The total Position Spread in mixed‐valence compounds: A study on the  model system

Bendazzoli, Gian Luigi; Khatib, Muammar El; Evangelisti, Stefano; Leininger, Thierry

doi:10.1002/jcc.23557

Cited by 9 publications

(9 citation statements)

References 42 publications

(49 reference statements)

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“…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.…”

Section: The Spin-summed Spreadmentioning

confidence: 99%

“…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. 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.…”

Section: Introductionmentioning

confidence: 99%

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The total position-spread tensor: Spin partition

Khatib

Brea

Fertitta

et al. 2015

The Journal of Chemical Physics

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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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Section: The Spin-summed Spreadmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The total position-spread tensor: Spin partition

Khatib

Brea

Fertitta

et al. 2015

The Journal of Chemical Physics

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“…The Position Spread [42], is a tensor defined as the second moment cumulant of the total position operator ̂ : where the sum runs over all the electron of the system. Then, the cumulant is computed, It is possible to partition the spread according to the electron spin: the position ̂ is written as the sum of the spin components ̂ +̂ , so that , which is quadratic in the position, becomes the sum of four terms.…”

Section: The Total Position Spreadmentioning

confidence: 99%

Conical intersection properties unraveled by the position spread tensor

et al. 2018

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We explore the application of the electron position spread tensor, i.e., a quantitative measure of the electron delocalization and mobility, to the conical intersection regions of three relevant compounds showing either photoisomerization or chemiluminescence properties. The electronic structure of the involved states has been solved using the complete active space self-consistent field method, and the position spread tensor has been computed at the same level of theory. In particular, we show that the total position spread tensor is degenerate between the ground and the excited states, because of the inversion of the electronic nature of the states happening at the crossing areas. We also show that the ground-state position spread tensor shows a discontinuity that may be used to locate conical intersections without the need to explicitly compute the excited-state wavefunction. Furthermore, we also report that the spin partition position spread tensor shows a peculiar behavior presenting values close to zero in two of its principal components. We associate those small values to the degeneracy-lifting coordinates and hence to the conical intersection branching space.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Fertitta

Khatib

Bendazzoli

et al. 2015

The Journal of Chemical Physics

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The spin partition of the Total Position-Spread (TPS) tensor has been performed for one-dimensional Heisenberg chains with open boundary conditions. Both the cases of a ferromagnetic (high-spin) and an anti-ferromagnetic (low-spin) ground-state have been considered. In the case of a low-spin ground-state, the use of alternating magnetic couplings allowed to investigate the effect of spin-pairing. The behavior of the spin-partitioned TPS (SP-TPS) tensor as a function of the number of sites turned to be closely related to the presence of an energy gap between the ground-state and the first excited-state at the thermodynamic limit. Indeed, a gapped energy spectrum is associated to a linear growth of the SP-TPS tensor with the number of sites. On the other hand, in gapless situations, the spread presents a faster-than-linear growth, resulting in the divergence of its per-site value. Finally, for the case of a high-spin wave function, an analytical expression of the dependence of the SP-TPS on the number of sites n and the total spin-projection Sz has been derived.

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The total Position Spread in mixed‐valence compounds: A study on the model system

Cited by 9 publications

References 42 publications

The total position-spread tensor: Spin partition

The total position-spread tensor: Spin partition

Conical intersection properties unraveled by the position spread tensor

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

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