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Insights into the Influence of Dispersion Correction in the Theoretical Treatment of Guanidine-Quinoline Copper(I) Complexes Alexander Hoffmann,[a] Richard Grunzke,[b] and Sonja Herres-Pawlis*[a] For the description of steric effects, dispersion correction is important in density functional theory. By investigation of sterically encumbered guanidine-quinoline copper bis(chelate) complexes, we could show that the correct description requires modern dispersion correction using Becke–Johnson (BJ) damping and that earlier dispersion corrections are not sufficient. The triple-zeta basis set def2-TZVP of the Ahlrichs series is balanced and converged for the structural description. With regard to functionals, the best structural description is obtained with the TPSSh functional but B3LYP is very suited as well. Cutting of ligand substituents leads to distortions which limit the predictive ability of such calculations.

We recommend the calculation of “full” chemical systems with inclusion of dispersion correction using BJ damping. In the further analysis of the regarded copper bis(chelate) complexes, we found that the theoretical description of optical and Raman spectra is not much affected by the dispersion although charge transfer excitations come into play and that B3LYP/def2-TZVP is the best choice. Hence, we can derive the result that the correct structural description with dispersion serves as crucial basis for subsequent C 2014 Wiley Periodicals, Inc. calculation steps. V

Introduction

the description of optical transitions remains a challenge to time-dependent density functional theory (TD-DFT).[11,16] Recently, we presented electron transfer models based on guanidine-quinoline-bis(chelate) complexes with the exceptional property that the coordination between copper(I) and copper(II) showed only minor differences residing in an intermediate coordination geometry between tetrahedron and square-planar geometry.[17] In a theoretical study,[15] we found that BP86/6-311g(d) showed the best performance in structural regard whereas for optical description B3LYP/def2-TZVP was best applicable. At that point in time, we used numerous pure and hybrid functionals as well as the long-range corrected B3LYP (CAM-B3LYP) and the dispersion-corrected wB97xD functional. Here, no substantial influence of the dispersion interaction was found. Meanwhile, different versions of Grimme’s dispersion are available in the latest versions of several quantum chemical codes. In this study, we present now an in-depth-study on the dispersion influence on the structural properties of the guanidinequinoline-bis(chelate) copper(I) complex cations [Cu(TMGqu)2]1

Copper is besides iron the most important metal in nature for redox processes. The most relevant fields are here oxygen transport and activation (e.g. in Type-3 copper proteins [1]) and electron transfer (e.g., Type-1 and Type-Zero copper proteins [1] ). Type-1 proteins use copper as a one electron relay, shuttling between the cuprous and cupric oxidation states. The inner coordination sphere most directly affects the redox properties of metal ions.[2] Thus, detailed tuning of the CuII/I redox couple is central for electron transfer in nature and also important in synthetic complexes for catalytic applications.[3] The tight relationship between redox potential and structure has therefore been investigated for many years.[3–5] There are multiple factors governing the redox potential: effects of first coordination sphere such as geometric constraints (tetrahedral vs. square planar) and ligand donor atoms but also second coordination sphere effects.[6–9] Copper(I) is a soft Lewis acid preferring soft donors (such as imines and cysteinates) in a trigonal-planar or tetrahedral environment, copper(II) a harder one accepting coordination of numerous nitrogen donors but also sulfur and oxygen donors in square-planar or square-pyramidal environment. The coordinative versatility of both ions makes their coordination chemistry so unique and useful for nature. The correct theoretical description of copper complexes is an ongoing topic owing to their importance in bioinorganic chemistry.[1] In spite of numerous efforts, the description of structural and optical properties of copper complexes is not straightforward at all but requires careful benchmarking.[10–12] Lots of work has been performed on the validation of functionals and basis sets[13,14] on test sets of small copper complexes[10] or selected examples of larger ones.[15] Especially,

DOI: 10.1002/jcc.23706

[a] A. Hoffmann, S. Herres-Pawlis Department of Chemistry, Ludwig-Maximilians-Universit€ at M€ unchen, Butenandtstr. 5 - 13, 81377 M€ unchen, Germany E-mail: [email protected] [b] R. Grunzke Zentrum f€ ur Informationsdienste und Hochleistungsrechnen, Technische Universit€ at Dresden, Zellescher Weg 12–14, 01062 Dresden, Germany. Dedicated to Dr. Klaus R€ omer on the occasion of his 75th birthday Contract grant sponsor: Deutsche Forschungsgemeinschaft; Contract grant number: FOR1405; Contract grant sponsor: European Commission’s Seventh Framework Programme (FP7/2007–2013); Contract grant number: 312579 (ER-flow) C 2014 Wiley Periodicals, Inc. V

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and its smaller congener [Cu(Gqu)2]1 where the methyl substituents are replaced by hydrogen atoms. By this medium-sized model, we can study the steric encumbrance of the tetramethylguanidine groups which considerably contributes to the strongly distorted coordination environment. In addition, we tested the basis set convergence of the Ahlrichs def2 series with regard to the structural description.[18] As the copper–nitrogen bond lengths and the angle between the chelate ligands are highly sensitive toward choice of functional, basis sets and dispersion correction we focused on the analysis of selected geometric parameters instead of using global indicators. With regard to the bioinorganic application in the context of excited state calculations, we also investigated the dispersion effect on the optical and Raman properties for the large system.

