Static electronic and vibrational first hyperpolarizability of meta-dinitrobenzene as studied by quantum chemical calculations R. Zales ´ny a, * , G. Wójcik a , I. Mossakowska a , W. Bartkowiak a , A. Avramopoulos b,c , M.G. Papadopoulos b a Institute of Physical and Theoretical Chemistry, Wrocław University of Technology, Wyb. Wyspian ´skiego 27, 50-370 Wrocław, Poland b Institute of Organic and Pharmaceutical Chemistry, The National Hellenic Research Foundation, 48 Vas. Constantinou Avenue, 11635 Athens, Greece c Department of Informatics and Computer Technology, Technological Educational Institute of Lamia, 35100 Lamia, Greece article info Article history: Received 3 February 2009 Received in revised form 15 April 2009 Accepted 16 April 2009 Available online 22 April 2009 Keywords: First hyperpolarizability Vibrational contributions meta-dinitrobenzene Electron correlation Nonlinear optical properties Anharmonicity abstract In the present study, we report on the results of computations of the electronic and the vibrational con- tributions to the static first hyperpolarizability ðbÞ of meta-dinitrobenzene molecule. It turned out that the electron correlation effects are much more important for reliable prediction of the electronic counter- part than for determining vibrational corrections: b e value is increased by about 500% passing from the HF to the CCSD(T) level of theory. The preliminary assessment of density functional theory in determina- tion of hyperpolarizabilities shows that harmonic contributions to b, contrary to the purely electronic contributions, are substantially underestimated in comparison with the wave function theory results. Another important finding of this study is that long-range corrected functionals tend to improve upon traditional functionals both in determining electronic as well as vibrational hyperpolarizabilities. It is also demonstrated that the vibrations of the nitro groups have a predominant influence on the vibrational contributions to b vib . The mechanical and electrical anharmonicity correction terms to the vibrational hyperpolarizability were found to be substantially larger than the lowest-order harmonic term. Ó 2009 Elsevier B.V. All rights reserved. 1. Introduction The electronic and vibrational contributions to the first hyper- polarizabilities have been studied theoretically for many organic and inorganic systems [1,2]. It should be underscored, however, that the electronic counterpart of the nonlinear optical response have been studied much more extensively than the vibrational one. The rationale for this is that the vibrational contributions are important only for selected nonlinear optical processes [3]. The other reason, perhaps of even higher importance, is that the evaluation of the vibrational corrections is much more computa- tionally demanding than the calculations of the electronic contri- butions. The values of the electronic first hyperpolarizability ðbÞ were found to be quite large for the so-called push–pull molecules, i.e. p-conjugated molecules with the electron donating and the electron withdrawing substituents attached to a p-bridge, compared to the monosubstituded systems [4–6]. This type of functionalization of organic materials, with the purpose of maxi- mizing NLO properties, is still commonly followed route. Likewise, structure–property relationships have already been established with the purpose of maximizing the two-photon absorption cross sections of molecules [7–9]. The relations between the electronic and the vibrational contri- butions to molecular hyperpolarizabilities, if any, are still not understood. According to Zerbi and co-workers [10–12], the ratio of the electronic and vibrational static hyperpolizabilities ought to be close to unity, as both, the electronic and vibrational contri- butions to b are two independent measures of the same physical quantity. As it was shown later on the basis of ab initio computa- tions the ratio is system specific and, in particular, depends cru- cially on the applied level of theory [13–16]. In the case of para- nitroaniline, the vibrational contributions to b were found at the HF level of theory to be comparable with the electronic counterpart [17]. As it was shown by Champagne [17], the vibrational part of b, at least within the double-harmonic oscillator approximation, is mainly determined by the normal modes describing the oscilla- tions between aromatic-like and quinoid-like molecular structures. On the other hand, our previous quantum chemical calculations of the nonlinear optical properties of the isolated meta-dinitroben- zene molecule, performed at the Hartree–Fock level of theory, re- vealed significant contribution of the nitro groups’ torsional vibrations to the static vibrational first-order hyperpolarizability and the predominant value of the vibrational hyperpolarizability as compared with its electronic counterpart [18]. Our variable- temperature X-ray diffraction studies of the meta-dinitrobenzene crystal, including the analysis of atomic thermal motions within the TLS (translation/libration/screw) rigid body approach [19,20], also revealed the important role of the nitro groups’ torsional 0166-1280/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2009.04.011 * Corresponding author. E-mail address: robert.zalesny@pwr.wroc.pl (R. Zales ´ny). Journal of Molecular Structure: THEOCHEM 907 (2009) 46–50 Contents lists available at ScienceDirect Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem