1. Introduction
Butadiene transition metal chemistry dates back to the 1930 discovery of butadiene iron tricarbonyl by Reihlen et al. [1], its subsequent reinvestigation by Hallam and Pauson in 1958 [2] after the 1951 discovery of ferrocene [3,4], and its structural elucidation by Mills and Robinson [5] using X-ray crystallography. The next major development was the nickel-catalyzed trimerization of butadiene to give 1,5,9-cyclododecatriene. Proposed organonickel intermediates in this process include (η3,2,3-C12H18)Ni with an acyclic C12H18 ligand and cyclo-(η2,2,2-C12H18)Ni with a complexed 1,5,9-cyclododecatriene ligand (Figure 1). The latter intermediate has been structurally characterized by X-ray crystallography [6]. However, the instability of the former intermediate has precluded similar definitive structural characterization. The bonding of the central C=C double bond of the acyclic C12H18 ligand to the nickel atom in the former intermediate is uncertain since our recent theoretical studies [7] suggest a η3,3-hexahapto ligand rather than the originally proposed η3,2,3-octahapto ligand. No stable homoleptic (C4H6)nNi (n = 2, 3) intermediates with unsubstituted separate butadiene ligands were observed in this system, even though the nickel atom in a hypothetical (C4H6)2Ni with two tetrahapto butadiene ligands would have the favored 18-electron configuration.
Synthesis of stable homoleptic butadiene metal complexes is found to require either substituted butadienes for the first-row transition metal derivatives or the second- and third-row transition metals for stable (C4H6)3M complexes of unsubstituted butadiene. It has been shown that 2,3-dimethylbutadiene forms an isolable crystalline homoleptic (2,3-MeC4H4)2Ni complex which is stable only below −10 °C [8]. Use of butadiene ligands with bulkier substituents leads to stable bis(butadiene)metal derivatives of first-row transition metals other than nickel. Thus, co-condensation of metal vapors with 1,4-bis(tert-butyl)butadiene gives corresponding [1,4-(Me3C)2C4H4]2M complexes (M = Ti [9], V [9], Co [10]). Similarly, the zerovalent 1,4-bis(trimethylsilyl)butadiene cobalt open sandwich [1,4-(Me3Si)2C4H4]2Co has been synthesized and structurally characterized [11].
In contrast to the first-row transition metals, the homoleptic tris(butadiene) complexes of the second- and third-row group 6 metals molybdenum and tungsten, (η4-C4H6)3M (M = Mo, W) are known as stable compounds. They can be synthesized by co-condensation of the metal vapors with butadiene [12] or by reduction of metal halides with activated magnesium in the presence of butadiene [13]. X-ray crystallography indicates trigonal prismatic coordination of the six C=C double bonds of the three butadiene ligands to the central metal atom [14]. Tris(butadiene)molybdenum and related substituted butadiene derivatives have been useful precursors to the synthesis of other zerovalent molybdenum compounds such as ditertiary phosphine derivatives of the type (diene)2Mo(diphosphane) [15] and the unusual Mo(GaC5Me5)6 cluster having a central molybdenum atom surrounded by six gallium atoms with octahedral coordination [16].
Although the tris(butadiene) derivatives of the heavier group 6 transition metals molybdenum and tungsten are stable compounds, the corresponding chromium derivative (C4H6)3Cr has never been synthesized. Furthermore, our recent theoretical studies [7] indicate that a singlet tris(butadiene)chromium structure, (η4-C4H6)3Cr, analogous to the stable molybdenum and tungsten derivatives, is energetically disfavored relative to a quintet (η3,3-C12H18)Cr structure with an open-chain bis(trihapto) C12H18 ligand. This observation suggests that the tris(butadiene) chemistry of the first-row transition metals is significantly different from that of their second- and third-row analogs. One factor may be the larger ligand field splitting in the second- and third-row transition metal complexes relative to their first-row transition metal analogs. An indication of this is the quintet ground state of the (C12H18)Cr system contrasted with the singlet state of the tris(butadiene) molybdenum and tungsten complexes.
