Near-infrared absorption and radiative cooling of naphthalene dimers (C10H8)2.

The radiative cooling of naphthalene dimer cations, (C10H8)2+ was studied experimentally through action spectroscopy using two different electrostatic ion-beam storage rings, DESIREE in Stockholm and Mini-Ring in Lyon. The spectral characteristics of the charge resonance (CR) band were observed to vary significantly with a storage time of up to 30 seconds in DESIREE. In particular, the position of the CR band shifts to the blue, with specific times (inverse of rates) of 0.64 s and 8.0 s in the 0-5 s and 5-30 s storage time ranges, respectively. These long-time scales indicate that the internal energy distribution of the stored ions evolves by vibrational radiative cooling, which is consistent with the absence of fast radiative cooling via recurrent fluorescence for (C10H8)2+. Density functional based tight binding calculations with local excitations and configuration interactions (DFTB-EXCI) were used to simulate the absorption spectrum for ion temperatures between 10 and 500 K. The evolution of the bandwidth and position with temperature is in qualitative agreement with the experimental findings. Furthermore, these calculations yielded linear temperature dependencies for both the shift and the broadening. Combining the relationship between the CR band position and the ion temperature with the results of the statistical model, we demonstrate that the observed blue shift can be used to determine the radiative cooling rate of (C10H8)2+.

Probing the electronic structure and ground state symmetry of gas phase C60+ via VUV photoionization and comparison with theory.

Recently, some of us reviewed and studied the photoionization dynamics of C60 that are of great interest to the astrochemical community as four of the diffuse interstellar bands (DIBs) have been assigned to electronic transitions in the C60+ cation. Our previous analysis of the threshold photoelectron spectrum (TPES) of C60 [Hrodmarsson et al., Phys. Chem. Chem. Phys. 22, 13880-13892 (2020)] appeared to give indication of D3d ground state symmetry, in contrast to theoretical predictions of D5d symmetry. Here, we revisit our original measurements taking account of a previous theoretical spectrum presented in the work of Manini et al., Phys. Rev. Lett. 91(19), 196402 (2003), obtained within a vibronic model parametrized on density functional theory/local-density approximation electronic structure involving all hg Jahn-Teller active modes, which couple to the 2Hu components of the ground state of the C60+ cation. By reanalyzing our measured TPES of the ground state of the C60 Buckminsterfullerene, we find a striking resemblance to the theoretical spectrum calculated in the work of Manini et al., Phys. Rev. Lett. 91(19), 196402 (2003), and we provide assignments for many of the hg modes. In order to obtain deeper insights into the temperature effects and possible anharmonicity effects, we provide complementary modeling of the photoelectron spectrum via classical molecular dynamics (MD) involving density functional based tight binding (DFTB) computations of the electronic structure for both C60 and C60+. The validity of the DFTB modeling is first checked vs the IR spectra of both species which are well established from IR spectroscopic studies. To aid the interpretation of our measured TPES and the comparisons to the ab initio spectrum we showcase the complementarity of utilizing MD calculations to predict the PES evolution at high temperatures expected in our experiment. The comparison with the theoretical spectrum presented in the work of Manini et al., Phys. Rev. Lett. 91(19), 196402 (2003), furthermore, provides further evidence for a D5d symmetric ground state of the C60+ cation in the gas phase, in complement to IR spectroscopy in frozen noble gas matrices. This not only allows us to assign the first adiabatic ionization transition and thus determine the ionization energy of C60 with greater accuracy than has been achieved at 7.598 ± 0.005 eV, but we also assign the two lowest excited states (2E1u and 2E2u) which are visible in our TPES. Finally, we discuss the energetics of additional DIBs that could be assigned to C60+ in the future.

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.

Electronic effects in the dissociative ionisation of pyrene clusters.

We present a combined experimental and theoretical study on the dissociative ionisation of clusters of pyrene. We measured the experimental appearance energies in the photon energy range 7.2-12.0 eV of the fragments formed from neutral monomer loss for clusters up to the hexamer. The results obtained show a deviation from statistical dissociation. From electronic structure calculations, we suggest that the role of excited states must be considered in the interpretation of experimental results, even in these relatively large systems. Non-statistical effects in the dissociative ionization process of polycyclic aromatic hydrocarbon (PAH) clusters may have an impact on the assessment of mechanisms determining the stability of these clusters in astrophysical environments.

