Addressing electronic and dynamical evolution of molecules and molecular clusters: DFTB simulations of energy relaxation in polycyclic aromatic hydrocarbons

We present a review of the capabilities of the density functional based Tight Binding (DFTB) scheme to address the electronic relaxation and dynamical evolution of molecules and molecular clusters following energy deposition via either collision or photoabsorption. The basics and extensions of DFTB for addressing these systems and in particular their electronic states and their dynamical evolution are reviewed. Applications to PAH molecules and clusters, carbonaceous systems of major interest in astrochemical/astrophysical context, are reported. A variety of processes are examined and discussed such as collisional hydrogenation, fast collisional processes and induced electronic and charge dynamics, collision-induced fragmentation, photo-induced fragmentation, relaxation in high electronic states, electronic-to-vibrational energy conversion and statistical versus non-statistical fragmentation. This review illustrates how simulations may help to unravel different relaxation mechanisms depending on various factors such as the system size, specific electronic structure or excitation conditions, in close connection with experiments.

Influence of the internal degrees of freedom of coronene molecules on the nonlinear dynamics of a columnar chain

The nonlinear dynamics of a one-dimensional molecular crystal in the form of a chain of planar coronene molecules is analyzed. Using molecular dynamics, it is shown that a chain of coronene molecules supports acoustic solitons, rotobreathers, and discrete breathers. An increase in the size of planar molecules in a chain leads to an increase in the number of internal degrees of freedom. This results in an increase in the rate of emission of phonons from spatially localized nonlinear excitations and a decrease in their lifetime. Presented results contribute to the understanding of the effect of the rotational and internal vibrational modes of molecules on the nonlinear dynamics of molecular crystals.

Aggregation of coronene: the effect of carboxyl and amine functional groups

The aggregation of coronene is relevant to understand the formation of carbon nanomaterials, including graphene quantum dots (GQDs) that show exceptional photophysical properties. This article evaluates the influence of carboxyl and amine substituting groups on the aggregation of coronene by performing a global optimization study based on a new potential energy surface. The structures of clusters with substituted coronene are similar to those formed by un-substituted monomers, that is, stacked (non-stacked) motifs are favoured for small-size (large-size) clusters. Nonetheless, the presence of carboxyl and amine groups leads to an increase of the number of local minima of comparable energy. The clusters with substituted monomers have also shown to enhance the attractive component interaction, which can be attributed to weak induction and charge transfer effects and to stronger electrostatic contributions. Moreover, the calculated height of magic-number structures of the clusters in this work is compatible with the morphology of the GQDs reported in the literature.

Dependence upon charge of the vibrational spectra of small Polycyclic Aromatic Hydrocarbon clusters: the example of pyrene

Infrared spectra are computed for neutral and cationic clusters of Polycyclic Aromatic Hydrocarbon clusters, namely( C 16 H 10 ) n = 1 , 4 ( 0 / + ) , using the Density Functional based Tight Binding scheme combined with a Configuration Interaction scheme (DFTB-CI) in the double harmonic approximation. Cross-comparison is carried out with DFT and simple DFTB. Similarly to the monomer cation, the IR spectra of cluster cations are characterized by a depletion of the intensity of the CH stretch modes around 3000 cm-1, with a weak revival for n = 3 and 4. The in-plane CCC modes in the region 1400-2000 cm-1 are enhanced while the CH bending modes in the range 700-1000 cm-1 are significantly weakened with respect to the monomer cation, in particular for n = 2. Finally, soft modes corresponding to diedral fluctuations of the monomers within the central stack of the ion structure, possibly mixed with monomer folding, are also observed in the region 70-120 cm-1.

