Solvation of cationic copper clusters in molecular hydrogen.

Multiply charged superfluid helium nanodroplets are utilized to facilitate the growth of cationic copper clusters (Cun+, where n = 1-8) that are subsequently solvated with up to 50 H2 molecules. Production of both pristine and protonated cationic Cu clusters are detected mass spectrometrically. A joint effort between experiment and theory allows us to understand the nature of the interactions determining the bonding between pristine and protonated Cu+ and Cu2+ cations and molecular hydrogen. The analysis reveals that in all investigated cationic clusters, the primary solvation shell predominantly exhibits a covalent bonding character, which gradually decreases in strength, while for the subsequent shells an exclusive non-covalent behaviour is found. Interestingly, the calculated evaporation energies associated with the first solvation shell markedly surpass thermal values, positioning them within the desirable range for hydrogen storage applications. This comprehensive study not only provides insights into the solvation of pristine and protonated cationic Cu clusters but also sheds light on their unique bonding properties.

N2+(2Σg) and Rb(2S) in a hybrid trap: modeling ion losses from radiative association paths.

By employing ab initio computed intermolecular potential energy surfaces we calculate the radiative association probabilities and rates for two different associative mechanisms involving trapped molecular ions N2+(2Σg) interacting either directly with ultracold Rb atoms or undergoing charge-exchange (CE) processes leading to the formation of complexes of the strongly exothermic products N2(X1Σg) plus Rb+(1S0). The two processes are expected to provide possible paths to ion losses in the trap within the timescale of experiments. The present calculations suggest that the associative rates for the 'vibrational' direct process are too small to be of any significant importance at the millikelvin temperatures considered in the experiments, while the 'vibronic' path into radiatively associating the CE products has a probability of occurring which is several orders of magnitude larger. However the reaction rate constants attributed to non-adiabatic CE [F. H. J. Hall and S. Willist, Phys. Rev. Lett., 2012, 109, 233202] are in turn several orders of magnitude larger than the radiative ones calculated here, thereby making the primary experimental process substantially unaffected by the radiative losses channel.

Quasiclassical trajectory and statistical quantum calculations for the C + OH → CO + H reaction on the first excited 1(2)A″ potential energy surface.

We report quasiclassical trajectory dynamical calculations for the C((3)P) + OH(X(2)Π) → CO(a(3)Π) + H((2)S) using a recently developed ab initio potential energy surface for the first electronic state of HCO of 1(2)A″ symmetry. The dependence of integral cross sections on the collision energy was determined. Product energy and angular distributions have also been calculated. Integral cross sections show no energy threshold and decrease as the collision energy increases. The comparison with results obtained from a statistical quantum method seems to confirm that the reaction is mainly dominated by an indirect mechanism in which a long-lived intermediate complex is involved.

H2, H3+ and the age of molecular clouds and prestellar cores.

Measuring the age of molecular clouds and prestellar cores is a difficult task that has not yet been successfully accomplished although the information is of paramount importance to help in understanding and discriminating between different formation scenarios. Most chemical clocks suffer from unknown initial conditions and are therefore difficult to use. We propose a new approach based on a subset of deuterium chemistry that takes place in the gas phase and for which initial conditions are relatively well known. It relies primarily on the conversion of H(3)(+) into H(2)D(+) to initiate deuterium enrichment of the molecular gas. This conversion is controlled by the ortho/para ratio of H(2) that is thought to be produced with the statistical ratio of 3 and subsequently slowly decays to an almost pure para-H(2) phase. This slow decay takes approximately 1 Myr and allows us to set an upper limit on the age of molecular clouds. The deuterium enrichment of the core takes longer to reach equilibrium and allows us to estimate the time necessary to form a dense prestellar core, i.e. the last step before the collapse of the core into a protostar. We find that the observed abundance and distribution of DCO(+) and N(2)D(+) argue against quasi-static core formation and favour dynamical formation on time scales of less than 1 Myr. Another consequence is that ortho-H(2) remains comparable to para-H(2) in abundance outside the dense cores.

An accurate study of the dynamics of the C+OH reaction on the second excited 1(4)A" potential energy surface.

