Cundari Th.R. -- Computational Organometallic Chemistry-0824704789

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state, and only a small number of investigations have focused on syntheses and reactivities (3). Moreover, only a limited number of theoretical studies have focused on main group metallocenes, because the different types of bonding character between the main group element (E) and Cp ligand (due to less involvement of d orbitals compared to the transition metal metallocenes) result in numerous structural possibilities with different bonding patterns. In main group metallocenes, π-type interactions become weaker due to the absence of d orbitals, and deviation from typical pentahapticity (η5) is often observed. The broad range of electronegativities of main group elements (E) also leads to either ionic or covalent bonding for Cp–E interactions. For example, bonding of Cp to s-block elements (Groups 1, 2) shows highly ionic character, while the p-block elements (Groups 13, 14), which have electronegativities similar to that of transition metals, exhibit large covalent bonding character to the Cp ligand.

This chapter will provide a review of previous theoretical studies of main group metallocene compounds and a guide for theoretical calculations of main group metallocenes. Owing to the tremendous progress of computational hardware and software in the last decade, computational chemistry has rapidly expanded to various fields of chemistry and now plays an important role as a real partner in most chemical research where experiment and theory are complementary tools to each other. This is because the accuracy of computed equilibrium geometries, energetics, and other molecular properties, such as vibrational frequencies and NMR chemical shifts, can often be comparable or even superior to experimental data. Therefore, a general overview of the application of computational chemistry to the main group metallocenes should be helpful for those who want to model these systems theoretically. Additionally, many of the methods and approaches discussed should be generally useful for quantum modeling for main group compounds.

The review part of this chapter will be limited to the calculation of metallocenes of Groups 1 and 2 (s-block elements) and Groups 13 and 14 (p-block elements). There have been good reviews of synthetic procedures, structural characterization, and other experimental features for main group metallocenes (4–6). We will restrict our discussion to simple main group metallocenes that have only one Cp ring bonded (half-sandwich) or two Cp rings bonded (full-sandwich) to the main group element, although there are various metallocenes that include more than two Cp ligands or contain substituted Cp ligands such as pentamethylcyclopentadienyl (abbreviated as Cp*) and trimethylsilylcyclopentadienyl ligands. However, we will include a few examples of the effect the bulky ligand Cp* has on the structure and electronic properties of main group metallocenes. Finally, some examples of calculations for main group metallocene will be presented in order to show fundamental differences between various computational techniques and theoretical methods.

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FIGURE 1 Possible structures of half-sandwich metallocenes. (R is either an electron lone pair or an auxiliary substituent.)

2.STRUCTURAL FEATURES OF MAIN GROUP METALLOCENES

The structural classification of metallocene compounds can be divided into halfsandwich complexes and full-sandwich complexes with respect to the number of Cp ligands bonded to the main group element (E). Half-sandwich metallocenes exhibit the possible structural forms in Figure 1. The parent structure of a halfsandwich metallocene is assumed to have C5v symmetry. These half-sandwich metallocenes can be bonded to auxiliary ligands or possess an electron lone pair. It is known that stable half-sandwich metallocenes exist for most main group elements with covalent bonded substituents or ligands, depending on the valence and the atomic radius of main group elements (5a). Half-sandwich metallocenes exist in a monomeric form in the gas phase, but a polymeric arrangement or highly symmetric cluster form occurs in the solid state. A full-sandwich metallocene generally has two Cp ligands, in which two Cp rings are either parallel or nonparallel (bent), as shown in Figure 2. The parallel structure can have staggered

FIGURE 2 Possible structures of full-sandwich metallocenes.

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D5d or eclipsed D5h conformations, while the bent structure can have C2v or Cs symmetry. In typical metallocenes, all of the C–C bond distances are equal and the rings are parallel. However, there are several cyclopentadienyl compounds in which the rings are tilted with respect to one another. Full-sandwich metallocenes of heavier elements of Group 2, such as Cp2Ca and Cp2Ba, have bent structures, which can be explained by the fact that larger metal cations increase core polarizability and decrease ligand–ligand repulsions, which results in less linear rigidity, or even bent, structures. One or more auxiliary substituents, such as a solvent molecule, can also lead to a bent conformation of full-sandwich metallocenes. Structure determinations of the simplest Group 14 full-sandwich compounds, such as Cp2Ge and Cp2Pb, have shown that they adopt a bent conformation in monomeric form due to the lone pair repulsion in Ge(II) and Pb(II)

(5).

