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Nonresonant frequency dispersion of the electronic second hyperpolarizability of all‐trans polysilane chains: An ab initio TDHF oligomeric approach
Author(s) -
Champagne Benoît,
Perpète Éric A.,
André JeanMarie
Publication year - 1998
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1998)70:4/5<751::aid-qua21>3.0.co;2-3
Subject(s) - hyperpolarizability , polysilane , chemistry , dispersion (optics) , ab initio , limit (mathematics) , molecular physics , computational chemistry , atomic physics , quantum mechanics , physics , nonlinear system , nonlinear optical , mathematics , organic chemistry , mathematical analysis , polymer
The frequency‐dependent electronic second hyperpolarizability of increasingly large polysilane chains is computed for the most common nonlinear optical (NLO) processes at the time‐dependent Hartree–Fock level with the 6‐31G atomic basis set. Due to σ‐conjugation, the longitudinal component (γ L e ) turns out to be dominant. Its nonresonant dispersion relations are described by the coefficients of the power expansion formula, γ L e (−ω σ ; ω 1 , ω 2 , ω 3 )=γ L e (0; 0, 0, 0)[1+ A ω L 2 + B ω L 4 + C ω L 6 +···], where ω L 2 =ω σ 2 +ω 1 2 +ω 2 2 +ω 3 2 and γ L e (0; 0, 0, 0) is the static limit value. In the infinite chain length limit, the CHF/6‐31G static longitudinal electronic second hyperpolarizability per Si 2 H 4 unit cell is estimated to attain 463±10×10 3 a.u. whereas the A coefficient reaches 27.8±0.9 a.u. The accuracy that could be reached from using this power expansion expression for estimating the second hyperpolarizability for other optical frequencies is discussed. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 751–761, 1998