Revisiting Numerical Solutions of Weakly Bound Noble Gases' Vibrational Energy Levels Modeled by the Improved Lennard-Jones Potential

We revisit the numerical solutions of vibrational eigenstates of weakly bound homonuclear and heteronuclear noble gas pairs by applying a Fortran program based on the Numerov method. The harmonic, Lennard-Jones (LJ), Morse, Tang-Toennies (TT), and Improved Lennard-Jones (ILJ) potential models have been implemented to represent the potential energy curves (PECs). The obtained vibrational energies spectrum was tested on the experimental data and accurate ab initio calculations at CCSD(T)/CBS level. The vibrational eigenvalues and eigenfunctions can be reproduced accurately within the ILJ potential model. Moreover, considering the calculated lifetime of van der Waals (vdW) complexes, the implementation of ILJ rather than standard LJ potential model has a significant impact on the systems dynamics by providing more representative atomic trajectories when the function is incorporated in force fields for molecular dynamics (MD) simulations. Overall, the ILJ function is the best suited potential model for the representation of vibrational motions and the determination of vibrational energy levels of weakly bound systems, both at equilibrium and non-equilibrium conditions.

Vibrational energy relaxation in shock-heated CO/N2/Ar mixtures

Experimental and numerical studies were performed on the vibrational energy relaxation in shock-heated CO/N2/Ar mixtures. A laser absorption technique was applied to the time-dependent rovibrational temperature time-history measurements. The vibrational relaxation data of reflected-shock-heated CO were summarized at 1720-3230 K. In shock-tube experiments, the rotational temperature of CO quickly reached equilibrium, whereas a relaxation process was found in the time-dependent vibrational temperature. For the mixture with 1.0% CO and 10.0% N2, the vibrational excitation caused a decrease in the macroscopic thermodynamic temperature of the test gas. In the simulations, the state-to-state (StS) approach was employed, where the vibrational energy levels of CO and N2 are treated as pseudo-species. The vibrational state-specific inelastic rate coefficients of N2-Ar collisions were calculated using the mixed quantum-classical method based on a newly developed three-dimensional potential energy surface. The StS predictions agreed well with the measurements, whereas deviations were found between the Schwartz-Slawsky-Herzfeld formula predictions and the measurements. The Millikan-White vibrational relaxation data of the N2-Ar system were found to have the most significant impact on the model predictions via sensitivity analysis. The vibrational relaxation data of the N2-Ar system were then modified according to the experimental data and StS results, providing an indirect way to optimize the vibrational relaxation data of a specific system. Moreover, the vibrational distribution functions of CO and N2 and the effects of the vibration-vibration-translation energy transfer path on the thermal nonequilibrium behaviors were highlighted.

Trihydrogen Cation Helium Clusters: A New Potential Energy Surface

We present a new analytical potential energy surface (PES) for the interaction between the trihydrogen cation and a He atom,H 3 + - H e ${{H}_{3}^{+}-He}$ , in its electronic ground state. The proposed PES has been built as a sum of two contributions: a polarization energy term due to the electric field generated by the molecular cation at the position of the polarizable He atom, and an exchange-repulsion and dispersion interactions represented by a sum of "atom-bond" potentials between the three bonds ofH 3 + ${{H}_{3}^{+}}$ and the He atom. All parameters of this new PES have been chosen and fitted from data obtained from high-level ab-initio calculations. Using this new PES plus the Aziz-Slaman potential for the interaction between Helium atoms and assuming pair-wise interactions, we carry out classical Basin-Hopping (BH) global optimization, semiclassical BH with Zero Point Energy corrections, and quantum Diffusion Monte Carlo simulations. We have found the minimum energy configurations of small He clusters doped withH 3 + ${{H}_{3}^{+}}$ ,H 3 + H e N ${{H}_{3}^{+}{\left(He\right)}_{N}}$ , with N=1-16. The study of the energies of these clusters allows us to find a pronounced anomaly for N=12, in perfect agreement with previous experimental findings, which we relate to a greater relative stability of this aggregate.