Some geometrical parameters must be defined in order to compare various structural patterns of metallocenes, as shown in Figure 3, that is, the angle α between the Cp ring planes and the angle β between Cp(centroid)–E–Cp(cen- troid) and the distances of C(Cp)–E and Cp(Centroid)–E. For example, parallel magnesocene (Cp2Mg) shows D5d symmetry and has α 0° and β 180° (7), while nonparallel stannocene (Cp2Sn) has α 47° and β 146° (8). For bond

˚

distances in Cp2Mg, X-ray diffraction shows 2.304(8) A for C(Cp)–Mg and

˚

1.977(8) A for Cp(centroid)–Mg (7).

Since main group metallocenes show weak proclivity toward directional bonding between the Cp ring and the central atom due to the lack of available d orbitals for π-type interaction, different hapticities (referred to as ring slippage) from η1 to η4 (Fig. 4) rather than prototype η5 can often be observed. If a metallocene has two or more equidistant C(Cp)–E bonds, it can be classified as a π complex with hapticities of η2–η5, while a metallocene with an η1–Cp has a σ type of interaction between C(Cp)–E (9). These different hapticities are due to

FIGURE 3 Geometrical descriptions of the metallocenes.

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FIGURE 4 Cp–E bonding arrangements with respect to different hapticities.

the nature of the main group elements, such as electronegativity and ionic radius, other substituents bonded to the main group element, and the substituted Cp ligand effect (10). However, the comparison of energetics among different haptometallocenes shows very small energy differences (4–8 kJ/mol) (11), which makes it difficult to determine a certain hapticity for main group metallocenes.

3.MOLECULAR ORBITAL INTERACTIONS OF CYCLOPENTADIENYL RINGS AND MAIN GROUP ELEMENTS (E)

In this section, we will state simply the general qualitative molecular orbital interactions between Cp and main group element for main group metallocenes. While these schemes have been presented and discussed elsewhere (5), we include a simple MO interaction diagram for a half-sandwich complex in Figure 5. Unlike ferrocene, where the bonding interaction results from the interaction of the a1 and e1 orbitals of Cp with the dz2, dxz, and dyz orbitals of iron, in main group metallocenes the comparable interaction involves the s, px, and py orbitals of the main group atom (Fig. 5).

Due to the broad range of electronegativities of the main group elements, the bonding in metallocenes can vary from being strongly ionic to being mainly covalent. The largest contributing factor to Cp–E interaction is the energy of the atomic orbitals of the main group element relative to the highest occupied molecular orbital (HOMO) of the Cp ligand. In the case of the half-sandwich metallocene, if the main group element’s valence orbitals are much higher in energy than the degenerate occupied e1 orbitals, this should make it easy to transfer electrons from the main group element to the Cp ligand, generating ionic bonding of Cp–E. For CpLi, the first ionization energy of Li (5.4 eV) (12) is much lower than that of Cp (8.4 eV) (13). On the other hand, Group 13, 14 elements have

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FIGURE 5 MO diagram for the half-sandwich main group metallocene (C5v symmetry).

valence orbitals comparable in energy with that of the Cp’s HOMO, which gives rise to much larger covalent bonding of Cp–E. For CpMg , the first ionization energy of Mg (7.6 eV) (12) is very compatible with that of Cp (8.4 eV) (13). In this complex, the direction of electron transfer is best described as being from the Cp ligand to the main group element. For full-sandwich metallocenes, we can split the metallocene compound into Cp2 and E units under either D5d or D5h symmetry, much like the ferrocene MO interaction example (12). However, the absence of available d orbitals in most main group elements leads to weaker π bonding with the degenerate e1 orbitals of Cp ligand due to poorer overlap of the px and py main group orbitals with the ligand compared to overlap with dxz and dyz orbitals. Since the degeneracy of these e1 orbitals easily breaks down by the second order Jahn–Teller effect, D5d or D5h parallel conformations tend to

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distort to lower-symmetry C2v or Cs bent structures for some main group metallocenes (14,15).

