Theoretical Equations of Zeeman Energy Levels for Distorted Metal Complexes with 3T1 Ground Terms
Round 1
Reviewer 1 Report
• The manuscript presents the calculations of the magnetization response for a family of compounds possessing a T symmetry of the ground state. The analysis presented is admittedly superficial and some of calculations are not clearly explained, although potentially straightforward.
• The presentation and scope of the manuscript must be largely expanded before this can be accepted in any scientific journal. The introduction to the problem is admittedly not existent.
• The Author presents the outcome of the evalution without any further analysis. Can these formulas be used to evaluate the energy splitting for some molecule on materials? Can the parameters of the Hamiltonian assume some value to evaluate the magnitude of the corrections? They said that a figure can be worth a thousand words...
I admittedly cannot recommend publication of the current manuscript.
Some more technical questions
1) For completeness, the derivation, or discussion of terms in the Hamiltonian should be provided or the Author should point to a source for it.
2) The choice of the 9 states is clearly arbitrary, what assures their orthogonality especially if they become degenerate?
3) I assume that with the matrices A, B. C, the Author means the Hamiltonian is separable into three subspaces spanned by different orthogonal vectors, and those matrices correspond to
the representation of H in each subspace.
4) Are the coefficients always real for the physical parameters? In particular, I have some doubts about V_4 and V_5.
5) The expressions for the coefficients c_1-c_13 can be simplified
by eliminating some of the ratios d_j/|d_j|. For example, d1/|d1|=1.
6) Clearly, not all the 13 c coefficients needed and some of them are fixed by the normalization conditions, other by orthogonality. But are the stakes \Psi_1 and \Psi_6 orthogonal? For example, <\psi_1|\psi_6>= c_1 * c_6 + c_2*c_7 + c_3*c_8 and it is not clear to see why this sum should vanish. If it does not, how the Author is certain not to loose physical information?
7) Some equations listed are admittedly useless, for example (63) to (73) can be compactified and (93) is equal to (91).
Author Response
Answers to reviewer 1
• The manuscript presents the calculations of the magnetization response for a family of compounds possessing a T symmetry of the ground state. The analysis presented is admittedly superficial and some of calculations are not clearly explained, although potentially straightforward.
---In fact, the first successful magnetic analysis of dinuclear octahedral high-spin cobalt(II) complexes with slightly distorted cobalt(II) ions was conducted using the closed-form expression. This has been added in the third paragraph of Introduction. Therefore, this kind of work has a meaning. Concerning the treatment of the wave functions, Kahn described in detail for 4T1g term. This has been added in Materials and Methods section, and the first paragraph of Results has been modified.
• The presentation and scope of the manuscript must be largely expanded before this can be accepted in any scientific journal. The introduction to the problem is admittedly not existent.
---The second paragraph of Introduction has been modified to expand the scope as much as possible.
• The Author presents the outcome of the evalution without any further analysis. Can these formulas be used to evaluate the energy splitting for some molecule on materials? Can the parameters of the Hamiltonian assume some value to evaluate the magnitude of the corrections? They said that a figure can be worth a thousand words...
---Simulation examples have been added in the manuscript. Although any new data has not been analyzed, earlier data have been analyzed and the correctness has been checked.
I admittedly cannot recommend publication of the current manuscript.
---Thank you for your comments. The manuscript has been modified to be better.
Answers to the technical questions
1) For completeness, the derivation, or discussion of terms in the Hamiltonian should be provided or the Author should point to a source for it.
---The source is reference 11 (O. Kahn, Molecular Magnetism), and the description has been added.
2) The choice of the 9 states is clearly arbitrary, what assures their orthogonality especially if they become degenerate?
---Nine orthogonal bases are used for considering the nine states. The orthogonality of the basis set assures the orthogonality of the states.
3) I assume that with the matrices A, B. C, the Author means the Hamiltonian is separable into three subspaces spanned by different orthogonal vectors, and those matrices correspond to the representation of H in each subspace.
---The nine by nine matrix can be reduced to the matrices A, B. and C. I have added a description in the manuscript.
4) Are the coefficients always real for the physical parameters? In particular, I have some doubts about V_4 and V_5.
---Yes. In V_4 and V_5, there were typos, which have been corrected. After the correction, the coefficients are always real. Thank you very much for your comment.
5) The expressions for the coefficients c_1-c_13 can be simplified by eliminating some of the ratios d_j/|d_j|. For example, d1/|d1|=1.
---Yes. They can be simplified, but I prefer using the general expression, because it is easy to check if the equations are correct. Some of the d_j/|d_j| values change from 1 to -1, and they cannot be eliminated. So, the general form is sometimes more useful.
