The total position-spread tensor: Spin partition

Abstract

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

The spin-partitioned total position-spread tensor: An application to Heisenberg spin chains

“…The general formalism of the spin-partitioned TPS tensor is fully unfolded in our previous works on the H 2 molecule 16 and hydrogen chains. 25 In the present paper, we summarize its main aspects and describe its application to the special case of Heisenberg chains.…”

“…The TPS presents important properties for molecules such as size-consistency 11,12 which is crucial to describe bond breaking and chemical processes. 8,[13][14][15][16] Hence, given that it encloses information about the overall wave function, the TPS is particularly appropriate to study finite-size systems.…”

“…Despite the fact that the TPS tensor has been subject of a variety of works in the last years, [13][14][15][17][18][19][20][21][22][23][24] the spinpartitioned TPS (SP-TPS) formalism is a new tool which has been introduced in our recent works on H 2 molecule 16 and hydrogen chains (H n ), 25 where we showed in detail how it allows to investigate separately the fluctuations of the same-spin and different-spin electrons in a system. In the present work, we focus our attention on the spin part of the wave function of linear systems, through the use of the Heisenberg model Hamiltonian.…”

Spatially resolved characterization of electron localization and delocalization in molecules: Extending the Kohn‐Resta approach

“…Possible applications of PST to the chemical bonding in molecules were given in Refs. . An important contribution was also been made by Ángyán and coworker who attempted to relate several known chemical localization descriptors to the density response function and to construct spatially resolved analog of PST.…”

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

“…Even a spin resolved version has also been studied. 30 It has been shown that the TPS is very sensitive to bond stretching, becoming large in the case of increased electron mobility. In simple diatomics, for instance, its parallel component is small at equilibrium, it increases as the interatomic distance is enlarged before achieving a maximum value close to the bond breaking region, and it decreases again towards the free atomic value at dissociation.…”