Stability of the three tetracoordinated dianions NiðCNÞ 2 4 , CrðSCNÞ 2 4 , and CuðN 3 Þ 2 4 Kasper Drenck a , Frank Jensen b, * , Jeppe Olsen b , Steen Brøndsted Nielsen a, * a Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark b Department of Chemistry, University of Aarhus, DK-8000 Aarhus C, Denmark article info Article history: Received 9 July 2008 Accepted 20 August 2008 Available online 23 August 2008 Keywords: Dianions Density functional theory Metal complexes Mass spectrometry abstract Using quantum chemistry calculations, we have explored the physical properties of three tetracoordinate dianions, NiðCNÞ 2 4 , CrðSCNÞ 2 4 , and CuðN 3 Þ 2 4 , and find that the electronic and geometrical stabilities are in qualitative accordance with previous experimental findings. Density functional theory reproduces results for NiðCNÞ 2 4 obtained by more elaborate coupled cluster calculations. At the B3LYP/6-311++G(3d,2p)// B3LYP/6-31+G(d,p) level of theory, the adiabatic electron binding energies are 1.43 eV, 0.11 eV, and 0.16 eV for NiðCNÞ 2 4 , CrðSCNÞ 2 4 , and CuðN 3 Þ 2 4 , respectively, and the reaction energies for loss of a nega- tively charged ligand are 1.43 eV, 0.56 eV, and 1.57 eV. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction Molecular dianions have become a field of intense research, both experimentally and theoretically [1–5]. The Coulomb repul- sion between the two excess charges renders small dianions elec- tronically unstable and/or unstable to dissociation into two singly charged fragments, i.e., Coulomb explosion process. Importantly, the Coulomb repulsion together with the electronic attraction to the nuclei of the molecule results in an internal Coulomb barrier to electron autodetachment, and dianions that are electronically unstable can have a long lifetime with respect to electron tunnel- ling through the barrier [2,6–8]. Dianions are especially interesting systems for quantum chemistry modelling since they present cases for which electron correlation is of utmost importance. An addi- tional complication arises when the electronic state is in the con- tinuum since large basis set dependencies are then expected [9,10]. On the other hand, the repulsive Coulomb barrier traps the electron and therefore limits the spatial extent of the wave- function. It is therefore possible to some extent to describe the proper physics of the shortlived dianion by confining the electron in a space close to the nuclei, not allowing it to explore the space on the other side of the barrier where the potential energy is lower. Methods have, however, been developed to overcome the problem of basis set dependence on the electronic energy of unbound an- ions, e.g., a repulsive Coulomb model [11], a stabilization-based model [12], and a model that is based on a simple correction to Koopman’s theorem [13–15]. Shortlived dianions cannot be studied experimentally in con- ventional mass spectrometers as these require lifetimes of several microseconds. Their existence can in certain cases be indirectly proven from the fragments formed in a Coulomb explosion due to the release of a significant amount of potential energy as trans- lational kinetic energy of the fragments. We have studied the for- mation, dissociation, and electron autodetachment processes of a whole series of dianions over the years [16–23]. Dianions are typ- ically formed by electron capture from sodium or cesium to monoanions travelling with large velocities, limiting the collision interaction time to a few femtoseconds (i.e., vertical electron trans- fer). Kinetic energies of fragment ions are measured with an elec- trostatic analyzer that allows us to identify the formation of a dianion even though it dissociates before detection. Typical kinetic energy release is of the order 2–4 eV [17,21]. Dianions that lose an electron are measured in the electrostatic ion storage ring, ELISA, from a detection of monoanions produced or the actual number of dianions in the ring as a function of time [23]. Storage rings can also be used for electron scattering experiments to identify high-energy states (resonances) [24–26]. One important class of dianions is inorganic metal ion com- plexes that have been subject for detailed investigations [16,17,21,26–49]. In this work we have addressed theoretically three types of complexes that have earlier been studied experi- mentally, NiðCNÞ 2 4 , CrðSCNÞ 2 4 , and AuðN 3 Þ 2 4 [16,17,21,50]. These dianions display differences in their behavior, NiðCNÞ 2 4 seems to be both electronically and geometrically stable, CrðSCNÞ 2 4 Cou- lomb explodes on a microsecond time scale into CrðSCNÞ  3 and SCN  , whereas AuðN 3 Þ 2 4 has a sub-microsecond lifetime with re- spect to Coulomb explosion into AuðN 3 Þ  3 and N  3 since no dianions 0301-0104/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2008.08.008 * Corresponding authors. E-mail addresses: frj@chem.au.dk (F. Jensen), sbn@phys.au.dk (S.B. Nielsen). Chemical Physics 353 (2008) 189–192 Contents lists available at ScienceDirect Chemical Physics journal homepage: www.elsevier.com/locate/chemphys