Electronic structure and spectra of ruthenium diimine complexes by density functional theory and INDO/S. Comparison of the two methods

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Abstract

Density functional theory calculations have been carried out on the series [Ru(bqdi)n(bpy)3−n]2+ (bpy=2,2′-bipyridine, bqdi=o-benzoquinonediimine) to explore the extent of coupling between metal 4d and ligand π and π* orbitals. Time-dependent density-functional response theory (TD-DFRT) has been used to predict the complex electronic spectra which are compared with their experimental data. The main thrust of the paper is a comparison of these calculations with those carried out using Zerner's frequently used INDO/S method. Different procedures for the electron population analysis of molecular orbitals are described and discussed. The agreement in terms of orbital energies, orbital mixing and electronic spectra is remarkably good. This confirms that for these species, and probably for all non-solvatochromic species in general, INDO/S is a good model reproducing very well the results of the computationally much more demanding, but also more reliable TD-DFRT calculations.

Density functional theory calculations have been carried out on the series [Ru(bqdi)n(bpy)3−n]2+ to explore the extent of coupling between metal and ligand orbitals, and to compare performance of time-dependent density-functional response theory and semi-empirical INDO/S method for prediction of electronic spectra. The agreement in terms of orbital energies, orbital mixing, and electronic spectra is remarkably good. This confirms that for these species, and probably for non-solvatochromic species in general, INDO/S is a good model reproducing well the results of the TD-DFRT calculations.

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Introduction

Electronic coupling in transition metal complexes and the prediction of their electronic spectra has been a topic of our interest for a long time. We are interested in studying how the covalent bonding in inorganic complexes affects their electronic spectra and electrochemistry. Currently two theoretical methods, namely density functional theory (DFT) [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11] and the semi-empirical INDO method [12], [13], [14], [15], [16], [17], [18], [19], [20] (or similar variants, as CINDO/CI [21], [22], [23], [24]), are commonly used to analyze the electronic structure and spectra of transition metal complexes. From the 1970s until the present the INDO/S method developed for transition metal systems by M.C. Zerner was a primary tool to study transition metal systems. During the past ten years DFT has been remarkably successful at evaluating a variety of ground state properties with high accuracy. The time-dependent generalization of DFT (TD-DFT) offered a rigorous route to calculate the dynamic response of the charge density. Combining this with the linear response theory allowed calculations of vertical electronic excitation spectra [4], [5], [6], [7], [8], [9], [10]. Several tests [6], [10] have shown that current exchange-correlation functionals, including hybrid functionals, provide results for excitation energies superior to those obtained by standard ab initio techniques. The reliability of TD-DFT approach in obtaining accurate predictions of excitation energies and oscillator strengths is by now well documented. It has been successfully used to calculate the electronic spectra of transition metal complexes such as metal fluorides [25], metal carbonyls [26], [27], nitrosyl complexes [28], [29], quinone–catechol complexes [30], and metalloporphyrins [31]. We are interested to explore how different are the wavefunctions and properties of excited states obtained with DFT and TD-DFT from those obtained with INDO/S and whether the electronic spectra predicted by the two methods are similar or not. Certainly TD-DFT is regarded today as the more accurate computational method, but given the high computational costs involved, especially with larger molecules, it is important to know how close are the predictions from these two methods. In fact, large molecular systems such as multi-nuclear transition metal complexes are very demanding computationally and out of reach for DFT and TD-DFT calculations for now. INDO/S still has an important role to play for such systems and is computationally inexpensive—but how does it perform relative to TD-DFT?

Here, we study four ruthenium complexes, [Ru(bqdi)n(bpy)3−n]2+ (n=0−3, bpy=2,2′-bipyridine, bqdi=o-benzoquinonediimine), to test and compare the performance of DFT and INDO/S methods. The diimine complexes of ruthenium have played an enormous role in the development of our understanding of the basic photochemistry and photophysics of transition metal systems. Among the fundamental questions that have been examined for these systems is the degree of spatial localization of transferred charge in the photoexcited states. We have previously studied these species using the INDO/S method [32], [33] and now we want to verify our earlier conclusions by applying DFT and TD-DFT. This series has been chosen because it spans a range from relatively little Ru–ligand interaction (Ru–bpy) to very strong Ru–ligand (bqdi) interaction (or coupling).

One additional effect which must be considered is that solvent molecules interact strongly with highly charged ions, and these interactions are central to electron-transfer energetics.

Section snippets

Computational details

The DFT calculations presented in this article have been carried out using the gaussian-98 program [34]. Becke's three parameter hybrid functional [35] with the LYP correlation functional [36] (B3LYP) and an effective core potential basis set LanL2DZ [37], [38], [39], [40] were employed in all the DFT calculations. The SCF convergence criterion was a change of less than 10−8 Hartree in the total energy.

The electronic spectra of these complexes were calculated with the INDO/S method [11], [12],

Structures

As can be seen from Table 1, DFT calculations with the B3LYP functional and LanL2DZ basis set are able to predict the structures of these complexes quite reasonably. The B3LYP/LanL2DZ calculations do over-estimate the RuN bond lengths in [Ru(bpy)3]2+ by 0.03–0.04 Å, but the local spin density calculations with the SVWN functional [48], [49], [50], [51] and the same basis set gave underestimated RuN distances (2.023 Å). This is not surprising, because local spin density methods usually lead to

Electronic spectra

The TD-DFRT and INDO/S methods were employed to evaluate the properties of the excited states of [Ru(bqdi)n(bpy)3−n]2+ complexes. TD-DFRT provides a first principles method for the calculation of excitation energies within a density functional framework. The reliability of the TD-DFRT approach in obtaining accurate predictions of excitation energies and oscillator strengths is established [4], [5], [6], [7], [8], [9], [10], [11], [25], [26], [27], [28], [29], [30], [31]. TD-DFRT calculations

Conclusions

The electronic spectra calculations for the [Ru(bqdi)n(bpy)3−n]2+ complexes show that both INDO/S and TD-DFRT are remarkably accurate. The average deviation between the calculated and experimental transition energies is 1100 cm−1 (0.14 eV) for INDO/S and 900 cm−1 (0.11 eV) for TD-DFRT. Agreement between the two models is also exceptionally good. For [Ru(bqdi)n(bpy)3−n]2+ complexes the INDO/S method provides reliable results close enough to those which could be obtained at much greater

Acknowledgements

We thank the Province of Ontario for an Ontario Graduate Fellowship (SIG) and NSERC (Ottawa) for financial support.

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