Computational Details The geometries of the complex cations [Cu(TMGqu)2]1 and [Cu(Gqu)2]1 are fully optimised at different levels of DFT using the Berny algorithm as implemented in Gaussian 09.[19] All optimised geometries are characterised as stationary points on the potential energy surface with vibrational frequency calculations. TD-DFT calculations are performed on the equilibrium ground state geometries with different DFT levels. For all calculations we used the ultrafine integration grid. The Gaussian 09 calculations are performed with the nonlocal hybrid GGAs B3LYP, [20–23] BHLYP, [20,21] the local meta GGA TPSS,[24] the nonlocal hybrid meta GGA TPSSh[24] and the pure, local functional M06-L[25]. Ahlrichs type basis sets def2-SVP, def2TZVP, and def2-QZVP are used.[18] Continuous UV/Vis spectra are plotted with the AOMix program [26] using the Gaussian model. The half-bandwidths were taken to be equal to 3000.0 cm21. Continuous Raman spectra are plotted with the SWizard program [27] using Lorentz functions with half-bandwidths of 15 cm21. As dispersion correction, we used the standard Grimme dispersion (named as D2[28] and D3[29,30]) as implemented in Gaussian, Revision D.01. The Becke–Johnson (BJ) dispersion was also used as implemented in Gaussian, Revision D.01 with the following parameters for the functionals (Table 1). Some of these calculations have been performed within the MoSGrid environment.[32,33]

Results and Discussion As already described in previous work,[15] the accurate structural description of copper complexes can be challenging. Table 1. Becke–Johnson damping factors. Functional

S8

a1

a2

References

B3LYP TPSSh

1.9889 2.2382

0.3981 0.4529

4.4211 4.6550

BHLYP TPSS

1.0354 1.9435

0.2793 0.4535

4.9615 4.4752

31 Grimme, private communication[a] 30 31

[a] For TPSSh, not the values of the paper were used. These corrected values have been kindly provided by Grimme.

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Especially when two types of donor functions compete with each other, the differences in CuAN bond lengths have to be predicted correctly for meaningful further description of spectroscopic properties. In the copper complexes regarded herein, we focus on the interplay of guanidine and quinoline units. The quinoline is in general a softer donor whereas the guanidine is slightly harder but being able to coordinate copper in all oxidation states.[34–48] Moreover, the guanidine unit is sterically very encumbering. In the [Cu(TMGqu)2]1 complex, we found that the guanidine groups impose steric pressure on the bis(chelate) complex resulting in different isomers. Especially with regard to the distorted coordination geometry of [Cu(TMGqu)2]1, the steric influence of the guanidine groups requires further analysis. In previous work,[15] we investigated a very small model with a small imine unit and a demethylated guanidine group for simulations using Green’s functions methods which allow at maximum the treatment of 20 non-H atoms. In fact, the interaction of the guanidine with the small imine was not realistic as the whole quinoline unit was missing but we could calibrate the TD-DFT methodology to manybody perturbation theory yielding the result that careful benchmarking is always required. For a more detailed analysis of the decisive interaction of guanidine and quinoline, we have chosen a medium-sized hypothetic model [Cu(Gqu)2]1 containing the demethylated guanidine group and the full quinoline group (Fig. 1). In previous work, we evaluated several pure and hybrid functionals for the structural and optical description and found that BP86 was ideal for an accurate structural description. Unfortunately, BP86 gives unrealistic results in TD-DFT. As we target on the long range the simulation of excited states by means of DFT and TD-DFT, we need a comprehensive description using one single functional for all steps, e.g. structural optimisation, TD-DFT, frequency calculation and following selected TD-DFT excitations with subsequent relaxation. Hence, we had to omit all pure functionals which gave unreasonable results in the last study and to focus on the classical B3LYP and on modern functionals for transition metal systems such as TPSSh, M06-L and BHLYP. The TPSSh functional is a nonempirical functional except for the a 5 0.1 coefficient of exact exchange; hence, it does not rely on the additional parameters optimised empirically for other functionals such as B3LYP and BP86.[49,50] It has widely been shown that this functional yields very good results for transition metal and especially bioinorganic systems.[51–53] M06-L belongs to the Minnesota family of functionals and is a local functional with 0% HF exchange. It has been reported to be useful for transition metal systems and organometallics and even convincing in the prediction of noncovalent interactions.[13,25] BHLYP[20,54] uses a 1:1 mixture of DFT and exact exchange energies and was recommended for charge transfer systems.[55] Tables 2 and 3 collect all data of the geometry optimisations of both complexes with the functionals B3LYP, TPSSh, M06-L, TPSS, and BHLYP using Ahlrichs basis sets and different types of dispersion. As the new Ahlrichs basis sets are more balanced and efficient as other common basis sets, we restrict our study to the use of def2-SVP, def2-TZVP, and def2-QZVP.[18] WWW.CHEMISTRYVIEWS.COM

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Figure 1. Molecular structure of a) [Cu(TMGqu)2]1 and b) [Cu(Gqu)2]1.

