Rotational Transitions in the N2 + Ion Induced by Collisions with Helium Atoms in Cold Helium Plasmas. A Quasiclassical Trajectory Study.

Cross-sections of state-to-state rotational transitions in electronically ground-state 14 N 2 + ${{\rm{N}}_2^ + }$ (X2 Σ g + ${{\Sigma }_{g}^{+}}$ ) ions induced by collisions with 4 He atoms have been calculated using a quasiclassical trajectory method and a set of artificial neural networks representing the N 2 + ${{\rm{N}}_2^ + }$ /He potential energy surface. The training points for the neural networks have been calculated at a MCSCF (multi-configuration self-consistent field)/aug-cc-pVQZ level. A broad range of the N 2 + ${{\rm{N}}_2^ + }$ /He collision energy has been considered ( E c o l l ≤ 100 ${{E}_{{\rm c}{\rm o}{\rm l}{\rm l}}\le 100}$  eV) and the efficiency of vibrational transitions in the N 2 + ${{\rm{N}}_2^ + }$ ion has also been analyzed. It has been found that vibrational transitions are negligible with respect to rotational transitions up to E c o l l ≈ 10 ${{E}_{{\rm c}{\rm o}{\rm l}{\rm l}}\approx 10}$  eV and that above this energy, both rotational and vibrational transitions in N 2 + ${{\rm{N}}_2^ + }$ are marginal in the N 2 + ${{\rm{N}}_2^ + }$ /He collisions.

Size Evolution of Photoabsorption Spectra of Small Clusters: A Computational Study.

Photoabsorption spectra of He N + ${{\rm{He}}_N^ + }$ clusters, N=5-9, have been calculated using a diatomics-in-molecules like electronic structure model and a path-integral Monte Carlo sampling method. A qualitative change in the calculated spectra has been observed at N=9, which has been interpreted in terms of a structural transformation in the clusters consisting in a transition from trimer-like ionic cores observed for N≤7 to dimer-like ionic cores prevailing in He 9 + ${{\rm{He}}_9^ + }$ through an intermediate state (comparable abundances of both types of ionic cores) observed in He 8 + ${{\rm{He}}_8^ + }$ . The calculated spectra have been thoroughly compared with an earlier calculation on He 3 + ${{\rm{He}}_3^ + }$ , He 4 + ${{\rm{He}}_4^ + }$ , and He 10 + ${{\rm{He}}_{10}^ + }$ reported from our group and data available for the same cluster sizes from an experiment.

Thermodynamics of small mercury clusters and the role of electronically excited states: a case study on Hg13.

Classical Monte Carlo simulations in the isothermal-isobaric ensemble have been performed for the Hg13 cluster with the main emphasis paid to structural changes in this cluster induced by elevated temperature and pressure. Broad ranges of temperatures and pressures have been considered so that a comprehensive picture of the structural changes in Hg13 could be obtained and represented in the form of a phase diagram constructed in the temperature-pressure plane. The effect of the complex electronic structure of the cluster on its electronic ground state potential energy surface and equilibrium thermodynamics has been studied within a semi-empirical electronic structure model based on the diatomics-in-molecules approach. The involvement of (three) lowest excited electronic states has been revealed while the higher excited states available within this model do not contribute.

Finite Systems under Pressure: Assessing Volume Definition Models from Parallel-Tempering Monte Carlo Simulations.

We have investigated different approaches to handling parallel-tempering Monte Carlo (PTMC) simulations in the isothermal-isobaric ensemble of molecular cluster/nanoparticle systems for predicting structural phase diagram transitions. We have implemented various methodologies that consist of treating pressure implicitly through its effect on the volume. Thus, the main problem in the simulations under nonzero pressure becomes the volume definition of the finite nonperiodic system, and we considered approaches based on the particles' coordinates. Various volume models, namely container-volume, particle-volume, average-volume, ellipsoids-volume, and convex hull-volume, were employed, and the required corrections for each of them in the Monte Carlo computations were introduced. Finally, we explored the effects of volume/pressure changes for all models on structural phase transitions of a test system, such as the small "icelike" (H2O)12 water cluster. The temperature and pressure dependence of the cluster's heat capacity and energy-volume Pearson correlation coefficient were studied, phase diagrams were constructed using a multiple-histogram method, and attempts were made to identify phase transitions to particular cluster structures. Our results show significant differences between the employed volume models, and we discuss all pressure-induced, such as solid-solid-, solid-liquid-, and liquid-gas-like, phase transformations in the present study.

Calculations of cross-sections, dissociation rate constants and transport coefficients of Xe2+ colliding with Xe.

