A number of structural rules and semi-empirical treatments have been proposed to elucidate the structure of cluster compounds113-93. In the present paper I tried to use four numbers (nxcπ) to describe the structural types of clusters and related molecules. 1. Organic and inorganic molecules including clusters are supposed to be composed of molecular fragments, A molecular fragment M#em/em# consists of a central atom A#em/em# and some ligands Lk attached to it, where i, j, k are numbers of valence electrons. 2. Ligands are here defined as atomic groups attached to one or more central atoms. There are four types of bonds between the ligand and the central atom; (1) the ligand and the central atom each contributes one electron to form a covalent bond; (2) the ligand contributes a pair of electrons to the vacant orbital of the central atom to form a dative bond; (3) a pi ligand contributes all its pi electrons to form a bond with the central atom; (4) a bridging ligand may contribute one electron to form an electron-deficient three-center bond with two central atoms. Ligands may be classified according to the total number of valence electrons k they contribute to the central atom as shown in Table 1. 3. Molecular fragments containing the same number of valence electrons #em/em# are called isoelectronic fragments and may be denoted by M#em/em# and arranged in a form like the periodic table as shown in Table 2. 4. The valency V#em/em# of a fragment M#em/em# is equal to the number of vacancies in the valence orbital of the fragment as shown in Table 3 and 4. 5. The structural type of any molecule may be specified by a set of four numbers (nxcπ), where n=no. of fragments, π=no. of pi bonds, c=no. of cycles in rings, polycyclic networks or clusters, x=∑x#em/em#, x#em/em#=4-V#em/em#=4+#em/em#-2(NV0)#em/em#. Table 5 gives the formulas of x for various cases derived from the above general formula. Let B equal to the number of bonds between the n fragments in a molecule, then Table 6 summarizes the (xBcπ) values of n-fragment molecules of various structural types. 6. Jn order to verify the above rules, we have used the HAM/3 semi-empirical SCF method proposed by Asbrink et al and Hoffmann's EHMO method to calculate the MO energy levels of a series of molecules of various typical structural types with the following results; (1) If a stable molecule with certain (nxcπ) values assumes a proper structural type as shown in Table 5, then its energy diagram should be such that all bonding orbitals are occupied, all antibonding orbitals are empty, with a certain gap between the HOMO and LUMO; (2) If the B. 0. are not fully occupied, the molecule will tend to gain more electrons or to assume a different structural type with less B. 0.; (3) If the A. B. O. are filled with some electrons, the molecule will lose some ligands with their valence electrons in A. B. 0. or to assume a different structural type with more B. 0.; (4) If the frontier orbitals are nonbonding, weakly bonding or weakly antibonding, the number of valence electrons may be varied with in a certain range. 7. The substitution of one or more fragments in a molecule by the same number of other fragments such that the NVE does not change or changes only in multiples of ten, then the four numbers (nxcπ) will remain unchanged, and consequently the structural type of the substituted molecule is the same as the original one. Examples were given to illustrate the applications of these structural rules and (nxcπ) formalism, such as the determination of structural type from molecular formula, the prediction of new cluster compounds and their possible route of syntheses, et cetera.
