2.3.1 Methodology
Although, from the previous section, we already know that EMACs as short as tri-nuclear chains are not enough to describe helical tenancy on ligands due to the chain end effects, it is still worthwhile to look into the influence of the helicity from these simpler EMACs before we move onto a longer EMAC. And hopefully we can find an answer to the distin-guish high conductivities of non-helical Mo2M(npo)4(NCS)2(M=Mn, Fe, Co, Ni) family.
The already synthesized unique non-helical Mo2M(npo)4(NCS)2(M=Mn, Fe, Co, Ni) are calculated and compared with the helical Mo2M(dpa)4(NCS)2EMACs family. In addition to the geometries of these two series of EMACs, the electronic structures are also been studied. For electronic structures, an additional single point calculation with UB3LYP functional are conducted with each optimized geometries.
2.3.2 Results and Discussions
The results of geometry optimizations are shown in Table 2.1. The pyramidality defined here is the average inner angle between metal-metal bonds and metal-nitrogen bonds or metal-oxygen bonds connecting ligands. Compared to the experimental crystal struc-tures (Table 1.1), DFT calculations give similar results on the EMACs geometries. In all these Mo-Mo-M EMACs, dimolybdenum form a strongly interacting unit. Through-out the series, the Mo-Mo bond lengths are short and almost still, which are around 2.1 Å and the bond orders between two molybdenum atoms are high over triple bond while the second molybdenum and the last metal bonds are weak, which have extremely high bond distances and bond order as small as not being over than 0.3.
Being the same period elements, from Mn to Ni, radius of the element shrinks as moving to the right side of the periodic table. At the same time, in Mo2M(L)4(NCS)2 (M=Mn, Fe, Co, Ni, L=npo, dpa), the Mo-M equilibrium bond length gradually grows
shorter and the Mo-M bond order increases while the total bond order alone the central metal chain remain almost the same as the third metal changed from manganese to nickel.
Table 2.1: Geometry of Mo2M(L)4(NCS)2(M= Mn, Fe, Co, Ni, L=npo, dpa) Dihedral Angle Pyramidality Bond Length Bond Order
(degree) (degree) (Å)
NMMoN NMoMoN MMo MoMo MMo MoMo MMo MoMo
dpa
Mn 17.13 11.88 82.68 92.42 2.82 2.10 0.16 3.15
Fe 19.17 12.33 83.27 92.30 2.74 2.11 0.20 3.13
Co 19.13 12.24 84.55 92.29 2.64 2.11 0.23 3.09
Ni 19.16 12.14 85.49 92.27 2.56 2.11 0.29 3.06
npo
Mn 0.20 0.11 82.55 92.64 2.90 2.11 0.14 3.12
Fe 0.02 0.07 83.69 92.57 2.80 2.12 0.20 3.10
Co 0.65 0.40 86.24 91.30 2.69 2.12 0.22 3.10
Ni 0.38 0.25 86.33 92.57 2.60 2.11 0.27 3.06
Comparing bond lengths between two ligands, we can see that metal-metal bond length are slightly longer in Mo2M(npo)4(NCS)2, especially for the M bonds. All these Mo-M bond lengths in both Mo-Mo2M(npo)4(NCS)2and Mo2M(dpa)4(NCS)2series are far over the critical bond length where ligands on EMACs should be exactly planar by Eq. 1.1.
However, from the previous section of Mo-Ni-Mo tri-nuclear EMACs model, we already know that being a tri-nuclear EMACs, chain end effects and steric hindrances strongly affect the ligand conformations, so it is no surprise that Mo2M(dpa)4(NCS)2complexes, having a more bulky dpa ligands, still shows a dihedral angle about 18 degrees, while the dihedral angles of Mo2M(npo)4(NCS)2are nearly zero. In the present of pyramidality at chain ends, ligands can compensate the unbalance of their lengths with the metal chain lengths and the steric effects arised from the hydrogens on the rings of the surrounding li-gands by deviating N(O)-Mo-N pyramidality angle from 90 degrees as Mo-M bond grows larger, especially in Mo2M(dpa)4(NCS)2, which have larger helicities. The slightly shorter of the metal-metal bonds in dpa ligand may also be the result of these compensations.
As for the electronic properties, firstly spin densities, which is defined as the electron density differences between alpha and beta orbitals, is studied and listed in the Table 2.2.
Coincided with the significant difference of bond lengths and bond orders between Mo-Mo and Mo-M indicating, all the spin densities mostly locate on the third metal M (M=Mn, Fe, Co, Ni) and close to the isolated M metal, which are all in their +2 oxidation state, while
Mo-Mo have slightly antiferromagnetic properties inside the units and have S=0 over the whole units.