Density-functional tight-binding: basic concepts and applications to molecules and clusters.

The scope of this article is to present an overview of the Density Functional based Tight Binding (DFTB) method and its applications. The paper introduces the basics of DFTB and its standard formulation up to second order. It also addresses methodological developments such as third order expansion, inclusion of non-covalent interactions, schemes to solve the self-interaction error, implementation of long-range short-range separation, treatment of excited states via the time-dependent DFTB scheme, inclusion of DFTB in hybrid high-level/low level schemes (DFT/DFTB or DFTB/MM), fragment decomposition of large systems, large scale potential energy landscape exploration with molecular dynamics in ground or excited states, non-adiabatic dynamics. A number of applications are reviewed, focusing on -(i)- the variety of systems that have been studied such as small molecules, large molecules and biomolecules, bare orfunctionalized clusters, supported or embedded systems, and -(ii)- properties and processes, such as vibrational spectroscopy, collisions, fragmentation, thermodynamics or non-adiabatic dynamics. Finally outlines and perspectives are given.

Threshold collision induced dissociation of pyrene cluster cations.

We report threshold collision induced dissociation experiments on cationic pyrene clusters, for sizes n = 2-6. Fragmentation cross sections are recorded as a function of the collision energy and analyzed with a statistical model. This model can account for the dissociation cascades and provides values for the dissociation energies. These values, of the order of 0.7 eV-1 eV, are in excellent agreement with those previously derived from thermal evaporation. They confirm the charge resonance stability enhancement predicted by theoretical calculations. In addition, remarkable agreement is obtained with theoretical predictions for the two smaller sizes n = 2 and 3. For the larger sizes, the agreement remains good, although the theoretical values obtained for the most stable structures are systematically higher by 0.2 eV. This offset could be attributed to approximations in the calculations. Still, there is an indication in the results of an incomplete description of the role of isomerization and/or direct dissociation upon collisions. Finally, by-product clusters containing dehydrogenated species are found to dissociate at energies comparable to the non-dehydrogenated ones, which shows no evidence for covalent bonds within the clusters.

Theoretical investigation of the electronic relaxation in highly excited chrysene and tetracene: The effect of armchair vs zigzag edge.

Non-adiabatic molecular dynamics of neutral chrysene and tetracene molecules is investigated using Tully's fewest switches surface hopping algorithm coupled to the time-dependent density functional based tight-binding (TD-DFTB) method for electronic structure calculations. We first assess the performance of two DFTB parameter sets based on the computed TD-DFTB absorption spectra. The main focus is given to the analysis of the electronic relaxation from the brightest excited state following absorption of a UV photon. We determine the dynamical relaxation times and discuss the underlying mechanisms. Our results show that the electronic population of the brightest excited singlet state in armchair-edge chrysene decays an order-of-magnitude faster than the one in zigzag-edge tetracene. This is correlated with a qualitatively similar difference of energy gaps between the brightest state and the state lying just below in energy, which is also consistent with our previous study on polyacenes.

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.

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.

Evidencing the relationship between isomer spectra and melting: the 20- and 55-atom silver and gold cluster cases.

The present work highlights the links between melting properties and structural excitation spectra of small gold and silver clusters. The heat capacity curves are computed for Ag20, Au20, Ag55, Au55 and their ions, using a parallel-tempering molecular dynamics scheme to explore the density functional based tight binding (DFTB) potential energy surfaces and the multiple histogram method. It is found that clusters having very symmetric lowest energy structures (Au20, Ag55 and their ions) present sharp or relatively sharp solid-to-liquid transitions and large melting temperatures, important structural excitation energies and a discrete isomer spectrum. Opposite trends are observed for less ordered clusters (Ag20, Au55 and their ions). Regarding the structural evolution with temperature, very symmetric clusters exhibit minor evolution up to the starting melting temperature. The present study also highlights that, in contrast with the case of Au20, a single electron excess or deficiency is not determinant regarding the melting characteristics, even quantitatively, for clusters containing 55 atoms, for gold as for silver.

Non-adiabatic molecular dynamics investigation of the size dependence of the electronic relaxation in polyacenes.

