Applying the Jellium model to octacarbonyl metal complexes

The recently reported octacarbonyl metal complexes M(CO)8 (M = Ca, Sr, Ba) feature interesting bonding structures. In these compounds, the bond order is 7, while accommodating 8 lone pairs of ligands in forming octa-coordinated complexes or ions. Here, by comparing [Ba(CO)8]2− and metal clusters of [BaBe8]2− analogically, we demonstrate that the Jellium model can not only be applied on metal clusters, but is also a useful tool to understand the electronic structures of [M(CO)8]q (M, q = Ca, 2−; Sc, 1−; Ti, 0; V, 1+; Cr, 2+; Ba, 2−). By applying the Jellium model, we find that a 20-e model with the configuration |1S2|1P6|1D10|1F2| is an appropriate description of the valence bonding structures of M(CO)8 species, where each coordinative bond contains 7/8ths of the bonding orbitals and 1/8th non-bonding orbitals.

The authors should add the calculated vibrational frequencies and the CO dissociation energies in SI.
We have added the corresponding energies in SI- Table S1. As for the dissociation M(CO)8→ M(CO)7 + CO, we do not find the stable conformation of [Ca(CO)7] 2-. But there are no virtual frequencies in the results of [Ca(CO)8] 2-, indicating [Ca(CO)8] 2is a stable structure on the PES. In the manuscript, we modified the paragraph in the revised manuscript as below: As for Ti(CO)8 (Fig. 2a) 1939.24, 1939.24, 1939.24, 1943.70, 1943.70, 1943.70, 1952.20

For completeness, the authors should include Sc(CO) 8 and V(CO) 8 + as well.
We have added the descriptions of Sc(CO)8and V(CO)8 + in the manuscript. Figure 2 has been revised, where all the numbers have been moved into Table 1. The details are listed below. The modifications of Figure 2 are showed in the answers of question 5 below.  |ONs|1 is the occupation number including the contribution of a2u orbital. |ONs|2 is the occupation number without the contribution of a2u orbital.
Ratio is the components of the a2u orbital, which is calculated as：  Figure 2 is very crowded and difficult to follow. The authors should clean the figure and put the numbers into a table.

5.
We have modified Figure 2 and removed all the details into Table 1 in the revised manuscript. Here are the detailed modifications: . 2) Regarding the Jellium model, why is 2S not occupied? Is it higher in energy than 1F2?
First, the energy level of 2S and 1F orbitals are close to each other. But 1F orbitals are more susceptible to the ligands. Secondly, it is a cubic field in all the M q (CO)8 complexes or ions, which affect the F orbital in the coordination. The 7-degenerate F orbitals can be simplified as Figure1 (a), where the a2u-symmetric Fxyz orbital matches the orbital symmetry in the cubic field of coordination. Therefore, as a bonding orbital, the energy of 1Fxyz orbital is lower than 2S orbital caused by the splitting of F orbitals affected by the cubic field. As showed in Figure1 (b) below, the a2u orbital of [Ba(CO)8] 2is showed below, where the eight ligands coordinate with Ba 2matching of orbitals symmetry.
In order to clarify our viewpoints, we also optimized [U(CO)8] 4+ to understand the splitting of the f orbitals in Figure 2, where the 5f atomic orbitals of U 4+ are contributed in the bonding structure. Obviously, all the MOs are similar with that of [Ba(CO)8] 2-, except for the orbital energies. The energy of a2u orbital is lower than d-type orbital because of the splitting of 5f AOs of U 4+ .
So in the manuscript, we descript the energy level as Figure 1 showed, where the electron first occupied a2u-symmetric 1Fxyz orbital rather than a1g-symmetric 2S orbital.
On the basis of the suggestion, we add some explanations in the manuscript as: It should be noticed that the a2u orbital is an 1F orbital rather than 2S orbital, where the energy of 1F orbital is in the middle of the two groups 1D orbitals.
Based on the calculation, a2u orbital adopts the f symmetry as showed in Fig. 1. Furthermore, there is a cubic field in all the M q (CO)8 complexes or ions, which affect the 7-degenerate 1F orbitals in the coordination, in which the a2u-symmetric 1Fxyz orbital matches the orbital symmetry in the cubic field of coordination. Therefore, the energy of 1Fxyz orbital is lower than 2S orbital caused by the splits of F orbitals ( Figure S1 in the supporting information). The sequences of energy levels of the orbitals are the results of the splitting of 1D and 1F orbitals.    Yes. It is an error in the previous manuscript. Now we have modified in the revised paper: As for Ti(CO)8 (Fig. 2a), the HOMO-LUMO gap of Ti(CO)8 is 5.47 eV under the same theoretical level of M062x/def2tzvpp. 6) In the caption of Figure 2, please add also the colors used for each of the three systems: red, black and blue. Figure 2 is very crowded and difficult to follow. Now we have modified Figure 2 and listed all the details into Table 1. Here are the detailed modifications:  7) Can the authors justify the reason why 1D(4) orbitals can be either lower ( Figure 3) or higher in energy than 1F(2) (Figure 1)? How does the change of M affect these trends? (2018)). In the revised paper, we summarize all the energy levels for the five compounds in the Table and put them into the Table S4 of supporting information. The results indicate the energy of 1F orbital is between 3-degenerate 1D orbitals (1Dxy, xz, yz) and 2-degenerate 1D orbitals (1D and 1D ). In our opinion, the energy level of |1F| 2 is lower than that of |1D| 4 , which is caused by the splitting of D orbitals and F orbitals in the cubic field. In the Jellium model, the energies of 1D orbitals are lower than that of 1F orbitals. But the 5-degenerate 1D orbitals split to two groups in the coordination, including 3-degenerate σ-type bonding orbitals with lower energies and 2-degenerate anti-bonding orbitals with higher energies. As for 1F orbital, we have analyzed in Fig. S1, where the splitting of 1F orbitals results in the 1Fxyz orbital as the non-bonding orbital, which takes part in the coordination as the ligand-only orbital.
And we also add the explanation for the sequences of the orbitals in the revised manuscript: Therefore, the 15 MOs should be composed as 7 bonding, 1 non-bonding, and 7 anti-bonding orbitals filled by 16 electrons successively. In the 15 MOs, the 7 bonding orbitals are corresponding to the a1g, t1u and t2g orbitals. The non-bonding orbital is exactly corresponding to the ligand-only a2u orbital. This is also consistent with the sequence of energies of orbital levels, where the energy of 1Fxyz orbital as a non-bonding orbital is between 3-degenerate 1D orbitals (1Dxy, xz, yz) and 2-degenerate 1D orbitals (1 and 1 ).