Table 2.2: Spin density of Mo2M(L)4(NCS)2(M= Mn, Fe, Co, Ni, L=npo, dpa) Mn(S=5/2) Fe(S=2) Co(S=3/2) Ni(S=1)
dpa npo dpa npo dpa npo dpa npo
Mo1 0.73 0.86 0.72 0.86 0.66 0.84 0.58 0.84 Mo2 -0.67 -0.81 -0.64 -0.81 -0.55 -0.75 -0.41 -0.71
M 4.79 4.78 3.73 3.72 2.65 2.66 1.54 1.61
Moreover, to gain further insight of their electronic structure, MOs of both series mo-lecules have been compared. Fig. 2.4 and Fig. 2.5 show the occupied orbitals near the HOMO of Mo2M(npo)4(NCS)2and Mo2M(dpa)4(NCS)2separately. In both npo and dap series, orbitals are strongly asymmetry and mostly located on either Mo-Mo of M (M=Mn, Fe, Co,Ni) side. Dimolybdenums are strongly bonded and have poor interaction with the third transition metal, since molybdenum is a 4d transition metal and from manganese to nickel all the third metal used here are 3d transition metals. Moreover, while looking at the periodic trend in both series, from M=Mn to M=Ni, orbitals which mainly located on the Mo-Mo side and also antibonding between Mo and M gradually go down. This may attribute to the fact that d orbital energies get lower and lower from Mn to Ni along the periodic table. Hence as the third metal changed from manganese to nickel, MO energies are dragged down and the interactions weaker between Mo and M.
Figure 2.4: Occupied orbitals near the HOMO (the highest one) of Mo2M(npo)4(NCS)2
Figure 2.5: Occupied orbitals near the HOMO (the highest one) of Mo2M(dpa)4(NCS)2
Comparing two seires of EMACs, in the npo series, since the ligands have C2 sym-metry instead of C4 symmetry, the degeneration of dxz and dyzbreaks and the paired mo-lecular orbitals split into to different energies. Furthermore, delta bond orbitals have lower energy with npo ligands compared to dpa ligands. This could be a result of its nearly planar ligand conformation.
DFT calculations show that the greater helicity of the ligands on Mo2M(dpa)4(NCS)2 (Fig. 2.6(a)) makes d orbitals between neighboring metal atoms twist along their ligands, and thus gives poorer overlaps. On the other hand, Mo2M(npo)4(NCS)2 (Fig. 2.6(b)), which has nearly planar ligands, has a perfectly face to face atomic orbital and a larger overlap between d orbitals, and hence results in a stronger interaction between central metal atoms and lower their energies. The heilicity of ligands directly influence the mo-lecular orbital energies and the orbital alignment and can possibly affect their other elec-tronic properties such as conductivities, since orbitals having energies near the Fermi level may promote conductivities.
Figure 2.6: (a)Delta orbital of Mo2Ni(npo)4(NCS)2(two delta orbitals have the same ori-entations, and have poor overlap) (b)Delta orbital of Mo2Ni(dpa)4(NCS)2(two delta or-bitals have a torsion angle between them)
2.4 Penta-nuclear MoMoMMoMo (M=Mn, Fe, Ni) sys-tem containing two Mo
2units
2.4.1 Methodology
Finally, we get back to the penta-nuclear EMACs, Mo2NiMo2(tpda)4(NCS)2 (Fig. 1.2).
Starting from both helical and meso conformation, full optimizations are firstly conduc-ted. The initial geometries for the calculations are taken from the crystal structures of Mo2NiMo2(tpda)4(NCS)2. After that, a series of constrained geometry optimization are done. Since Mo-Mo bond lengths, listed in Table 1.2, are almost the same in two confor-mations, we focus on Mo-Ni bonds to see the changes when Mo-Ni bond lengths differ.
Mo-Ni bonds (r1and r2labeled in Fig. 2.7) are tuned from 2.30 Å to 2.70 Å separately, and then these two bond lengths are fixed in the followed constrained geometry optimizations.
In other words, two types of stretching Mo-Ni bonds are done, symmetrically and asym-metrically. For symmetrical one, we lengthen both Mo-Ni bonds simultaneously from 2.30 Å to 2.70 Å at the same time with r1 = r2. And as for the asymmetrical case, while r1 is lengthen from 2.30 Å to 2.70 Å, different r2 > r1form 2.30 to 2.70 Å are calculated at each r1.