The Tully's fewest switches surface hopping algorithm is implemented within the framework of the time-dependent density functional based tight binding method (TD-DFTB) to simulate the energy relaxation following absorption of a UV photon by polycyclic aromatic hydrocarbons (PAHs). This approach is used to study the size effect on the ultrafast dynamics in excited states for a special class of PAH species called polyacenes. We determine the dynamical relaxation times and discuss the underlying mechanisms. Our results show that there is a striking alternation in decay times of the brightest singlet state for neutral polyacenes with 3 to 6 aromatic cycles. The alternation corresponds to an order-of-magnitude variation between roughly 10 and 100 fs and is correlated with a qualitatively similar alternation of energy gaps between the brightest state and the state lying just below in energy.

Density-functional tight-binding approach for metal clusters, nanoparticles, surfaces and bulk: application to silver and gold.

Density-functional based tight-binding (DFTB) is an efficient quantum mechanical method that can describe a variety of systems, going from organic and inorganic compounds to metallic and hybrid materials. The present topical review addresses the ability and performance of DFTB to investigate energetic, structural, spectroscopic and dynamical properties of gold and silver materials. After a brief overview of the theoretical basis of DFTB, its parametrization and its transferability, we report its past and recent applications to gold and silver systems, including small clusters, nanoparticles, bulk and surfaces, bare and interacting with various organic and inorganic compounds. The range of applications covered by those studies goes from plasmonics and molecular electronics, to energy conversion and surface chemistry. Finally, perspectives of DFTB in the field of gold and silver surfaces and NPs are outlined.

Au147 nanoparticles: Ordered or amorphous?

Structural aspects of the Au147 cluster have been investigated through a density functional based tight binding global optimization involving a parallel tempering molecular dynamics scheme with quenching followed by geometries relaxation at the Density Functional Theory (DFT) level. The focus is put on the competition between relaxed ordered regular geometries and disordered (or amorphous) structures. The present work shows that Au147 amorphous geometries are relevant low energy candidates and are likely to contribute in finite temperature dynamics and thermodynamics. The structure of the amorphous-like isomers is discussed from the anisotropy parameters, the atomic coordinations, the radial and pair distribution functions, the IR spectra, and the vibrational DOS. With respect to the regular structures, the amorphous geometries are shown to be characterized by a larger number of surface atoms, a less dense volume with reduced coordination number per atom, a propensity to increase the dimension of flat facets at the surface, and a stronger anisotropy. Moreover, all amorphous clusters have similar IR spectra, almost continuous with active frequencies over the whole spectral range, while symmetric clusters are characterized by a few lines with large intensities.

Melting of the Au20 Gold Cluster: Does Charge Matter?

We investigate the dependence upon the charge of the heat capacities of magic gold cluster Au20 obtained from density functional-based tight binding theory within parallel tempering molecular dynamics and the multiple histogram method. The melting temperatures, determined from the heat capacity curves, are found to be 1102 K for neutral Au20 and only 866 and 826 K for Au20+ and Au20-. Both the canonical and the microcanonical aspects of the transition are discussed. A convex intruder, associated with a negative heat capacity, is evidenced in the microcanonical entropy in the case of the neutral cluster but is absent in the melting processes of the ions. The present work shows that a single charge quantitatively affects the thermal properties of the gold 20mer.

Molecular Dynamics Study of the Collision-Induced Reaction of H with CO on Small Water Clusters.

The successive hydrogenation of CO is supposed to be the main mechanism leading to the formation of complex oxygenated species in the interstellar medium, possibly mediated by ice layers or ice grains. In order to simulate the dynamical influence of a water environment on the first step of the hydrogenation process, we perform molecular dynamics simulations of the reactive collision of H with CO adsorbed on water clusters in the framework of the self-consistent-charge density functional based tight-binding approach (SCC-DFTB) to calculate potential energy surfaces. The reaction probabilities and the reactive cross sections are determined for water cluster sizes up to ten water molecules. The collision results are analyzed in terms of different reaction pathways: reactive or nonreactive, sticking or desorption of the products or reactants. We show that the HCO radical, although potentially formed as an intermediate regardless of the size of the water cluster, is significantly stabilized for cluster sizes larger than one water molecule and may remain adsorbed on water clusters with more than three molecules. This behavior is shown to be linked with the dissipation of the collision energy into vibrational excitation of the water cluster.

Theoretical investigation of the solid-liquid phase transition in protonated water clusters.

