Unraveling the Metastability of Cn2+ (n = 2–4) Clusters

Pure carbon clusters have received considerable attention for a long time. However, fundamental questions, such as what the smallest stable carbon cluster dication is, remain unclear. We investigated the stability and fragmentation behavior of Cn2+ (n = 2–4) dications using state-of-the-art atom probe tomography. These small doubly charged carbon cluster ions were produced by laser-pulsed field evaporation from a tungsten carbide field emitter. Correlation analysis of the fragments detected in coincidence reveals that they only decay to Cn–1+ + C+. During C22+ → C+ + C+, significant kinetic energy release (∼5.75–7.8 eV) is evidenced. Through advanced experimental data processing combined with ab initio calculations and simulations, we show that the field-evaporated diatomic 12C22+ dications are either in weakly bound 3Πu and 3Σg– states, quickly dissociating under the intense electric field, or in a deeply bound electronic 5Σu– state with lifetimes >180 ps.


Mathematical model of the fragmentation track
For the fragmentation process AB i+j+ → A i+ + B j+ sketched in Figure 1, in case it takes place at the potential , after a potential drop − = d (U is the potential of the field emitter's surface), the velocity of the fragment A i+ should be Ad ⃗⃗⃗⃗⃗⃗ = ABd ⃗⃗⃗⃗⃗⃗⃗⃗ + A ⃗⃗⃗⃗⃗⃗ , where ABd ⃗⃗⃗⃗⃗⃗⃗⃗ is the velocity of the parent cluster ion AB i+j+ at the instant of fragmentation, and A ⃗⃗⃗⃗⃗⃗ is the velocity resulting from the kinetic energy release (KER). The KER is usually of the order of a few electron volts, 1 much smaller than Ud, which means that A is much smaller than ABd . Therefore, Here, is the fragmentation angle for the fragment A i+ , i.e. the angle between the Coulomb force Fci and the local electric field. For the fragment B j+ , the fragmentation angle is = − . Assuming the repulsion between the fragments is only active during a very short period after fragmentation, then the velocity of the fragment A i+ on the detector 0 can be calculated based from the conservation of energy along the trajectory between the fragmentation point and the detector: Using the approximation of the instantaneous acceleration suggested by Saxey, 2 the measured mass-to-charge ratio of the fragment A i+ can be expressed as is the ratio of the KER A provided to the fragment A i+ over the potential energy that this fragment would have accumulated on a complete flight from the emitter's surface to the detector. A similar equation can also be obtained for fragment B j+ .
When A is very small and can be neglected, or the cluster axis is perpendicular to the electric field, i.e. = 2 , Equation S1 can be rewritten as which is just the formula given by Saxey. 2

Ab initio calculation
For C2 2+ , the potential energy curves (PEC) of the 1 3 u -, 1 3 u and 1 5 gwere calculated at the multi-reference configuration interaction (MRCI) level, following the calculation performed by Hogreve. 3 All calculations were done with the MOLCAS quantum chemistry software 4 in the C2v symmetry group with ANO-RCC_VQZP basis set. 5 The scalar relativistic effects were taken into account by means of the Douglas-Kroll Hamiltonian. 5 To obtain the PEC for each symmetry, we have performed a state-average restricted active space self-consistent field (SA-RASSCF) calculation over a large number of states (typically 50 states).
The configurations in the active spaces were obtained by keeping the innermost 1s orbitals inactive with 4 electrons, while the 2s and 2p orbitals were considered active with 6 electrons distributed among them. The configurations were restricted to those with at most two holes in the 2s orbitals.
This SA-RASSCF calculation provides us with a set of molecular orbitals.
The generated orbitals were then used to compute the PEC by means of a MRCI calculation. In The lifetimes obtained from our calculation are given in table ST1 for the five lowest vibrational states of the 1 5 ustate PEC and for the lowest rotational number. Since the lifetimes are shorter for the projection of total angular momentum = 2, we simply used this lifetime in our simulation. 8