Excited-state properties from ground-state DFT descriptors: A QSPR approach for dyes

https://doi.org/10.1016/j.jmgm.2009.11.001Get rights and content

Abstract

This work presents a quantitative structure–property relationship (QSPR)-based approach allowing an accurate prediction of the excited-state properties of organic dyes (anthraquinones and azobenzenes) from ground-state molecular descriptors, obtained within the (conceptual) density functional theory (DFT) framework. The ab initio computation of the descriptors was achieved at several levels of theory, so that the influence of the basis set size as well as of the modeling of environmental effects could be statistically quantified. It turns out that, for the entire data set, a statistically-robust four-variable multiple linear regression based on PCM-PBE0/6-31G calculations delivers a Radj2 of 0.93 associated to predictive errors allowing for rapid and efficient dye design. All the selected descriptors are independent of the dye's family, an advantage over previously designed QSPR schemes. On top of that, the obtained accuracy is comparable to the one of the today's reference methods while exceeding the one of hardness-based fittings. QSPR relationships specific to both families of dyes have also been built up. This work paves the way towards reliable and computationally affordable color design for organic dyes.

Introduction

Organic chromogens play a crucial industrial role since 1880, not only as dyes or pigments, but also in more technological fields, such as thermal transfer systems, molecular switches, media storages or photovoltaic devices [1], [2], [3]. Often, industrial applications imply the design of specific dyes possessing given spectroscopic (and sometimes photochromic) properties. In that framework, beside the traditional synthesis tools belonging to the chemist cultural background, simulation approaches can provide an efficient and complementary approach for the screening of new molecules. Of course, such theoretical approaches should rely upon the development of effective tools for the prediction of the color of dyes, a great challenge in the field of theoretical chemistry. Indeed, modeling the color generated by photon absorption requires the description of low-lying excited-state(s), a demanding task. If physico-chemical properties related to the electronic distribution (such as light absorption and emission), can be accurately evaluated by quantum chemical models, the bottleneck remains the balance between accuracy and computing times. On the one hand, post-Hartree-Fock methods (EOM-CC, MR-CI or CAS-PT2) are accurate but time consuming and present a problematic scaling with the system dimension; on the other hand, semi-empirical methods (CNDO/S, INDO/S) are applicable for large systems but with a significant loss in accuracy [4], [5]. In the last years, the time-dependent density functional theory (TD-DFT) [6], [7], [8] has emerged as a popular scheme able to deliver remarkable accuracies with “reasonable” computational times for both organic and inorganic species [9], [10], [11], [12], [13], [14], [15], [16]. Nevertheless, the TD-DFT methods, even in their most modern implementations, scale as O(N3), N being the number of basis functions, the pre-factor being large. As a matter of fact, TD-DFT studies are limited to medium-size molecules (100–150 atoms, 1000–3000 basis functions), especially when atomic basis sets including diffuse/polarized orbitals are mandatory.

It is therefore interesting, to search for alternative theoretical protocols coupling speed and accuracy, especially by estimating electronic spectra from directly-available ground-state properties. In that sense, the quantitative structure activity/properties relationship (QSAR/QSPR) methods appear as ideal candidates. Nowadays such approaches are mainly used in the toxic property screening (i.e. the nitrobenzene molecule [17]) and their primary applications mainly encompass biology [18], [19], toxicology [20], [21] and drug design [22], [23], [24]. However, a growing number of applications have recently appeared for the prediction of physico-chemical properties [25], [26], [27]. Apart from the usual drawbacks of numerical methods (neural networks [28], genetic algorithms [29] and statistical regressions [30]) used for obtaining the relationship, the main limit for building up such chemical QSPR models remains the reliability of the experimental training data set.

In this paper we propose the development of a QSPR protocol for the prediction of the main π–π* transition of two families of industrial organic dyes: 9,10-anthraquinones (AQ) and azobenzenes (AB, see Fig. 1). Together they represent about 90% of today's world dye production [2], [31]. We are aware of only a few previous works using information theory for the spectral properties of these dyes. The first two, by three of us [32], [33], aims at an optimal combination of TD-DFT results obtained with different functionals, in order to reproduce the absorption wavelengths of AQ dyes, a computationally successful but demanding approach. The third, by Åstrand and coworkers [34] relates the nitrogen double bond lengths (and critical points of the electron density) to the transition energies of a large set of AB compounds. While such approach delivers accurate transition energies, it remains difficult to generalize as a family-specific geometrical parameter appears necessary to obtain valuable predictions. We have found several QSPR works carried out for dyes but these studies focus on ground-state related properties (thermal stability [35], affinity with fibres [36], adsorption [37] or acidity [38]), and excludes, to the best of our knowledge, properties related to the excited-states, such as the color. Here, the developed protocol starts from DFT calculations of the ground electronic states and includes general molecular descriptors belonging to the so-called family of “conceptual” DFT [39], [40]. Correlations between these data and the experimental ones have been brought to light to obtain a predictive model for the most important excited-state property. Our results are compared to these of TD-DFT calculations.