The dynamics of the C((3)P)+OH(X(2)Π) → CO(a(3)Π)+H((2)S) on its second excited potential energy surface, 1(4)A", have been investigated in detail by means of an accurate quantum mechanical (QM) time-dependent wave packet (TDWP) approach. Reaction probabilities for values of the total angular momentum J up to 50 are calculated and integral cross sections for a collision energy range which extends up to 0.1 eV are shown. The comparison with quasi-classical trajectory (QCT) and statistical methods reveals the important role played by the double well structure existing in the potential energy surface. The TDWP differential cross sections exhibit a forward-backward symmetry which could be interpreted as indicative of a complex-forming mechanism governing the dynamics of the process. The QM statistical method employed in this study, however, is not capable to reproduce the main features of the possible insertion nature in the reactive collision. The ability to stop individual trajectories selectively at specific locations inside the potential energy surface makes the QCT version of the statistical approach a better option to understand the overall dynamics of the process.

Communication: Quantum Zeno-based control mechanism for molecular fragmentation.

A quantum control mechanism is proposed for molecular fragmentation processes within a scenario grounded on the quantum Zeno effect. In particular, we focus on the van der Waals Ne-Br(2) complex, which displays two competing dissociation channels via vibrational and electronic predissociation. Accordingly, realistic three-dimensional wave packet simulations are carried out by using ab initio interaction potentials recently obtained to reproduce available experimental data. Two numerical models to simulate the repeated measurements are reported and analyzed. It is found that the otherwise fast vibrational predissociation is slowed down in favor of the slow electronic (double fragmentation) predissociation, which is enhanced by several orders of magnitude. Based on these theoretical predictions, some hints to experimentalists to confirm their validity are also proposed.

Weakly bound finite systems: (4He)N-Rb2(³Σu), clustering structures from a quantum Monte Carlo approach.

We report here ((4)He)(N)-Rb(2)((3)Σ(u)) complexes, 2 ≤ N ≤ 20, analysed through a quantum diffusion Monte Carlo stochastic approach. The calculations show that the spin stretched dimer molecule is bound outside the pure He sub-complex, due to the stronger He-He potential as compared with the He-Rb(2) interaction, while the rare gas atom moiety presents, in turn, a shell-like structure with ten He adatoms completing the first shell. Our results agree with previous findings on this and similarly weakly interacting systems.

Spin-polarized Rb2 interacting with bosonic He atoms: potential energy surface and quantum structures of small clusters.

A new full-dimension potential energy surface of the three-body He-Rb2(³Σ(u)(+)) complex and a quantum study of small (4He)(N)-Rb2(³Σ(u)(+)) clusters, 1 ≤ N ≤ 4, are presented. We have accurately fitted the ab initio points of the interaction to an analytical form and addressed the dopant's vibration, which is found to be negligible. A Variational approach and a Diffusion Monte Carlo technique have been applied to yield energy and geometric properties of the selected species. Our quantum structure calculations show a transition in the arrangements of the helium atoms from N = 2, where they tend to be separated across the diatomic bond, to N = 4, in which a closer packing of the rare gas particles is reached, guided by the dominance of the He-He potential over the weaker interaction of the latter adatoms with the doping dimer. The deepest well of the He-Rb2 interaction is placed at the T-shape configuration, a feature which causes the dopant to be located as parallel to the helium "minidroplet". Our results are shown to agree with previous findings on this and on similar systems.

Quantum mechanical study of the proton exchange in the ortho-para H2 conversion reaction at low temperature.

Ortho-para H(2) conversion reactions mediated by the exchange of a H(+) proton have been investigated at very low energy for the first time by means of a time independent quantum mechanical (TIQM) approach. State-to-state probabilities and cross sections for H(+) + H(2) (v = 0, j = 0,1) processes have been calculated for a collision energy, E(c), ranging between 10(-6) eV and 0.1 eV. Differential cross sections (DCSs) for H(+) + H(2) (v = 0, j = 1) → H(+) + H(2) (v' = 0, j' = 0) for very low energies only start to develop a proper global minimum around the sideways scattering direction (θ≈ 90°) at E(c) = 10(-3) eV. Rate coefficients, a crucial information required for astrophysical models, are provided between 10 K and 100 K. The relaxation ortho-para process j = 1 → j' = 0 is found to be more efficient than the j = 0 → j' = 1 conversion at low temperatures, in line with the extremely small ratio between the ortho and para species of molecular hydrogen predicted at the temperature of interstellar cold molecular clouds. The results obtained by means of a statistical quantum mechanical (SQM) model, which has previously proved to provide an adequate description of the dynamics of the title reactions at a higher collision energy regime, have been compared with the TIQM results. A reasonable good agreement has been found with the only exception of the DCSs for the H(+) + H(2) (v = 0, j = 1) → H(+) + H(2) (v' = 0, j' = 0) process at very low energy. SQM cross sections are also slightly below the quantum results. Estimates for the rate coefficients, in good accord with the TIQM values, are a clear improvement with respect to pioneering statistical studies on the reaction.

