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

Abstract

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.

Inducing a Finite In-Plane Piezoelectricity in Graphene with Low Concentration of Inversion Symmetry-Breaking Defects

“…The present computational setup is the same as that used in a previous investigation on large Carbon nanotubes 41 which led to an accurate description of electronic properties such as the band gap. At variance with the case of polyacetylene (PA), 42 the calculation of the piezoelectric response of BN-doped graphene is not much sensitive to the adopted DFT functional (see comparison with LDA results in Supporting Information). We recently utilized the same approach for investigating the piezoelectric response of 3D systems such as SrTiO 3 , 35 BaTiO 3 , 43 Ge-doped quartz 44 and low-dimensional systems such as h-BN, 45 h-ZnO, 46 and BeO nanotubes.…”

Static and dynamic coupled perturbed Hartree-Fock vibrational (hyper)polarizabilities of polyacetylene calculated by the finite field nuclear relaxation method

“…9 for details). Optimal parameter values have been found in our previous work, 32 which shows that the smaller the band gap E g the larger the values of S and T x that need to be used. PA has a small energy gap due to π -electron conjugation (1.6 ≤ E g ≤ 1.8 eV) (Ref.…”

“…34) which, we note in passing, is severely underestimated by pure DFT methods (for local-density approximation, LDA, and generalized-gradient approximation, GGA, 10 −2 ≤ E g ≤ 10 −1 eV). 32 Although HF overestimates the band gap it yields much more reasonable (hyper)polarizabilities. Thanks to the large HF gap (about 7 eV), 32 it is sufficient to use S = 30 and T x = 100.…”

“…Two computational parameters have been shown 32 to have a large influence on the calculated (hyper)polarizability tensors, namely, the shrinking factor S -defining the number of k points at which the self-consistent field (SCF) and CPHF equations are solved -and the pair of tolerances, collectively denoted as T x , controlling the accuracy of the Hartree-Fock exchange series. 9,33 We set T x = T 4 = 1 2 T 5 for the current calculations (see Ref.…”

“…We have chosen to employ the HF level of theory in order to avoid the large overshoot in calculating the electronic (hyper)polarizability of PA (and other quasi-linear systems) [15][16][17][18][29][30][31][32] obtained with conventional DFT functionals, a phenomenon sometimes described as the DFT catastrophe.…”