Metallic clusters basis states

In practice, however, already with a comparatively small number of metal atoms it is no longer feasible to investigate all possible spin states with all potential realizations by various local spin distributions. Assumptions on the interaction of the metal centers on the basis of their structural arrangement and experimental susceptibility measurements have to be made. For example, for the BS state of a tetranuclear transition-metal cluster, one has to decide which of the four metal atoms couple in an antiferromagnetic fashion with each other. Prominent coupling schemes are, e.g., the dimer-of-dimers 2-plus-2-type or the 3-plus-... 

The idea of fractional occupation numbers was introduced by Slater [71], already in 1969. This approach is not limited for the JT systems, e.g. it was explored by Dunlap and Mei [32] for molecules, by Filatov and Shaik [36] for diradicals, and is also used for calculations of solids and metal clusters [8], It rests on a Arm basis in cases when the ground state density has to be represented by a weighted sum of single determinant densities [53,79], One should remember that molecular orbitals (MO) themselves have no special meaning. Thus, using partial occupation is just a way of obtainning electron density of a proper symmetry (HS). 

The improved numerical stability of the new deMon2K version also opened the possibility for accurate harmonic Franck-Condon factor calculations. Based on the combination of such calculations with experimental data from pulsed-field ionization zero-electron-kinetic energy (PFl-ZEKE) photoelectron spectroscopy, the ground state stmcture of V3 could be determined [272]. Very recently, this work has been extended to the simulation of vibrationaUy resolved negative ion photoelectron spectra [273]. In both works the use of newly developed basis sets for gradient corrected functionals was the key to success for the ground state stmcture determination. These basis sets have now been developed for aU 3d transition metal elements. With the simulation of vibrationaUy resolved photoelectron spectra of small transition metal clusters reliable stmcture and... 

Each low oxidation state metal cluster cage possesses a characteristic number of valence electrons (ve) as Table 23.5 shows. We shall not describe the MO basis for these numbers, but merely apply them to rationalize observed structures. Look back to Section 23.2 for the numbers of electrons donated by ligands. Any organometallic complex with a triangular M3 framework requires 48 valence electrons, for example ... 

The duster 14 contains 121 valence electrons, one electron less than predicted by the 18e rule. An electron counting rule for centered metal clusters, as proposed by Mingos, [30-33] states that the number of valence electrons in dose-packed metal clusters should be (12n, + A), where n, is the number of peripheral metal atoms and is 18 or 24 for centered cubic polyhedra. On this basis, 14 should possess either 114 or 120 valence electrons. 

Characterization is relatively simple since the dusters contain only metal atoms, and usually of only a single element. However, there is one problem asso-dated with the characterization of metal clusters in cages. In contrast to the situation for metal carbonyl dusters, there is no base data set for these metal clusters themselves in a pure state to be used for comparison. This means that spectra of encaged metal dusters cannot be compared with those of their analogues in the liquid or solid state because they simply are not known. Thus the basis for structure determination is in a sense weaker than that for metal carbonyl dusters. 

Couple cluster methods differ from perturbation theory in that they include specific corrections to the wavefunction for a particular type to an infinite order. Couple cluster theory therefore must be truncated. The exponential series of functions that operate on the wavefunction can be written in terms of single, double and triple excited states in the determinantl " . The lowest level of truncation is usually at double excitations since the single excitations do not extend the HF solution. The addition of singles along with doubles improves the solution (CCSD). Expansion out to the quadruple excitations has been performed but only for very small systems. Couple cluster theory can improve the accuracy for thermochemical calculations to within 1 kcal/mol. They scale, however, with increases in the number of basis functions (or electrons) as N . This makes calculations on anything over 10 atoms or transition-metal clusters prohibitive. 

---