For ease of data presentation, we have summarised the basis set effect for B3LYP and TPSSh for [Cu(TMGqu)2]1 in Figure 2. Figure 2 illustrates that TPSSh predicts the coordinational bond lengths better than B3LYP. Both functionals reflect the

donor difference very well. With regard to Table 2, it has to be remarked that BHLYP predicts both bond lengths too long whereas M06-L comes very close to the experimental CuANgua value and gives a reasonable result for the CuANqu bond

Table 2. Selected bond lengths [A ], angles [ ] and structural parameter s4[56] of the [Cu(TMGqu)2]1 cation. Dispersion Experimental average B3LYP/def2-SVP B3LYP/def2-SVP B3LYP/def2-SVP B3LYP/def2-SVP B3LYP/def2-TZVP B3LYP/def2-TZVP B3LYP/def2-TZVP B3LYP/def2-TZVP B3LYP/def2-TZVP/SMD (MeCN) B3LYP/def2-TZVP/SMD (MeCN) B3LYP/def2-QZVP B3LYP/def2-QZVP B3LYP/def2-QZVP TPSSh/def2-SVP TPSSh/def2-SVP TPSSh/def2-SVP/SMD (MeCN) TPSSh/def2-SVP/SMD (MeCN) TPSSh/def2-TZVP TPSSh/def2-TZVP TPSSh/def2-TZVP/SMD (MeCN) TPSSh/def2-TZVP/SMD (MeCN) TPSSh/def2-QZVP M06L/def2-SVP M06L/def2-SVP M06L/def2-TZVP M06L/def2-TZVP TPSS/def2-TZVP TPSS/def2-TZVP BHLYP/def2-TZVP BHLYP/def2-TZVP [a] s4 ¼ 360



– GD2 GD3 GD3BJ – GD2 GD3 GD3BJ GD3BJ – – GD3 GD3BJ – GD3BJ GD3BJ – – GD3BJ GD3BJ – – – GD3 – GD3 – GD3BJ – GD3BJ

CuANgua

CuANqu

2.082 2.145 2.105 2.109 2.098 2.175 2.123 2.133 2.121 2.137 2.228 2.173 2.130 2.119 2.103 2.067 2.088 2.138 2.110 2.073 2.091 2.134 2.110 2.088 2.088 2.091 2.111 1.903 1.893 2.165 2.127

1.991 2.065 2.056 2.045 2.041 2.051 2.044 2.031 2.024 2.055 2.060 2.047 2.028 2.022 2.031 2.013 2.025 2.045 2.014 1.995 2.012 2.027 2.011 2.032 2.031 2.012 2.019 1.874 1.856 2.106 2.081

s4

[a]

0.59 0.66 0.68 0.62 0.62 0.67 0.61 0.64 0.64 0.64 0.65 0.67 0.64 0.64 0.66 0.64 0.62 0.67 0.67 0.65 0.65 0.68 0.67 0.59 0.59 0.62 0.62 0.52 0.55 0.67 0.64

CuN2,CuN’2 76.1 74.7 66.3 69.9 69.9 77.6 70.3 73.2 73.5 73.5 75.8 77.8 73.1 73.6 74.0 70.5 70.1 76.7 76.2 73.0 74.8 77.6 76.2 66.5 66.9 70.2 70.6 55.1 58.0 78.6 73.6

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Table 3. Selected bond lengths (A ), angles ( ) and structural parameter s4[56] of the [Cu(Gqu)2]1 cation and the [Cu(TMGqu)2]1 cation for comparison. CuANgua

CuANqu

s4[a]

CuN2,CuN’2

– GD3BJ GD3BJ

2.154 2.150 2.104

1.989 1.976 2.013

0.67 0.66 0.70

67.1 64.7 80.2

– GD3BJ GD3BJ

2.110 2.073 2.091

2.014 1.995 2.012

0.67 0.65 0.65

76.2 73.0 74.8

Dispersion 1

[Cu(Gqu)2] TPSSh/def2-TZVP TPSSh/def2-TZVP TPSSh/def2-TZVP/SMD (MeCN) [Cu(TMGqu)2]1 TPSSh/def2-TZVP TPSSh/def2-TZVP TPSSh/def2-TZVP/SMD (MeCN) [a] s4 ¼ 360

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length. The pure functional TPSS predicts both CuAN bonds ˚ too short. In summary, this structural benchlength 0.1 A marking shows that the bond lengths to not change significantly between the use of the triple-zeta def2-TZVP basis set and its quadruple-zeta relative. Hence, the structural convergence is reached here and for further calculations, triple-zeta quality is sufficient. As next question we dealt with the structural influence of the dispersion correction. London dispersion forces are present in all molecules but become only critical in medium-range interactions.[57] The dispersion has its origin in induced dipole moments between atoms in molecules and between molecules, which can be regarded as charge fluctuations or instantaneous electron correlations.[58] There are many ways to treat this complicated process, but the semiclassical way in terms of DFT-D is most common. Originally, this approach dates back to the 1970s using Hartree–Fock theory,[59,60] has been rediscovered around 2000.[61–64] Grimme further developed this approach,[65] and presented then an update named DFT-D2 which was most widely used.[28] In the next generation, DFTD3 offers less empiricism and higher accuracy because Grimme included the atom pairwise-specific dispersion coefficients and a new set of cutoff radii, which were both calculated ab initio.[29] DFT-D3 is available for all elements up to Z 5 94 and can be coupled with more than 45 common density functionals.[58] All these DFT-D methods use damping functions which determine the range of the dispersion correction to avoid near singularities for small interatomic distances and double-