Helium nanodroplets as an efficient tool to investigate hydrogen attachment to alkali cations

We report a novel method to reversibly attach and detach hydrogen molecules to positively charged sodium clusters formed inside a helium nanodroplet host matrix. It is based on the controlled production of multiply charged helium droplets which, after picking up sodium atoms and exposure to H2 vapor, lead to the formation of Nam+(H2)n clusters, whose population was accurately measured using a time-of-flight mass spectrometer. The mass spectra reveal particularly favorable Na+(H2)n and Na2+(H2)n clusters for specific "magic" numbers of attached hydrogen molecules. The energies and structures of these clusters have been investigated by means of quantum-mechanical calculations employing analytical interaction potentials based on ab initio electronic structure calculations. A good agreement is found between the experimental and the theoretical magic numbers.

Semiempirical Potential in Kinetics Calculations on the HC3N + CN Reaction

The reaction between the cyano radical CN and cyanoacetylene molecule HC3N is of great interest in different astronomical fields, from star-forming regions to planetary atmospheres. In this work, we present a new synergistic theoretical approach for the derivation of the rate coefficient for gas phase neutral-neutral reactions. Statistic RRKM calculations on the Potential Energy Surface are coupled with a semiempirical analysis of the initial bimolecular interaction. The value of the rate coefficient for the HC3N + CN → H + NCCCCN reaction obtained with this method is compared with previous theoretical and experimental investigations, showing strengths and weaknesses of the new presented approach.

Vibrational Energy Transfer in CO+N2 Collisions: A Database for V-V and V-T/R Quantum-Classical Rate Coefficients

Knowledge of energy exchange rate constants in inelastic collisions is critically required for accurate characterization and simulation of several processes in gaseous environments, including planetary atmospheres, plasma, combustion, etc. Determination of these rate constants requires accurate potential energy surfaces (PESs) that describe in detail the full interaction region space and the use of collision dynamics methods capable of including the most relevant quantum effects. In this work, we produce an extensive collection of vibration-to-vibration (V-V) and vibration-to-translation/rotation (V-T/R) energy transfer rate coefficients for collisions between CO and N2 molecules using a mixed quantum-classical method and a recently introduced (A. Lombardi, F. Pirani, M. Bartolomei, C. Coletti, and A. Laganà, Frontiers in chemistry, 7, 309 (2019)) analytical PES, critically revised to improve its performance against ab initio and experimental data of different sources. The present database gives a good agreement with available experimental values of V-V rate coefficients and covers an unprecedented number of transitions and a wide range of temperatures. Furthermore, this is the first database of V-T/R rate coefficients for the title collisions. These processes are shown to often be the most probable ones at high temperatures and/or for highly excited molecules, such conditions being relevant in the modeling of hypersonic flows, plasma, and aerospace applications.

Energy exchange rate coefficients from vibrational inelastic O2(Σg-3) + O2(Σg-3) collisions on a new spin-averaged potential energy surface

A new spin-averaged potential energy surface (PES) for non-reactive O₂(Σg-3) + O₂(Σg-3) collisions is presented. The potential is formulated analytically according to the nature of the principal interaction components, with the main van der Waals contribution described through the improved Lennard-Jones model. All the parameters involved in the formulation, having a physical meaning, have been modulated in restricted variation ranges, exploiting a combined analysis of experimental and ab initio reference data. The new PES is shown to be able to reproduce a wealth of different physical properties, ranging from the second virial coefficients to transport properties (shear viscosity and thermal conductivity) and rate coefficients for inelastic scattering collisions. Rate coefficients for the vibrational inelastic processes of O₂, including both vibration-to-vibration (V-V) and vibration-to-translation/rotation (V-T/R) energy exchanges, were then calculated on this PES using a mixed quantum-classical method. The effective formulation of the potential and its combination with an efficient, yet accurate, nuclear dynamics treatment allowed for the determination of a large database of V-V and V-T/R energy transfer rate coefficients in a wide temperature range.

Spherical harmonics representation of the potential energy surface for the H2⋯H2 van der Waals complex

We perform a study of the molecular anisotropy for the H₂⋯H₂ van der Waals system using a spherical harmonics expansion. We use six leading stable configurations to construct our analytical potential energy surface (PES) from ab initio calculations guided qualitatively by the symmetry-adapted perturbation theory (SAPT) analyses. We extrapolate the energies of the PES performed at the CCSD(T)/aug-cc-pVnZ (n = 2 and 3) levels to the complete basis set (CBS) limit. To best fit the shallow potential energy surface of each leading configuration with the intermolecular distance, it was employed an extended version of the Rydberg potential. To assess the quality of our extrapolated analytical PES, we calculate the second virial coefficients, which are in relatively good agreement with the experimental data. As a result, the spherical harmonics coefficients obtained might be of considerable relevance in spectroscopy and dynamics applications.