4.RESULTS AND DISCUSSIONS OF PREVIOUS COMPUTATIONAL STUDIES OF MAIN GROUP METALLOCENES

Tables 1 and 2 show available experimental and calculated geometrical parameters for known s-block metallocenes of main group elements in Groups 1 and 2, while Table 3 gives the same information for p-block elements in Groups 13 and 14. As mentioned before, main group metallocenes can be classified into two categories: s-block metallocenes and p-block metallocenes, depending on the main group element. The s-block metallocenes (Groups 1, 2) are considered to have mainly ionic bonding, while most p-block metallocenes (Groups 13, 14) show covalent interaction of Cp–E. However, there is not enough data from highlevel theoretical calculations to have a quantitative understanding of the factors involving covalent or ionic bonding between the Cp ligand and the main group element.

4.1. s-Block Metallocenes

LiCp and Cp2Li are the simplest metallocenes and have been of considerable interest in terms of the interaction between lithium and the π electron system.

TABLE 1 Experimental and Calculated Geometrical Parameters for Group 1 Metallocenes

	˚	˚	β ( Cp–E–Cp) (°)
	C(Cp)–E (A)	Cp(centroid)–E (A)
LiCp		2.06(XD) [16]
		1.700(MNDO) [17]
		1.957(PM3) [17]
		1.79(SCF) [18]
Cp2Li		2.008(XD) [19]	Linear (expt.; calc.)
		1.974(MNDO) [17]
		2.034(PM3) [17]
		2.015(B3LYP) [20]
Cp2Na	2.630(XD) [22]	2.366(XD) [22]	Linear (expt.; calc.)
	2.600(VWN) [23]	2.461(VWN) [23]
	2.700(BP) [23]	2.566(BP) [23]
Cp2K	2.800(VWN) [23]	2.671(VWN) [23]	Linear (VWN, BP)
	2.820(BP) [23]	2.692(BP) [23]

ED electron diffraction; XD X-ray diffraction; VWN, BP, B3LYP DFT level. Source: Reference numbers appear in brackets.

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TABLE 2 Experimental and Calculated Geometrical Parameters for Group 2 Metallocenes

	˚	˚	β ( Cp–E–Cp) (°)
	C(Cp)–E (A)	Cp(centroid)–E (A)
CpBeH	1.920(XD) [24]	1.49(XD) [24]
	1.991(MNDO) [24]	1.557(MNDO) [24]
	1.976(SCF) [24]	1.563(SCF) [24]
Cp2Bea	1.94(XD) [25]	1.52(XD) [25]
	1.624(SCF) [24]	1.466(SCF) [24]
MgCp	2.251(MP2) [26]
Cp2Mg	2.339(ED) [27]	2.008(ED) [27]	Linear (exptl.; calc.)
	2.304(XD) [7]	1.977(XD) [7]
	2.376(SCF) [28]	2.050(SCF) [28]
	2.270(VWN) [23]	1.930(VWN) [23]
	2.360(BP) [23]	2.040(BP) [23]
	2.357(B3LYP) [28]	2.022(B3LYP) [28]
Cp2Ca	2.80(XD) [29]		119(XD) [29]
	2.714(SCF) [30]	2.428(SCF) [29]	Linear (SCF, MP2) [30]
	2.611(MP2) [30]	2.321(MP2) [30]	150(VWN, BP) [23]
	2.540(VWN) [23]	2.240(VWN) [23]	149.6 (B3LYP) [28]
	2.580(BP) [23]	2.290(BP) [23]
	2.613(B3LYP) [28]	2.317(B3LYP) [28]
Cp2Sr	2.883(SCF) [30]	2.623(SCF) [30]	Linear (SCF, MP2) [30]
	2.801(MP2) [30]	2.533(MP2) [30]	145 (VWN, BP) [23]
	2.600(VWN) [23]	2.310(VWN) [23]
	2.680(BP) [23]	2.440(BP) [23]
Cp2Ba	3.083(SCF) [30]	2.842(SCF) [30]	Linear (SCF) [30]
	2.976(MP2) [30]	2.725(MP2) [30]	142.7(MP2) [30]

a Cp2Be is a Cs slipped sandwich structure.

