vibrational effects can be rationalized in terms of bending, and to a lesser extent, stretching distortion enhancing transition to the Kr+ -NO2 charge state.     

Collision energy transfer in collision of NH(4) (+)(NH(3))(n-1) (n=3-9) with ND(3)

An incorporation of ND(3) into protonated ammonia cluster ions NH(4)(+)(NH(3))(n-1) (n=3-9), together with a dissociation of the cluster ions, was observed in the collision of the cluster with ND(3) at collision energies ranging from 0.04 to 1.4 eV in the center-of-mass frame. The branching fractions of the cluster ion species produced in the reactions were obtained as a function of the collision energy. The branching fractions of the incorporation products were successfully explained in terms of the Rice-Ramsperger-Kassel (RRK) theory at collision energies lower than the binding energy of the cluster ion. In addition, the internal energy distributions of the parent cluster ions were determined, and found to be in good agreement with those predicted using the evaporative ensemble model. In incorporations at collision energies lower than the binding energy of the cluster ion, all of the collision energy was transferred to the internal energy of the cluster ions; subsequently, an evaporation of ammonia molecules occurred in an equilibrium process after a complete energy redistribution in the clusters. In contrast, at collision energies higher than the binding energy of the cluster ion, a release of an ammonia molecule from the incorporation products occurred in a nonequilibrium process. The transition from the complex mode to the direct mode in the incorporation was observed at collision energies approximately equal to the binding energy. On the other hand, the collision energy dependence of the cross sections for the dissociation and for a nonreactive collision were estimated by a RRK simulation in which the collision energy transfer was interpreted by using the classical hard-sphere collision model. A relationship between reactivity and reaction modes in the collision of NH(4)(+)(NH(3))(4) with ND(3) is discussed via a comparison of the experimental results with the RRK simulation.     

Investigation of energy deposited by femtosecond electron transfer in collisions using hydrated ion nanocalorimetry

Ion nanocalorimetry is used to investigate the internal energy deposited into M (2+)(H 2O) n , M = Mg ( n = 3-11) and Ca ( n = 3-33), upon 100 keV collisions with a Cs or Ne atom target gas. Dissociation occurs by loss of water molecules from the precursor (charge retention) or by capture of an electron to form a reduced precursor (charge reduction) that can dissociate either by loss of a H atom accompanied by water molecule loss or by exclusively loss of water molecules. Formation of bare CaOH (+) and Ca (+) by these two respective dissociation pathways occurs for clusters with n up to 33 and 17, respectively. From the threshold dissociation energies for the loss of water molecules from the reduced clusters, obtained from binding energies calculated using a discrete implementation of the Thomson liquid drop model and from quantum chemistry, estimates of the internal energy deposition can be obtained. These values can be used to establish a lower limit to the maximum and average energy deposition. Not taking into account effects of a kinetic shift, over 16 eV can be deposited into Ca (2+)(H 2O) 33, the minimum energy necessary to form bare CaOH (+) from the reduced precursor. The electron capture efficiency is at least a factor of 40 greater for collisions of Ca (2+)(H 2O) 9 with Cs than with Ne, reflecting the lower ionization energy of Cs (3.9 eV) compared to Ne (21.6 eV). The branching ratio of the two electron capture dissociation pathways differs significantly for these two target gases, but the distributions of water molecules lost from the reduced precursors are similar. These results suggest that the ionization energy of the target gas has a large effect on the electron capture efficiency, but relatively little effect on the internal energy deposited into the ion. However, the different branching ratios suggest that different electronic excited states may be accessed in the reduced precursor upon collisions with these two different target gases.     

Fragmentation of ionized doped helium nanodroplets: theoretical evidence for a dopant ejection mechanism

We report a theoretical study of the effect induced by a helium nanodroplet environment on the fragmentation dynamics of a dopant. The dopant is an ionized neon cluster Ne(n) (+) (n=4-6) surrounded by a helium nanodroplet composed of 100 atoms. A newly designed mixed quantum/classical approach is used to take into account both the large helium cluster zero-point energy due to the light mass of the helium atoms and all the nonadiabatic couplings between the Ne(n) (+) potential-energy surfaces. The results reveal that the intermediate ionic dopant can be ejected from the droplet, possibly with some helium atoms still attached, thereby reducing the cooling power of the droplet. Energy relaxation by helium atom evaporation and dissociation, the other mechanism which has been used in most interpretations of doped helium cluster dynamics, also exhibits new features. The kinetic energy distribution of the neutral monomer fragments can be fitted to the sum of two Boltzmann distributions, one with a low kinetic energy and the other with a higher kinetic energy. This indicates that cooling by helium atom evaporation is more efficient than was believed so far, as suggested by recent experiments. The results also reveal the predominance of Ne(2) (+) and He(q)Ne(2) (+) fragments and the absence of bare Ne(+) fragments, in agreement with available experimental data (obtained for larger helium nanodroplets). Moreover, the abundance in fragments with a trimeric neon core is found to increase with the increase in dopant size. Most of the fragmentation is achieved within 10 ps and the only subsequent dynamical process is the relaxation of hot intermediate He(q)Ne(2) (+) species to Ne(2) (+) by helium atom evaporation. The dependence of the ionic fragment distribution on the parent ion electronic state reached by ionization is also investigated. It reveals that He(q)Ne(+) fragments are produced only from the highest electronic state, whereas He(q)Ne(2) (+) fragments originate from all the electronic states. Surprisingly, the highest electronic states also lead to fragments that still contain the original ionic dopant species. A mechanism is conjectured to explain this fragmentation inhibition.     