In order to explore this matter further, we undertook density functional theory studies of the second-row transition metal butadiene complexes (C4H6)3M (M = Zr–Pd). In general, our results confirm low-spin structures to be the lowest-energy structures for all of the second-row transition metals in accord with the larger ligand field splitting in the second-row transition metal complexes relative to the corresponding first-row transition metal complexes. More specifically, our results confirm the experimental singlet (C4H6)3Mo structure to be the lowest-energy isomer by a significant margin in contrast to our earlier studies of the (C4H6)3Cr system. In addition, the low-energy low-spin (C4H6)3M structures of the second-row transition metals are found to exhibit an interesting trend. Thus, in (C4H6)3M complexes of the late transition metals requiring fewer electrons to attain the favored 18-electron configuration, the three butadiene ligands are found to couple to form a single open-chain C12H18 unit functioning as a hexahapto or octahapto ligand. However, for the early transition metals requiring more electrons to attain the favored 18-electron configuration, the three butadiene ligands remain as separate units thereby providing a total of 12 electrons for the central metal atom.
2. Theoretical Methods
Density functional theory (DFT) has been found to be a practical and effective computational tool, especially for organometallic compounds [17,18,19,20,21,22,23]. We used four DFT methods in this study. The first DFT method was the M06-L method, which has been claimed to be suitable for the study of organometallic and inorganic thermochemistry [24]. The second DFT method was the BP86 method, which combines Becke’s 1988 exchange functional with Perdew’s 1986 gradient corrected correlation functional [25,26]. Furthermore, in order to compare our current results with our earlier results on the first-row transition metal (C4H6)3M complexes [7], we also adopted the B3LYP [27,28] and B3LYP* [29] methods in the present paper. The results show that the four DFT methods predict similar results. The B3LYP and B3LYP* results are listed in the Supplementary Materials, and the M06-L results are those mainly discussed in the text.
The Stuttgart double-ζ basis sets with an effective core potential (ECP) [30,31] were used for the second-row transition metals from zirconium to palladium. In these basis sets, 28 core electrons in the transition metal atoms are replaced by an effective core potential. This effective core approximation includes scalar relativistic contributions, which may become significant for heavy transition metal atoms. The valence basis sets are contracted from (8s7p6d) primitive sets to (6s5p3d). For the carbon and hydrogen atoms, the all-electron double-ζ plus polarization (DZP) basis sets were used. These are derived from Huzinaga and Dunning’s contracted double-ζ contraction set [32] by adding spherical harmonic polarization functions with the orbital exponents αd(C) = 0.75 and αp(H) = 0.75. All of the computations were performed using the Gaussian 09 program [33], in which the fine grid (75,302) is the default for evaluating integrals numerically [34].
The present paper discusses systems of the type (C4H6)3M, where M is a second-row transition metal. Thus, the (C4H6)3M (M = Zr, Mo, Ru, Pd) structures were optimized in singlet and triplet electronic states and the (C4H6)2M (M = Nb, Tc, Rh)—in doublet and quartet electronic states. The harmonic vibrational frequencies and the corresponding infrared intensities were determined at the same levels by evaluating force constants analytically.
The energetically low-lying (C4H6)3M species are shown in the figures. Each structure is designated as M-nZ, where M is the symbol of the central metal atom, n orders the structure according to their relative energies predicted by the M06-L method, and Z designates the spin states using S, D, T, and Q for the singlet, doublet, triplet, and quartet states, respectively.
3. Results and Discussion
3.1. (C4H6)3Pd
The four lowest-energy (C4H6)3Pd structures are all singlets with hexahapto straight-chain C12H18 ligands of various types, leaving one uncomplexed C=C double bond (Figure 2 and Table 1). This corresponds to a 16-electron configuration for the central palladium atom. In the lowest-energy (C4H6)3Pd structure Pd-1S, the three carbon atoms at each end of the C12 chain are bonded to the central palladium atom as trihapto allylic units leaving an uncomplexed C=C double bond of length 1.342 Å (M06-L) in the center of the chain. Structures Pd-2S and Pd-3S, lying 9.0 and 9.1 kcal/mol (M06-L), respectively, in energy above Pd-1S, have similar geometries with a hexahapto η3,2,1-C12H18 ligand. In Pd-2S and Pd-3S, a terminal allylic unit, the central C=C double bond, and an interior carbon atom from the other terminal allylic unit are all within bonding distance of the palladium atom. The difference between Pd-2S and Pd-3S is the orientation of their terminal uncomplexed C=C double bonds. Structure Pd-4S, with a hexahapto η3,2,1-C12H18 ligand, lies 9.5 kcal/mol in energy above Pd-1S. The hexahapto coordination includes a terminal allylic unit at one end of the C12 chain and the carbon atom at the other end of the C12 chain in addition to the central C=C double bond. These four structures correspond to the four lowest-energy structures for the nickel (C4H6)3Ni system [7] with similar relative energies (Table 1).
