TD-DFT Research Papers - Academia.edu (original) (raw)

A series of divinyl-pyrene derivatives of the form D-vinyl-pyrene-vinyl-A, in which D corresponds to an electron donor group and A to an electron acceptor group, were studied in this work. The first purpose was to determine the optimal HF % exchange as incorporated in a range of hybrid functionals (M06HF, M062X, M06L, CAM-B3LYP, PBE0, BMK, and B3LYP) capable to produce, reliably and as close as possible to those obtained from MP2 calculations, NLO parameters and, in particular, first-order static hyperpolarizabilities. The CAM-B3LYP functional was revealed to be the most suitable one. The pair N(CH 3) 2 /NO 2 was then determined as the most efficient pair of groups in producing appreciable NLO responses. The effect of the substitution position on the pyrene moiety was also investigated, whereby aligning the two substituents involving the D and A groups in the direction of the dipole moment as in the (1,6 DVP) derivatives was shown to be most favorable for increasing the NLO parameters. ■ INTRODUCTION Because of their numerous applications in the areas of photonics and optoelectronics, 1−3 various types of NLO active materials have been developed over the recent years. These materials are used in technical applications like lasers, 4 optical data storage devices, biological imaging, 5 signal processing, and in electro-optical modulation as well. 6,7 These materials range from being inorganic to organic to organometallic. 8−11 In order to identify additional and more efficient materials for further NLO applications, many studies were conducted on organic materials, including, for instance, the polycyclic aromatic hydrocarbons (PAH) or, polynuclear aromatic hydrocarbons. 12−15 These latter are a series of hydrocarbons in which carbon atoms are arranged in multiple aromatic rings sharing one or more C−C bond. The resulting structures are molecules wherein all carbon and hydrogen atoms are lying in the same plane. Accordingly, their physical and chemical characteristics make them eligible as π-conjugated bridges 16 or chromophores in push−pull systems, 17 which contain a donor (D) and an acceptor (A) group end-capping the π-conjugated backbone. 18−20 Thereby, an enhancement of the intramolecular charge transfer (ICT) is obtained, 21−23 which results in a strong NLO response. The latter is closely connected to several factors such as the energy gap (ΔE H-L = ε LUMO − ε HOMO), the occupation quotient π*/π, the central bond length, the bond-length alternation (BLA), the delocalization energy E(2), the electronic transitions parameters, the polarizability α, and, finally, the most important factors: the static first order hyper-polarizability β 0 and the dipole moment μ 0 , 24−26 which have been at the center of much interest from theoretical chemists 27−34 for the past couple of decades. In this field, pure and hybrid DFT methods have been demonstrated to fail in calculating reliable hyperpolarizabilities, 35−38 while post-HF methods reproduce hyperpolarizabilities with a good accuracy 39 and are considered in the present work as a reference. The wrong asymptotic behavior of DFT methods 40 has been shown to be at the origin of the resulting inaccurate values. 41,42 Therefore, enhancing the incorporated HF exchange (X) fraction in hybrid DFT fuctionals as well as long-range corrections become very important in order to improve results, and many papers have appeared dealing with this goal. 43,44,37,38 Despite the popularity of the Minnesota M06 functionals, 45,46 their performance in calculating NLO responses of push−pull molecules has not been extensively tested. In this work, we focus on calculating NLO responses of various divinylpyrene derivatives that we consider as sufficiently large systems to test to what extent DFT methods can produce satisfactory results. Actually, as a special case of a PAH, we have pyrene, which consists of four fused benzene rings 47,48 (Figure 1). Since some years, pyrene and its derivatives have attracted considerable attention in the field of NLO because of their remarkable ICT. Actually, they have been frequently used as materials in organic light emitting diodes (OLED), in organic field effect transistors (OFET), and in organic photovoltaic cells. 49,50 So far, some 1-monosubstituted pyrene derivatives have been studied using the DFT-B3LYP/6-31g (d,p) level of theory. 51 It was demonstrated that the pyrene structure is strongly affected by the nature of the substituent. These variations are then obviously reflected in appreciable changes in the dipole moments values. Another work also using the B3LYP/6-31g (d,p) and dealing with some 1,3,6,8 tetra-hologeno-substituted