Postcollision relaxation of small atomic clusters

Molecular-dynamics simulations are performed to investigate the effects caused by the lack of internal equilibration on the dynamics and properties of atomic clusters. The studied systems consist of Lennard-Jones clusters of five to ten atoms and a colliding vapor monomer. Cluster radius and potential energy are shown to reach a time-independent value within 30 ps after a collision with a vapor monomer. The relaxation in terms of rotational energy takes at least 200 ps. During the first couple of picoseconds after the collision time-dependent cluster decay rates are observed. The unrelaxed cluster states are expected to have minimal effect on gas-liquid nucleation rates.     

Generating Excess Protons in Microsolvated Acid Clusters under Ambient Conditions: An Issue of Configurational Entropy versus Internal Energy

Acid dissociation, and thus liberation of excess protons in small water droplets, impacts on diverse fields such as interstellar, atmospheric or environmental chemistry. At cryogenic temperatures below 1 K, it is now well established that as few as four water molecules suffice to dissociate the generic strong acid HCl, yet temperature-driven recombination sets in simply upon heating that cluster. Here, the fundamental question is posed of how many more water molecules are required to stabilize a hydrated excess proton at room temperature. Ab initio path integral simulations disclose that not five, but six water molecules are needed at 300 K to allow for HCl dissociation independently from nuclear quantum effects. In order to provide the molecular underpinnings of these observations, the classical and quantum free energy profiles were decomposed along the dissociation coordinate in terms of the corresponding internal energy and entropy profiles. What decides in the end about acid dissociation, and thus ion pair formation, in a specific microsolvated water cluster at room temperature is found to be a fierce competition between classical configurational entropy and internal energy, where the former stabilizes the undissociated state whereas the latter favors dissociation. It is expected that these are generic findings with broad implications on acid–base chemistry depending on temperature in small water assemblies.     

Quantum and classical studies of the O(3P) + H2(v = 0-3,j = 0) --> OH + H reaction using benchmark potential surfaces

We present results of time-dependent quantum mechanics (TDQM) and quasiclassical trajectory (QCT) studies of the excitation function for O(3P) + H2(v = 0-3,j = 0) --> OH + H from threshold to 30 kcal/mol collision energy using benchmark potential energy surfaces [Rogers et al., J. Phys. Chem. A 104, 2308 (2000)]. For H2(v = 0) there is excellent agreement between quantum and classical results. The TDQM results show that the reactive threshold drops from 10 kcal/mol for v = 0 to 6 for v = 1, 5 for v = 2 and 4 for v = 3, suggesting a much slower increase in rate constant with vibrational excitation above v = 1 than below. For H2(v > 0), the classical results are larger than the quantum results by a factor approximately 2 near threshold, but the agreement monotonically improves until they are within approximately 10% near 30 kcal/mol collision energy. We believe these differences arise from stronger vibrational adiabaticity in the quantum dynamics, an effect examined before for this system at lower energies. We have also computed QCT OH(v',j') state-resolved cross sections and angular distributions. The QCT state-resolved OH(v') cross sections peak at the same vibrational quantum number as the H2 reagent. The OH rotational distributions are also quite hot and tend to cluster around high rotational quantum numbers. However, the dynamics seem to dictate a cutoff in the energy going into OH rotation indicating an angular momentum constraint. The state-resolved OH distributions were fit to probability functions based on conventional information theory extended to include an energy gap law for product vibrations.     