counting effects of correlation at medium distances. Most damping formulae approach zero for very small distances. Thus, the atoms experience a repulsive force which may lead (counter-intuitively) to longer interatomic distances with dispersion correction than without. A finite damping, the socalled Becke-Johnson (BJ) damping, provides small but finite correlation energies for each spatially close-lying atom pair and hence no significant “over-correlation”.[31] The inclusion of this BJ damping (which requires only one additional parameter) into DFT-D3 yields the latest development level which can be used in common quantum chemical codes. This modern description of dispersion can be used in challenging fields such as electron transfer,[66] agostic interactions,[67] and transorganometallic species.[68] Figure 3 shows the effect of the different levels of dispersion correction on the critical CuAN bond lengths. Upon consideration of the attractive London forces, all CuAN bonds are shortened which points into the “right” direction in this case. In general, it can be stated that both for B3LYP and TPSSh a more advanced dispersion correction yields more realistic results. However, in the case of TPSSh/def2-TZVP, the use of GD3BJ leads to a slightly too strong CuANgua bond shortening. Using M06-L, with the def2-SVP basis set, no effect of the dispersion can be observed, as the dispersion is already included by other corrections.[13] Using def2-TZVP, the dispersion inclusion shifts bond lengths to the unrealistic direction which seems to be a strange countereffect between this modern functional and the D3 dispersion. The BHLYP functional

Figure 2. Dependence of CuAN bond lengths on basis set quality and functional for [Cu(TMGqu)2]1.

Figure 3. Dependence of CuAN bond lengths on the inclusion of dispersion correction for [Cu(TMGqu)2]1. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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does not yield better results,[15] and the inclusion of dispersion correction does not help sufficiently. The predictive force of TPSS is not enhanced either by the inclusion of dispersion correction; the CuAN bond lengths become even shorter. The solvent effect tested with B3LYP and TPSSh has to be considered as minor to the structural effect of dispersion correction. The coordination environment is not only defined by the CuAN bond lengths but also by the angle between the chelate planes CuNquNgua and the so-called s4-value which determines the degree of distortion between tetrahedral and square-planar environment.[56] A value of 1 indicates an ideal tetrahedron whereas 0 assigns a square-planar geometry. Figure 4 depicts the dispersion effect on the s4-value whereas Figure 5 shows the effect of the dispersive description on the angles between the two chelate planes CuNquNgua. The coordination environment is highly sensitive towards the degree of dispersion correction as can be seen by the example of B3LYP/def2-TZVP. In fact, the nice agreement to experimental data for GD2 can only be regarded as serendipity. This fine agreement using GD2 is also observed for the angles between the chelate planes (ligands) in Figure 5. However, the description with B3LYP/def2-SVP and TPSSh/def2-SVP is reasonable as well. In summary, the best structural description for [Cu(TMGqu)2]1 is possible with TPSSh/def2-SVP and def2-TZVP with GD3BJ dispersion correction. Using B3LYP with GD3BJ dispersion or M06-L without dispersion yields reasonable results as well. With this information, the smaller congener of [Cu(TMGqu)2]1 is now investigated towards the bulky effect of the guanidine groups. Especially in the regarded bis(chelate) complexes, the steric bulk of the guanidine is crucial for the final coordination between tetrahedral and square-planar coordination with relevance to electron transfer systems. Even without the methyl substituents, the [Cu(Gqu)2]1 system appears sterically encumbered (Fig. 1b). It has to be noticed that in [Cu(Gqu)2]1, the intramolecular interactions are not sterically repulsive. On the contrary, attractive H bridging bonds between the amine NAH groups and the partially negatively charged imine N atoms distort the structure strongly which yields another conformer. This result clearly shows that simplifications of theoretical models have to be performed with great care. Using TPSSh/def2-TZVP ˚ as NHN bond. Table 3 collects the with GD3BJ yields 2.152 A corresponding bond lengths and structural parameters for both cations. To account for the strong polarity effects resulting in this strong NAHN bond, we included also simulations with the implicite SMD solvent model for MeCN.[69] In general, the CuANgua bonds are shorter in [Cu(Gqu)2]1 which indicates stronger binding. As expected, the quinolineACu bond is not so strongly affected. In this case, the indicative difference between s4-value and angle between chelate planes comes clear: whereas the s4-value is in both complexes rather similar, the angle deviates significantly between both models: at TPSSh/ def2-TZVP level, the angle between the chelate planes in [Cu(TMGqu)2]1 amounts to 73.0 whereas it is only 64.7 in [Cu(Gqu)2]1. The addition of the solvent model changes the situation again which shows that this medium sized model is not