Figure 2.7: Mo2NiMo2(tpda)4(NCS)2 used in the constrain geometry optimization with Mo-Ni bond length r1 and r2 fixed from 2.30 Å to 2.70 Å
Furthermore, to demonstrate that the origin of helical and meso conformation is mostly geometrical, beside Mo2NiMo2(tpda)4(NCS)2, hypothetical Mo2FeMo2(tpda)4(NCS)2and Mo2MnMo2(tpda)4(NCS)2 are also been calculated to see whether different element in the metallic chain effect the results. Again, the full optimizations and the constrained geometry optimizations with Mo-M (M=Mn, Fe) bond lengths varying from 2.30 to 2.70 Å are calculated.
2.4.2 Results and Discussions
In the full optimization of helical and meso Mo2NiMo2(tpda)4(NCS)2, the meso conforma-tion has a 0.011eV lower energy than the helical one. The small energy different indicates that the stability of two conformations are roughly the same and both of the conformations can exist at the same time. Similar to other EMACs containing dimolybdenum, the Mo-Mo bonds are strong with a bond order about 3, while the molybdenum-nickel bond are weak. All of these geometry properties are shown in Table 2.3, and are similar to the X-ray result list in Table 2.1, which shows the DFT calculation did quite a good job here. The optimized bond length also show a complementary trend of short dimolybdenum bonds and long molybdenum-nickel bonds.
Table 2.3: Optimized geometries of Mo2NiMo2(tpda)4(NCS)2
Bond length Dihedral angle Bond order
(Å) (degree)
Mo-Mo Mo-Ni N-Mo-Mo-N N-Mo-Ni-N Mo-Mo Mo-Ni
meso 2.10 2.54 8.04 4.43 2.99 0.33
Hehical 2.10 2.45 11.87 19.50 2.94 0.48
However, comparing two conformations, with the same chemical formula, their geo-metry are quite different. In the meso conformation, the metal-metal bond length of Mo-Mo and Mo-Mo-Ni are 2.10 Å and 2.54 Å. As for the helical one, the corresponding bond lengths are 2.10 Å and 2.45 Å. Mo-Mo bond lengths are nearly identical in both con-formations while a relatively short Mo-Ni bond lengths appear in the helical form. To have helical perversion at the center, the meso conformation have a rather small dihedral angles, which is 8.04 degrees for ∠NMoMo and 4.43 degrees for ∠NMoNi, while the
corresponding dihedral angles in helical conformation are much large at the scale of 11.87 and 19.50.
Figure 2.8: The potential energy surface of meso and helical conformations with different Mo-Ni bond length r1and r2. The color bar and the color map at the bottom represent the energy difference ∆E=EHemi− EHat different Mo-Ni bond length r1and r2.
In Fig. 2.8, the two surfaces present the potential energy surface of meso and helical conformation with different Mo-Ni distance separately. And the color bar and the color map at the bottom represent the energy difference ∆E=EHemi−EHat different Mo-Ni bond length r1and r2. As Mo-Ni bonds lengthened, meso conformation gradually become the more stable one. In both conformations, equal Mo-Ni bond length ones are more stable than the asymmetry ones. However, from the figure we can see that if r1+ r2= const. the energy different is almost the same. No matter two Mo-Ni bonds symmetric or not, the energy difference of two conformations remains almost still at the same average Mo-Ni
bond length, and declines as total Mo-Ni-Mo length grows longer. M eso conformations are gradually stabilized and became the lower energy one when the average Mo-Ni bond length is over 2.50 Å.
Figure 2.9: (a) N-Mo-Ni-N Dihedral angles at different Mo-Ni bond length plotted at equal Mo-Ni bond length. (b) N-Mo-Ni-N Dihedral angles at different average Mo-Ni bond length as Mo-Ni-Mo asymmetrized. Blue lines represent the helical conformation while the red lines representing the meso ones. Square, star, cross and circle line represent r1+ r2=4.8, 4.9, 5.0, 5.1 Å separately
Consisting with previous assumption, Fig. 2.9(a) shows that as Mo-Ni bond length grow longer, the average N-Mo-Ni-N dihedral angle become smaller. Furthermore, shown in Fig. 2.9(b), the average N-Mo-Ni-N dihedral angles also stay unchanged as molybdenum-nickel bond goes asymmetry. The pyridyl at the center are bent about 28.43 degrees backward (Fig. 2.10) in the meso conformation. In fact, in spite of N-M-M-N dihedral angles are quite different in two conformation, if we measure the dihedral angle between two the top carbons in the ring to their corresponding central metals ∠C-Mo-Ni-C are 32.71 degrees for the meso conformation and 36.95 degrees for the helical conformation.