6) Clearly, not all the 13 c coefficients needed and some of them are fixed by the normalization conditions, other by orthogonality. But are the stakes \Psi_1 and \Psi_6 orthogonal? For example, <\psi_1|\psi_6>= c_1 * c_6 + c_2*c_7 + c_3*c_8 and it is not clear to see why this sum should vanish. If it does not, how the Author is certain not to loose physical information?
---The orthogonality is clear from the basis set. I have added the explanation in the manuscript.
7) Some equations listed are admittedly useless, for example (63) to (73) can be compactified and (93) is equal to (91).
---Following the advice, the equations have been compactified.
Reviewer 2 Report
The paper submitted by Hiroshi Sakiyama reports theoretical equations of Zeeman energy levels for distorted metal complexes with 3T1(g) ground terms. The equations will be important for the understanding (simulating) of magnetic properties of the complexes with 3T1(g) ground terms. This is well written paper and results are clearly presented. The work should be of interest to readers of Magnetochemistry.
Author Response
Answers to reviewer 2
Thank you very much for your kind comment.
Reviewer 3 Report
The manuscript by Sakiyama presents solutions to a model Hamiltonian for the 3T1 state of a t22 electron configuration under axial distortion. Equations are given for the energies, wavefunctions, and first and second order Zeeman coefficients.
The author motivates this work by saying that "the equations [...] are useful in analyzing the magnetic data of complexes." and this "without solving the secular equation each time".
The content of the paper consists of a listing of a large number of equations resulting from a tedious but trivial algebraic calculation (at most, a quadratic equation needs to be solved). Very little if any commentary on these equations is provided, and no attempt has been made to condense the results in a limited, more digestible number of equations. The claimed usefulness of the equations for the simulation of magnetic data is not illustrated. In particular, it is not shown that using these equations provides any practical advantage over the straightforward numerical diagonalisation of the (very small) Hamiltonian matrix.
In my opinion, no theoretical or practical scientific advance is demonstrated in this manuscript. I therefore cannot recommend publication.
Author Response
Answers to reviewer 3
The manuscript by Sakiyama presents solutions to a model Hamiltonian for the 3T1 state of a t22 electron configuration under axial distortion. Equations are given for the energies, wavefunctions, and first and second order Zeeman coefficients.
The author motivates this work by saying that "the equations [...] are useful in analyzing the magnetic data of complexes." and this "without solving the secular equation each time".
The content of the paper consists of a listing of a large number of equations resulting from a tedious but trivial algebraic calculation (at most, a quadratic equation needs to be solved). Very little if any commentary on these equations is provided, and no attempt has been made to condense the results in a limited, more digestible number of equations. The claimed usefulness of the equations for the simulation of magnetic data is not illustrated. In particular, it is not shown that using these equations provides any practical advantage over the straightforward numerical diagonalisation of the (very small) Hamiltonian matrix.
In my opinion, no theoretical or practical scientific advance is demonstrated in this manuscript. I therefore cannot recommend publication.
---Equations have been simplified as much as possible. Although any new data have not been analyzed, simulation results have been added. One of the advantages is that anyone who wants to obtain Zeeman energy values and so on can calculate them without any specific programs. This has been added in the first paragraph of Discussion. In the case of the previous expression for the 4T1g ground term, in fact, the first successful magnetic analysis of dinuclear octahedral high-spin cobalt(II) complexes with slightly distorted cobalt(II) ions was conducted using the closed-form expression. In the same way, the present expressions for the 3T1 ground term are expected to be useful, although it has not been proven. This has been added in the third paragraph of Introduction.
Reviewer 4 Report
This paper establishes the theoretical equations of Zeeman energy levels of metal complexes with a 3T1 ground state together with a simulation of magnetic susceptibility and magnetization via a MagSaki software. The Zeeman energy levels play an important role in the field of molecule magnets, and this work presents a new feasibility in the understanding of Zeeman energy levels of distorted complexes with a 3T1 ground state. It is therefore a pleasure for me to recommend the paper for publication to Magnetochemistry.
Author Response
Answers to reviewer 4
Thank you very much for your kind comment.
Round 2
Reviewer 1 Report
I am content with the modifications done by the Author. I maintain that some more extensive introduction can help the readers.
Reviewer 3 Report
l.23: "simulation can be freely performed only by those who have programs to solve matrix equations"
Such programs or programming environments have in fact been freely available for a long time. Matrix algebra operations are available in, e.g., Python, Maxima, Octave, and Julia. They are all readily and freely downloadable from the internet.
Figure 2: The caption does not agree with the text in the preceding paragraph.
l.79 "positive \lambda" versus l.82 "\lambda takes [the] negative values"