Figure 4. Dependence of the s4-value on the inclusion of dispersion correction for [Cu(TMGqu)2]1. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

very robust: the larger [Cu(TMGqu)2]1 changes its angle only to 74.8 whereas the small [Cu(Gqu)2]1 widens this angle to 80.2 . The angle of the medium sized model without solvent model accords well to the experimental value of 67 of the large complex but this is due to coincidence as the consideration of solvent effects shows. Hence, the steric effects of the large model seem to dominate the angle between the ligands. When the methyl groups are omitted, this structural feature cannot be correctly predicted which shows the limited comparability of the medium sized model. Optical benchmarking Compared to the fundamental optical benchmarking in previous work for this complex,[15] we used now the simulation of a larger number of states (200 instead of 80) to account for the intensive high-energy region of ligand-to-ligand charge transfer transitions below 280 nm. Furthermore, the dispersion effect on the UV response has been studied. Table 4 collects all data for the positions of the absorption bands whereas Figures 6–8 give a visual impression of the accordance between calculated spectra and experimental data. The most

Figure 5. Dependence of the angles between the chelate planes CuNquNgua on the inclusion of dispersion correction for [Cu(TMGqu)2]1. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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Table 4. Calculated HOMO-LUMO gaps and positions of absorption bands at various theory levels.[a] Level of theory

Eg [eV]

E1 [eV]

E2 [eV]

E3 [eV]

E4 [eV]

E5 [eV]

B3LYP/def2-SVP B3LYP/def2-SVP-GD3BJ B3LYP/def2-TZVP B3LYP/def2-TZVP-GD3BJ TPSSh/def2-SVP TPSSh/def2-SVP-GD3BJ TPSSh/def2-TZVP TPSSh/def2-TZVP-GD3BJ M06L/def2-TZVP TPSS/def2-TZVP Experiment Assignment [15]

1.95 1.81 2.09 1.94 1.51 1.43 1.65 1.55 1.61 1.46 2.15 MLCTqu

2.50 2.52 2.63 2.62 2.12 2.15 2.23 2.25 2.04 2.21 2.84 MLCTqu

3.42 3.40 3.43/3.84 3.52/3.74 3.30 3.32 3.38 3.32 3.05/3.18 3.34 3.80 MLCTqu

4.53 4.61 4.66 4.68 4.10 4.19 4.28 4.32 4.05 4.29 broad MLCTgua

5.19 5.17 5.14 5.16 5.06 5.08 5.05 5.06 4.78/4.98 4.97 5.07 mixed

6.37/6.84 6.35/6.84 6.25/6.74 6.24/6.71 6.47 6.47 6.24 6.30 6.31 6.24 5.95 LLCT

[a] The start geometry was optimised with the same functional and basis set as used for the TD-DFT calculations.

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apparent result of the calculations using B3LYP (Fig. 6) and TPSSh (Fig. 7) functional is that the inclusion of dispersion does not change the UV/Vis spectra significantly. This can be interpreted as being a shallow conformational minimum where the small structural change of using dispersion or not yields only a negligible effect in the UV spectra. The choice of the functional is again found to be crucial for an accurate description of the optical transitions. B3LYP yields an astonishingly nice description of the features of the spectrum in the visible range as well as in the UV range although different kinds of metal-to-ligand charge transfer (MLCT) and ligand-to-ligand charge transfer (LLCT) processes are involved. This accordance comprises position and intensity of bands. The Cu d to quinoline p* transitions Eg, E1, and E2 are slightly red-shifted compared to experiment but the extent is negligible. The shoulder at 4.66 eV (E3) is reproduced as well. Moreover, the very strong absorption bands at 5 and 6 eV are extremely well reproduced. The fifth transition is split but this

cannot be resolved experimentally. The triple-zeta basis set gives a slightly better description in the visible region. Using the meta-hybrid-GGA TPSSh, the six transitions are well described, too, but the accordance in the visible range is worse than using B3LYP (error of 0.5 eV). The basis set has no influence here. When taking into account M06-L with 0% HF exchange, the visible bands move even more into the redshifted region with an error of 0.8 eV to the experiment. This behavior has already been observed for other pure GGAs such as BP86 and PW91.[15] Using the pure functional TPSS, the optical behavior is slightly better and more similar to TPSSh then to the other pure functionals. Unfortunately, the structures are predicted not reasonably by TPSS which makes it not to the best choice for combined structural and optical studies (or studies targeting excited states). In summary, B3LYP predicts all transitions very reasonably with both basis sets. Hence, our previous recommendation for B3LYP/def2-TZVP is furthermore valid.[15] The use of dispersion correction does not affect the optical description but for the

Figure 6. Calculated absorption spectra of [Cu(TMGqu)2]1 with the B3LYP functional and varying basis sets and dispersion corrections in comparison to experimental data.[15] [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 7. Calculated absorption spectra of [Cu(TMGqu)2]1 with the TPSSh functional and varying basis sets and dispersion corrections in comparison to experimental data.[17] [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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very sensitive to distortions of the coordination sphere. Even here, the accordance fits to the very detail.