Inelastic rate coefficients based on an improved potential energy surface for N2 + N2 collisions in a wide temperature range

Vibration-to-translation and vibration-to-vibration rate coefficients for N₂–N₂ inelastic scattering are calculated on an improved potential including high temperature regimes.

Complexes of Alkali Metal Cations and Molecular Hydrogen: Potential Energy Surfaces and Bound States

Complexes between metal cations and molecular hydrogen are systems quite amenable for precise spectroscopic and theoretical studies, and at the same time, they are relevant for applications in hydrogen storage and astrochemistry. In this work, we report new intermolecular potential energy surfaces and rovibrational states calculations for complexes involving molecular hydrogen and alkaline metal cations, M⁺-H₂ (M⁺ = Na⁺, K⁺, Rb⁺, Cs⁺). The intermolecular potentials, formulated in an internally consistent way to emphasize differences in the properties of the systems, are represented by simple analytical expressions whose parameters have been optimized from comparison with accurate ab initio calculations. Properties of the low-lying bound states-binding energies, frequencies, and rotational constants-are compared with previous measurements or computations and an overall good agreement is achieved, supporting the reliability of the present formulation. Variations of these properties as a function of the cation size and isotopic substitution, with a proper sequence of ortho and para rotational levels, are also discussed.

Full Dimensional Potential Energy Function and Calculation of State-Specific Properties of the CO+N2 Inelastic Processes Within an Open Molecular Science Cloud Perspective

A full dimensional Potential Energy Surface (PES) of the CO + N₂ system has been generated by extending an approach already reported in the literature and applied to N₂-N₂ (Cappelletti et al., 2008), CO₂-CO₂ (Bartolomei et al., 2012), and CO₂-N₂ (Lombardi et al., 2016b) systems. The generation procedure leverages at the same time experimental measurements and high-level ab initio electronic structure calculations. The procedure adopts an analytic formulation of the PES accounting for the dependence of the electrostatic and non-electrostatic components of the intermolecular interaction on the deformation of the monomers. In particular, the CO and N₂ molecular multipole moments and electronic polarizabilities, the basic physical properties controlling the behavior at intermediate and long-range distances of the interaction components, were made to depend on relevant internal coordinates. The formulated PES exhibits substantial advantages when used for structural and dynamical calculations. This makes it also well suited for reuse in Open Molecular Science Cloud services.

Closer versus Long Range Interaction Effects on the Non-Arrhenius Behavior of Quasi-Resonant O2 + N2 Collisions

We report in this paper an investigation on energy transfer processes from vibration to vibration and/or translation in thermal and subthermal regimes for the O₂ + N₂ system performed using quantum-classical calculations on different empirical, semiempirical, and ab initio potential energy surfaces. In particular, the paper focuses on the rationalization of the non-Arrhenius behavior (inversion of the temperature dependence) of the quasi-resonant vibration-to-vibration energy transfer transition rate coefficients at threshold. To better understand the microscopic nature of the involved processes, we pushed the calculations to the detail of the related cross sections and analyzed the impact of the medium and long-range components of the interaction on them. Furthermore, the variation with temperature of the dependence of the quasi-resonant rate coefficient on the vibrational energy gap between initial and final vibrational states and the effectiveness of quantum-classical calculations to overcome the limitations of the purely classical treatments were also investigated. These treatments, handled in an open molecular science fashion by chaining data and competencies of the various laboratories using a grid empowered molecular simulator, have allowed a rationalization of the dependence of the computed rate coefficients in terms of the distortion of the O₂-N₂ configuration during the diatom-diatom collisions. A way of relating such distortions to a smooth and continuous progress variable, allowing a proper evolution from both long to closer range formulation of the interaction and from its entrance to exit channel (through the strong interaction region) relaxed graphical representations, is also discussed in the paper.