ED electron diffraction; XD X-ray diffraction; VWN, BP, B3LYP DFT level. Source: Reference numbers appear in brackets.

Many calculations on LiCp have been done at various levels (17,18,42,43–46). Using a double-zeta basis set, Schaefer and coworkers (42) found that LiCp had

˚

a pentahapto structure with a Cp–Li distance of 1.79 A, with the CH bonds bent slightly out of the Cp plane away from the Li atom. Jemmis and Schleyer (18)

˚

optimized the Cp–Li distance to 1.79A at the HF/3-21G level. Waterman et al. (44) reinvestigated the out-of-plane bending of the CH bonds and concluded (in agreement with Schaefer) that the interaction was mainly Coulombic. Jemmis and Schleyer (18) explained the bonding of CpLi as an aromatic six-membered nido polyhedron in terms of ‘‘aromaticity in three dimensions.’’ High-level ab initio calculations with larger basis sets reproduced the experimental Cp–Li dis-

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TABLE 3 Experimental and Calculated Geometrical Parameters for Groups 13 and 14 Metallocenes

	˚	˚	β ( Cp–E–Cp) (°)
	C(Cp)–E (A)	Cp(centroid)–E (A)
BCp	2.136(SCF) [18]	1.764(SCF) [18]
AlCp	2.468(MP2) [31]	2.037(MP2) [31]
Cp2Al	2.204(SCF) [32]	1.843(SCF) [32]	Linear
	2.174(MP2) [32]
GaCp	2.420(MP2) [33]	2.096(MP2) [33]
InCp	2.62(ED) [5b]	2.32(ED) [5b]
	2.688(SCF) [34]
TlCp	2.705(ED) [5b]	2.41(ED) [5b]
	2.832(SCF) [34]
Cp2Tl		2.66(XD) [35]	155(XD) [35]
	3.01–3.27(SCF) [35]	2.85,2.90(SCF) [35]	144(SCF) [35]
CCp	1.822(SCF) [36]	1.357(SCF) [36]
Cp2C	η3–Cp2C is the most
	stable conformer [37]
SiCp	2.126(SCF) [36]	1.745(SCF) [36]
Cp2Si	η3–Cp2Si is the most
	stable conformer [37]
GeCp	2.32(SCF) [38]	1.99(SCF) [38]
Cp2Ge		2.23(XD) [5b]	152(XD) [5b]
		2.34[SCF] [39]	Linear (SCF) [39]
SnCp	2.474(SCF) [34]
Cp2Sn	2.70(XD) [8]	2.42(XD) [5b,8]	146(XD) [5b,8]
	2.56–3.09(SCF) [40]
Cp2Pb	2.78(ED) [41a]	2.55–2.82(ED) [41a]	135 15(ED) [41a]
	2.76(XD) [41b]	2.50(XD) [41b]
	2.71–2.97(SCF) [40]

ED electron diffraction; XD X-ray diffraction.

Source: Reference numbers appear in brackets.

tance, while the semiempirical MNDO method overestimated the C(Cp)–Li strength (17,45). Kwon and Kwon (20) showed that density functional theory (B3LYP/6-31G*) results for the Cp2Li anion were far superior to Hartree–Fock (HF) or semiempirical in terms of Cp–Li distance and CH bending (which is inward toward the Li atom in contrast to the case of LiCp). The staggered Cp2Li anion was predicted (DFT) to be more stable than the eclipsed form by 0.26 kJ/ mol, which is much less than in Cp2Fe ( 5 kJ/mol).

