Ionization potentials, dissociation energies and statistical fragmentation of neutral and positively charged small carbon clusters

Brazilian Journal of Physics, vol. 36, no. 2B, June, 2006 529 Ionization Potentials, Dissociation Energies and Statistical Fragmentation of Neutral and Positively Charged Small Carbon Clusters S. Dı́az-Tendero1 , G. Sánchez1 , P.-A. Hervieux2 , M. Alcamı́1 , and F. Martı́n1 1 Departamento de Quı́mica, C-9, Universidad Autónoma de Madrid, 28049 Madrid, Spain 2 Institut de Physique et Chimie des Matériaux de Strasbourg, GONLO, 23 rue du Loess, 67034 Strasbourg, France Received on 29 July, 2005 Dissociation energies, ionization potentials and fragmentation dynamics of neutral, singly- and doubly charged small carbon clusters have been theoretically studied with a combination of the density functional theory, the coupled cluster method and the the statistical model microcanonical Metropolis Monte Carlo. The second ionization potential decreases with the cluster size and is larger than the first one, which also decreases with the size showing oscillations. Dissociation energies also oscillate with the cluster size, being those with an odd number of atoms more stable. C3 cluster has the largest dissociation energy. The combination of a statistical treatment for the cluster fragmentation with experimental results has allowed us to evaluate the energy distribution in collisions experiments. Keywords: Carbon clusters; Fragmentation; Dissociation energy and ionization potential I. INTRODUCTION The decay of excited small carbon clusters has been experimentally widely studied [1–19]. In these experiments, the loss of neutral C3 has been found to be the dominant dissociation process for both charged and neutral clusters. Understanding the deexcitation processes observed in clusters collision experiments implies the knowledge of dissociation energies and ionization potentials of the evaporated fragments. The aim of q+ this paper is to provide these values for small Cn carbon clusters (n = 2 − 12 and q = 0 − 2). A large number of theoretical studies focussing on the structural properties of these systems can be found in the literature (see the reviews [20, 21] and references therein), but there is no theoretical work that treats all the clusters at the same level of theory. In order to obtain the energetic properties presented in this work, we have consistently evaluated neutral, singly- and doubly-charged small carbon clusters at the same level of theory. In addition, a statistical treatment of the fragmentation process has been carried out. These simulations have allowed us to have a direct comparison with recent fragmentation experiments [19] and the evaluation of energetic properties as a function of the cluster charge and size. The paper is organized as follows. In section II, we briefly summarize the computational methods employed. Dissociation energies, ionization potentials and fragq+ mentation properties of Cn clusters are presented and discussed in section III. We summarize our results in section IV. statistical weight measures the number of physically accessible states at a fixed energy and is entirely determined by the microscopic properties of the fragments. These properties (geometries, harmonic frequencies, rotational constants and binding energies) have been evaluated with standard quantum chemistry calculations. In particular, we have applied the density functional theory (DFT) with the B3LYP functional for exchange and correlation. This functional combines the Becke’s three parameter nonlocal hybrid exchange potential [23] with the nonlocal correlation functional of Lee, Yang and Parr [24]. The geometries have been optimized by using the 6-311+G(3df) basis set (B3LYP/6-311+G(3df)). The B3LYP functional has been proved to be a good choice for the description of carbon clusters [25]. In the case of small carbon clusters, the calculated geometries and the vibrational frequencies are very close to those obtained at higher levels of calculations [26–28]. More accurate values of electronic and binding energies have been obtained with the coupled cluster theory CCSD(T)/6-311+G(3df), which includes all single and double excitations, as well as triple excitations in a perturbative way [29], and made use of the B3LYP optimized geometry. The electronic energies obtained at this level of theory have been corrected with the zero point energy (ZPE) obtained from DFT vibrational analysis. All structure calculations have been performed with the Gaussian-98 program package [30]. III. RESULTS II. COMPUTATIONAL DETAILS The statistical fragmentation has been carried out with the microcanonical Metropolis Monte Carlo (MMMC) method as described in reference [22]. In this method, one moves in phase space until a region with maximum statistical weight is found. A physical observable is then evaluated as a statistical average in this region of maximum probability. The We have evaluated several properties of carbon clusters with linear and cyclic geometries and with different spin multiplicities (singlet and triplet for the neutral and doubly charged species and doublet and quadruplet for the singly charged ones) [28]. To introduce all the isomers in the MMMC simulations has been shown to be crucial to correctly describe the fragmentation process [19, 22]. Dissociation energies and ionization potentials have been calculated taking Brazilian Journal of Physics, vol. 36, no. 2B, June, 2006 530 8 27 Dissociation Energy (eV) 24 21 18 15 st 1 IP 7 6 Cn→ Cn-1 + C 5 Cn→ Cn-5 + C5 Cn→ Cn-3 + C3 4 2 9 4 6 8 10 12 Cluster size, n 6 8 10 12 (a) + + 8 n C →Cn-5 + C5 + + + Cn →Cn-3 + C3 Cn →Cn-1 + C 4 6 + + 2 + Cn →Cn-1 + C + + + + 4 + 6 Cn →Cn-4 + C4 7 8 10 Cluster size, n We first present the results obtained for the adiabatic ionization potentials. Fig. 1 shows the first and second ionization potentials as a function of the cluster size evaluated at both B3LYP and CCSD(T) levels of theory. Differences between both methods in the first ionization potentials are never larger than 0.5 eV. Although for the second ionization potentials the differences are larger, they never exceed 1 eV. As a general trend, first IP slowly decreases with cluster size, but this decrease is not monotonic and present some oscillations. The first ionization potencial has been measured by different authors [31–39] and theoretically calculated by Giuffreda et al. [40]. We have also included in Fig. 1 the available experimental data. Our results agree reasonably well with the experimental measurements and those reported in ref. [40]. Second IP decreases with cluster size showing a stabilization for n = 8 − 10. The observed behavior is quite predictable: the second IP is larger than the first IP and the difference between them is larger the smaller the system due to the ability of the larger cluster to accommodate multiple charges. Except for atomic C, we are not aware of any experimental determination of the second ionization potential to compare with. Cn →Cn-2 (...truncated)