Orbitals vacant atomic, population

Population of vacant atomic orbitals and electron density distribution... 

It is instructive to study the vacant atomic orbital population in dimers and trimers. As mentioned in the Introduction, in the 80 s Bauschlicher et al. [10,11] came to the conclusion that the promotion of ns-electrons to np-orbitals leading to sp-hybridization is the main mechanism responsible for binding in alkaline-earth clusters. This conclusion was based on a study of the SCF Mulliken population analysis for tetramers, which are stable at the SCF level. At present, we can perform more precise analysis using the Natural Bond Orbital Analysis and calculate it at the electron correlation level. 

It is important to check is the effect of a rather large population of vacant atomic orbitals at the electron correlation level specific for alkaline-earth atoms or it has a general character. In Table VII we present the results of net valence population calculations for noble-gas atoms performed by the Natural Bond Orbital Analysis at the MP4 level. We found non-negligible valence orbital population, especially for the d-orbitals. The results obtained for three different basis sets are quite close. Thus, the population of vacant orbitals in noble-gas atoms is not an artifact of the calculations. From this follows that elements traditionally assumed as closed-shell (noble gases) or closed-subshell (alkaline earths) atoms can to some extent manifest an anisotropic p-or d-symmetry behavior. It would be very interesting to obtain experimental evidence confirming this theoretical prediction. 

The crystal orbitals were calculated by the DFT method in the plane-wave basis set with the CASTEP code [377] in the GGA density functional. A set of special points k in the Brillouin zone for all the crystals was generated by the snperceU method (see Chap. 3) with a 5 x 5 x 5 diagonal symmetric extension, which corresponds to 125 points. In all cases, the pseudopotentials were represented by the normconserving optimized atomic pseudopotentials [621], which were also used to calculate the atomic potentials of free atoms. In the framework of both techniques (A, B), the population analysis was performed in the minimal atomic basis set i.e. the basis set involved only occupied or partially occupied atomic orbitals of free atoms. It is well known that the inclusion of diffuse vacant atomic orbitals in the basis set can substantially change the results of the population analysis. For example, if the Mg 2p vacant atomic orbitals are included in the basis set, the charge calculated by technique A for the Mg... 

We have also calculated the NBO valence population at the MP4 level for the isolated atoms. It could be expected that the inclusion of the electron correlation effects leads to some population of vacant (in the SCF approximation) atomic orbitals. But the values obtained are surprisingly large. The p-population in the Mg and Ca atoms are only slightly smaller than that in their dimers, and in the Be atom the population is 0.7 of the p-population in Be2. 

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