Diagrammatic valence‐bond theory for finite model Hamiltonians

Ramasesha, S.; Soos, Z. G.

doi:10.1002/qua.560250606

Cited by 103 publications

(42 citation statements)

References 45 publications

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“…A suitable choice for a basis is obtained by choosing states corresponding to Rumer-Pauling diagrams. [35][36][37][38] The advantage of this is that for appropriate normalization, the matrix elements of the M -matrix then remain integer, and we may again make use of exact integer arithmetic. 33 We further used the mirror symmetry of the cell C along one of its diagonals.…”

Section: The Square Latticementioning

confidence: 99%

Linear independence of nearest-neighbor valence bond states in several two-dimensional lattices

Wildeboer¹,

Seidel²

2011

Phys. Rev. B

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We show for several two-dimensional lattices that the nearest neighbor valence bond states are linearly independent. To do so, we utilize and generalize a method that was recently introduced and applied to the kagome lattice by one of the authors. This method relies on the choice of an appropriate cell for the respective lattice, for which a certain local linear independence property can be demonstrated. Whenever this is achieved, linear independence follows for arbitrarily large lattices that can be covered by such cells, for both open and periodic boundary conditions. We report that this method is applicable to the kagome, honeycomb, square, squagome, two types of pentagonal, square-octagon, the star lattice, two types of archimedean lattices, three types of "martini" lattices, and to fullerene-type lattices, e.g., the well known "Buckyball". Applications of the linear independence property, such as the derivation of effective quantum dimer models, or the constructions of new solvable spin-1/2 models, are discussed.

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Section: The Square Latticementioning

confidence: 99%

Linear independence of nearest-neighbor valence bond states in several two-dimensional lattices

Wildeboer¹,

Seidel²

2011

Phys. Rev. B

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“…We compare the VIP performed on the full aggregate (noted AM1) and the VIP extracted from the VB/HF procedure when one fragment is defined as X n and the second one as (mH 2 O) n (noted VB/HF). The last two columns of Table I give the differences between the VIP of the dimers and the VIP of the monomers (⌬PI 21 ), and between trimers and monomers (⌬PI 31 ). The AM1 and VB/HF VIP are quite similar, except for G n .…”

Section: Beyond the Rigid Gas-phase Supramoleculementioning

confidence: 99%

“…[30]) have been calculated by solving Eq. (18) using the AOVB program package [31], and by performing a Maxwell-Bolzmann statistic over the various eigenstates of the system. The charge density on a given site i in state n is then given by…”

Section: Simulation Of Photocleavage Experimentsmentioning

confidence: 99%

From organic superconductors to DNA: Fragment orbital‐based model

Castet

Ducasse

Fritsch

2005

Int J of Quantum Chemistry

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ABSTRACT:A semi-empirical valence bond/Hartree-Fock (VB/HF) method is developed to calculate one-and two-electron interactions between molecular fragments in conducting supramolecular stacks. This fragment orbital-based formalism allows for consistent extraction of an effective Hamiltonian defined as a "frontier orbital" model. This Hamiltonian quantitatively describes transfer and electrostatic interactions between conducting electrons, while reducing the active space so dramatically that the electronic eigenstates of very large systems may be investigated. The capabilities of the VB/HF method are illustrated on two different supramolecular stacks involving ainteracting fragment. In the first part of this study, the framework of the VB/HF method is used to evaluate the relative magnitude of the electronic interactions between conduction electrons in organic conductors and superconductors derived from Bechgaard salts. In the second part of this study, the VB/HF formalism is extended to derive an effective model for conduction holes along doped DNA double strands. Transferable intra-and intersite parameters were first evaluated from VB/HF calculations carried out on nucleoside pairs. From this interaction databank, the effective Hamiltonian of any type of nucleoside sequence can be defined. The thermalized charge distribution for a single hole delocalized along a DNA sequence containing 240 Watson-Crick pairs is then calculated and compared with the experimental yields of damage revealed by photocleavage experiments.

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“…Perhaps the most detailed and profound analyses have been performed by Klein and coworkers 1–4. Important contributions to understanding the structure of the PPP Hamiltonian are due to Paldus and coworkers 5–10 and Soos and Ramasesha 11–13. Works on the Heisenberg Hamiltonian are, perhaps, even more numerous.…”

Section: Introductionmentioning

confidence: 99%

Relations between Pariser–Parr–Pople and Heisenberg models

Karwowski¹,

Flocke

2002

Int J of Quantum Chemistry

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ABSTRACT:Necessary conditions under which the lowest-energy states obtained as exact (full configuration interation) solutions of the Pariser-Parr-Pople (PPP) model may be interpreted in terms of the Heisenberg model are analyzed. In particular, for a set of model lattices the range of empirical parameters in which the lowest part of the PPP spectrum corresponds to the covalent states has been determined. It has been demonstrated that the energy gap between the lowest ionic and the highest covalent states of the PPP model, as a function of empirical parameters and of the geometric structure of the lattice, behaves in a specific and regular way. The results may be useful for determining limits of applicability of the Heisenberg model and for further studies aimed at a construction of an effective, Heisenberg-type Hamiltonian that could reproduce the lowest part of the PPP spectrum.

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Diagrammatic valence‐bond theory for finite model Hamiltonians

Cited by 103 publications

References 45 publications

Linear independence of nearest-neighbor valence bond states in several two-dimensional lattices

Linear independence of nearest-neighbor valence bond states in several two-dimensional lattices

From organic superconductors to DNA: Fragment orbital‐based model

Relations between Pariser–Parr–Pople and Heisenberg models

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