Conclusions

Figure 8. Calculated absorption spectra of [Cu(TMGqu)2]1 with the hybrid functionals B3LYP, TPSSh and the pure functional TPSS and M06-L in comparison to experimental data.[17] [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

correct structural description (for excited states for instance) it might become important. Vibrational analysis In the context of resonance Raman studies,[17] the accurate vibrational analysis is crucial for the assignment of experimental data. Here, the influence of dispersion has to be clarified as well. In previous work,[17] we have shown that the accordance between experimental spectra and B3LYP/def2-TZVP calculated spectra is excellent (without scaling). Figure 9 shows that the accordance in band position and intensity between calculations considering the dispersion with BJ damping and those without is extremely good. Thus, our previous assignments are still valid. The inset region in Figure 9 depicts the region of CuAN vibrations[17] which should be

In summary, we could show that the correct description of copper bis(chelate) complexes requires modern dispersion correction using BJ damping. The triple-zeta basis set def2-TZVP of the Ahlrichs series is balanced and converged for the structural description. The best structural description is obtained with the TPSSh functional but B3LYP is very suited as well. Especially when application for the calculation of optical transitions (and the resulting structures) as well as Raman spectra prediction is targeted, B3LYP seems to be the best choice. Cutting of ligand substituents leads to distortions which limit the predictive ability of such calculations. We recommend the calculation of “full” chemical systems with inclusion of dispersion correction using BJ damping. In the further analysis of the regarded copper bis(chelate) complexes, we found that the theoretical description of optical and Raman spectra is not much affected by the dispersion although charge transfer excitations come into play. Hence, we can derive the result that the correct structural description with dispersion serves as crucial basis for subsequent calculation steps and very much attention has to be paid here as all errors propagate from this step.

Acknowledgments The authors would like to thank the BMBF (German Federal Ministry of Education and Research) for the opportunity to do research in the MoSGrid project (reference 01IG09006). Generous grants of computing time at the Leibniz-Rechenzentrum and the Paderborn Center for Parallel Computing PC2 are gratefully acknowledged. The authors thank Prof. Dr. S. Grimme for providing the Becke–Johnson damping parameters for TPSSh. Keywords: copper  N-donor ligands  DFT  dispersion

How to cite this article: A. Hoffmann, R. Grunzke, S. Herres-Pawlis. J. Comput. Chem. 2014, 35, 1943–1950. DOI: 10.1002/jcc.23706

Figure 9. Calculated Raman spectra of [Cu(TMGqu)2]1 using B3LYP/defTZVP with (red lines) and without dispersion (black). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

[1] E. I. Solomon, D. E. Heppner, E. M. Johnston, J. W. Ginsbach, J. Cirera, M. Qayyum, M. T. Kieber-Emmons, C. H. Kjaergaard, R. G. Hadt, L. Tian, Chem. Rev. 2014, 114, 3659. [2] A. B. P. Lever, Inorg. Chem. 1990, 29, 1271. [3] D. B. Rorabacher, Chem. Rev. 2004, 104, 651. [4] P. Comba, M. Kerscher, Coord. Chem. Rev. 2009, 253, 564. [5] H. B. Gray, B. G. Malmstr€ om, R.J. Williams, J. Biol. Inorg. Chem. 2000, 5, 551. [6] K. M. Lancaster, S. DeBeer George, K. Yokoyama, J. H. Richards, H. B. Gray, Nat. Chem. 2009, 1, 711. [7] K. M. Lancaster, O. Farver, S. Wherland, E. J. Crane, III, J. H. Richards, I. Pecht, H. B. Gray, J. Am. Chem. Soc. 2011, 133, 4865. [8] K. M. Lancaster, M.-E. Zaballa, S. Sproules, M. Sundararajan, S. DeBeer, J. H. Richards, A. J. Vila, F. Neese, H. B. Gray, J. Am. Chem. Soc. 2012, 134, 8241. [9] J. J. Warren, K. M. Lancaster, J. H. Richards, H. B. Gray, J. Inorg. Biochem. 2012, 155, 119.