3.2. (C4H6)3Rh
Four low-energy (C4H6)3Rh doublet structures were found within ~17 kcal/mol of the lowest-energy structure Rh-1D (Figure 3 and Table 2). In the two lowest-energy (C4H6)3Rh structures Rh-1D and Rh-2D, the three butadiene ligands are coupled to form a C12H18 chain. Structure Rh-1D has an octahapto η3,2,3-C12H18 ligand, thereby giving the central rhodium atom a 17-electron configuration. The second (C4H6)3Rh structure Rh-2D, lying 8.9 kcal/mol (M06-L) in energy above Rh‑1D, has a hexahapto η3,2,1-C12H18 ligand with an uncomplexed C=C double bond at the end of the C12H18 chain.
The significantly higher-energy (C4H6)3Rh structures Rh-3D and Rh-4D, lying 14.6 and 16.5 kcal/mol (M06-L), respectively, in energy above Rh-1D, have three separate butadiene ligands. One of these butadiene ligands is a tetrahapto ligand, whereas the two remaining butadiene ligands are dihapto ligands. Structures Rh-3D and Rh-4D differ only in the relative orientations of their terminal uncomplexed C=C double bonds.
The previous DFT study [7] of the analogous cobalt system (C4H6)3Co found quartet structures with the lowest-energy quartet structure lying ~15 kcal/mol above the lowest-energy isomer, which is a doublet. The lowest-energy quartet structure for (C4H6)3Rh structure is a very high-energy structure, lying more than 29 kcal/mol in energy above Rh-1D. Thus, quartet (C4H6)3Rh structures do not appear to be chemically relevant and therefore are not discussed in detail in this paper. The high energy of the quartet (C4H6)3Rh structures as compared with the analogous cobalt system is a consequence of the higher ligand field strengths in the second-row transition metal complexes as compared with the analogous first-row transition metal complexes.
3.3. (C4H6)3Ru
Four low-energy (C4H6)3Ru structures were optimized, namely, two singlets and two triplets (Figure 4 and Table 3). The lowest-energy (C4H6)3Ru structure Ru-1S has a singlet spin state with an octahapto η3,2,3-C12H18 ligand, thereby providing the ruthenium atom with a 16-electron configuration. A second singlet (C4H6)3Ru structure Ru-2S, lying only 4.3 kcal/mol (M06-L) in energy above Ru-1S, has three separate butadiene ligands. Two of the butadiene ligands in Ru-2S are tetrahapto ligands, whereas the third butadiene ligand is only a dihapto ligand. This gives the central ruthenium atom the favored 18-electron configuration.
The lowest-energy triplet (C4H6)3Ru structures lie ~20 kcal/mol in energy above the lowest-energy singlet structure Ru-1S (Figure 4 and Table 3). This contrasts with the analogous (C4H6)3Fe system for which the lowest-energy structures are triplet spin state structures [7]. Furthermore, for (C4H6)3Fe, even a quintet structure has a lower energy than the lowest-energy singlet structure. This, again, is an example of the preference of the second-row transition metals for lower spin states relative to analogous complexes of the first-row transition metals. The triplet (C4H6)3Ru structure Ru-1T has an octahapto η3,2,3-C12H18 ligand, thereby giving the ruthenium atom a 16-electron configuration consistent with a triplet spin state in a high-spin complex. The second triplet (C4H6)3Ru structure Ru-2T with a similar energy as Ru-1T has a hexahapto η3,3-C12H18 ligand similar to that in Pd-1S, with an uncomplexed central C=C double bond. This gives the ruthenium atom in Ru-2T only a 14-electron configuration, which can also be the basis for a triplet spin state structure. Note that the M06-L method predicts Ru-1T and Ru-2T to have essentially the same energies, while the BP86 method predicts Ru-2T to lie ~7 kcal/mol in energy above Ru-1T.