Enhanced Flexibility of the O2 + N2 Interaction and Its Effect on Collisional Vibrational Energy Exchange

Prompted by a comparison of measured and computed rate coefficients of Vibration-to-Vibration and Vibration-to-Translation energy transfer in O2 + N2 non-reactive collisions, extended semiclassical calculations of the related cross sections were performed to rationalize the role played by attractive and repulsive components of the interaction on two different potential energy surfaces. By exploiting the distributed concurrent scheme of the Grid Empowered Molecular Simulator we extended the computational work to quasiclassical techniques, investigated in this way more in detail the underlying microscopic mechanisms, singled out the interaction components facilitating the energy transfer, improved the formulation of the potential, and performed additional calculations that confirmed the effectiveness of the improvement introduced.

Energy transfer dynamics and kinetics of elementary processes (promoted) by gas-phase CO2 -N2 collisions: Selectivity control by the anisotropy of the interaction

In this work, we exploit a new formulation of the potential energy and of the related computational procedures, which embodies the coupling between the intra and intermolecular components, to characterize possible propensities of the collision dynamics in energy transfer processes of interest for simulation and control of phenomena occurring in a variety of equilibrium and nonequilibrium environments. The investigation reported in the paper focuses on the prototype CO2 -N2 system, whose intramolecular component of the interaction is modeled in terms of a many body expansion while the intermolecular component is modeled in terms of a recently developed bonds-as-interacting-molecular-centers' approach. The main advantage of this formulation of the potential energy surface is that of being (a) truly full dimensional (i.e., all the variations of the coordinates associated with the molecular vibrations and rotations on the geometrical and electronic structure of the monomers, are explicitly taken into account without freezing any bonds or angles), (b) more flexible than other usual formulations of the interaction and (c) well suited for fitting procedures better adhering to accurate ab initio data and sensitive to experimental arrangement dependent information. Specific attention has been given to the fact that a variation of vibrational and rotational energy has a higher (both qualitative and quantitative) impact on the energy transfer when a more accurate formulation of the intermolecular interaction (with respect to that obtained when using rigid monomers) is adopted. This makes the potential energy surface better suited for the kinetic modeling of gaseous mixtures in plasma, combustion and atmospheric chemistry computational applications. © 2016 Wiley Periodicals, Inc.

Interaction of O2 with CH4, CF4, and CCl4 by Molecular Beam Scattering Experiments and Theoretical Calculations

Gas phase collisions of O2 by CH4, CF4, and CCl4 have been investigated with the molecular beam technique by measuring both the integral cross section value, Q, and its dependence on the collision velocity, v. The adopted experimental conditions have been appropriate to resolve the oscillating "glory" pattern, a quantum interference effect controlled by the features of the intermolecular interaction, for all the three case studies. The analysis of the Q(v) data, performed by adopting a suitable representation of the intermolecular potential function, provided the basic features of the anisotropic potential energy surfaces at intermediate and large separation distances and information on the relative role of the physically relevant types of contributions to the global interaction. The present work demonstrates that while O2-CH4 and O2-CF4 are basically bound through the balance between size (Pauli) repulsion and dispersion attraction, an appreaciable intermolecular bond stabilization by charge transfer is operative in O2-CCl4. Ab initio calculations of the strength of the interaction, coupled with detailed analysis of electronic charge displacement promoted by the formation of the dimer, fully rationalizes the experimental findings. This investigation indicates that the interactions of O2, when averaged over its relative orientations, are similar to that of a noble gas (Ng), specifically Ar. We also show that the binding energy in the basic configurations of the prototypical Ng-CF4,CCl4 systems [ Cappelletti , D. ; Chem. Eur. J. 2015 , 21 , 6234 - 6240 ] can be reconstructed by using the interactions in Ng-F and Ng-Cl systems, previously characterized by molecular beam scattering experiments of state-selected halogen atom beams. This information is fundamental to approach the modeling of the weak intermolecular halogen bond. On the basis of the electronic polarizability, this also confirms [ Aquilanti , V. ; Angew. Chem., Int. Ed. 2005 , 44 , 2356 - 2360 ] that O2 can be taken as a proper reference partner for simulating the behavior of some basic noncovalent components of the interactions involving water. Present results are of fundamental relevance to build up the force field controlling the hydrophobic behavior of prototypical apolar CX4 (X = H, F, Cl) molecules.

