Cooperative Spin Transitions Triggered by Phonons in Metal Complexes Coupled to Molecular Vibrations

Round 1

Reviewer 1 Report

In a review, the authors explore an interesting problem of spin crossover in the case of mononuclear, binuclear, and tetra-nuclear systems when the spin change takes place due to the phonon influence leading to the cooperative interaction between the centers. The problem was considered before by the same authors, but it got a better presentation in this publication. The paper is publishable, provided the author make corrections and improvement, outlined below.

1. From the very title, the authors separate the systems’ atomic displacements in “molecular vibration” and “phonons”, but nowhere in the paper they show how is this separation actually realized. In particular, in the Hamiltonian, eq. (1), the first term describes “molecular” displacements, and the second term in parenthesis contains all the atomic displacements including, the molecular ones, and hence the latter are included twice (!). If the “molecular” atomic displacements are not included in the second, “crystal” term, it is not shown (and it would be very difficulties to show) how this separation is realized, and what is the meaning of the crystal parameters (without the molecular vibrations), to be used in the numerical estimates.
2. With regard to the numerical parameters employed to confirm the theory, they are not justified or discussed in detail, but referred to the authors’ previous publications (in which they are not discussed too). As they are so many (in fact, all constants), the results of comparison with experimental data look unconvincing. For instance, the maximum frequency of the long-wave vibrations in one system is taken as ω_m=23cm^-1 which, in view of the crystal including molecular centers, is absolutely no trustworthy. Similarly, wherefrom is taken the numerical relation between the three parameters of the ls-hs correlation over the four centers of the tetra-nuclear system as 59 : 1.26 : 1 ? . And there are more such questions. In a review, the reader is expected to find fully clarified description of the subject with clear trustworthy, well-grounded estimates of the results.

The paper can be recommended for publication in Magnetochemistry after corrections and improvements in according to the comments above, and after a second review.  

Author Response

In a review, the authors explore an interesting problem of spin crossover in the case of mononuclear, binuclear, and tetra-nuclear systems when the spin change takes place due to the phonon influence leading to the cooperative interaction between the centers. The problem was considered before by the same authors, but it got a better presentation in this publication. The paper is publishable, provided the author make corrections and improvement, outlined below.

1. From the very title, the authors separate the systems’ atomic displacements in “molecular vibration” and “phonons”, but nowhere in the paper they show how is this separation actually realized. In particular, in the Hamiltonian, eq. (1), the first term describes “molecular” displacements, and the second term in parenthesis contains all the atomic displacements including, the molecular ones, and hence the latter are included twice (!). If the “molecular” atomic displacements are not included in the second, “crystal” term, it is not shown (and it would be very difficulties to show) how this separation is realized, and what is the meaning of the crystal parameters (without the molecular vibrations), to be used in the numerical estimates.

Reply: Probably, our presentation in this point has not been clear enough. That is why n the revisised beginning of  section “Background of the model” a more detailed explanation is given of the different role of crystalline and molecular vibrations in spin crossover compounds. In particular, Equation (1) does not represent the Hamiltonian of the model, it shows that the symmetry adapted coordinates of the ligand surrounding can be represented as the linear superposition of the coordinates of molecular vibrations (first term)  and crystalline (second term)  vibrations (phonons).  In order to make this issue more clear we have added an additional Figure (Fig. 1 in the revised version. In order emphasize the main point of the article we have modified the title.

 

2. With regard to the numerical parameters employed to confirm the theory, they are not justified or discussed in detail, but referred to the authors’ previous publications (in which they are not discussed too). As they are so many (in fact, all constants), the results of comparison with experimental data look unconvincing. For instance, the maximum frequency of the long-wave vibrations in one system is taken as ω_m=23cm^-1 which, in view of the crystal including molecular centers, is absolutely no trustworthy. Similarly, wherefrom is taken the numerical relation between the three parameters of the ls-hs correlation over the four centers of the tetra-nuclear system as 59 : 1.26 : 1 ?

Reply: For mononuclear and binuclear systems the ration between the parameters of cooperative interaction was taken : : = 1.59 : 1.26 : 1, for tetranuclear systems the ratio for these parameters was  :   : : = 3.22 : 1.79 : 1. The difference can be explained as follows. In the first case for calculations the numerical values of the frequencies were ω_hs=161 cm^-1, ω_hs=200 cm^-1 [39], in the second case the frequency values 97 cm^-1 and 151 cm^-1 for the hs and ls configurations, respectively, were taken from reference [41]. No ratio 59 : 1.26 : 1 was employed in the calculations and listed in the paper.