3.4. (C4H6)3Tc
Three low-energy doublet structures were optimized for (C4H6)3Tc (Figure 5 and Table 4). Quartet and sextet (C4H6)3Tc structures have energies at least 13 kcal/mol in energy above the lowest-energy doublet (C4H6)3Tc structure Tc-1D. This contrasts with the (C4H6)3Mn system for which the lowest energy structures are sextet structures and the lowest- energy doublet structure lies ~24 kcal/mol in energy above the lowest-energy sextet structure [7]. This, again, is an indication of the higher ligand field strength in the second-row transition metals relative to analogous complexes of the first-row transition metals.
The lowest-energy (C4H6)3Tc structures Tc-1D and Tc-2D are almost degenerate in energy within 1.0 kcal/mol (M06-L) (Figure 5 and Table 4). Both structures have two tetrahapto butadiene ligands and one dihapto butadiene ligand with an uncomplexed C=C double bond of length ~1.35 Å. This arrangement of butadiene ligands gives the technetium atoms in these structures 17-electron configurations, consistent with the doublet spin state. Structures Tc-1D and Tc-2D differ only in the orientations of their butadiene ligands. The other doublet (C4H6)3Tc structure Tc-3D, lying 11.3 kcal/mol (M06-L) in energy above Tc-1D, has three butadiene units coupled to form an octahapto η3,2,3-C12H18 ligand, thereby giving the technetium atom a 15-electron configuration.
3.5. (C4H6)3Mo
Six low-energy (C4H6)3Mo structures were found, namely, three singlets and three triplets (Figure 6 and Table 5). The theoretical singlet structure Mo-1S is predicted to be the global minimum, and is experimentally known as a stable species [12,13,14,15]. Structure Mo‑1S has three separate tetrahapto butadiene ligands, thereby giving the molybdenum atom the favored 18‑electron configuration. Table 6 shows that our predicted geometric parameters agree with experiment, especially with the more reliable low-temperature X‑ray crystallographic structures in the 2002 paper [14]. For example, the predicted Mo–C1 distances (~2.28 Å) and the Mo–C2 distances (~2.35 Å) agree within 0.02 Å. The C1–C2 distances (~1.44 Å) and C2–C2A distances (~1.41 Å) also agree within 0.02 Å. Our predicted C1-C2-C2A angle (118.9° or 119.1°) agrees with the experimental result (119.7°) within 1°. Kaupp et al. also carried out a computational study on Mo-1S [14]. We found that the geometry parameters from different computational methods are in reasonable agreement (Table S8 in the Supporting Information).
The singlet (C4H6)3Mo structure Mo-2S, with two tetrahapto butadiene ligands and one dihapto butadiene ligand similar to Ru-2S and Tc-1D, is predicted to lie 12.8 kcal/mol (M06-L) in energy above Mo-1S. The molybdenum atom in Mo-2S has a 16-electron configuration. The singlet Mo-3S, lying 13.3 kcal/mol (M06-L) in energy above Mo-1S, has a geometry similar to that of Mo-1S, i.e., with three tetrahapto butadiene ligands, but in a different orientation. Thus, in Mo-3S, the molybdenum atom has the favored 18-electron configuration.
In contrast to their molybdenum analogs, the singlet (C4H6)3Cr structures are high-energy structures relative to the triplet and especially the quintet state (C4H6)3Cr isomers [7]. This difference is another example of the increased ligand field strength of the second-row transition metal complexes relative to the corresponding first-row transition metal complexes, leading to lower-spin state preferred structures for the second-row transition metals. Furthermore, the high energy of singlet (η4-C4H6)3Cr relative to higher-spin state isomers with coupled butadiene ligands as compared with the low energy of its molybdenum analog (η4-C4H6)3Mo explains why the chromium derivative is unknown but the molybdenum structure is a stable species.
The lowest-energy triplet (C4H6)3Mo structure Mo-1T, lying 16.5 kcal/mol (M06-L) in energy above Mo-1S, has a coupled straight-chain η3,3-C8H12 ligand and a separate η4-C4H6 ligand, thereby giving the molybdenum atom a 16-electron configuration consistent with the triplet spin state (Figure 6 and Table 5). The second triplet (C4H6)3Mo structure Mo-2T, lying 29.3 kcal/mol (M06-L) in energy above Mo-1S, has a ligand arrangement similar to Mo-2S with two tetrahapto η4-C4H6 ligands and one dihapto η2-C4H6 ligand. This gives the molybdenum atom in Mo-2T a 16-electron configuration similar to Mo-2S. Thus, Mo-2T can be regarded as the high-spin analog of Mo-2S. The significantly higher-energy triplet structure Mo-3T, lying 36.2 kcal/mol (M06-L) in energy above Mo-1S, has a long-chain octahapto η3,2,3-C12H18 ligand, thereby giving the molybdenum atom a 14-electron configuration.