Protonated water clusters have received a lot of attention as they offer tools to bridge the gap between molecular and bulk scales of water. However, their properties are still not fully understood and deserve further theoretical and experimental investigations. In this work, we simulate the caloric curves of protonated water clusters (H2O)nH+ (n = 20-23). These curves, which have recently been measured experimentally, are characteristic of the phase changes occurring in the aggregates with respect to temperature. The present simulations are achieved by combining parallel-tempering molecular dynamics and the self-consistent-charge density-functional based tight-binding approach and are focused on a restricted size range around (H2O)21H+ which presents singular properties. The shape of the experimental caloric curves and their size dependence are satisfactorily reproduced by the simulations which allows us to further provide a description of the phase transition in terms of structural modifications, dynamics of water molecules and proton mobility. Similar to the experiments, we observe that (H2O)21H+ exhibits a sharper phase transition than the neighbouring size clusters, which can be traced back to both structural and dynamic peculiarities.

Structural Characterization of Sulfur-Containing Water Clusters Using a Density-Functional Based Tight-Binding Approach.

A global optimization search of low-energy isomers is carried out to investigate the structural and stability properties of sulfur-containing water clusters, including both (H2O)nSO42- and (H2O)nH2SO4 aggregates. The systematic optimization algorithm involves a combination of parallel-tempering molecular dynamics and periodic gradient-driven quenches with energy and energy-gradient calculations performed using the Self-Consistent-Charge Density-Functional based Tight-Binding (SCC-DFTB) scheme. Comparisons with new MP2 and DFT calculations on the smallest systems and previous ab initio investigations of the literature show that the SCC-DFTB approach provides a fairly accurate description of both neutral and ionic species, comparable to that of DFT. Structural and stability features of larger sulfur-containing clusters, with up to 20 water molecules, are also determined using the SCC-DFTB scheme. The interest of this work is 2-fold: (i) the benchmark on small species demonstrates the ability of SCC-DFTB to describe complex potential energy landscapes involving hydrogen-bonds and proton transfers; (ii) it opens the way to the study of large clusters that can hardly be performed within ab initio approaches.

Benchmarking Density Functional Based Tight-Binding for Silver and Gold Materials: From Small Clusters to Bulk.

We benchmark existing and improved self-consistent-charge density functional based tight-binding (SCC-DFTB) parameters for silver and gold clusters as well as for bulk materials. In the former case, our benchmarks focus on both the structural and energetic properties of small-size AgN and AuN clusters (N from 2 to 13), medium-size clusters with N = 20 and 55, and finally larger nanoparticles with N = 147, 309, and 561. For bulk materials, structural, energetics and elastic properties are discussed. We show that SCC-DFTB is quite satisfactory in reproducing essential differences between silver and gold aggregates, in particular their 2D-3D structural transitions, and their dependency upon cluster charge. SCC-DFTB is also in agreement with DFT and experiments in the medium-size regime regarding the energetic ordering of the different low-energy isomers and allows for an overall satisfactory treatment of bulk properties. A consistent convergence between the cohesive energies of the largest investigated nanoparticles and the bulk's is obtained. On the basis of our results for nanoparticles of increasing size, a two-parameter analytical extrapolation of the cohesive energy is proposed. This formula takes into account the reduction of the cohesive energy for undercoordinated surface sites and converges properly to the bulk cohesive energy. Values for the surface sites cohesive energies are also proposed.

An extended DFTB-CI model for charge-transfer excited states in cationic molecular clusters: model studies versus ab initio calculations in small PAH clusters.

We present an extension of the constrained density functional tight binding scheme combined with configuration interaction (DFTB-CI) to efficiently compute excited states of molecular cluster cations and their oscillator strengths from the ground state. The present extension consists of generalizing the initial model, relying on configurations with holes in the monomer HOMOs only, to configurations involving sub-HOMO holes, allowing for the description of higher excited states. The extended scheme is benchmarked on selected energy pathways with respect to available ab initio and new CASPT2 reference calculations on the benzene, naphthalene and pyrene dimer cations. The ability of the model to describe the potential energy surfaces and the transition dipole moments is discussed. The vertical electronic absorption spectra of the three dimer cations are calculated and compared with the theoretical litterature and available experimental data. Finally, the electronic absorption spectra of low energy isomers of the trimer and tetramer pyrene cluster cations are also predicted.