On the electrostatic potential in linear periodic polymers

Saunders, V. R.; Freyria-Fava, C.; Dovesi, Roberto; Roetti, C.

doi:10.1016/0010-4655(94)90209-7

Cited by 50 publications

(36 citation statements)

References 19 publications

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“…The electron-electron interaction was modelled by a 1D Coulomb potential [32]. The charge neutrality of each wire was maintained by introducing a uniform line of positive background charge.…”

Section: B Diffusion Monte Carlo (Dmc) Calculationsmentioning

confidence: 99%

Anomalous nonadditive dispersion interactions in systems of three one-dimensional wires

Misquitta

Drummond

Stone³

et al. 2014

Phys. Rev. B

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The non-additive dispersion contribution to the binding energy of three one-dimensional (1D) wires is investigated using wires modelled by (i) chains of hydrogen atoms and (ii) homogeneous electron gases. We demonstrate that the non-additive dispersion contribution to the binding energy is significantly enhanced compared with that expected from Axilrod-Teller-Muto-type triple-dipole summations and follows a different power-law decay with separation. The triwire non-additive dispersion for 1D electron gases scales according to the power law d −β , where d is the wire separation, with exponents β(r s ) smaller than 3 and slightly increasing with r s from 2.4 at r s = 1 to 2.9 at r s = 10, where r s is the density parameter of the 1D electron gas. This is in good agreement with the exponent β = 3 suggested by the leading-order charge-flow contribution to the triwire nonadditivity, and is a significantly slower decay than the ∼ d −7 behaviour that would be expected from triple-dipole summations.

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Section: B Diffusion Monte Carlo (Dmc) Calculationsmentioning

confidence: 99%

Anomalous nonadditive dispersion interactions in systems of three one-dimensional wires

Misquitta

Drummond

Stone³

et al. 2014

Phys. Rev. B

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“…T 2 defines the set of direct space g vectors within which these bielectronic integrals are calculated exactly, otherwise a multipolar expansion is used to describe the interacting charge distributions. [36][37][38] The effect of T C (here T 1 has been set equal to T 2 ) on the ground state and its optical properties is documented in Table III. Both α and γ show high stability with respect to T c , so that T c = 10 can be used safely (despite the small energy variation at higher T c values), extending the TABLE III.…”

Section: B Convergence With Respect To the Two-electron Series Rangementioning

confidence: 99%

Calculation of longitudinal polarizability and second hyperpolarizability of polyacetylene with the coupled perturbed Hartree-Fock/Kohn-Sham scheme: Where it is shown how finite oligomer chains tend to the infinite periodic polymer

Lacivita¹,

Rérat²,

Orlando³

et al. 2012

The Journal of Chemical Physics

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Articles you may be interested inThe longitudinal polarizability, α xx , and second hyperpolarizability, γ xxxx , of polyacetylene are evaluated by using the coupled perturbed Hartree-Fock/Kohn-Sham (HF/KS) scheme as implemented in the periodic CRYSTAL code and a split valence type basis set. Four different density functionals, namely local density approximation (LDA) (pure local), Perdew-Becke-Ernzerhof (PBE) (gradient corrected), PBE0, and B3LYP (hybrid), and the Hartree-Fock Hamiltonian are compared. It is shown that very tight computational conditions must be used to obtain well converged results, especially for γ xxxx , that is, very sensitive to the number of k points in reciprocal space when the band gap is small (as for LDA and PBE), and to the extension of summations of the exact exchange series (HF and hybrids). The band gap in LDA is only 0.01 eV: at least 300 k points are required to obtain well converged total energy and equilibrium geometry, and 1200 for well converged optical properties. Also, the exchange series convergence is related to the band gap. The PBE0 band gap is as small as 1.4 eV and the exchange summation must extend to about 130 Å from the origin cell. Total energy, band gap, equilibrium geometry, polarizability, and second hyperpolarizability of oligomers −(C 2 H 2 ) m −, with m up to 50 (202 atoms), and of the polymer have been compared. It turns out that oligomers of that length provide an extremely poor representation of the infinite chain polarizability and hyperpolarizability when the gap is smaller than 0.2 eV (that is, for LDA and PBE). Huge differences are observed on α xx and γ xxxx of the polymer when different functionals are used, that is in connection to the well-known density functional theory (DFT) overshoot, reported in the literature about short oligomers: for the infinite model the ratio between LDA (or PBE) and HF becomes even more dramatic (about 500 for α xx and 10 10 for γ xxxx ). On the basis of previous systematic comparisons of results obtained with various approaches including DFT, HF, Moller-Plesset (MP2) and coupled cluster for finite chains, we can argue that, for the infinite chain, the present HF results are the most reliable.

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“…Strictly speaking, some of the terms such as E(NR) are divergent for a periodic system, and a formulation based on e.g. the Ewald and related methods would be more suitable [28,29]. However, the main issue of the present paper can easiest be demonstrated with a notation consistent with references [6,7,26], and convergence issues of the Coulomb sums shall be ignored.…”

Section: Zero Temperaturementioning

confidence: 96%

On the gradient for metallic systems with a local basis set

Doll

2012

Chemical Physics Letters

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The analytical gradient for periodic systems is presented, for the case of metallic systems. The total energy and the free energy are computed on the Hartree-Fock or density functional level, with the wave function being expanded in terms of Gaussian type orbitals. The expression for the gradient is similar to the case of insulating systems, when no thermal broadening is applied. When the occupation of the states is according to the Fermi function, then the gradient is consistent with the gradient of the free energy. By comparing with numerical derivatives, examples demonstrate that a reasonable accuracy is achieved.

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On the electrostatic potential in linear periodic polymers

Cited by 50 publications

References 19 publications

Anomalous nonadditive dispersion interactions in systems of three one-dimensional wires

Anomalous nonadditive dispersion interactions in systems of three one-dimensional wires

Calculation of longitudinal polarizability and second hyperpolarizability of polyacetylene with the coupled perturbed Hartree-Fock/Kohn-Sham scheme: Where it is shown how finite oligomer chains tend to the infinite periodic polymer

On the gradient for metallic systems with a local basis set

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