3.6. (C4H6)3Nb
Two low-energy doublet (C4H6)3Nb structures were found (Figure 7 and Table 7). The lowest-energy (C4H6)3Nb structure Nb-1D has three separate tetrahapto butadiene ligands, thereby giving the niobium atom a 17-electron configuration consistent with the doublet spin state. The second doublet (C4H6)3Nb structure Nb-2D, lying 10.7 kcal/mol (M06-L) in energy above Nb-1D, has a coupled long-chain η3,2,3-C12H18 ligand, thereby giving the niobium atom a 13-electron configuration (Figure 7 and Table 7). Quartet (C4H6)3Nb structures are high-energy structures lying at least 26 kcal/mol in energy above Nb-1D and thus are not considered in detail. This contrasts with the (C4H6)3V system for which quartet structures are the lowest-energy structures.
3.7. (C4H6)3Zr
Two low-energy (C4H6)3Zr structures were found (Figure 8 and Table 8). The global minimum by M06-L is the singlet structure Zr-1S. In Zr-1S, the Zr–C distances clearly indicate that one of the C4H6 ligands is tetrahapto, and the remaining two C4H6 ligands are coupled to form an acyclic η3,3-C8H12 ligand. The other singlet structure Zr-2S, lying 8.9 kcal/mol (M06-L) in energy above Zr-1S, is shown by its Zr–C distances to have three separate tetrahapto η4-C4H6 ligands, thereby giving the zirconium atom a 16-electron configuration. The lowest energy triplet (C4H6)3Zr structure lies ~27 kcal/mol in energy above Zr-1S and therefore is not considered in detail.
4. Summary
The lowest-energy (C4H6)3M structures for the second-row transition metals from zirconium to palladium are all low-spin singlet and doublet structures, in contrast to the corresponding derivatives of the first-row transition metals. This is a reflection of the higher ligand field strength of the second-row transition metal derivatives relative to the analogous first-row transition metal derivatives.
In addition to the preference for low-spin structures, the energetically preferred structure types for the second-row transition metal (C4H6)3M derivatives are found to depend on the electronic requirements of the central metal atom to attain the favored 18-electron configuration. Thus, attaining the 18-electron configuration for the late second-row transition metals from palladium to ruthenium leaves one or two uncomplexed C=C double bonds in the set of three surrounding butadiene ligands. In such complexes, the uncomplexed C=C double bonds provide reactive sites to couple with adjacent butadiene ligands to form structures with an open-chain C12H18 ligand. As a result, the three butadiene ligands in the lowest-energy (C4H6)3M structures of the late second-row transition metals couple to form a C12H18 ligand that binds to the central metal atom as a hexahapto ligand for M = Pd but as an octahapto ligand for M = Rh and Ru. Thus, the four lowest-energy (C12H18)Pd structures resemble their nickel analogs with similar relative energies. However, attaining or even approaching the favored 18-electron configuration for (C4H6)3M complexes of the early transition metals from zirconium to technetium requires complexation of all six C=C double bonds of three surrounding butadiene ligands. As a result, the lowest-energy (C4H6)3M structures have three tetrahapto butadiene ligands for M = Zr, Nb, and Mo or two tetrahapto butadiene ligands and one dihapto butadiene ligand for M = Tc. The low energy of the experimentally known singlet (C4H6)3Mo structure contrasts with the very high energy of its experimentally unknown singlet chromium (C4H6)3Cr analog relative to quintet (C12H18)Cr isomers with an open-chain C12H18 ligand. The (C4H6)3M complexes studied in this work are potentially accessible by reactions of the metal vapors with butadiene under suitable conditions similar to the reported synthesis of the molybdenum derivative (C4H6)3Mo.
Supplementary Materials
The following are available online, Tables S1–S25: Atomic coordinates of the optimized structures for the (C4H6)3M (M = Pd, Rh, Ru, Tc, Mo, Nb, Zr) complexes.