Efficiency of Collisional O2 + N2 Vibrational Energy Exchange

By following the scheme of the Grid Empowered Molecular Simulator (GEMS), a new O2 + N2 intermolecular potential, built on ab initio calculations and experimental (scattering and second virial coefficient) data, has been coupled with an appropriate intramolecular one. On the resulting potential energy surface detailed rate coefficients for collision induced vibrational energy exchanges have been computed using a semiclassical method. A cross comparison of the computed rate coefficients with the outcomes of previous semiclassical calculations and kinetic experiments has provided a foundation for characterizing the main features of the vibrational energy transfer processes of the title system as well as a critical reading of the trajectory outcomes and kinetic data. On the implemented procedures massive trajectory runs for the proper interval of initial conditions have singled out structures of the vibrational distributions useful to formulate scaling relationships for complex molecular simulations.

Energy transfer upon collision of selectively excited CO2 molecules: State-to-state cross sections and probabilities for modeling of atmospheres and gaseous flows

Carbon dioxide molecules can store and release tens of kcal/mol upon collisions, and such an energy transfer strongly influences the energy disposal and the chemical processes in gases under the extreme conditions typical of plasmas and hypersonic flows. Moreover, the energy transfer involving CO2 characterizes the global dynamics of the Earth-atmosphere system and the energy balance of other planetary atmospheres. Contemporary developments in kinetic modeling of gaseous mixtures are connected to progress in the description of the energy transfer, and, in particular, the attempts to include non-equilibrium effects require to consider state-specific energy exchanges. A systematic study of the state-to-state vibrational energy transfer in CO2 + CO2 collisions is the focus of the present work, aided by a theoretical and computational tool based on quasiclassical trajectory simulations and an accurate full-dimension model of the intermolecular interactions. In this model, the accuracy of the description of the intermolecular forces (that determine the probability of energy transfer in molecular collisions) is enhanced by explicit account of the specific effects of the distortion of the CO2 structure due to vibrations. Results show that these effects are important for the energy transfer probabilities. Moreover, the role of rotational and vibrational degrees of freedom is found to be dominant in the energy exchange, while the average contribution of translations, under the temperature and energy conditions considered, is negligible. Remarkable is the fact that the intramolecular energy transfer only involves stretching and bending, unless one of the colliding molecules has an initial symmetric stretching quantum number greater than a threshold value estimated to be equal to 7.

Line mixing effects in isotropic Raman spectra of pure N2: a classical trajectory study

Line mixing effects in the Q branch of pure N2 isotropic Raman scattering are studied at room temperature using a classical trajectory method. It is the first study using an extended modified version of Gordon's classical theory of impact broadening and shift of rovibrational lines. The whole relaxation matrix is calculated using an exact 3D classical trajectory method for binary collisions of rigid N2 molecules employing the most up-to-date intermolecular potential energy surface (PES). A simple symmetrizing procedure is employed to improve off-diagonal cross-sections to make them obeying exactly the principle of detailed balance. The adequacy of the results is confirmed by the sum rule. The comparison is made with available experimental data as well as with benchmark fully quantum close coupling [F. Thibault, C. Boulet, and Q. Ma, J. Chem. Phys. 140, 044303 (2014)] and refined semi-classical Robert-Bonamy [C. Boulet, Q. Ma, and F. Thibault, J. Chem. Phys. 140, 084310 (2014)] results. All calculations (classical, quantum, and semi-classical) were made using the same PES. The agreement between classical and quantum relaxation matrices is excellent, opening the way to the analysis of more complex molecular systems.

Line interference effects using a refined Robert-Bonamy formalism: the test case of the isotropic Raman spectra of autoperturbed N2

A symmetrized version of the recently developed refined Robert-Bonamy formalism [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] is proposed. This model takes into account line coupling effects and hence allows the calculation of the off-diagonal elements of the relaxation matrix, without neglecting the rotational structure of the perturbing molecule. The formalism is applied to the isotropic Raman spectra of autoperturbed N2 for which a benchmark quantum relaxation matrix has recently been proposed. The consequences of the classical path approximation are carefully analyzed. Methods correcting for effects of inelasticity are considered. While in the right direction, these corrections appear to be too crude to provide off diagonal elements which would yield, via the sum rule, diagonal elements in good agreement with the quantum results. In order to overcome this difficulty, a re-normalization procedure is applied, which ensures that the off-diagonal elements do lead to the exact quantum diagonal elements. The agreement between the (re-normalized) semi-classical and quantum relaxation matrices is excellent, at least for the Raman spectra of N2, opening the way to the analysis of more complex molecular systems.