Section snippets

Data set

The choice of the training set of experimental data, a critical point in any QSPR analysis, is difficult here, as experimental conditions (solvent) might significantly influence the measured spectral properties, i.e. the wavelength of maximal absorption (λmax). Therefore, to allow straightforward and consistent comparisons with previous TD-DFT benchmarks [41], we have chosen 24 anthraquinones and 22 azobenzenes. For each series, a large panel of substituents has been included, so that the

Results and discussion

The QSPR methodology was applied to predict the wavelength of maximum absorption (λmax). The eight descriptors have been calculated for the 24 AQ with the 6-311+G(2d,p) and 6-31G basis sets with and without ethanol solvent (see Supporting Information, Tables S1–S3). The corresponding information for the AB set are located at Table S4–S6. Note that we have not carried out gas-phase calculations with the most extended atomic basis set as including the solvent effects does not provoke a

Conclusions

Using a QSPR methodology relying on ground-state “conceptual DFT” descriptors, models have been designed to predict an essential excited-state property: the wavelength of maximal absorption of organic dyes. Our training set contained 24 anthraquinones and 22 azobenzenes, solvated in polar media, as these two families present the largest industrial interest. First the influence of the theoretical level used to compute the descriptors was tested and it turned out that the selection of a large

Acknowledgements

DJ and EAP thank the Belgian National Fund for their research associate and senior research associate positions, respectively. DJ, EAP, and CA thank the Commissariat Général aux Relations Internationale and the Egide agency for supporting this work within the framework of the Tournesol Scientific cooperation between France and the Communauté Française de Belgique. DFT calculations have been performed on the Interuniversity Scientific Computing Facility (ISCF), installed at the Facultés

References (62)

  • D. Jacquemin et al.

    Chem. Phys. Lett.

    (2006)
  • D. Jacquemin et al.

    Chem. Phys. Lett.

    (2005)
  • V.K. Agrawal et al.

    Bioorg. Med. Chem.

    (2001)
  • S.P. Bradbury

    Toxicol. Lett.

    (1995)
  • M. Grover et al.

    Pharm. Sci. Technol. Today

    (2000)
  • M. Grover et al.

    Pharm. Sci. Technol. Today

    (2000)
  • J. Taskinen et al.

    Adv. Drug Deliv. Rev.

    (2003)
  • D. Jacquemin et al.

    Spectrochim. Acta A

    (2007)
  • S. Timofei et al.

    Dyes Pigments

    (2000)
  • D. Jacquemin et al.

    J. Chem. Theory Comput.

    (2008)
  • P. Thanikaivelan et al.

    Chem. Phys. Lett.

    (2000)
  • J. Padmanabhan et al.

    Bioorg. Med. Chem.

    (2006)
  • I. Ciofini et al.

    Chem. Phys.

    (2005)
  • P.C. Chen et al.

    J. Mol. Struct. (Theochem)

    (2005)
  • A. Natansohn et al.

    Chem. Rev.

    (2002)
  • H. Zollinger

    Color Chemistry, Syntheses Properties and Applications of Organic Dyes and Pigments

    (2003)
  • V. Balzani et al.

    Molecular Devices and Machines

    (2004)
  • J. Fabian

    Theor. Chem. Acc.

    (2001)
  • J.P. Perdew et al.

    J. Chem. Phys.

    (2005)
  • E. Runge et al.

    Phys. Rev. Lett.

    (1984)
  • K. Burke et al.

    J. Chem. Phys.

    (2005)
  • D. Jacquemin et al.

    J. Am. Chem. Soc.

    (2006)
  • L. Petit et al.

    J. Phys. Chem. B

    (2006)
  • A.D. Quartarolo et al.

    Chem. Eur. J.

    (2006)
  • L. Petit et al.

    J. Phys. Chem. B

    (2005)
  • R. Improta et al.

    Angew. Chem. Int. Ed. Engl.

    (2007)
  • M. Dierksen et al.

    J. Phys. Chem. A

    (2004)
  • M.J.G. Peach et al.

    J. Chem. Phys.

    (2008)
  • H. Gao et al.

    Chem. Rev.

    (1999)
  • D.A. Winkler

    Brief Bioinform.

    (2002)
  • C.D. Selassie et al.

    Chem. Rev.

    (2002)
  • Cited by (0)

    View full text