Author Contributions
Y.Z., Q.C., M.H., Z.Z. performed the calculations to generate the data; X.F. supervized the group at Changzhou University and provided an initial summary of the data; Y.X. did the initial editing of the material provided by X.F.; R.B.K. suggested the original project, wrote the Introduction, and edited the remainder of the manuscript; H.F.S. reviewed and edited the final version of the manuscript. All authors have read and agreed to the published version of the manuscript.
Funding
National Science Foundation (Grant No. CHE-1661604).
Institutional Review Board Statement
Not applicable.
Informed Consent Statement
Not applicable.
Data Availability Statement
Not applicable.
Acknowledgments
This work was supported by the Jiangsu Key Laboratory of Advanced Catalytic Materials and Technology, Changzhou University in China, Advanced Catalysis and Green Manufacturing Collaborative Innovation Center, Changzhou University in China. Research at The University of Georgia was supported by the U.S. National Science Foundation (grant No. CHE-1661604).
Conflicts of Interest
There authors declare no conflict of interest.
Sample Availability
Not applicable.
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Figures and Tables
Enlarge this image.Figure 1. Comparison of the experimentally known nickel complexes with C12H18 ligands obtained from butadiene with the molybdenum and tungsten (C4H6)3M complexes with three separate butadiene ligands.
Enlarge this image.Figure 2. The optimized (C4H6)3Pd structures. The upper and lower distances (in Å) are from the M06-L and BP86 methods, respectively.
Enlarge this image.Figure 3. Optimized (C4H6)3Rh structures. The upper and lower distances (in Å) are from the M06-L and BP86 methods, respectively.
Enlarge this image.Figure 4. The optimized (C4H6)3Ru structures. The upper and lower distances (in Å) are from the M06-L and BP86 methods, respectively.
Enlarge this image.Figure 5. The optimized (C4H6)3Tc structures. The upper and lower distances (in Å) are from the M06-L and BP86 methods, respectively.
Enlarge this image.Figure 6. The optimized (C4H6)3Mo structures. The upper and lower distances (in Å) are from the M06-L and BP86 methods, respectively.
Enlarge this image.Figure 7. The optimized (C4H6)3Nb structures. The upper and lower distances (in Å) are from the M06-L and BP86 methods, respectively.
Enlarge this image.Figure 8. The optimized (C4H6)3Zr structures. The upper and lower distances (in Å) are from the M06-L and BP86 methods, respectively.
Total energies with ZPVE (zero potential vibrational energy) correction (E in hartrees), relative energies with ZPVE corrections (ΔE in kcal/mol), relative enthalpies (ΔH in kcal/mol), and relative free energies (ΔG298 in kcal/mol) for the (C4H6)3Pd structures; comparison with the (C4H6)3Ni system [7].
| Pd-1S (C1) | Pd-2S (C1) | Pd-3S (C1) | Pd-4S (C1) | ||
|---|---|---|---|---|---|
| M06-L | E | −595.76525 | −595.75132 | −595.75118 | −595.75072 |
| ∆E (∆H) | 0.0 (0.0) | 9.0 (9.0) | 9.1 (8.9) | 9.5 (9.3) | |
| ∆G298 | 0.0 | 8.2 | 8.9 | 9.4 | |
| BP86 | E | −595.85507 | −595.84924 | −595.84701 | −595.84689 |
| ∆E (∆H) | 0.0 (0.0) | 3.6 (3.7) | 5.0 (5.0) | 5.0 (5.1) | |
| ∆G298 | 0.0 | 2.8 | 4.5 | 4.7 | |
| (C4H6)3Ni (B3LYP*) | ∆E | 0.0 | 6.7 | 8.9 | 9.5 |
Total energies with ZPVE correction (E in hartrees), relative energies with ZPVE corrections (ΔE in kcal/mol), relative enthalpies (ΔH in kcal/mol), and relative free energies (ΔG298 in kcal/mol) for the (C4H6)3Rh structures.