Continuum Modelling for Interacting Coronene Molecules with a Carbon Nanotube

The production of single dimensional carbon structures has recently been made easier using carbon nanotubes. We consider here encapsulated coronene molecules, which are flat and circular-shaped polycyclic aromatic hydrocarbons, inside carbon nanotubes. Depending on the radius of the nanotube, certain specific configurations of the coronene molecules can be achieved that give rise to the formation of stacked columns or aid in forming nanoribbons. Due to their symmetrical structure, a coronene molecule may be modelled by three inner circular rings of carbon atoms and one outer circular ring of hydrogen atoms, while the carbon nanotube is modelled as a circular tube. Using the continuous model and the Lennard-Jones potential, we are able to analytically formulate an expression for the potential energy for a coronene dimer and coronene inside a carbon nanotube. Subsequently, stacking of coronene molecules inside a nanotube is investigated. We find that the minimum energy tilt angle of coronenes in a stack differs from that of a single coronene within the same nanotube. More specifically, for both (18, 0) and (19, 0) zigzag carbon nanotube, we find that the minimum energy tilt angles of the single coronene case (≈42° and ≈20° respectively) do not occur in the stack model.

Thermal evaporation of pyrene clusters

This work presents a study of the thermal evaporation and stability of pyrene (C16H10)n clusters. Thermal evaporation rates of positively charged mass-selected clusters are measured for sizes in the range n = 3-40 pyrene units. The experimental setup consists of a gas aggregation source, a thermalization chamber, and a time of flight mass spectrometer. A microcanonical Phase Space Theory (PST) simulation is used to determine the dissociation energies of pyrene clusters by fitting the experimental breakdown curves. Calculations using the Density Functional based Tight Binding combined with a Configuration Interaction (CI-DFTB) model and a hierarchical optimization scheme are also performed in the range n = 2-7 to determine the harmonic frequencies and a theoretical estimation of the dissociation energies. The frequencies are used in the calculations of the density of states needed in the PST simulations, assuming an extrapolation scheme for clusters larger than 7 units. Using the PST model with a minimal set of adjustable parameters, we obtain good fits of the experimental breakdown curves over the full studied size range. The approximations inherent to the PST simulation and the influence of the used parameters are carefully estimated. The derived dissociation energies show significant variations over the studied size range. Compared with neutral clusters, significantly higher values of the dissociation energies are obtained for the smaller sizes and attributed to charge resonance in line with CI-DFTB calculations.

Structures and Energetics of Neutral and Cationic Pyrene Clusters

The low energy structures of neutral and cationic pyrene clusters containing up to seven molecules are searched through a global exploration scheme combining parallel tempering Monte Carlo algorithm and local quenches. The potential energies are computed at the density functional based tight binding level for neutrals and configuration interaction density functional based tight binding for cations in order to treat properly the charge resonance. New simplified versions of these schemes are also presented and used during the global exploration. Neutral clusters are shown to be made of compact assemblies of sub-blocs containing up to three units whereas cations present a charged dimer or trimer core surrounded by neutral units. The structural features of the clusters are analyzed and correlated for the cation with the charge distribution. The stability of clusters is also discussed in terms of cohesive and evaporation energies. Adiabatic and vertical ionization potentials are also discussed.

The Structure of Adamantane Clusters: Atomistic vs. Coarse-Grained Predictions From Global Optimization

Candidate structures for the global minima of adamantane clusters, (C₁₀H₁₆)_N, are presented. Based on a rigid model for individual molecules with atom-atom pairwise interactions that include Lennard-Jones and Coulomb contributions, low-energy structures were obtained up to N = 42 using the basin-hopping method. The results indicate that adamantane clusters initially grow accordingly with an icosahedral packing scheme, followed above N = 14 by a structural transition toward face-centered cubic structures. The special stabilities obtained at N = 13, 19, and 38 are consistent with these two structural families, and agree with recent mass spectrometry measurements on cationic adamantane clusters. Coarse-graining the intermolecular potential by averaging over all possible orientations only partially confirm the all-atom results, the magic numbers at 13 and 38 being preserved. However, the details near the structural transition are not captured well, because despite their high symmetry the adamantane molecules are still rather anisotropic.