A quantum formalism and classical treatment have been used for electrons and nuclei, respectively, in a hybrid method in order to study the dynamics of electronically ground-state ionic xenon dimer, Xe2+, in its parent gas. A semiempirical Diatomics In Molecules approach has been used to model the effective electronic Hamiltonian with different sets of input diatomic potentials (ionic and neutral). Non-reactive scattering and collision induced dissociation cross-sections have first been calculated and then injected in a Monte Carlo code for the simulations of the transport coefficients and dissociation rate constant calculated at ambient temperature and atmospheric pressure. Selected transport coefficients, such as Xe2+ mobility for which experimental measurements are available, have been compared to experimental results while transversal and longitudinal diffusion coefficients are compared to pseudo-experimental data obtained from inverse method calculations. Investigation of rotational-vibrational effects and the influence of different sets of ionic and neutral diatomic potentials have been studied.

Photoabsorption spectra of small mercury clusters: a computational study.

Photoabsorption spectra of small HgN clusters (N = 2-5) have been calculated using a diatomics-in-molecules interaction model and an atoms-in-molecules approach for transition probability calculations. Absorption cross-sections are provided over a broad range of photon energies, Ephot = 4.0-7.5 eV, as calculated for various cluster temperatures ranging between T = 0 K and T = 40 K. Quantum as well as temperature-induced delocalization of nuclear positions has been taken into account at various levels using classical and quantum (path-integral) Monte Carlo methods as well as sampling from the square of cluster vibrational ground-state wavefunctions. A thorough comparison of the calculated data with available experimental records is also provided.

Fragmentation of KrN+ clusters after electron impact ionization. Short-time dynamics simulations and approximate multi-scale treatment.

Post-ionization fragmentation of small ionic krypton clusters, KrN+ (N = 3-13), has been investigated using a semiclassical non-adiabatic dynamics approach consisting of classical treatment of atomic nuclei and full quantum treatment of electrons, and an extended diatomics-in-molecules model including the spin-orbit coupling as well as leading three-body interaction corrections. Electronic quantum decoherence has also been considered via a simplified scheme proposed previously. The positive charge has been initially localized on a randomly selected atom in the form of a localized 2P1/2 positive hole. It follows from the calculations that the data are not converged at timescales usually considered in dynamical calculations (t = 200 ps in this work) and that an extension to t ≈ 1 µs is needed. An approximate multi-scale treatment developed recently has been used to provide such an extension of the output of dynamical calculations. A qualitative agreement with available experimental data has been achieved, in particular, the experimental observation that the monomer fragment, Kr+, completely dominates has been reproduced. Interestingly, stabilized neutral dimer and trimer fragments have been observed in our calculations at non-negligible abundances despite extremely weak bonding in these species.

Fragmentation of KrN+ clusters after electron impact ionization II. Long-time dynamics simulations of Kr7+ evolution and the role of initial electronic excitation.

Long time simulations, up to 100 ns, have been performed for the fragmentation of Kr7+ clusters after electron impact ionization. They rely on DIM approaches and hybrid non-adiabatic dynamics combining mean field and decoherence driven either by Tully fewest switches (TFS) algorithm or through electronic amplitude (AMP) calculations. With both methods, for the first time, when the initial electronic excited state belongs to group II correlating to P1/2 atomic ions, the fragmentation ratio in mainly monomer and dimer ions agrees very well with known experimental results. A complex non-adiabatic dynamics is found where initial neutral monomer evaporations due to gradual deexcitation over electronic states of group II are followed by a non-adiabatic transition across a wide energy gap of the spin-orbit origin to electronic states of group I. The resulting excess of kinetic energy causes the final fragmentation of charged intermediate fragments to stable ionic monomers or dimers. Characteristic times of these processes have been estimated. The kinetic energy distribution of the neutral and ionic monomers (the dominating final fragments) has been analyzed in detail. Interestingly they exhibit some signature of the initial excited electronic state which could allow for an experimental identification.

Phase transitions in free water nanoparticles. Theoretical modeling of [H2O]48 and [H2O]118.

Classical parallel-tempering Monte Carlo simulations of [H2O]48 and [H2O]118 have been performed in the isothermal-isobaric ensemble and a two-dimensional multiple-histogram method has been used to calculate the heat capacity of the two clusters. A semiempirical procedure is proposed for the inclusion of quantum effects and transformed heat capacity profiles are compared with state-of-the-art experimental data [C. Hock et al., Phys. Rev. Lett., 2009, 103, 073401]. A very good agreement is achieved. A detailed analysis of the simulation data is provided to gain an insight into the nature of the phase change which takes place in the two clusters at T ≈ 100 K.

Photodissociation of medium-sized argon cluster cations in the visible region.

