Electron correlation effects on the first hyperpolarizability of push–pull π-conjugated systems

Abstract

The first hyperpolarizability (β) of representative push-pull π-conjugated compounds has been calculated at several levels of approximation to assess the effects of electron correlation. First, the 6-31+G(d) basis set has been shown to give the best balance between accuracy and computational resources for a polyene linker whereas for polyyne linker, the 6-31G(d) basis set is already an optimal choice. As a result of cancellations between higher order contributions, the MP2 method turns out to be the method of choice to predict β of push-pull π-conjugated systems since it closely reproduces the values obtained with the reference CCSD(T) scheme. Moreover, the SDQ-MP4 and CCSD approaches provide rarely improved estimates over MP2 while the MP4 method does not represent an improvement over MP4-SDQ or the SCS-MP2 method, over MP2. Among density functional theory exchange-correlation functionals, LC-BLYP is reliable when characterizing the changes of first hyperpolarizability upon enlarging the π-conjugated linker or upon changing the polyyne linker into a polyene segment. Nevertheless, its reliability is very similar to what can be achieved with the Hartree-Fock method and the MP2 scheme is by far more accurate. On the other hand, the BLYP, B3LYP, and BHandHLYP functionals perform quantitatively better in a number of cases but the trends are poorly described. This is also the case of the B2-PLYP and mPW2-PLYP functionals, which are often the most accurate, though they underestimate the increase of β when going from polyyne to polyene linkers and overestimate the enhancement of β with chain length.

Can Gap Tuning Schemes of Long-Range Corrected Hybrid Functionals Improve the Description of Hyperpolarizabilities?

“…This Table illustrates the improvement of tuned over standard LC-DFT when comparing with static β tot values calculated by the MP2 method, which has been shown to produce reasonably accurate molecular hyperpolarizabilities. 22,40,67,[76][77][78] The qualitative observations that can be drawn from Table 5 are similar to those obtained when using experimental data as reference; LC-DFT tends to underestimate hyperpolarizabilities, the tuning procedure roughly halves this error, and the improvement is more noticeable in polar environments. We also note that, although MP2 tends to somehow overshoot β ijk values compared to coupled cluster calculations, this effect is usually small when using large enough basis sets, similar to the ones used here (see, e.g., Refs.…”

“…Numerous studies have found that LC-DFT methods provide better estimates for hyperpolarizabilities and related properties in chargetransfer compounds as compared to hybrid and GGA functionals. 18,[32][33][34][35][36][37][38][39][40][41][42] However, some recent works have also concluded that LC-DFT does not consistently outperform hybrids and GGAs; for example, in Ref. 43, the range-separated CAM-B3LYP provides the best results in some solvents, but the standard hybrid B3LYP is better in others.…”

Can Short- and Middle-Range Hybrids Describe the Hyperpolarizabilities of Long-Range Charge-Transfer Compounds?

“…All of these can be expected to be reasonably accurate. 24,26,42,46,70,73 We hope that this work will stimulate more extensive studies on the adequacy of SR and MR hybrids for the prediction of NLO properties of organic materials.…”

“…This is the idea behind long-range corrected (LC)-DFT functionals, [29][30][31][32][33][34] which have been shown to provide an improved description of long-range properties (including CT excitations and hyperpolarizabilities) as compared to global hybrids and GGAs. [35][36][37][38][39][40][41][42][43][44][45][46][47][48] Furthermore, the range-separation parameter of LC-DFT can be optimized ab initio for the system of interest by demanding that the molecule, and its corresponding anion, obey the Coulomb operator is divided in three parts). However, these functionals are rarely used in hyperpolarizability calculations since it is believed that the incorrect asymptotic behavior of the exchange potential would lead to catastrophic overshooting of GGAs.…”

Double-hybrid density functionals: merging wavefunction and density approaches to get the best of both worlds

“…Other recent applications, the (necessarily limited and biased) following selection tries only to show the wide and rich range of systems being currently afforded, include the modelling of ionic liquids [175], gas adsorption in metalorganic frameworks [176,177], isomerism in monosaccharides [178], conformational analysis [179,180], nonlinear optical responses [181], magnetic couplings in organometallics [182], enzymatic catalysis [183,184], electron paramagnetic resonance hyperfine coupling tensors [185], inclusion complexes and nanoencapsulation [186], electronic circular dichroism [187], organometallic complexes of graphene [188], interfacial chemistry [189], photosynthetic water oxidation [190], hyperpolarizability of pushpull systems [191], lightharvesting complexes [192], adsorbate-zeolite interactions [193], or harmonic and anharmonic vibrational frequency calculations [194], among others. • Figure 1.…”