Recursive Density-Matrix-Spectral-Moment Algorithm for Molecular Nonlinear Polarizabilities
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چکیده
Relations between chemical and electronic structure and linear and nonlinear optical polarizabilities of conjugated molecule have drawn much attention of chemists and physicists over the past 20 years [1–4]. Resonant nonlinear spectroscopy provides most valuable information on states that are inaccessible by linear techniques [5–9], whereas off-resonant measurements probe the collective response of many molecular eigenstates [1–3]. The size-scaling of various optical properties has been studied extensively, both theoretically [10–12] and experimentally [5,9,13,14]. Linear absorption of short oligomers with N < 12 − 20 carbon atoms shows an Ω ∼ N−μ scaling of the optical gap with μ ∼ 0.4 − 0.6 [5]. The Hückel model yields μ = 1 [12]. An important relation is the scaling of nonlinear susceptibilities with molecular size. The power scaling law γ ∼ N b for the third-order polarizability, where N is the number of carbon atoms, has been established experimentally in the early 70’th [15], and supported by theoretical calculations using the free electron model [16]. Numerous subsequent studies showed that for short chains, the exponent b can vary between 3 and 8, depending on the system and model, and eventually approaches 1 (saturates) for long molecules. The crossover between these two behaviors is related to the exciton coherence size [4,5,13]. Calculations performed using the Hückel model (which neglects Coulomb interactions) predict saturation at long chains (N ∼ 50) and b ∼ 5 − 9 [12,17], whereas calculations based on the Pariser-ParrPople (PPP) Hamiltonian which includes electronic correlations predict a shorter saturation size (N ∼ 20 − 30) and b ∼ 4−5 [4,18,1]. Sum-over-states calculations of γ in short oligomers yield a scaling exponents b ≈ 8 for symmetric linear cyanites and b ≈ 4 for linear polyenes [19]. Difficulties with the controlled synthesis and poor solubility of polyenic oligomers restricted early experimental studies to molecules with up to 30-40 carbon atoms [14,15,20] which showed no saturation. These problems have been overcome, and the saturation of γ has been observed experimentally at ∼ 200 double bonds [13], which is much larger than early estimates.
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تاریخ انتشار 1997