Journal of Computational Chemistry 2014, 35, 1943–1950

1949

FULL PAPER

WWW.C-CHEM.ORG

[10] S. F. Sousa, G. R. P. Pinto, A. J. M. Ribeiro, J. T. S. Coimbra, P. A. Fernandes, M. Jo~ao Ramos, J. Comput. Chem. 2013, 34, 2079. [11] F. Neese, Coord. Chem. Rev. 2009, 253, 526. [12] A. Tsipis, Coord. Chem. Rev. 2014, 272, 1. [13] R. Peverati, D. G. Truhlar, Philos. Trans. R. Soc. A 2014, 372, 1471. [14] A. D. Becke, J. Chem. Phys. 2014, 140, 18A301. [15] A. Jesser, M. Rohrm€ uller, W. G. Schmidt, S. Herres-Pawlis, J. Comput. Chem. 2014, 35, 1. [16] A. D. Laurent, D. Jacquemin, Int. J. Quantum Chem. 2013, 113, 2019. [17] (a) A. Hoffmann, S. Binder, A. Jesser, R. Haase, U. Fl€ orke, M. Gnida, M. Salomone Stagni, W. Meyer-Klaucke, B. Lebsanft, L. E. Gr€ unig, S. Schneider, M. Hashemi, A. Goos, A. Wetzel, M. R€ ubhausen, S. Herres-Pawlis, Angew. Chem. 2014, 126, 305; (b) A. Hoffmann, S. Binder, A. Jesser, R. Haase, U. Fl€ orke, M. Gnida, M. Salomone Stagni, W. Meyer-Klaucke, B. Lebsanft, L. E. Gr€ unig, S. Schneider, M. Hashemi, A. Goos, A. Wetzel, M. R€ ubhausen, S. Herres-Pawlis, Angew. Chem. Int. Ed. 2014, 53, 299. [18] F. Weigend, R. Ahlrichs, Phys. Chem. Chem. Phys. 2005, 7, 3297. [19] Gaussian 09, Revision D.01, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, T. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, D. J. Fox, Gaussian, Inc: Wallingford CT, 2013. [20] C. Lee, W. Yang, R. G. Parr, Phys. Rev. B 1988, 37, 785. [21] B. Miehlich, A. Savin, H. Stoll, H. Preuss, Chem. Phys. Lett. 1989, 157, 200. [22] P. J. Stephens, F. J. Devlin, C. F. Chabalowski, M. J. Frisch, J. Phys. Chem. 1994, 98, 11623. [23] C. Adamo, V. Barone, J. Chem. Phys. 1999, 110, 6158. [24] J.-D. Chai, M. Head-Gordon, Phys. Chem. Chem. Phys. 2008, 10, 6615. [25] Y. Zhao, D. G. Truhlar, J. Chem. Phys. 2006, 125, 194101. [26] S. I. Gorelsky, AOMix: Program for Molecular Orbital Analysis; version 6.80, University of Ottawa, Ottawa, Canada, 2013, Available at: http:// www.sg-chem.net/. Accessed on January 2, 2014. [27] S. I. Gorelsky, SWizard program; University of Ottawa: Ottawa, Canada, 2013. Available at: http://www.sg-chem.net/, accessed on January 2, 2014. [28] S. Grimme, J. Comput. Chem. 2006, 27, 1787. [29] S. Grimme, J. Antony, S. Ehrlich, H. Krieg, J. Chem. Phys. 2010, 132, 154104. [30] L. Goerigk, S. Grimme, Phys. Chem. Chem. Phys. 2011, 13, 6670. [31] S. Grimme, E. Ehrlich, L. Goerigk, J. Comput. Chem. 2011, 32, 1456. [32] J. Kr€ uger, R. Grunzke, S. Gesing, S. Breuers, A. Brinkmann, L. de la Garza, O. Kohlbacher, M. Kruse, W. Nagel, L. Packschies, R. M€ uller-Pfefferkorn, P. Sch€afer, C. Sch€arfe, T. Steinke, T. Schlemmer, K. Warzecha, A. Zink, S. Herres-Pawlis, J. Chem. Theory Comput. 2014, 10, 2232. [33] S. Herres-Pawlis, A. Hoffmann, A. Balasko, P. Kacsuk, G. Birkenheuer, A. Brinkmann, L. de la Garza, J. Kr€ uger, S. Gesing, R. Grunzke, G. Terstyansky, N. Weingarten, Concurrency Computat.: Pract. Exper. (in press). Doi: 10.1002/cpe.3292. [34] S. Herres-Pawlis, R. Haase, G. Henkel, S. Binder, A. Eich, B. Schulz, M. R€ ubhausen, G. Wellenreuther, W. Meyer-Klaucke, Chem. Eur. J. 2009, 35, 8678. [35] S. Herres-Pawlis, T. Seshadri, U. Fl€ orke, G. Henkel, Z. Anorg. Allg. Chem. 2009, 635, 1209. [36] S. Herres-Pawlis, G. Berth, V. Wiedemeier, L. Schmidt, A. Zrenner, H.-J. Warnecke, J. Lumin. 2010, 130, 1958. [37] R. Haase, T. Beschnitt, U. Fl€ orke, S. Herres-Pawlis, Inorg. Chim. Acta 2011, 374, 546. [38] O. Bienemann, A. Hoffmann, S. Herres-Pawlis, Rev. in Inorg. Chem. 2011, 3, 83.