The Debye frequency =23 cm^-1 of the acoustic lattice vibrations used for the description of the Fe(II) SCO compounds was evaluated in [39] from their parabolic dependence on the wave vector  in the center of the Brillouin zone. For FeCo complex demonstrating CTIST this frequency was evaluated with the use of equation from the classical book of Anselm (ref.[44] in the corrected version of the paper). The obtained value   = 24 cm⁻¹ is practically the same as that used for the Fe(II) complexes. The value ω_m=23cm^-1  looks like being  too small, but one should take into account that it is interrelated with  the weak intermolecular interactions of heavy molecular units. The corresponding explanation was added to the paper.

 

3. And there are more such questions. In a review, the reader is expected to find fully clarified description of the subject with clear trustworthy, well-grounded estimates of the results.The paper can be recommended for publication in Magnetochemistry after corrections and improvements in according to the comments above, and after a second review.

Reply: The review contains a brief description of the main points of the model and of the results obtained on the explanation of the observed characteristics of spin crossover compounds of different nuclearity as well as of compounds  exhibiting charge transfer induced spin transitions. We have omitted many of the details given in our previous papers in order to facilitate the understanding of the main results obtained earlier and to draw the attention of theoretical and experimental groups to this new model of spin transitions. Actually  the aim of this mini-review was to give the description of the fundamentals  of the new model  and to attract the reader to the further more deep  acquaintance with this model published in our papers [27-30] cited in the list of references

 

         We thank the Reviewer for his helpful Comments that have been taken into       

        account in the revised version.

Author Response File: Author Response.docx

Reviewer 2 Report

This is a very nice piece of work. The authors have put together a collection of models that are being used to describe spin transition in cluster with one, two and four magnetic centers. The models are carefully described and the approximations made clearly outlined. The connection between spin crossover and charge transfer induced transitions is very interesting and in some way the two phenomena were unified in this contribution. The text can be very helpful for other researchers to understand all the systems and use the different models for analysis of experimental data. I have just three minor observations that might be considered for improvement.

line 31: not more than 100 years (it's almost 100 years)

lines 196 and 272: Is there any intuitive explanation for the change in the ratio of the interaction parameters from two-center clusters to four-center clusters?

line 357: The theoretical prediction is indeed quite good, but not as spot on as for the SCO cases. It might be interesting to mention soem possible improvements to increase the abruptness of the transition in the theoretical model. In the description fo the model quite a few approximations (which appear to be reasonable at first sight) were introduced. Any of these can be at the origin of smearing out the transition?

Author Response

This is a very nice piece of work. The authors have put together a collection of models that are being used to describe spin transition in cluster with one, two and four magnetic centers. The models are carefully described and the approximations made clearly outlined. The connection between spin crossover and charge transfer induced transitions is very interesting and in some way the two phenomena were unified in this contribution. The text can be very helpful for other researchers to understand all the systems and use the different models for analysis of experimental data. I have just three minor observations that might be considered for improvement.

line 31: not more than 100 years (it's almost 100 years)

 

Reply: In the new version of the paper it is written now “The phenomenon of SCO was discovered almost one hundred years ago”

 

lines 196 and 272: Is there any intuitive explanation for the change in the ratio of the interaction parameters from two-center clusters to four-center clusters?

 

Reply: The ratio of the interaction parameters is different in the two-center and four-center problems, because in the former case for the frequencies of molecular vibrations in the ls- and hs-states the values ω_hs=161 cm^-1, ω_hs=200 cm^-1 were taken from the classical paper of  P. Guetlich and co-workers[39], while in the case of tetranuclear spin crossover systems the frequencies of the full-symmetric vibrations 97 cm^-1 and 151 cm^-1 for the hs and ls configurations obtained in [41] by DFT calculations were employed. The corresponding references are given in the paper.

 

line 357: The theoretical prediction is indeed quite good, but not as spot on as for the SCO cases. It might be interesting to mention some possible improvements to increase the abruptness of the transition in the theoretical model. In the description for the model quite a few approximations (which appear to be reasonable at first sight) were introduced. Any of these can be at the origin of smearing out the transition?

 

Reply: We agree, an improvement can be achieved if the real phonon densities of the phonons are taken into account.

We thank the Reviewer for his helpful Comments that have been taken into account in the revised version.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors made reasonable corrections, following the previous comments. I recommend publication.