8) Finally, several misprints along the manuscript should be corrected.
We  orbital is an 1F orbital rather than 2S orbital, where the energy of 1F orbital is in the middle of the two groups 1D orbitals.
Based on the calculation, a2u orbital adopts the f symmetry as showed in Fig. 1.
Furthermore, there is a cubic field in all the M q (CO)8 complexes or ions, which affect the 7-degenerate 1F orbitals in the coordination, in which the a2u-symmetric 1Fxyz orbital matches the orbital symmetry in the cubic field of coordination. Therefore, the energy of 1Fxyz orbital is lower than 2S orbital caused by the splits of F orbitals ( Figure S1 in the supporting information  As for Ti(CO)8 (Fig. 2a) Fig. 2a) are very close to the ideal value 2.0 |e|, suggesting reasonable valence properties.
method 22 . The AdNDP analyses are showed in Fig. 2a.
In order to make clear whether the a2u orbital in any M q (CO)8 (M q =Ca 2-, Sc -, Ti, V + or Cr 2+ ) participates in the formation of eight coordinative bonds, we apply AdNDP method to compare the |ONs| of eight Ti-C orbitals of Ti(CO)8 with and without the participation of a2u orbital (showed in Fig. 2b and 2c).
Page 5 Therefore, it can be concluded that the bonding orbitals occupy around 7/8 components (non-bonding orbital contribute 1/8 components) in the coordination.
So in conclusion, the octacarbonyl metal complex (M(CO)8), it is more reasonable to view the ligand-only a2u orbital as a non-bonding orbital contributes to form the eight coordinative orbitals (a1g 2 t1u 6 t2g 6 a2u 2 ), where each coordinative bonds contains 1/8 non-bonding orbital and 7/8 bonding orbital as showed in Fig.   3.
Therefore, it can be concluded that the bonding orbitals occupy around 7/8 components (non-bonding orbital contribute 1/8 components) in the coordination.  As for the t1u orbitals in Fig.2, we tuned the isovalue of the density surfaces and showed the AOs of metal in the AdNDP analysis, which can be clearly found the t1u orbitals are mainly contributed from the 3-degenerate p -type orbitals of the metal. On the basis of the suggestions, the pictures have been also updated in Fig.1 and Fig.2 of the revised manuscript, which also showed as below:

1) On Pg 2, line 13(left column) "alkali metal" should be "alkaline earth metal";
We have modified "alkali metal" should be "alkaline earth metal" as the suggestions: 2) on Pg 3, line 2 of the second paragraph, the computational method "BP86/def2tzvpp" should be "M06-2X/def2tzvpp" according to their supporting information.
Yes. It is an error in the previous manuscript. Now we have modified in the revised paper: As for Ti(CO)8 (Fig. 2a), the HOMO-LUMO gap of Ti(CO)8 is 5.47 eV under the same theoretical level of M062x/def2tzvpp.