Sphere Encapsulated Monte Carlo: Obtaining Minimum Energy Configurations of Large Aromatic Systems

We introduce a simple global optimization approach that is able to find minimum energy configurations of clusters containing aromatic molecules. The translational and rotational perturbations required in Monte Carlo-based methods often lead to unrealistic configurations within which two or more molecular rings intersect, causing many of the computational steps to be rejected and the optimization process to be inefficient. Here we develop a modification of the basin-hopping global optimization procedure tailored to tackle problems with intersecting molecular rings. Termed the Sphere Encapsulated Monte Carlo (SEMC) method, this method introduces sphere-based rearrangement and minimization steps at each iteration, and its performance is shown through the exploration of potential energy landscapes of polycyclic aromatic hydrocarbon (PAH) clusters, systems of interest in combustion and astrophysics research. The SEMC method provides clusters that are accurate to 5% mean difference of the minimum energy at a 10-fold speed up compared to previous work using advanced molecular dynamics simulations. Importantly, the SEMC method captures key structural characteristics and molecular size partitioning trends as measured by the molecular radial distances and coordination numbers. The advantages of the SEMC method are further highlighted in its application to previously unstudied heterogeneous PAH clusters.

Aggregation enhancement of coronene molecules by seeding with alkali-metal ions

Microsolvation constitutes the first step in the formation of cluster structures of molecules that surround a solute in the bulk and it allows for a deep insight into the relationship between the structure of the solvation shells and other physical properties. We propose semiempirical potential energy functions that are able to describe the interaction between K+ or Cs+ with coronene. Such functions were calibrated through the comparison with accurate estimations of the interaction between the cation and the planar hydrocarbon, obtained by means of ab initio electronic-structure calculations. By employing the potential energy functions and an evolutionary algorithm (EA), we have investigated the structure and energetics of the clusters resulting from the microsolvation of either K+ or Cs+ with coronene molecules. The reliability of the results for smaller clusters was checked by performing geometry re-optimization exploiting a suitable DFT level of theory. This has allowed for the characterization of the first solvation shells of planar molecules of coronene around an alkali-metal ion. It has also been found that the presence of metal ion impurities considerably enhances the formation of small coronene clusters leading to much stronger binding energies for heterogeneous with respect to homogeneous aggregates. These clusters could represent relevant species involved in the early stages of soot nucleation.

Coarse-grained modeling of the nucleation of polycyclic aromatic hydrocarbons into soot precursors

The aggregation and physical growth of polycyclic aromatic hydrocarbon (PAH) molecules was simulated using a coarse-grained (CG) approach based on the Paramonov-Yaliraki (PY) potential and a stochastic Monte Carlo framework, following earlier efforts in which the structure [Phys. Chem. Chem. Phys., 2016, 18, 13736] and equilibrium thermodynamics [Phys. Chem. Chem. Phys., 2017, 19, 1884] were investigated and critically compared to the predictions of all-atom models. Homomolecular and heteromolecular assemblies of pyrene, coronene, and circumcoronene were considered at various temperatures and compositions, and the distributions of aggregation products were characterized. Under the simulated conditions, and in agreement with earlier studies, the clusters are rather small and, in the case of pyrene-rich systems, only formed below 1000 K. The clusters obtained by spontaneous aggregation of isolated molecules are statistically analysed. For the selected sizes of tetramers and octamers, broad distributions of isomers are obtained with a clear entropic stabilization. In heteronuclear assemblies, our results suggest a minor spontaneous segregation towards pure and equi concentrations at variance with purely statistical expectations.

Coarse-graining strategy for molecular pair interactions: A reaction coordinate study for two- and three-dimensional systems

We investigate and provide optimal sets of reaction coordinates for mixed pairs of molecules displaying polar, uniaxial, or spherical symmetry in two and three dimensions. These coordinates are non-redundant, i.e., they implicitly involve the molecules' symmetries. By tabulating pair interactions in these coordinates, resulting tables are thus minimal in length and require a minimal memory space. The intended fields of application are computer simulations of large ensembles of molecules or colloids with rather complex interactions in a fluid or liquid crystalline phase at low densities. Using effective interactions directly in the form of tables can help bridging the time and length scales without introducing errors stemming from any modeling procedure. Finally, we outline an exemplary computational methodology for gaining an effective pair potential in these coordinates, based on the Boltzmann inversion principle, by providing a step-by-step recipe.

Dynamics and thermodynamics of the coronene octamer described by coarse-grained potentials

Coarse-grained models developed for polycyclic aromatic hydrocarbons based on the Paramonov–Yaliraki potential have been employed to investigate the finite temperature thermodynamics, out-of-equilibrium dynamics, energy landscapes, and rearrangement pathways of the coronene octamer.