Line coupling effects in the isotropic Raman spectra of N2: a quantum calculation at room temperature

We present quantum calculations of the relaxation matrix for the Q branch of N2 at room temperature using a recently proposed N2-N2 rigid rotor potential. Close coupling calculations were complemented by coupled states studies at high energies and provide about 10,200 two-body state-to state cross sections from which the needed one-body cross-sections may be obtained. For such temperatures, convergence has to be thoroughly analyzed since such conditions are close to the limit of current computational feasibility. This has been done using complementary calculations based on the energy corrected sudden formalism. Agreement of these quantum predictions with experimental data is good, but the main goal of this work is to provide a benchmark relaxation matrix for testing more approximate methods which remain of a great utility for complex molecular systems at room (and higher) temperatures.

Refinement of the Robert-Bonamy formalism: considering effects from the line coupling

Since it was developed in 1979, the Robert-Bonamy (RB) formalism has been widely used in calculating pressure broadened half-widths and induced shifts for many molecular systems. However, this formalism contains several approximations whose applicability has not been thoroughly justified. One of them is that lines of interest are well isolated. When these authors developed the formalism, they have relied on this assumption twice. First, in calculating the spectral density F(ω), they have only considered the diagonal matrix elements of the relaxation operator. Due to this simplification, effects from the line mixing are ignored. Second, when they applied the linked cluster theorem to remove the cutoff, they have assumed the matrix elements of the operator exp(-iS1 - S2) can be replaced by the exponential of the matrix elements of -iS1 - S2. With this replacement, effects from the line coupling are also ignored. Although both these two simplifications relied on the same approximation, their validity criteria are completely different and the latter is more stringent than the former. As a result, in many cases where the line mixing becomes negligible, significant effects from the line coupling have been completely missed. In the present study, we have developed a new method to evaluate the matrix elements of exp(-iS1 - S2) and have refined the RB formalism such that line coupling can be taken into account. Our numerical calculations of the half-widths for Raman Q lines of the N2-N2 pair have demonstrated that effects from the line coupling are important. In comparison with values derived from the RB formalism, new calculated values for these lines are significantly reduced. A recent study has shown that in comparison with the measurements and the most accurate close coupling calculations, the RB formalism overestimates the half-widths by a large amount. As a result, the refinement of the RB formalism goes in the right direction and these new calculated half-widths become closer to the "true" values.

Coping with the anisotropy in the analytical representation of an ab initio potential energy surface for the Cl2 dimer

The intermolecular potential energy surface (PES) of the Cl2 dimer is calculated at the MP2/aTZ + b level of ab initio theory. A quantitative measure is proposed for comparison of the anisotropy of PESs of different systems at different intermolecular distances. A high degree of anisotropy at short and intermediate distances results in the failure of fitting strategies that are based on the angular expansion of the potential energy. To tackle this problem, a step-by-step fitting strategy is designed for analytical representation of the PES. The global minimum energy configuration of the dimer is found to be a distorted L-shape structure with a well depth of around 615 cm(-1). The PES is finally scaled to minimize deviations between calculated and experimental second virial coefficients.

Beyond the Lennard-Jones model: a simple and accurate potential function probed by high resolution scattering data useful for molecular dynamics simulations

Scattering data, measured for rare gas-rare gas systems under high angular and energy resolution conditions, have been used to probe the reliability of a recently proposed interaction potential function, which involves only one additional parameter with respect to the venerable Lennard-Jones (LJ) model and is hence called Improved Lennard-Jones (ILJ). The ILJ potential eliminates most of the inadequacies at short- and long-range of the LJ model. Further reliability tests have been performed by comparing calculated vibrational spacings with experimental values and calculated interaction energies at short-range with those obtained from the inversion of gaseous transport properties. The analysis, extended also to systems involving ions, suggests that the ILJ potential model can be used to estimate the behavior of unknown systems and can help to assess the different role of the leading interaction components. Moreover, due to its simple formulation, the physically reliable ILJ model appears to be particularly useful for molecular dynamics simulations of both neutral and ionic systems.