Ortho-para H2 conversion by proton exchange at low temperature: an accurate quantum mechanical study.

We report extensive, accurate fully quantum, time-independent calculations of cross sections at low collision energies, and rate coefficients at low temperatures for the H⁺ + H2(v = 0, j) → H⁺ + H2(v = 0, j') reaction. Different transitions are considered, especially the ortho-para conversion (j = 1 → j' = 0) which is of key importance in astrophysics. This conversion process appears to be very efficient and dominant at low temperature, with a rate coefficient of 4.15 × 10⁻¹° cm³ molecule⁻¹ s⁻¹ at 10 K. The quantum mechanical results are also compared with statistical quantum predictions and the reaction is found to be statistical in the low temperature regime (T < 100 K).

The O((1)D) + H2 (X (1)Σ+, v, j) → OH(X (2)Π, v', j') + H((2)S) reaction at low collision energy: when a simple statistical description of the dynamics works.

In this communication, we highlight that statistical approaches for chemical reactions describe reasonably well the low energy dynamics of the title process. Consequently, such methods prove to be valuable to compute rate constants from low to room temperatures. Results are compared with experiment and recent precise quantum wave packet calculations [J. Phys. Chem. A, 2009, 113, 5285].

Energy dependent dynamics of the O(1D) + HCl reaction: a quantum, quasiclassical and statistical study.

The dynamics of the reaction O((1)D) + HCl → ClO + H, OH + Cl has been investigated in detail by means of a time-dependent wave packet (TDWP) method in comparison with quasiclassical trajectory (QCT) and statistical approaches on the ground potential energy surface by Martínez et al. [Phys. Chem. Chem. Phys., 2000, 2, 589]. Fully coupled quantum mechanical (QM) reaction probabilities for high values of the total angular momentum (J≤ 50) are reported for the first time. At the low collision energy regime (E(c)≤ 0.4 eV) the TDWP probabilities are well reproduced by the QCT and statistical results for the ClO forming product channel, but for the OH + Cl arrangement, only QCT probabilities are found to agree with the QM values. The good accordance found between the rigorous statistical models and the dynamical QM and QCT calculations for the O + HCl → ClO + H process underpins the assumption that the reaction pathway leading to ClO is predominantly governed by a complex-forming mechanism. In addition, to further test the statistical character of this reaction channel, the laboratory angular distribution and time-of-flight spectra obtained in a crossed molecular beam study by Balucani et al. [Chem. Phys. Lett. 1991, 180, 34] at a collision energy as high as 0.53 eV have been simulated using the state resolved differential cross section obtained with the statistical approaches yielding a satisfactory agreement with the experimental results. For the other channel, O + HCl → OH + Cl, noticeable differences between the statistical results and those found with the QCT calculation suggest that the dynamics of the reaction are controlled by a direct mechanism. The comparison between the QCT and QM-TDWP results in the whole range of collision energies lends credence to the QCT description of the dynamics of this reaction.

A path-integral Monte Carlo study of a small cluster: The Ar trimer.

The Ar(3) system has been studied between T=0 K and T=40 K by means of a path-integral Monte Carlo (PIMC) method. The behavior of the average energy in terms of the temperature has been explained by comparison with results obtained with the thermal averaged rovibrational spectra estimated via: (i) a quantum mechanical method based on distributed Gaussian functions for the interparticle distances and (ii) an analytical model which precisely accounts for the participation of the dissociative continua Ar(2)+Ar and Ar+Ar+Ar. Beyond T approximately 20 K, the system explores floppier configurations than the rigid equilateral geometry, as linear and Ar-Ar(2)-like arrangements, and fragmentates around T approximately 40 K. A careful investigation of the specific heat in terms of a confining radius in the PIMC calculation seems to discard a proper phase transition as in larger clusters, in apparent contradiction with previous reports of precise values for a liquid-gas transition. The onset of this noticeable change in the dynamics of the trimer occurs, however, at a remarkably low value of the temperature in comparison with Ar(n) systems formed with more Ar atoms. Quantum mechanical effects are found of relevance at T

The dynamics of the O(1D) + HCl --> OH + Cl reaction at a 0.26 eV collision energy: a comparison between theory and experiment.