| Rh-1D (C1) | Rh-2D (C1) | Rh-3D (C1) | Rh-4D (C1) | ||
|---|---|---|---|---|---|
| M06-L | E | −578.40533 | −578.39125 | −578.38207 | −578.37905 |
| ∆E (∆H) | 0.0 (0.0) | 8.9 (8.9) | 14.6 (16.4) | 16.5 (18.1) | |
| ∆G298 | 0.0 | 9.0 | 11.8 | 14.2 | |
| BP86 | E | −578.52088 | −578.50221 | −578.49830 | −578.49439 |
| ∆E (∆H) | 0.0 (0.0) | 11.6 (11.8) | 14.1 (15.8) | 16.5 (18.2) | |
| ∆G298 | 0.0 | 11.6 | 11.5 | 14.1 |
Total energies with ZPVE corrections (E in hartrees), relative energies with ZPVE corrections (ΔE in kcal/mol), relative enthalpies (ΔH in kcal/mol), and relative free energies (ΔG298 in kcal/mol) for the (C4H6)3Ru structures; comparison with the (C4H6)3Fe system [7].
| Ru-1S (C1) | Ru-2S (C1) | Ru-1T (C1) | Ru-2T (Cs) | ||
|---|---|---|---|---|---|
| M06-L | E | −562.75206 | −562.74555 | −562.71903 | −562.72023 |
| ∆E (∆H) | 0.0 (0.0) | 4.3 (5.1) | 20.7 (21.3) | 20.2 (20.7) | |
| ∆G298 | 0.0 | 3.4 | 19.0 | 18.0 | |
| BP86 | E | −562.87730 | −562.86819 | −562.84327 | −562.83165 |
| ∆E (∆H) | 0.0 (0.0) | 6.0 (6.6) | 21.4 (21.7) | 28.7 (29.2) | |
| ∆G298 | 0.0 | 5.4 | 20.7 | 26.8 | |
| (C4H6)3Fe (B3LYP*) | ∆E | 9.8 | 31.0 | 0.0 | 0.9 |
Total energies with ZPVE corrections (E in hartrees), relative energies with ZPVE corrections (ΔE in kcal/mol), relative enthalpies (ΔH in kcal/mol), and relative free energies (ΔG298 in kcal/mol) for the (C4H6)3Tc structures; comparison with the (C4H6)3Mn system [7].
| Tc-1D (C1) | Tc-2D (C1) | Tc-3D (C1) | ||
|---|---|---|---|---|
| M06-L | E | −548.63293 | −548.63130 | −548.61490 |
| ∆E (∆H) | 0.0 (0.0) | 1.0 (0.8) | 11.3 (10.4) | |
| ∆G298 | 0.0 | 1.3 | 12.8 | |
| BP86 | E | −548.76092 | −548.76018 | −548.73899 |
| ∆E (∆H) | 0.0 (0.0) | 0.5 (0.3) | 13.8 (12.4) | |
| ∆G298 | 0.0 | 0.6 | 15.5 | |
| (C4H6)3Mn (B3LYP*) | ∆E | 23.9 | 25.9 | 27.5 |
Total energies with ZPVE corrections (E in hartrees), relative energies with ZPVE corrections (ΔE in kcal/mol), relative enthalpies (ΔH in kcal/mol), and relative free energies (ΔG298 in kcal/mol) for the (C4H6)3Mo structures; comparison with the (C4H6)3Cr system [7].
| Mo-1S (C3h) | Mo-2S (C1) | Mo-3S (C1) | Mo-1T (C1) | Mo-2T (C1) | Mo-3T (Cs) | ||
|---|---|---|---|---|---|---|---|
| M06-L | E | −536.04474 | −536.02426 | −536.02360 | −536.01838 | −535.99805 | −535.98708 |
| ∆E (∆H) | 0.0 (0.0) | 12.8 (13.5) | 13.3 (13.5) | 16.5 (17.0) | 29.3 (30.5) | 36.2 (36.8) | |
| ∆G298 | 0.0 | 10.9 | 12.2 | 14.2 | 25.9 | 34.3 | |
| BP86 | E | −536.16875 | −536.15267 | −536.14640 | −536.14416 | −536.12279 | −536.11094 |
| ∆E (∆H) | 0.0 (0.0) | 10.1 (10.7) | 14.0 (14.3) | 15.4 (15.8) | 28.8 (30.0) | 36.3 (36.2) | |
| ∆G298 | 0.0 | 8.1 | 12.9 | 13.1 | 25.4 | 34.3 | |
| (C4H6)3Cr (B3LYP*) | ∆E | − | 28.5 | 39.5 | 2.3 | 15.3 | 17.4 |
Computed structural parameters of Mo-1S compared to experimental data a.