Tandem mass spectrometry of protein—Protein complexes: Cytochrome c—Cytochrome b 5

An improved method to interpret triple quadrupole MS/MS experiments of complexes of large ions is presented and applied to a study of the complex formed by the proteins cytochrome c and cytochrome b5. Modeling of the activation and dissociation process shows that most of the reaction occurs near the collision cell exit where ions have the highest internal energies. Experiments at different collision cell pressures or with different collision gases (Ne, Ar, Kr) are interpreted with a previously proposed collision model (Chen et al., Rapid Commun. Mass Spectrom. 1998, 12, 1003-1010) to calculate the internal energy added to ions to cause dissociation. Small but systematic differences under different experimental conditions are attributed to different times available for reaction. A method to correct for this is presented. Ne, Ar, and Kr are found to have similar energy transfer efficiencies. Complexes of cytochrome c and cytochrome b5 are detected in ESI mass spectra but with abundances less than expected from the solution equilibrium. Dissociation of the cytochrome c-cytochrome b5 complexes with charge k gives as the most abundant fragments, cytochrome b5(+3) and cytochrome c+(k-3). Adding charges to the complex destabilizes it. A series of cytochrome c variants with Lys residues thought to be involved in solution binding replaced by Ala showed no differences in the energy required to induce dissociation of the gas phase complex. The implications for the binding of the gas phase ions are inconclusive.     

On the statistical nature of collision and surface-induced dissociation: a theoretical investigation of aluminum clusters

The unimolecular dissociation dynamics of aluminum clusters following collision with either a rare gas atom or a surface is investigated by classical trajectory simulations with model potentials. Two conformers of Al(6) with very distinct shapes, i.e., the spherical O(h) and planar C(2)(h) clusters, are considered in this work. The initial vibrational energy and angular momentum distributions resulting from collision, as well as the energy and angular momentum resolved lifetime distributions, of excited clusters were determined for both collision-induced dissociation (CID) and surface-induced dissociation (SID) processes. The partitioning of excitation energy acquired upon collision was found to depend on the excitation mechanism (CID or SID), as well as on the cluster molecular shape, especially in the case of CID. For both types of processes, the energy and angular momentum resolved excited cluster lifetime distributions were found to decay exponentially, in agreement with statistical theories of chemical reactions, suggesting intrinsic Rice-Ramsperger-Kassel-Marcus (RRKM) behavior. Moreover, the simulated microcanonical rate constants determined from the cluster lifetime distributions are in good agreement with the predictions of the orbiting transition state model of phase space theory (OTS/PST), which further supports the statistical character of cluster CID and SID. Thus, in the CID and SID of highly fluxional systems such as aluminum clusters, the rate of intramolecular vibrational energy redistribution (IVR) is much faster than the dissociation rate, which validates one of the key assumptions, i.e., post-collision statistical behavior, underlying the models that are routinely used to determine cluster binding energies from experimental CID/SID cross sections.     

Alkali chloride cluster ion dissociation examined by the kinetic method: heterolytic bond dissociation energies,effective temperatures,and entropic effects

Branching ratios have been measured as a function of collision energy for the dissociation of mass-selected chloride-bound salt cluster ions, [Rb-³⁵Cl-M_i]⁺, where M_i = Na, K, Cs. The extended version of the kinetic method was used to determine the heterolytic bond dissociation energy (HBDE) of Rb-Cl. The measured value of 480.8 ± 8.5 kJ/mol, obtained under single collision conditions, agrees with the HBDE value (482.0 ± 8.0 kJ/mol), calculated from a thermochemical cycle. The observed effective temperature of the collisionally activated salt clusters increases with laboratory-frame collision energy under both single- and multiple-collision conditions. Remarkably, the effective temperatures under multiple collision conditions are lower than those recorded under single-collision conditions at the same collision energy, a consequence of the inability of the triatomic ions to store significant amounts of internal energy. Laboratory-frame kinetic energy to internal energy transfer (T→V) efficiencies range from 3.8 to 13.5%. For a given cluster ion, the T→V efficiency decreases with increasing collision energy. Many features of the experimental results are accounted for using MassKinetics modeling (Drahos and Vékey, J. Mass Spectrom. 2001, 36, 237).     

Reaction products with internal energy beyond the kinematic limit result from trajectories far from the minimum energy path: an example from H + HBr --> H2 + Br

The importance of reactive trajectories straying far from the minimum energy path is demonstrated for the bimolecular reaction H + HBr --> H2(v', j') + Br at 53 kcal/mol collision energy. Product quantum state distributions are measured and calculated using the quasi-classical trajectory technique, and the calculations indicate that highly internally excited H2 products result from indirect reactive trajectories with bent transition states. A general argument is made suggesting that reaction products with internal energy exceeding a kinematic constraint can, in general, be attributed to reactive collisions straying far from the minimum energy path.     

Trajectory-based solution of the nonadiabatic quantum dynamics equations: an on-the-fly approach for molecular dynamics simulations

The non-relativistic quantum dynamics of nuclei and electrons is solved within the framework of quantum hydrodynamics using the adiabatic representation of the electronic states. An on-the-fly trajectory-based nonadiabatic molecular dynamics algorithm is derived, which is also able to capture nuclear quantum effects that are missing in the traditional trajectory surface hopping approach based on the independent trajectory approximation. The use of correlated trajectories produces quantum dynamics, which is in principle exact and computationally very efficient. The method is first tested on a series of model potentials and then applied to study the molecular collision of H with H(2) using on-the-fly TDDFT potential energy surfaces and nonadiabatic coupling vectors.     

