Review Reports - Modeling the Eu(III)-to-Cr(III) Energy Transfer Rates in Luminescent Bimetallic Complexes

Round 1

Reviewer 1 Report

The work presented a theoretical model to calculate the ET rates between a transition metal and a lanthanide ion in [EuCrL3]6+ complex. The values obtained by the theoretical model were in good agreement with the experiment. However, there are some questions that need to be answered.

1 The expression “ [Cr(phen)2(bipy)](BF4)3 ” is incomplete.

2 Why is it difficult to get the absorption data for Cr(III) in the [EuCrL3]6+ complex, while it is possible in the Cr(phen)2(bipy)](BF4)3 system?

3 What are the assumptions for the equations developed by Malta and collaborators?

4 Please explain more in the figure captions of figures 3,4 and 5. What is the green line in figure 3? What is the black line in figure 5?

5 Please describe in detail the fitting process in figure 6 and 7.

6 The sentence in line 243“Ward [26] reported ET rates for M–Ln(III) systems with large intermetallic distances, suggesting that the most likely ET mechanism is the Dexter one (exchange) because of the forbidden transitions character of Ln(III) and the large separation distances between Cr(III) and Eu(III) ions are unfavorable for the dipole–dipole (Förster) mechanism.”

The Dexter mechanism features a double electron transfer during which an electron of the donor in the excited state is transferred to the acceptor, while simultaneously, an electron of the acceptor in its ground state is transferred to the donor. This process requires donor-acceptor wavefunction overlap and a short donor-acceptor distance. Thus, is the description of the ET mechanism accurate?

7 Many sentences should be rewritten, such as “This adjustment used the dipole strengths obtained from radiative lifetimes of the acceptor level (Eq. 7)” in line 262, “The model reported here is distinguished because considers the Judd-Ofelt formalism for Ln(III) ions, in which the forbidden character of their transitions is circumvented through the forced electric dipole mechanism.” in line 249 and so on.

8 The sentence in line 316 “A question can be raised regarding the role of the exchange mechanism in the Eu(III)→Cr(III) ET process.” is confusing. For the distance of 9.3 Å, the d-f overlap integral is negligible, and the exchange mechanism is not dominant. So what is the question?

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

This article presented a theoretical model to calculate the energy transfer rate from transition metal to lanthanide ion, which agrees well with the experimental value. The proposed model reveals the predominant mechanisms maximizing the energy transfer rates and efficiencies. This contribution should suit for Inorganics upon a minor revision.

1. In the Abstract, the calculated energy transfer rate may be better expressed by W_cal, while the experimental available date with W_exp.

2. The rate range, for example, 1-2*10³s^-1 can be re-expressed as 1*10³-2*10³ s^-1, otherwise the rates of 966-2*10³s^-1 could be corrected.

3. In Eq. 1, the dipole strength transitions of the metal M and Lu are all considered, so the expression of “The equations were adapted to consider the dipole strength transitions of the metal M (Cr(III)), represented by the ” could be corrected to “The equations were adapted to consider the dipole strength transitions of the metal M Cr(III) and Ln (III), represented by the and ”.

In line 88, you have explain that h is Planck’s constant, I think it would be better if you state that “ћ is Reduced Planck constant” (Eq.1).

4. Please also describe the physical quantity represented by m in Eq. 9.

5. In Figure 6, correct “Bandwith” to “Bandwidth”.

6. To express the “Energy transfer rate”, the author specifies “Et Rate” in Figure 7a, “ET Rate” in Figure 7b, but “Energy Transfer Rate” in Figure 6. Please unify the expression.

7. In Figure 8, the authors need to correct the value of overlap integral for the distance of 9.3 Å.

8. There are some errors in the grammar and punctuation, for example, line 73, “The shielding factors σ₁ e σ₂…”; line 121-122, “However, it is not possible to distinguish in the absorption spectrum the peaks and bandwidths”. Please check throughout the text.

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

Coelho and co-workers demonstrate a theoretical model to calculate the ET rates between Cr3+ and Eu3+ ion. The theoretical part is based on one coauthor's (O.L. Malta) previous reports, while the experimental spectra are adapted from other reports. Thus the novelty of this paper is not high.

The writing of this manuscript is bad. In page 2, in the theoretical methodology part, the descriptions for each factor listed in the four equations are not appropriate. For example, the authors uses W_d-dand W_d-m in the equations, but the following descriptions ignored them, and the sequence for each factor is disordered which makes it difficult to follow. The authors should describe the items step by step.

In addition, the description for the complex [CrEuL₃]⁶⁺ is funny, sometimes it is [CrEuL3]⁶⁺(Page 4, line 126), and [EuCrL₃]⁶⁺in the conclusions. The authors should unify it.

Author Response

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Author Response File: Author Response.docx

Reviewer 4 Report

This contribution reports on some theoretical modeling of an Eu(III)-to-Cr(III) energy transfer operating in a helical heterometallic helicate designed, prepared, characterized and studied by an other research group two decades ago and for which only partial photophysical data could be retrieved by the current authors from ref. [46]. This reviewer is astonished that the authors prefer to use some parent trigonal [Cr(diimine)3] compounds from ref. [54] in order to imagine (deduce ?) some inaccurate absorption spectra for the CrEu helicate (Figure 5) instead of taking the pertinent missing data from a recently published paper in the same topic (Golesorkhi et al. Dalton Trans. 2021, 50 (23), 7955-7968).