Semiclassical methods for non-adiabatic dynamics simulations, based on a semiempirical diatomics-in-molecules model of intracluster interactions and the mean-field dynamical approach with the inclusion of quantum decoherence, have been used to study the photodissociation of argon cluster cations, Ar(N)(+)(N = 6-19), at E(phot) = 2.35 eV. Time periods upto t = 200 ps have been considered and abundance of ionic and neutral fragments, their time evolution and stability have been investigated and compared with available experimental data as well as earlier theoretical studies. A good agreement has been achieved between our predictions and the experimental data and deviations from earlier dynamical calculations are discussed.

First principles transport coefficients and reaction rates of Ar2(+) ions in argon for cold plasma jet modeling.

Momentum-transfer collision cross-sections and integral collision cross-sections for the collision-induced dissociation are calculated for collisions of ionized argon dimers with argon atoms using a nonadiabatic semiclassical method with the electronic Hamiltonian calculated on the fly via a diatomics-in-molecules semiempirical model as well as inverse-method modeling based on simple isotropic rigid-core potential. The collision cross-sections are then used in an optimized Monte Carlo code for evaluations of the Ar 2 (+) mobility in argon gas, longitudinal diffusion coefficient, and collision-induced dissociation rates. A thorough comparison of various theoretical calculations as well as with available experimental data on the Ar 2 (+) mobility and collision cross-sections is performed. Good agreement is found between both theoretical approaches and the experiment. Analysis of the role of inelastic processes in Ar 2 (+)/Ar collisions is also provided.

Multiscale approach combining nonadiabatic dynamics with long-time radiative and non-radiative decay: dissociative ionization of heavy rare-gas tetramers revisited.

A multiscale approach is proposed to address short-time nonadiabatic dynamics and long-time decay. We show the role of both radiative and non-radiative processes in cluster decay mechanisms on examples of rare-gas cluster fragmentation after electron impact ionization. Nonadiabatic molecular dynamics is used as an efficient tool for theoretical study on femto- and picosecond scales and a multiscale approach based on kinetic rates of radiative as well as non-radiative transitions, both considered as parallel reaction channels, is used for the analysis of the long-time system relaxation spanning times over microseconds to infinity. While the radiative processes are typically slow, the system relaxation through non-radiative electronic transitions connected with electron-nuclear interchange of energy may, on the other hand, significantly vary in kinetic rates according to kinetic couplings between relevant adiabatic states. While the predictions of picosecond molecular dynamics themselves fail, the results of the multiscale model for the electron-impact post-ionization fragmentation of krypton and xenon tetramers are in agreement with experiment, namely, in leading to the conclusion that charged monomers prevail. More specifically, on microsecond and longer scales, mainly slow radiative processes are substantial for krypton cluster decay, while for xenon the radiative and slow non-radiative processes compete. In general, the role of slow decay processes through non-radiative transitions is comparable with the role of radiative decay mechanism. The novel multiscale model substantially improves theoretical predictions for the xenon tetramer decay and also further improves the good agreement between theory and experiment we reached previously for krypton.

Photoabsorption spectrum of helium trimer cation--theoretical modeling.

The photoabsorption spectrum of He3(+) is calculated for two semiempirical models of intracluster interactions and compared with available experimental data reported in the middle UV range [H. Haberland and B. von Issendorff, J. Chem. Phys. 102, 8773 (1995)]. Nuclear delocalization effects are investigated via several approaches comprising quantum samplings using either exact or approximate (harmonic) nuclear wavefunctions, as well as classical samplings based on the Monte Carlo methodology. Good agreement with the experiment is achieved for the model by Knowles et al., [Mol. Phys. 85, 243 (1995); Mol. Phys. 87, 827 (1996)] whereas the model by Calvo et al., [J. Chem. Phys. 135, 124308 (2011)] exhibits non-negligible deviations from the experiment. Predictions of far UV absorption spectrum of He3(+), for which no experimental data are presently available, are reported for both models and compared to each other as well as to the photoabsorption spectrum of He2(+). A simple semiempirical point-charge approximation for calculating transition probabilities is shown to perform well for He3(+).

Thermodynamics of water clusters under high pressures. A case study for (H2O)15 and (H2O)15CH4.

Thermal properties and structures of the water cluster containing fifteen molecules, either pure or doped with methane, are studied via classical parallel tempering Monte Carlo calculations in the isothermal-isobaric ensemble. The main emphasis is on structural transformations the cluster undergoes with increasing temperature and pressure. A simple TIP4P interaction model is employed for water and the unified-atom approximation with a Lennard-Jones potential is used to model the methane-water interaction. The results are compared with the data obtained recently for zero temperature via evolutionary algorithm calculations [Hartke, J. Chem. Phys., 2009, 130 art. no. 024905].