The difference is not that significant as expected, and shows that in meso conformation Mo2NiMo2(tpda)4(NCS)2, back bending of the central pyridyl ring is formed to avoid steric hindrance at an almost planar geometry, and this back bending effect may further favor the meso conformation, since in a helical conformation, the pyridyl ring next to the back
bending one would be vary close to the bent ring.
Figure 2.10: Central pyridyls bent backward (highlight in red).
After analyzing the Mo2NiMo2(tpda)4(NCS)2, to gain a more general point of view on the origin of meso conformation surrounding ligands, the central transition metal nickel is changed, and hypothetical Mo2FeMo2(tpda)4(NCS)2and Mo2MnMo2(tpda)4(NCS)2are calculated. As central metals changed, similar trends as in the Mo2NiMo2(tpda)4(NCS)2 molecule are shown in both calculation results of related EMACs containing iron and manganese.
Table 2.4: Equilibrium bond lengths and energy difference of meso and helical confor-mation.
meso/helical Mo-Mo (Å) Mo-Ni (Å) EHemi− EH(eV)
Ni 2.10/2.10 2.54/2.45 -0.011
Fe 2.11/2.10 2.55/2.46 -0.17
Mn 2.10/2.09 2.58/2.50 -0.34
As indicated in Table 2.4, for Mo2FeMo2(tpda)4(NCS)2the equilibrium bond lengths of dimolybdenum in meso and helical conformation are 2.11 Å and 2.10 Å separately. And as for the Mo2MnMo2(tpda)4(NCS)2complex, dimolybdenum units are 2.10 Å and 2.09 Å long for the meso and helical conformation. Along with the Mo2NiMo2(tpda)4(NCS)2 calculation, in six cases dimolybdenum bond lengths stay short and still, and can be seen as dimer units at chain ends. As for the central Mo-M bond, one the other hand, though shorter than the Mo-M bonds in the tri-nuclear Mo-Mo-M EMACs, these bonds show the same properties of extremely long Mo-M bonds as the tri-nuclear ones. Mo-Fe bond length are 2.55 Å for meso conformation and 2.46 Å for helical conformation. In
Mo2MnMo2(tpda)4(NCS)2, even longer Mo-Mn distances are shown, 2.58 Å and 2.50 Å for meso and helical conformation separately. Both of them are longer than the Mo-Ni bonds in Mo2NiMo2(tpda)4(NCS)2and consist with the trend that Mo-Mn>Mo-Fe>Mo-Ni in tri-nuclear Mo-Mo-M EMACs. Furthermore, as in Mo2NiMo2(tpda)4(NCS)2, longer Mo-M bond appear in the meso conformation.
As shown in Fig. 2.11 and Fig. 2.12, the potential well have a similar shape in the M=Mn and Fe case, expect the positions of the well changed. The zero energies defined here is the lowest energy in each complex, and the energy differences are again defined as
∆E=EHemi− EH, which means meso conformation become the more stable one when ∆E is negative.
Figure 2.11: The potential energy curve and the energy differences of two conformations ( ∆E= EHemi− EH) of Mo2MMo2(tpda)4(NCS)2 with M=Mn, Fe, Ni at different Mo-M bond lengths.
Figure 2.12: The potential energy surface of both Mo2FeMo2(tpda)4(NCS)2and
Mo2MnMo2(tpda)4(NCS)2with different Mo-M bond length r1and r2from 2.30 Å to 2.70 Å.
As in Mo2NiMo2(tpda)4(NCS)2, when the Mo-M bonds lengthen, the meso confor-mation gradually become the more stable one. And since the equilibrium Mo-M bond lengths are longer when nickel is replaced by iron and manganese, the meso conforma-tion became even more stable than their helical conformaconforma-tion than in the M=Ni case. In Mo2FeMo2(tpda)4(NCS)2, the energy difference further rise to 0.17eV and in
Mo2MnMo2(tpda)4(NCS)2, the energy of meso conformation is 0.34eV lower than the he-lical one. And from the energy surfaces, we can see that the energy crossing points, where the more stable conformation changes, also occur at a shorter and shorter Mo-M when the central metal in Mo2NiMo2(tpda)4(NCS)2is changed to iron and manganese. In the case of Mo2FeMo2(tpda)4(NCS)2the crossing point is at an average Mo-Fe bond length of 2.45 Å, and as for the Mo2MnMo2(tpda)4(NCS)2, the energy crossing average Mo-Mn bond length decline to 2.40 Å.
