The bond nature in beryllium dimer has been theoretically investigated using high-level ab initio methods. A series of ANO basis sets of increasing quality, going from sp to spdf ghi contractions, has been employed, combined with HF, CAS-SCF, CISD, and MRCI calculations with several different active spaces. The quality of these calculations has been checked by comparing the results with valence Full-CI calculations, performed with the same basis sets. It is shown that two quasi-degenerated partly occupied orbitals play a crucial role to give a qualitatively correct description of the bond. Their nature is similar to that of the edge orbitals that give rise to the quasi-degenerated singlet–triplet states in longer beryllium chains.

The behavior of the Position-Spread Tensor (Λ) in a series of light diatomic molecules (either neutral or negative ions) is investigated at a Full Configuration Interaction level. This tensor, which is the second moment cumulant of the total position operator, is invariant with respect to molecular translations, while its trace is also rotationally invariant. Moreover, the tensor is additive in the case of noninteracting subsystems and can be seen as an intrinsic property of a molecule. In the present work, it is shown that the longitudinal component of the tensor, Λ∥, which is small for internuclear distances close to the equilibrium, tends to grow if the bond is stretched. A maximum is reached in the region of the bond breaking, then Λ∥ decreases and converges toward the isolated-atom value. The degenerate transversal components, Λ⊥, on the other hand, usually have a monotonic growth toward the atomic value. The Position Spread is extremely sensitive to reorganization of the molecular wave function, and it becomes larger in the case of an increase of the electron mobility, as illustrated by the neutral-ionic avoided crossing in LiF. For these reasons, the Position Spread can be an extremely useful property that characterizes the nature of the wave function in a molecular system.

The electronic structure of planar molecular edifices obtained by joining polyacene fragments (polyacene stripes) is investigated at tight-binding and ab initio levels. It is shown that the presence of 60° angles in the molecular skeleton induces the formation of singly-occupied molecular orbitals, whose combination gives rise to quasi-degenerate electronic states. The ab initio investigation requires therefore the use of CAS-SCF and MR-PT approaches. The three types of possible convex polygons having a unique side length (hexagons, rhombuses and triangles) have been considered in this work. The spin multiplicity of these quasi-flat molecular structures is found to be in systematical accord with the Ovchinnikov rule.

The Total Position Spread (TPS) tensor, defined as the second moment cumulant of the position operator, is a key quantity to describe the mobility of electrons in a molecule or an extended system. In the present investigation, the partition of the TPS tensor according to spin variables is derived and discussed. It is shown that, while the spin-summed TPS gives information on charge mobility, the spin-partitioned TPS tensor becomes a powerful tool that provides information about spin fluctuations. The case of the hydrogen molecule is treated, both analytically, by using a 1s Slater-type orbital, and numerically, at Full Configuration Interaction (FCI) level with a V6Z basis set. It is found that, for very large inter-nuclear distances, the partitioned tensor growths quadratically with the distance in some of the low-lying electronic states. This fact is related to the presence of entanglement in the wave function. Non-dimerized open chains described by a model Hubbard Hamiltonian and linear hydrogen chains H n (n ≥ 2), composed of equally spaced atoms, are also studied at FCI level. The hydrogen systems show the presence of marked maxima for the spin-summed TPS (corresponding to a high charge mobility) when the inter-nuclear distance is about 2 bohrs. This fact can be associated to the presence of a Mott transition occurring in this region. The spin-partitioned TPS tensor, on the other hand, has a quadratical growth at long distances, a fact that corresponds to the high spin mobility in a magnetic system. C 2015 AIP Publishing LLC. [http://dx

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The behavior of the Total Position Spread (TPS) tensor, which is the second moment cumulant of the total position operator, is investigated in the case of a mixed-valence model system. The system consists of two H2 molecules placed at a distance D. If D is larger than about 4 bohr, the singly ionized system shows a mixed-valence character. It is shown that the magnitude of the TPS has a strong peak in the region of the avoided crossing. We believe that the TPS can be a powerful tool to characterize the behavior of the electrons in realistic mixed-valence compounds.

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