The dynamics of the O((1)D) + HCl(v = 0, j = 0) --> Cl + OH reaction at a 0.26 eV collision energy has been investigated by means of a quasiclassical trajectory (QCT) and statistical quantum and quasiclassical methods. State-resolved cross sections and Cl atom velocity distributions have been calculated on two different potential energy surfaces (PESs): the H2 surface (Martinez et al. Phys. Chem. Chem. Phys. 2000, 2, 589) and the latest surface by Peterson, Bowman, and co-workers (PSB2) (J. Chem. Phys. 2000, 113, 6186). The comparison with recent experimental results reveals that the PSB2 PES manages to describe correctly differential cross sections and the velocity distributions of the departing Cl atom. The calculations on the H2 PES seem to overestimate the OH scattering in the forward direction and the fraction of Cl at high recoil velocities. Although the comparison of the corresponding angular distributions is not bad, significant deviations with a statistical description are found, thus ruling out a complex-forming mechanism as the dominant reaction pathway. However, for the ClO + H product channel, the QCT and statistical predictions are found to be in good agreement.

Differential cross sections and product rotational polarization in A + BC reactions using wave packet methods: H+ + D2 and Li + HF examples.

The state-to-state differential cross sections for some atom + diatom reactions have been calculated using a new wave packet code, MAD-WAVE3, which is described in some detail and uses either reactant or product Jacobi coordinates along the propagation. In order to show the accuracy and efficiency of the coordinate transformation required when using reactant Jacobi coordinates, as recently proposed [ J. Chem. Phys. 2006 , 125 , 054102 ], the method is first applied to the H + D(2) reaction as a benchmark, for which exact time-independent calculations are also performed. It is found that the use of reactant coordinates yields accurate results, with a computational effort slightly lower than that when using product coordinates. The H(+) + D(2) reaction, with the same masses but a much deeper insertion well, is also studied and exhibits a completely different mechanism, a complex-forming one which can be treated by statistical methods. Due to the longer range of the potential, product Jacobi coordinates are more efficient in this case. Differential cross sections for individual final rotational states of the products are obtained based on exact dynamical calculations for some selected total angular momenta, combined with the random phase approximation to save the high computational time required to calculate all partial waves with very long propagations. The results obtained are in excellent agreement with available exact time-independent calculations. Finally, the method is applied to the Li + HF system for which reactant coordinates are very well suited, and quantum differential cross sections are not available. The results are compared with recent quasiclassical simulations and experimental results [J. Chem. Phys. 2005, 122, 244304]. Furthermore, the polarization of the product angular momenta is also analyzed as a function of the scattering angle.

Effects of the rotational excitation of D2 and of the potential energy surface on the H+ + D2 --> HD + D+ reaction.

The H(+) + D(2) --> HD + D(+) reaction has been theoretically investigated by means of an exact quantum mechanical approach, a quasiclassical trajectory method, and two statistical methods based in the propagation of either wave functions or trajectories. The study addresses the possible changes on the overall dynamics of the title reaction when the D(2) diatom is rotationally excited to its v = 0, j = 1 state. In addition, the reactivity for the ground rotational state on two different potential energy surfaces (PESs), namely, the surface by Aguado et al. [J. Chem. Phys. 112, 1240 (2000)] and the PES by Kamisaka et al. [J. Chem. Phys. 116, 654 (2002)], is examined. Reaction probabilities and cross sections at 0.524 and 0.1 eV collision energies are calculated. The major differences with respect to the reaction initiated with D(2) in its ground rovibrational state are observed for the lowest collision energy E(c) = 0.1 eV. Differential cross sections have been found to depend to some extend on the PES employed. In addition, at E(c) = 0.1 eV further discrepancies in the total and rotational cross sections are noticeable.

A theoretical investigation on the spectrum of the Ar trimer for high rotational excitations.