As for the ligand geometries, changing from M=Ni to M=Mn and Fe gives a nearly identical results. Shown in Fig. 2.13, as in Mo2NiMo2(tpda)4(NCS)2, dihedral angels shrinks as bond lengths grow longer, and as Mo-Ni-Mo become asymmetric, the aver-age dihedral angle remain. Moreover, with the same metal-metal bond lengths, the dihe-dral angles are similar even with different metals, which indicates that the species of the transition metal used only determine the favorites of the metal-metal bond lengths, and its effect on the ligand conformation is rather non-chemical but geometric. The ligand helicities and the formation of the meso conformations are determined by the metal-metal chain lengths and geometric unbalanced chain lengths.
To this point, we can finally make some conclusions that although the steric effect does affect the ligand geometry, being a long chain, the formation of the meso conformation is from a rather geometrical aspect. Since the metal-metal bond lengths are different with the surrounding organic ligands, N-M-M-N dihedral angles arise. To balance the length of central metal chain and the surrounding ligands, the shorter the central metal chain is, the greater helicities arise. Two extremely long molybdenum-nickel bonds at the center of Mo2NiMo2(tpda)4(NCS)2favor a planer geometry, and hence the meso conformation, which is relativity flat at the helical perverse point, is stabilized. And if changed to metal that favored a even longer bonds at the center, meso conformation can be further stabilized.
Figure 2.13: Figures show the N-Mo-M-N (M=Mn and Fe) dihedral angles at different Mo-M bond lengths. For each complex, the left-hand side of the picture are dihedral angles plotted at equal Mo-M bond length. And as for the right-hand side, N-Mo-Ni-N dihedral angles at different average Mo-M bond length as Mo-M-Mo geos asymmetry.
Blue lines represent the helical conformation while the red lines represent the meso ones.
Square, star, cross and circle line represent r1+ r2=4.8, 4.9, 5.0, 5.1 Å separately
2.5 Conclusion
Rather than the traditional interpretation on the helicities of EMACs ligand conformation with steric effects, in this work we try to explain it in a more geometrical approach, and try to give an explanation of why ligands in EMACs are helical and why meso conforma-tion, which have hemihelical ligands, is formed in the unique Mo2NiMo2(tpda)4(NCS)2. Compared to the metallic chains, bonds containing carbons and nitrogens are seen as rigid bonds, hence the organic ligands on EMACs have a similar length in different central metal chain EMACs. The unbalance of metallic chain length and the organic ligand lengths are the origin of helices in EMACs. When these two have exactly the same length, planer con-formation should be formed. However, this is usually not the case in EMACs molecules.
The longer one, the surrounding organic ligands in EMACs, curve into helical conforma-tion and forming dihedral angles, which can be simplified by Eq. 1.1, to shorten the total length. As the metal-metal bond grows longer, the dihedral angle between neighbor M-N bonds gradually vanish again.
We start with the shortest tri-nuclear EMACs. Comparing hypothetical Mo-Ni-Mo model with bulky and non-bulky surrounding ligands, we can see that the size of dihedral angles does decline as metal-metal bond lengthen as expected. However, with only three metals in a chain, the geometries are strongly affected by chain end effects and steric hindrances at the persent of chain end∠NMM pyramidalities. With crowed ligands such as dpa, ligand helicity cannot be eliminated at long central metal-metal bonds due to the hydrogen hindrance on pyridyls. On the other hand, with a spare ligand, for example npo, ligand helicity arise when central metal chain is shorter than the surrounding ligand. And if one can synthesized an EMACs with these ligands and long enough metal-metal bonds, one may get an non-helical EMACs.
We start with the shortest tri-nuclear EMACs. Comparing hypothetical Mo-Ni-Mo model with bulky and non-bulky surrounding ligands, we can see that the size of dihedral angles does decline as metal-metal bond lengthen as expected. However, with only three metals in a chain, the geometries are strongly affected by chain end effects and steric hindrances at the persent of chain end∠NMM pyramidalities. With crowed ligands such as dpa, ligand helicity cannot be eliminated at long central metal-metal bonds due to the hydrogen hindrance on pyridyls. On the other hand, with a spare ligand, for example npo, ligand helicity arise when central metal chain is shorter than the surrounding ligand. And if one can synthesized an EMACs with these ligands and long enough metal-metal bonds, one may get an non-helical EMACs.