This modest reviewer does realize that these authors are well-recognized experts of the Judd-Ofelt theory and of the antenna effect pertinent to lanthanide sensitization in lanthanide complexes (particularly with beta-diketonate ligands, see for instance Brito, H. F.; Malta, O. M. L.; Felinto, M. C. F. C.; Teotonio, E. E. S., Luminescence phenomena involving metal enolates. The Chemistry of Metal Enolates 2009, chapter 3, 131-1849) but they should consider that [CrN6] chromophores have slightly different characteristics, even if the basis of photophysics remains identical.

Firstly, [CrN6] chromophores, which are build from three helically wrapped polyaromatic diimine ligands, as found in the selected EuCr complex, display numerous intense LMCT amd MLCT transitions covering the 19000-30000 cm-1 energy range which mask the weak spin-allowed Cr(4T2-4A2) transition (for theoretical justifications and for the authors’ perusal, please see for instance Jimenez et al, Chiral Molecular Ruby [Cr(dqp)2](3+) with Long-Lived Circularly Polarized Luminescence. J. Am. Chem. Soc. 2019, 141 (33), 13244-13252, Sinha et al., A Near-Infrared-II Emissive Chromium(III) Complex. Angew. Chem. Int. Ed. 2021, 60, 23722-23728 and/or Forster, C.; Heinze, K., Photophysics and photochemistry with Earth-abundant metals - fundamentals and concepts. Chem. Soc. Rev. 2020, 49 (4), 1057-1070.) In this context, the analysis depicted in Figure 4 is of very limited use because only a careful (and difficult) deconvolution of the absorption spectra could give access to some realistic molar absorption coefficients for the spin-allowed Cr(4T2-4A2) transition in this chromophore. Using the proposed ratio is really subjective at this level of analysis.

Secondly, trigonal [CrN6] chromophores are known to display molar exctinction coefficients not larger than 0.2 M-1cm-1 for the spin-flip Cr(2T1,2E-4A2) transitions (see ref [54]). Figure 5, on which is based the rest of the calculations and predictions is therefore a non-sense. This reviewer is further surprised that the authors did not consider the available experimental data reported for these transitions in the closely related CrLnCr helicate (see Figure 9 in Golesorkhi and coworkers. Molecular light-upconversion: we have had a problem! When excited state absorption (ESA) overcomes energy transfer upconversion (ETU) in Cr(III)/Er(III) complexes. Dalton Trans. 2021, 50 (23), 7955-7968). As expected, the experimental molar extinction coefficients are more than three orders of magnitude smaller than that proposed by the authors in their Figure 5.

In conclusion, some deeper consideration of the Cr(III) absorption properties is probably required together with the use of additional references prior to perform a novel set of simulations.

In conclusion, this reviewer regrets for not being more positive, but this contribution cannot be considered for publication in its current form and with its current content.

Author Response

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Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

I suggest an acceptance of the revised manuscript.

Author Response

Many thanks for the positive recommendation.

Reviewer 4 Report

Upon reading the second version of this ms, reviewer #4 is really impressed by (i) the complete re-writing and re-analysis of the kinetic processes proposed by the authors and (ii) their careful consideration of the original suggestions of this reviewer for improving their ms. This reviewer must confess that it is the first time in her/his career that she/he is not insulted by the authors after having written that some errors were detected in the original work.

For being faced, once in her/his life, with this innovative feeling, reviewer #4 would like to warmly thank the authors for their respect of her/his advice and for their scientific pertinence in modifying their conclusions.

The second version now proposes a phonon-assisted mechanism for modeling the Eu-to-Cr energy transfer operating in the triple-stranded helicate. The theoretical calculations are far beyond the pertinence and the capacities of this modest reviewer, but the final interpretation now makes sense.

The three following points could be considered by the authors when preparing the final version of their ms.

1) Page 3, line 100. C-N does not correspond to a high-vibrational mode. Please replace it with C=N.

2) Page 8, line 268. The authors probably mixed the concept of aromatic amines (as found in phenyl amine) with aromatic imines (as found in pyridine). Replace aromatic amines with aromatic imines

3) Page 11, line 348. The authors should mention (and compare) their modern finding of a phonon bath of 2x1000 cm-1 for modeling their phonon-assisted energy transfer with that proposed, twenty years ago by Reinhard and Güdel (2000 cm-1….and the same Huang-Rhys approach) for explaining the indirect lanthanide sensitization induced in related triple-helical complexes (see Reinhard, C.; Güdel, H. U., High-resolution optical spectroscopy of Na3[Ln(dpa)3].13H2O with Ln = Er, Tm, Yb. Inorg. Chem. 2002, 41, 1048-1055).

Author Response

Reply: We thank the reviewer for the careful revisions and analyses. Indeed, they contribute significantly to improving and enriching the manuscript. We are grateful.

The three following points could be considered by the authors when preparing the final version of their ms.

1) Page 3, line 100. C-N does not correspond to a high-vibrational mode. Please replace it with C=N.

Reply: We do agree and acknowledge the reviewer for pointing out this error, which was corrected in the revised version of the manuscript.

2) Page 8, line 268. The authors probably mixed the concept of aromatic amines (as found in phenyl amine) with aromatic imines (as found in pyridine). Replace aromatic amines with aromatic imines

Reply: We apologize for this misunderstanding and the manuscript has been corrected.

Reply: We thank the reviewer for pointing out this reference. We were aware of the single-configurational coordinate (SCC) model; however not this application to triple-helical complexes. Despite the SCC model is quite different from the model employed here, the phonon-assisted parts are quite consistent. So, the following comparison was included in the discussion (lines 270-273):

These values of the average phonon energies are consistent with the single-configurational coordinate model applied to related triple-helical complexes, Na₃[Ln(dpa)₃]·13H₂O, which employed a phonon energy of 1200 cm^–1 [69]. However, this same work employed a Huang-Rhys factor of 2 to estimate the energy transfer rates, which could be considered too large for Ln(III) complexes.