3) Thus, the authors should check the main text carefully again.
We orbital is an 1F orbital rather than 2S orbital, where the energy of 1F orbital is in magic number '20' appearing the magical stability. the middle of the two groups 1D orbitals.
Based on the calculation, a2u orbital adopts the f symmetry as showed in Fig. 1.
Furthermore, there is a cubic field in all the M q (CO)8 complexes or ions, which affect the 7-degenerate 1F orbitals in the coordination, in which the a2u-symmetric 1Fxyz orbital matches the orbital symmetry in the cubic field of coordination. Therefore, the energy of 1Fxyz orbital is lower than 2S orbital caused by the splits of F orbitals ( Figure S1 in the supporting information). The As for Ti(CO)8 (Fig. 2a) Fig. 2a) are very close to the ideal value 2.0 |e|, suggesting reasonable valence properties.
orbital (NBO) analysis by using the adaptive natural density partitioning (AdNDP) method 22 . The AdNDP analyses are showed in Fig. 2a.
In order to make clear whether the a2u orbital in any M q (CO)8 (M q =Ca 2-, Sc -, Ti, V + or Cr 2+ ) participates in the formation of eight coordinative bonds, we apply AdNDP method to compare the |ONs| of eight Ti-C orbitals of Ti(CO)8 with and without the participation of a2u orbital (showed in Fig. 2b and 2c).
For another aspect, the diminution of |ONs| from 1.94 |e| to 1.73 |e| suggests around 1/8 components (Table 1)  suggest the both the a2u orbitals contribute around 1/8 components in the coordinative orbital (Table 1).
For another aspect, the diminution of |ONs| from 1.94 |e| to 1.71 |e| suggests around 1/8 components ( We hope to explain this query in the following 2 aspects.

I) M q (CO)7 and M q (CO)8 systems can be both synthesized successfully
It is truly that M q (CO)7 systems are more stable than that of M q ( That is the significance of this study.
Therefore, we theoretically design six Oh-symmetric octacarbonyl metal complexes or ions with 20-e on purpose. Actually, if we apply Jellium model, there are no differences of the valence orbitals among the experimental alkaline earth complexes   It should be noticed that the a2u orbital is an 1F orbital rather than 2S orbital, where the energy of 1F orbital is in the It should be noticed that the a2u orbital is a 1F orbital rather than the 2S orbital, where the energy level of 1F orbital is in 6 middle of the two groups 1D orbitals the middle of the two groups of 1D orbitals Based on the calculation, a2u orbital adopts the f symmetry as showed in Fig. 1 Based on the calculation, a2u orbital with f symmetry is shown in Fig. 1.
Therefore, the energy of 1Fxyz orbital is lower than 2S orbital caused by the splits of F orbitals Therefore, the energy of 1Fxyz orbital is lower than 2S orbital caused by the splitting of F orbitals Page 2 The comparison of the molecular orbitals of [Ba(CO)8] 2and [Ba(Be)8] 2are showed in Fig. 1 The comparison of the molecular orbitals of [Ba(CO)8] 2and [Ba(Be)8] 2are shown in Fig. 1.
The eg MOs are corresponding to the 1D and 1D orbitals as two π-type orbitals, corresponding to the two dπ* bonds donated from 5d AOs of Ba (5d and 5d AOs) to the 2p AOs of eight CO groups.
The eg MOs are corresponding to the 1D and 1D orbitals as two π-type orbitals, which are the two dπ* bonds donated from 5d AOs of Ba (5d and 5d AOs) to the 2p AOs of eight CO groups This is also consistent with the sequence of molecular orbital level energy, where the energy of 1Fxyz orbital as the non-bonding orbital is higher than that of (1Dxy, xz, yz) and lower than the energy of 1D and 1D orbitals.  (SI-table S3) where each coordinative bonds contains 1/8 non-bonding orbital and 7/8 bonding orbital as showed in Fig. 3.