| M06-L b | BP86 b | Expt c | Expt d | Expt e | |
|---|---|---|---|---|---|
| r(Mo-C1) | 2.270 | 2.291 | 2.29 (1) | 2.301 (8) | 2.284 (2), 2.273 (6) |
| r(Mo-C2) | 2.340 | 2.364 | 2.29 (1) | 2.317 (7) | 2.325 (2), 2.330 (5) |
| r(C1-C2) | 1.430 | 1.443 | 1.32 (2) | 1.336 (11) | 1.414 (4), 1.414 (7) |
| r(C2-C2A) | 1.402 | 1.414 | 1.55 (3) | 1.560 (18) | 1.403 (5), 1.388 (9) |
| r(C1-H1) | 1.092 | 1.100 | 1.14 (8) | ||
| r(C1-H2) | 1.088 | 1.097 | 0.96 (10) | ||
| r(C2-H3) | 1.088 | 1.098 | 1.12 (10) | ||
| ∠C1-C2-C2A | 118.9 | 119.1 | 114.84 (88), 119.20 (15) | 119.7 (4) | |
| ∠H1-C1-C2 | 117.2 | 117.6 | 121.99 (5.30) | ||
| ∠H2-C1-C2 | 117.5 | 117.1 | 119.10 (6.33) | ||
| ∠H3-C2-C2A | 119.0 | 118.9 | 125.24 (5.32) | ||
| Σ∠(C1) f | 348.6 | 348.6 | 349.9 |
a Distances in Å, angles in degrees. b The present work. c Skell, P.S.; McGlinchey, M.J. Angew. Chem. Int. Ed. 1975, 14, 195. d Green, J.C.; Kelly, M.R.; Grebenik, P.D.; Briant, C.E.; McEvoy, N.A.; Mingos, D.M.P. J. Organomet. Chem. 1982, 228, 239. e Ref. [14]. f Sum of angles around C1 (the terminal carbon).
Table 7Total energies with ZPVE corrections (E in hartrees), relative energies with ZPVE corrections (ΔE in kcal/mol), relative enthalpies (ΔH in kcal/mol), and relative free energies (ΔG298 in kcal/mol) for the (C4H6)3Nb structures; comparison with the (C4H6)3V system [7].
| Nb-1D (C1) | Nb-2D (C1) | ||
|---|---|---|---|
| M06-L | E | −524.79243 | −524.77533 |
| ∆E (∆H) | 0.0 (0.0) | 10.7 (9.8) | |
| ∆G298 | 0.0 | 11.5 | |
| BP86 | E | −524.91119 | −524.89914 |
| ∆E (∆H) | 0.0 (0.0) | 7.6 (6.7) | |
| ∆G298 | 0.0 | 8.1 | |
| (C4H6)3V (B3LYP) | ∆E | 9.8 | 4.4 |
Total energies with ZPVE correction (E in hartrees), relative energies with ZPVE correction (ΔE in kcal/mol), relative enthalpies (ΔH in kcal/mol), and relative free energies (ΔG298 in kcal/mol) for the (C4H6)3Zr structures.
| Zr-1S (C1) | Zr-2S (C1) | ||
|---|---|---|---|
| M06-L | E | −514.89112 | −514.87692 |
| ∆E (∆H) | 0.0 (0.0) | 8.9 (9.4) | |
| ∆G298 | 0.0 | 8.5 | |
| BP86 | E | −515.00107 | −514.98811 |
| ∆E (∆H) | 0.0 (0.0) | 8.1 (8.5) | |
| ∆G298 | 0.0 | 8.1 | |
| (C4H6)3Ti (B3LYP) | ∆E | 0.0 | 15.5 |
© 2021 by the authors.
Details
; Feng, Xuejun 3 ; Xie, Yaoming 4
; King, Robert Bruce 4 ; Schaefer, Henry F 4 1 School of Petrochemical Engineering, Changzhou University, Changzhou 213164, China;
2 School of Petrochemical Engineering, Changzhou University, Changzhou 213164, China;
3 School of Petrochemical Engineering, Changzhou University, Changzhou 213164, China;
4 Department of Chemistry and Center for Computational Quantum Chemistry, University of Georgia, Athens, GA 30602, USA;