Translational to rotational energy transfer in molecule-surface collisions

A theoretical approach that combines classical mechanics for treating translational and rotational degrees of freedom and quantum mechanics for describing the excitation of internal molecular modes is applied to the scattering of diatomic molecules from metal surfaces. Calculations are carried out for determining the extent of energy transfer to the rotational degrees of freedom of the projectile molecule. For the case of observed spectra of intensity versus final rotational energy, quantitative agreement with available experimental data for the scattering of NO and N(2) from close packed metal surfaces is obtained. It is shown that such measurements can be used to determine the average rotational energy of the incident molecular beam. Measurements of the exchange of energy between translational and rotational degrees of freedom upon collision are also described by calculations for these same systems.     

Uptake of phenol on aerosol particles

We present a study of the interaction between a phenol molecule and an aerosol particle. The aerosol particle is represented by a cluster of 128 water molecules. Using a classical approach, we present interaction energy surfaces for different relative distances and for three orientations of phenol relative to the particle. From the energy surfaces we find the reaction pathways with the largest interaction between the molecule and the particle. We use a quantum mechanics/molecular mechanics (QM/MM) method to calculate a potential energy curve for each reaction path. Coupled cluster methods are used for the part of the system described by quantum mechanics, while the part described by molecular mechanics is represented by a polarizable force field. We compare results obtained from the classical approach with the QM/MM results. Furthermore, we use the QM/MM results to calculate mass accommodation coefficients using a quantum-statistical (QM-ST) model and show how the mass accommodation coefficient depends on the relative orientation of phenol with respect to the aerosol particle.     

Six-dimensional quasiclassical and quantum dynamics of H2 dissociation on the c(2 × 2)-Ti/Al(100) surface

Based on a slab model of H(2) dissociation on a c(2 × 2) structure with Ti atoms in the first and third layers of Al(100), a six-dimensional (6D) potential energy surface (PES) has been built. In this PES, a molecular adsorption well with a depth of 0.45 eV is present in front of a barrier of height 0.13 eV. Using this PES, H(2) dissociation probabilities are calculated by the classical trajectory (CT), the quasiclassical trajectory (QCT), and the time-dependent wave-packet (TDWP) method. The QCT study shows that trajectories can be trapped by the molecular adsorption well. Higher incident energy can lead to direct H(2) dissociation. Vibrational pre-excitation is the most efficient way to promote direct dissociation without trapping. We find that both rotational and vibrational excitation have efficacies close to 1.0 in the entire range of incident energies investigated, which supports the randomization in the initial conditions making the reaction rate solely dependent on the total (internal and translational) energy. The H(2) dissociation probabilities from quantum dynamics are in reasonable agreement with the QCT results in the energy range 50-200 meV, except for some fluctuations. However, the TDWP results considerably exceed the QCT results in the energy range 200-850 meV. The CT reaction probabilities are too low compared with the quantum dynamical results.     

Non-adiabatic molecular dynamics with quantum solvent effects

Three novel approaches extending quantum-classical non-adiabatic (NA) molecular dynamics (MD) to include quantum effects of solvent environments are described. In a standard NA-MD the solute subsystem is treated quantum mechanically, while the larger solvent part of a system is treated classically. The three novel approaches presented here are based on the Bohmian formulation of quantum mechanics, the stochastic Schrödinger equation for the evolution of open quantum systems and the quantized Hamilton dynamics generalization of classical mechanics. The approaches extend the standard NA-MD to incorporate the following quantum effects of the solvent. (1) Branching, i.e. the ability of solvent quantum wave packets to split and follow asymptotically diverging trajectories correlated with different quantum states of the solute. (2) Decoherence, i.e. loss of quantum interference within the solute subsystem induced by the diverging solvent trajectories. (3) Zero point energy that contributes to NA coupling and must be preserved during the energy exchange between solvent and solute degrees of freedom. The Bohmian quantum-classical mechanics, stochastic mean-field and quantized mean-field approximations incorporate the quantum solvent effects into the standard quantum-classical NA-MD in a straightforward and efficient way that can be easily applied to quantum dynamics of condensed phase chemical systems.     

Collision complexes in dissociative single electron transfer between Ne2+ and N2

Experiments involving the coincident detection of the two monocationic products (Ne+ and N+) from the dissociative electron transfer reaction between Ne2+ and N2 at 7.8 eV collision energy allow the nascent velocity vectors of the ionic and neutral (N) products to be determined. Examination of the correlations between these vectors shows that one pathway to the products involves the dissociation of a transitory collision complex (N2Ne2+).