page_title: Total position spread
section_title: Monitor the wave function
hierarchical_section_title: Total position spread / Applications / Monitor the wave function
caption_attribution_description: Figure 1: SS-TPS as a function of the internuclear distance R for the hydrogen dimer.
context_page_description: In physics, the total position-spread tensor is a quantity originally introduced in the modern theory of electrical conductivity. In the case of molecular systems, this tensor measures the fluctuation of the electrons around their mean positions, which corresponds to the delocalization of the electronic charge within a molecular system. The total position-spread can discriminate between metals and insulators taking information from the ground state wave function. This quantity can be very useful as an indicator to characterize Intervalence charge transfer processes, the bond nature of molecules, and Metal–insulator transition.
context_section_description: The total position-spread is a powerful tool to monitor the wave function. In Figure 3 is shown the longitudinal spin-summed total position-spread (Λ∥) computed at full configuration interaction level for the H₂ diatomic molecule. The Λ∥ in the high repulsive region shows a value that is lower than in the asymptotic limit. This is a consequence of nuclei being near to each other's causing and enhancement of the effective nuclear charge that makes electrons to be more localized. When stretching the bond, the total position-spread starts growing until it reaches a maximum (strong delocalization of the wave function) before the bond is broken. Once the bond is broken, the wave function becomes a sum of disconnected localized regions and the tensor decreases until it reaches twice the value of the atomic limit (1 bohr² for each hydrogen atom).
caption: Figure 3: Spin-summed total position-spread as a function of the internuclear distance R for the hydrogen dimer.
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