Assessment of Conventional Density Functional Schemes for Computing the Dipole Moment and (Hyper)polarizabilities of Push−Pull π-Conjugated Systems

Abstract

DFT schemes based on conventional exchange-correlation (XC) functionals have been employed to determine the dipole moment (μ), polarizability (α), and first (β) and second (γ) hyperpolarizabilities of push−pull π-conjugated systems. In addition to the failures already pointed out for α and γ in a recent study on polyacetylene chains [J. Chem. Phys. 1998, 109, 10489; Phys. Rev. Lett. 1999, 83, 694], these functionals are also unsuitable for the evaluation of μ and β. In the case of β, in particular, an almost catastrophic behavior with respect to increasing chain length is found. We show that the C functional has a negligible effect on the calculated μ, α, β, and γ whereas the X-part is responsible for the large property overestimations when the size of the system increases. The overly large μ values are associated with an overestimation of the charge transfer between the donor and the acceptor whereas for α, β, and γ, incomplete screening of the external electric field is responsible for the large discrepancies with respect to accurate values. Our results show that current XC functionals incorrectly describe the polarization of conjugated systems when the polarization is due to donor/acceptor substitution or an external field or both.

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.…”

“…It is generally recognized, here and elsewhere, [21][22][23][24][25] that pure GGAs tend to overestimate NLO responses, whereas the opposite is true when including large amounts of HF exchange. Tuned LC-DFT can interpolate between these two extremes leading to a more balanced description of hyperpolarizabilities.…”

“…However, these methods have an incorrect asymptotic exchange potential behavior, which leads to an underestimation of charge-transfer excitation energies and, consequently, a large (at times catastrophic) overestimation of hyperpolarizabilities. [21][22][23][24][25] Although inclusion of 100% Hartree-Fock (HF) exchange should in principle fix this problem, in practice results are often unsatisfactory due to the reliance of DFT in the error cancellation between inexact exchange and correlation terms. …”

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

“…[8][9][10][11] This has generated much interest around this kind of compounds owing to the applications of materials with large hyperpolarizabilities in nonlinear optics [12][13][14][15][16][17][18][19] (NLO), and a considerable amount of effort in this area of research has been devoted to the theoretical prediction of NLO properties via computational methods of quantum chemistry. [19][20][21][22][23][24][25][26][27][28] It was recognized early on that the theoretical determination of hyperpolarizabilities was very challenging for ab initio and semi-empirical methods. 8,12,20 The advent of modern density functional theory (DFT) methods, very successful in many areas across chemistry and materials science, does not solve this problem.…”

“…In fact, the description of CT excitations by time-dependent (TD)DFT using popular global hybrids and generalized gradient approximations (GGAs) is fundamentally flawed, often leading to gross underestimations of E CT and, consequently, exaggeration of β T z . [23][24][25] In TDDFT, the approximate expression for E CT comparable to eq 1 yields 1,2…”