Model Calculation of Electron–phonon Couplings in a Dimer With a Non-Degenerate Orbital

Acquarone, M.; Noce, Canio

doi:10.1142/s0217979299003052

Cited by 5 publications

(5 citation statements)

References 14 publications

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“…, where b † i , b i are bosonic creation and annihilation operators of the system deformation and the set {ξ i } defines a new set of microscopic parameters -the electron-ion coupling constants. They can be derived by differentiation in a way similar to that of [23,24] (cf. Appendix B for details).…”

Section: Adiabatic Approximation For the Electron-ion Couplingmentioning

confidence: 99%

H₂and (H₂)₂molecules with anab initiooptimization of wave functions in correlated state: electron–proton couplings and intermolecular microscopic parameters

Kądzielawa¹,

Bielas

Acquarone

et al. 2014

New J. Phys.

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The hydrogen molecules H 2 and ( ) H 2 2 are analyzed with electronic correlations taken into account between the s 1 electrons in an exact manner. The optimal single-particle Slater orbitals are evaluated in the correlated state of H 2 by combining their variational determination with the diagonalization of the full Hamiltonian in the second-quantization language. All electron-ion coupling constants are determined explicitly and their relative importance is discussed. Sizable zero-point motion amplitude and the corresponding energy are then evaluated by taking into account the anharmonic contributions up to the ninth order in the relative displacement of the ions from their static equilibrium value. The applicability of the model to solid molecular hydrogen is briefly analyzed by calculating intermolecular microscopic parameters for the × H 2 2 rectangular configuration, as well its ground state energy.Keywords: hydrogen molecules, electron-proton coupling for hydrogen molecule, electronic correlations for hydrogen molecule, intermolecular hopping and interaction parameters MotivationThe few-site models of correlated fermions play an important role in singling out, in an exact manner, the role of various local intra-and inter-site interactions against hopping (i.e., containing both covalent and the ionic factors) and thus, in establishing the optimal correlated state of fermions [1-8] on a local (nanoscopic) scale. The model has also been used to obtain a realistic analytic estimate of the hydrogen-molecule energies of the ground and the excited states in the correlated state [9]. For this purpose, we have developed the so-called EDABI method, which combines Exact Diagonalization in the Fock space with a concomitant Ab Initio determination of the single-particle basis in the Hilbert space. So far, the method has been implemented by taking only s 1 Slater orbitals, one per site [10]. The method contains no parameters; the only approximation made is taking a truncated single-particle basis (i.e., one Slater orbital per site) when constructing the field operator, that in turn is used to derive the starting Hamiltonian in the second-quantization representation. This Hamiltonian represents an extended Hubbard Hamiltonian, with all two-site interactions taken into account and the solution comprises not only the exact eigenvalues of the few-site Hamiltonian, but also at the same time an evaluation of the adjustable single-particle wave functions in the correlated state. Also, the calculated thermodynamic properties rigorously exemplify [12,11] the low-and highenergy scales, corresponding to spin and local charge fluctuations, respectively. The former represents the precursory magnetic-ordering effect whereas the latter represents local effects accompanying the Mott-Hubbard transition. In general, our approach follows the tradition of accounting for interelectronic correlations via the second-quantization procedure, with the adjustment of single-particle wave functions, contained in microscopic parameters of the startin...

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Section: Adiabatic Approximation For the Electron-ion Couplingmentioning

confidence: 99%

H₂and (H₂)₂molecules with anab initiooptimization of wave functions in correlated state: electron–proton couplings and intermolecular microscopic parameters

Kądzielawa¹,

Bielas

Acquarone

et al. 2014

New J. Phys.

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“…The case of Γ = 2.Å −1 (discussed in ref. 3) shows that, the more localized are the orbitals, the more relevant is the role of g cf in relation to the other admissible couplings. Fig.3 shows the couplings derived from the two-body electronic interactions for the same parameters as Fig.2.…”

Section: Coupling Terms In the Anti-adiabatic Limitmentioning

confidence: 99%

“…, is due to the modulation of the hopping amplitude t. To preserve the invariance of H SSH under site permutation, γ (12) = −γ (21) (see e.g refs.6 and 7). Indeed, its explicit expression [3] is:…”

Section: Coupling Terms In the Anti-adiabatic Limitmentioning

confidence: 99%

“…It has a formal similarity with the Holstein coupling term [4], but it has a physically different origin, as Holstein [4] considered electrons moving along a chain of fixed spacing with vibrating diatomic molecules at its nodes. On site 1, its explicit evaluation [3] yields:…”

Section: Coupling Terms In the Anti-adiabatic Limitmentioning

confidence: 99%

“…Therefore for the dimer as a whole one writes this term as g 12 cf σ (n 1σ u 2 − n 2σ u 1 ). The explicit evaluation [3] for site 1 yields:…”

Section: Coupling Terms In the Anti-adiabatic Limitmentioning

confidence: 99%

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Distance-Depending Electron-Phonon Interactions From One- And Two-Body Electronic Terms in a Dimer

Acquarone

Noce

2000

Int. J. Mod. Phys. B

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For a dimer with a non-degenerate orbital built from atomic wave functions of Gaussian shape we evaluate all the electron-phonon couplings derived from the one-body and two-body electronic interactions, considering both the adiabatic and extreme non-adiabatic limit. Not only the values of the coupling parameters in the two limits, but also the expressions of the corresponding terms in the Hamiltonian differ. Depending on the distance between the dimer ions, some of the two-body couplings are comparable, or even larger than the one-body ones.

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Effect of the intersite Coulomb interaction in the Hubbard–Holstein model on a four-site chain

Acquarone

Cuoco

Noce

et al. 2000

Physica B: Condensed Matter

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Model Calculation of Electron–phonon Couplings in a Dimer With a Non-Degenerate Orbital

Cited by 5 publications

References 14 publications

H₂and (H₂)₂molecules with anab initiooptimization of wave functions in correlated state: electron–proton couplings and intermolecular microscopic parameters

H₂and (H₂)₂molecules with anab initiooptimization of wave functions in correlated state: electron–proton couplings and intermolecular microscopic parameters

Distance-Depending Electron-Phonon Interactions From One- And Two-Body Electronic Terms in a Dimer

Effect of the intersite Coulomb interaction in the Hubbard–Holstein model on a four-site chain

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Model Calculation of Electron–phonon Couplings in a Dimer With a Non-Degenerate Orbital

Cited by 5 publications

References 14 publications

H2and (H2)2molecules with anab initiooptimization of wave functions in correlated state: electron–proton couplings and intermolecular microscopic parameters

H2and (H2)2molecules with anab initiooptimization of wave functions in correlated state: electron–proton couplings and intermolecular microscopic parameters

Distance-Depending Electron-Phonon Interactions From One- And Two-Body Electronic Terms in a Dimer

Effect of the intersite Coulomb interaction in the Hubbard–Holstein model on a four-site chain

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Product

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H₂and (H₂)₂molecules with anab initiooptimization of wave functions in correlated state: electron–proton couplings and intermolecular microscopic parameters

H₂and (H₂)₂molecules with anab initiooptimization of wave functions in correlated state: electron–proton couplings and intermolecular microscopic parameters