On the competition between linear and perpendicular isomers in photodynamics of cationic argon trimers.

Photoabsorption and subsequent photodissociation of two structural isomers of Ar(3) (+) are studied via semiclassical non-adiabatic dynamics simulations. Several experimental observables are simulated under various plausible experimental conditions with the main emphasis on the differences between the data produced for the two isomers. They include photoabsorption cross section, total kinetic energy released, fragments kinetic energy distributions, and distribution of the total kinetic energy among photofragments represented via Dalitz plots. The ability of the parameters to discriminate between the two isomers is analyzed through a thorough comparison with available experimental data. We show that the recently recorded experimental Dalitz plots [V. Lepère, Y. J. Picard, M. Barat, J. A. Fayeton, B. Lucas, and K. Béroff, J. Chem. Phys. 130, 194301 (2009)] correspond to a hot mixture of distorted linear-like and perpendicular-like structures where linear-like structures prevail.

Theoretical modeling of ionization energies of argon clusters: nuclear delocalization effects.

Temperature dependence of vertical ionization energies is modeled for small argon clusters (N ≤ 13) using classical parallel-tempering Monte Carlo methods and extended interaction models based on the diatomics-in-molecules approach. Quantum effects at the zero temperature are also discussed in terms of zero-point nuclear vibrations, either at the harmonic approximation level or at the fully anharmonic level using the diffusion Monte Carlo calculations. Both approaches lead to a considerable improvement of the theoretical predictions of argon clusters ionization energies and represent a realistic way of modeling of ionization energies for weakly bound and floppy complexes in general. A thorough comparison with a recent electron-impact experiment [O. Echt et al., J. Chem. Phys. 123, 084313 (2005)] is presented and a novel interpretation of the experimental data is proposed.

Vibrational spectrum of Ar3(+) and relative importance of linear and perpendicular isomers in its photodissociation.

The photodissociation dynamics of the argon ionized trimer Ar(3)(+) is revisited in the light of recent experimental results of Lepère et al. [J. Chem. Phys. 134, 194301 (2009)], which show that the fragment with little kinetic energy is always a neutral one, thus the available energy is shared by a neutral and ionic fragments as in Ar(2)(+). We show that these results can be interpreted as the photodissociation of the linear isomer of the system. We perform a 3D quantum computation of the vibrational spectrum of the system and study the relative populations of the linear (trimer-core) and perpendicular (dimer-core) isomers. We then show that the charge initially located on the central atom in the ground electronic state of the linear isomer migrates toward the extreme ones in the photoexcitation process such that photodissociation of the linear isomer produces a neutral central atom at rest in agreement with measured product state distributions.

Structural changes in the water tetramer. A combined Monte Carlo and DFT study.

The heat capacity curve of the water tetramer has been calculated at various levels of theory and over a broad range of temperatures, T = 50-200 K. Parallel-tempering and multiple-histogram Monte Carlo methods have been used and combined with the Density Functional Theory calculations of intra-cluster interactions via the Boltzmann-reweighting approach. It is demonstrated that such a combination can yield well converged thermodynamic data even for a modest number of sample configurations, which makes the methodology particularly appropriate for the inclusion of quantum chemistry calculations in Monte Carlo simulations. The B97-1 exchange-correlation functional has been used in the present work together with augmented correlation-consistent basis sets of atomic orbitals up to triple-zeta quality. A structural change has been detected in the water tetramer in the temperature range considered. It is demonstrated that the change corresponds to the onset of rotations of the water molecules around hydrogen bonds with an almost rigid skeleton of the cluster (square cycle) conserved.

Photodissociation dynamics of ionic argon pentamer.

Photodissociation of the ionized argon pentamer, Ar(5)(+), is studied using an extended diatomics-in-molecules interaction model with the inclusion of the spin-orbit coupling and various dynamical approaches. A thorough comparison with the experimental data available in the literature is presented, including photofragment abundances and their kinetic and internal energy distributions. New predictions are reported for ultraviolet photoexcitation energies, a range that has not been studied before either experimentally or theoretically.

Structures and energetics of helium cluster cations: equilibrium geometries revisited through the genetic algorithm approach.

Equilibrium geometries and dissociation energies of He(N)(+) clusters have been calculated for N=3-35 using an extended genetic algorithm approach and a semiempirical model of intracluster interactions [P. J. Knowles, J. N. Murrell, and E. J. Hodge, Mol. Phys. 85, 243 (1995)]. A general aufbau principle is formulated for both ionic cores and neutral solvation shells, and the results are thoroughly compared with other theoretical data available for helium cluster cations in literature.