1950

Journal of Computational Chemistry 2014, 35, 1943–1950

[39] A. Hoffmann, J. B€ orner, U. Fl€ orke, S. Herres-Pawlis, Inorg. Chim. Acta, 2009, 362, 1185. [40] (a) M. Schatz, V. Raab, S. P. Foxon, G. Brehm, S. Schneider, M. Reiher, M. C. Holthausen, J. Sundermeyer, S. Schindler, Angew. Chem. 2004, 116, 4460; (b) M. Schatz, V. Raab, S. P. Foxon, G. Brehm, S. Schneider, M. Reiher, M. C. Holthausen, J. Sundermeyer, S. Schindler, Angew. Chem. Int. Ed. 2004, 43, 4360. [41] (a) C. W€ urtele, E. Gaoutchenova, K. Harms, M.C. Holthausen, J. Sundermeyer, S. Schindler, Angew. Chem. 2006, 118, 3951; (b) C. W€ urtele, E. Gaoutchenova, K. Harms, M.C. Holthausen, J. Sundermeyer, S. Schindler, Angew. Chem., Int. Ed. 2006, 45, 3867. [42] (a) D. Maiti, D.-H. Lee, K. Gaoutchenova, C. W€ urtele, M. C. Holthausen, A. A. Narducci Sarjeant, J. Sundermeyer, S. Schindler, K. D. Karlin, Angew. Chem. 2008, 120, 88; (b) D. Maiti, D.-H. Lee, K. Gaoutchenova, C. W€ urtele, M. C. Holthausen, A. A. Narducci Sarjeant, J. Sundermeyer, S. Schindler, K. D. Karlin, Angew. Chem., Int. Ed. 2008, 47, 82. [43] J. S. Woertink, L. Tian, D. Maiti, H. R. Lucas, R. A. Himes, K. D. Karlin, F. Neese, C. W€ urtele, M. C. Holthausen, E. Bill, J. Sundermeyer, S. Schindler, E. I. Solomon, Inorg. Chem. 2010, 49, 9450. [44] A. Peters, C. Trumm, M. Reinmuth, D. Emeljanenko, E. Kaifer, H.-J. Himmel, Eur. J. Inorg. Chem. 2009, 3791. [45] C. Trumm, O. H€ ubner, E. Kaifer, H.-J. Himmel, Eur. J. Inorg. Chem. 2010, 3102. [46] D. Emeljanenko, A. Peters, N. Wagner, J. Beck, E. Kaifer, H.-J. Himmel, Eur. J. Inorg. Chem. 2010, 1839. [47] D. Maiti, D.-H. Lee, A. A. Narducci Sarjeant, M. Y. Pau, E. I. Solomon, K. Gautchenova, J. Sundermeyer, K. D. Karlin, J. Am. Chem. Soc. 2008, 130, 6700. [48] C. Saracini, D. G. Liakos, J. E. Zapata Rivera, F. Neese, G. J. Meyer, K. D. Karlin, J. Am. Chem. Soc. 2014, 136, 1260. [49] A. D. Becke, J. Chem. Phys. 1993, 98, 5648. [50] J. P. Perdew, Phys. Rev. B 1986, 33, 8822. [51] K. P. Jensen, Inorg. Chem. 2008, 47, 10357. [52] A. Hoffmann, S. Herres-Pawlis, Chem. Commun. 2014, 50, 403. [53] (a) A. Hoffmann, C. Citek, S. Binder, A. Goos, M. R€ ubhausen, O. Troeppner, I. Ivanovic´-Burmazovic´, E. C. Wasinger, T. D. P. Stack, S. Herres-Pawlis, Angew. Chem. 2013, 125, 5508; (b) A. Hoffmann, C. Citek, S. Binder, A. Goos, M. R€ ubhausen, O. Troeppner, I. Ivanovic´Burmazovic´, E. C. Wasinger, T. D. P. Stack, S. Herres-Pawlis, Angew. Chem. Int. Ed. 2013, 52, 5398. [54] A. D. Becke, Phys. Rev. A 1988, 38, 3098. [55] O. Bixner, V. Lukes, T. Mancˇal, J. Hauer, F. Milota, M. Fischer, I. Pugliesi, M. Bradler, W. Schmid, E. Riedle, H. F. Kauffmann, N. Christensson, J. Chem. Phys. 2012, 136, 204503. [56] L. Yang, D. R. Powell, R. P. Houser, Dalton Trans. 2007, 9, 955. [57] S. Ehrlich, J. Moellmann, S. Grimme, Acc. Chem. Res. 2013, 46, 916. [58] S. Grimme, WIREs Comput. Mol. Sci. 2011, 1, 211. [59] J. Hepburn, G. Scoles, R. Penco, Chem. Phys. Lett. 1975, 36, 451. [60] R. Ahlrichs, R. Penco. G. Scoles. Chem. Phys. 1977, 19, 119. [61] M. Elstner, P. Hobza, T. Frauenheim, S. Suhai, E. Kaxiras, J. Chem. Phys. 2001, 114, 5149. [62] Q. Wu, W. Yang, J. Chem. Phys. 2002, 116, 515. [63] F. A. Gianturco, F. Paesani, M. F. Laranjeira, V. Vassilenko, M. A. Cunha, J. Chem. Phys. 1999, 110, 7832. [64] J. S. Cohen, R. T. Pack, J. Chem. Phys. 1974, 61, 2372. [65] S. Grimme, J. Comput. Chem. 2004, 25, 1463. [66] G. B. Hall, R. Kottani, G. A. N. Felton, T. Yamamoto, D. H. Evans, R. S. Glass, D. L. Lichtenberger, J. Am. Chem. Soc. 2014, 136, 4012. [67] E. F. van der Eide, P. Yang, R. Morris Bullock, Angew. Chem. Int. Ed. 2013, 52, 10190. [68] K. K. Pandey, J. Organomet. Chem. 2014, 761, 134. [69] A. V. Marenich, C. J. Cramer, D. G. Truhlar, J. Phys. Chem. B 2009, 113, 6378.

Received: 10 June 2014 Revised: 14 July 2014 Accepted: 16 July 2014 Published online on 14 August 2014

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