Behavior of the Position–Spread Tensor in Diatomic Systems

Abstract

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 total position-spread tensor: Spin partition

“…In Figure 8, the FCI energies per atom are reported as a function of the inter-atomic distances R, for the HL_n (n = 2, 4,6,8,10,12,14,16). For all the involved chains except the dimer, there is a minimum of the potential energy surfaces (PES) in the region of 2.0 bohrs.…”

“…8,9 In recent years, our group has been investigating the properties of what we named the TPS tensor, Λ. 10 Notice that LT and TPS are trivially related, since the original LT introduced by Resta is nothing but our TPS tensor divided by the number of electrons. In our investigation, we considered several structures (atoms, molecules, clusters), treated either by ab initio, [11][12][13][14] or model 15,16 Hamiltonians.…”

“…In our investigation, we considered several structures (atoms, molecules, clusters), treated either by ab initio, [11][12][13][14] or model 15,16 Hamiltonians. Although essentially equivalent quantities, we believe that, in a molecular context, the TPS tensor is more pertinent than the LT. 10,17,18 In fact, in this context, it is useful to have a property like TPS that is strongly dependent upon the number of electrons or the size of the system, in order to follow processes like chemical reactions or fragmentation. Moreover, the contribution of the different electronic shells to the TPS is extremely inhomogeneous, so performing an average on these different terms has little meaning.…”

An unexpected bridge between chemical bonding indicators and electrical conductivity through the localization tensor

“…In the last few years, several works by Leininger, Evangelisti and coworkers 28,29 have examined the role of k in molecular instead of extended systems. To that end, these authors have preferred to use the total second cumulant, which they have called the total position-spread tensor, K or TPS, and not the per electron quantity.…”

“…Leininger et al, 28 mean-field and correlated descriptions of the dissociation process differ essentially. Interestingly, these qualitative differences are also observed when the delocalization index is examined by itself.…”