Calculation of electric dipole (hyper)polarizabilities by long-range-correction scheme in density functional theory: A systematic assessment for polydiacetylene and polybutatriene oligomers

Kirtman, Bernard; Bonness, Sean; Ramı́rez-Solı́s, A.; Champagne, Benoı̂t; Matsumoto, Hironori; Sekino, Hideo

doi:10.1063/1.2885051

Cited by 122 publications

(73 citation statements)

References 14 publications

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“…On this basis our LDA and GGA data give catastrophically exaggerated values (DFT catastrophe), whereas hybrid data are more reasonable but still far apart by orders of magnitude when γ xxxx is considered. LR corrections 52,53 have been claimed, in the case of finite oligomer chains, to limit catastrophic divergence on (hyper)polarizabilities, but still performance depends parametrically on the system 52 and no clear improvements of LR corrected functionals over HF have been shown. 52,53 Besides the wide family of small-gap organic polymers, there is a connection with the optical properties of more complex systems such as carbon nanotubes (CNT) (1D systems characterized by a small band gap).…”

Section: Discussionmentioning

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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Section: Discussionmentioning

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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“…According to previous studies on (hyper)polarizabilities [24][25][26][27][28][29][30][31], a bigger impact can be expected for larger molecules. More importantly, this work confirms the conclusion of a previous study on excitation energies and oscillator strengths of a few small molecules [46] in that the TDRSH method is a reasonably accurate method even using only a LDA-type density functional and without adding an explicit treatment of long-range correlation.…”

Section: Discussionmentioning

confidence: 99%

“…It has been demonstrated that the LC scheme corrects the underestimation of Rydberg excitation energies of small molecules [23] and the overestimation of (hyper)polarizabilities of long conjugated molecules [24][25][26][27][28][29][30][31] usually obtained with standard (semi)local densityfunctional approximations. A variety of other similar range-separated TDDFT schemes have also been employed, which for example use an empirically modified correlation density functional depending on the rangeseparation parameter [32], or introduce a fraction of HF exchange at shorter range as well [33][34][35][36][37][38][39][40][41][42][43][44][45], such as in the CAM-B3LYP approximation [33].…”

Section: Introductionmentioning

confidence: 99%

Assessment of range-separated time-dependent density-functional theory for calculating C6 dispersion coefficients

Toulouse¹,

Rebolini²,

Gould³

et al. 2013

The Journal of Chemical Physics

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We assess a variant of linear-response range-separated time-dependent density-functional theory (TDDFT), combining a long-range Hartree-Fock (HF) exchange kernel with a short-range adiabatic exchange-correlation kernel in the local-density approximation (LDA) for calculating isotropic C6 dispersion coefficients of homodimers of a number of closed-shell atoms and small molecules. This range-separated TDDFT tends to give underestimated C6 coefficients of small molecules with a mean absolute percentage error of about 5%, a slight improvement over standard TDDFT in the adiabatic LDA which tends to overestimate them with a mean absolute percentage error of 8%, but close to time-dependent Hartree-Fock which has a mean absolute percentage error of about 6%. These results thus show that introduction of long-range HF exchange in TDDFT has a small but beneficial impact on the values of C6 coefficients. It also confirms that the present variant of rangeseparated TDDFT is a reasonably accurate method even using only a LDA-type density functional and without adding an explicit treatment of long-range correlation.

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“…For example, positively large b was reported for a tictoid at twisted angle h ¼ 49 at CASSCF (2,2)/6-31G(d,p) level, whereas b becomes negatively large at h ¼ 53 [44]. On the other hand, DFT methods, in particular to functionals with long-range correction (LC-DFT) to exchange term, are successfully used in evaluating NLO properties for large pextended systems [45][46][47]. We notice that DFT, MP2, and CASSCF produce similar energy variation with twist angle for tictoids [44].…”

mentioning

confidence: 99%

Theoretical study of static (Hyper)polarizabilities of twisted intramolecular charge transfer chromophores

Liu¹,

Yang²,

Wang³

et al. 2011

Int J of Quantum Chemistry

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Density functional theory calculations are performed to study the (hyper)polarizabilities of a series of planar and twisted intramolecular charge transfer molecules (tictoids) with different electron-donating and electron-withdrawing groups. Both similarity and difference between the planar and twisted molecules are noted in their (hyper)polarizability variation with respect to substituent and solvent dielectric constant. When compared with dramatic enhancements resulting from geometry twist and solvent effect, substitution to D/A pairs leads to relatively moderate variation in (hyper) polarizability. In addition, tictoids with different substituents may exhibit different solvent effects in their hyperpolarizability magnitudes. Our calculations suggest that the nonlinear optical response of the tictoids could be tuned by appropriately selecting the donor/acceptor pairs and solvents.

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Calculation of electric dipole (hyper)polarizabilities by long-range-correction scheme in density functional theory: A systematic assessment for polydiacetylene and polybutatriene oligomers

Cited by 122 publications

References 14 publications

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

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

Assessment of range-separated time-dependent density-functional theory for calculating C6 dispersion coefficients

Theoretical study of static (Hyper)polarizabilities of twisted intramolecular charge transfer chromophores

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