A detailed study of the rovibrational spectrum of the Ar trimer is performed by means of an exact hyperspherical coordinate (HC) method and a variational approach based on distributed Gaussian functions (DGFs) to describe the interparticle distances. The good agreement observed between the energy levels obtained with both procedures for high values of the total angular momentum (J=15 and 20) reveals the quality of the DGF method to describe the rotation of the title system. Rotational constants for the lowest bound states, obtained as averages for each vibrational state, have been obtained and compared to previous results. A detailed analysis of density probability functions obtained by means of the HC approach for rovibrational states at J=0 and 20 shows close similitudes thus supporting the vibration-rotation separation adopted within the DGF scheme for the Ar(3) system.

A comparison of quantum and quasiclassical statistical models for reactions of electronically excited atoms with molecular hydrogen.

A detailed comparison of statistical models based on the quasiclassical trajectory (SQCT) and quantum mechanical (SQM) methods is presented in this work for the C((1)D)+H(2), S((1)D)+H(2), O((1)D)+H(2) and N((2)D)+H(2) insertion reactions. Reaction probabilities, integral (ICS) and differential (DCS) cross sections at different levels of product's state resolution are shown and discussed for these reactions. The agreement is in most cases excellent and indicates that the effect of tunneling through the centrifugal barrier is negligible. However, if there exists a dynamical barrier, as in the case of the N((2)D)+H(2) reaction, some of the SQM results can be slightly different than those calculated with the SQCT model. The rationale of the observed similarities and discrepancies can be traced back to the specific topologies of the potential energy surfaces for each of the reactions examined. The SQCT model is sensitive enough to show the relatively small inaccuracies resulting from the decoupling inherent to the centrifugal sudden approximation when used in the SQM calculations. In addition, the effect of ignoring the parity conservation is also examined. This effect is in general minor except in particular cases such as the DCS from initial rotational state j=0, which requires, in order to reproduce the sharp forward and backward peaks, the explicit conservation of parity.

Stringent test of the statistical quasiclassical trajectory model for the H+3 exchange reaction: a comparison with rigorous statistical quantum mechanical results.

A complete formulation of a statistical quasiclassical trajectory (SQCT) model is presented in this work along with a detailed comparison with results obtained with the statistical quantum mechanical (SQM) model for the H+ +D2 and H+ +H2 reactions. The basic difference between the SQCT and the SQM models lies in the fact that trajectories instead of wave functions are propagated in the entrance and exit channels. Other than this the two formulations are entirely similar and both comply with the principle of detailed balance and conservation of parity. Reaction probabilities, and integral and differential cross sections (DCS's) for these reactions at different levels of product's state resolution and from various initial states are shown and discussed. The agreement is in most cases excellent and indicates that the effect of tunneling through the centrifugal barrier is negligible. Some differences are found, however, between state resolved observables calculated by the SQCT and the SQM methods which makes use of the centrifugal sudden (coupled states) approximation (SQM-CS). When this approximation is removed and the full close coupling treatment is used in the SQM model (SQM-CC), an almost perfect agreement is achieved. This shows that the SQCT is sensitive enough to show the relatively small inaccuracies resulting from the decoupling inherent to the CS approximation. In addition, the effect of ignoring the parity conservation is thoroughly examined. This effect is in general minor except in particular cases such as the DCS from initial rotational state j=0. It is shown, however, that in order to reproduce the sharp forward and backward peaks the conservation of parity has to be taken into account.

A statistical quasiclassical trajectory model for atom-diatom insertion reactions.

A statistical model based on the quasiclassical trajectory method is presented in this work for atom-diatom insertion reactions. The basic difference between this and the corresponding statistical quantum model (SQM) lies in the fact that trajectories instead of wave functions are propagated in the entrance and exit channels. Other than this the two formulations are entirely similar. In particular, it is shown that conservation of parity can be taken into account in a natural and precise way in the statistical quasiclassical trajectory (SQCT) model. Additionally, the SQCT model complies with the principle of detailed balance and overcomes the problem of the zero point energy in the products. As a test, the model is applied to the H3+ and H+D2 exchange reactions. The excellent agreement between the SQCT and SQM results, especially in the case of the differential cross sections, indicates that the effect of tunneling through the centrifugal barrier is negligible. The effect of ignoring quantum mechanical parity conservation is also investigated.