Bridgeman (23) calculated Cp2Na , Cp2K , and Cp2Rb using DFT methods (BP and VWN) and showed that calculated geometries were in reasonable

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agreement with the available experimental data. The alkali metal metallocenes were predicted to have parallel equilibrium structures, and Mulliken orbital population analysis indicated that d orbitals of heavier alkali metals contributed largely to π-type interactions in Cp2K and Cp2Rb .

Although a number of beryllium compounds containing only one Cp ligand have been synthesized, there is no evidence of the simple BeCp cationic compound to our knowledge. Theoretical calculations at different levels have been done for BeCpH (24). It has been shown that CpBeH prefers C5v symmetry and η5-type bonding with a large covalent character. The direction of the calculated dipole moment, which has a negative end toward the BeH group, contradicts an ionic bonding view of Cp BeH and implies considerable electron donation from the Cp ligand to the Be atom. The structure of Cp2Be is unusual and still somewhat uncertain. Both X-ray and electron diffraction data have been interpreted in terms of a ‘‘slipped-sandwich’’ complex with a Cs symmetry in which one Cp ring is pentahapto and the other is either weakly π bonded or perhaps even ρ bonded (see Fig. 6) (25,47). However, a previous SCF calculation (24) indicated that the lowest-energy form has one η5–Cp ring and one η1–Cp ring bonded to the Be atom, which differs from the experimental structures (see Fig. 6). Recently, MP2 and DFT (B3LYP) calculations on Cp2Be revealed that DFT reproduced the experimental Cs slipped-sandwich structure as the lowest conformer, while MP2 failed (48). When comparing experiment and theory, there is still disagreement about the equilibrium geometry of Cp2Be. Cotton and Wilkinson postulated that the radius of the Be atom is so small that even at the closest distance of

FIGURE 6 Experimental and calculated structures of Cp2Be: (a) solid-state structure, (b) optimized structure at the SCF level.

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the two parallel Cp rings, the Be atom cannot be bonded to both Cp ligands simultaneously (49).

There is no available structural characterization of the MgCp cation due to its instability in the gas phase. Recently, a combination of tandem mass spectrometry and high-level ab initio calculations (26) revealed that the η5 bonded structure with C5v symmetry is the lowest conformer at the MP2/6-31G** level. With a natural bond orbital (NBO) analysis (50) of the Cp–Mg interactions, the authors (26) obtained a natural charge of 1.8 for Mg, which implies ionic bonding between the Mg2 cation and a Cp anion. Cp2Mg has a staggered parallel conformation in the solid state but is reported to be eclipsed in the gas phase (5a). However, the rotational barrier is computed to be only 0.13 kJ/mol at the HF level (51). A D5d symmetry structure of Cp2Mg has been identified by previous theoretical calculations (23,28,51) in which DFT produces a better optimized geometry of Cp2Mg than the HF method. However, the nature of the bonding between the Cp ligand and Mg atom (ionic or covalent) is still controversial. Because the ionic chemistry of Mg2 is quite similar to that of Li , one might expect that the bonding of Cp2Mg is comparable to that of Cp2Li anion. However, the Mulliken analysis at the HF level of theory revealed an atomic charge of 1.39 for Mg (51), while the Mulliken charge for Mg at the DFT level predicted 0.66, which would suggest somewhat covalent character in metal–ligand bonding (23).

Heavier alkaline earth metallocenes such as Cp2Ca, Cp2Sr, and Cp2Ba have bent polymeric structures due to the d orbital contribution from the Ca, Sr, and Ba atoms (5a). However, with sufficiently bulky substituents on the Cp ring, the heavier Group 2 metallocenes can also be isolated in a monomeric form (5a). Previous calculations (23,30) showed that they have strong ionic bonding character and structurally nonrigid systems. The energy barrier from the bent to the parallel form for Cp2Ca was computed to be about 10 kJ/mol at DFT levels (B3LYP, BP, VWN) (23,28). Mulliken population analysis at the DFT level of theory revealed that the greater π bonding in Cp2Ca and Cp2Sr was influenced by metal d orbitals, while the d orbital populations of Mg were found to be negligible in Cp2Mg (23).

4.2. P-Block Metallocenes

Due to the inert-pair effect, Group 13 elements sometimes produce low-valent monomeric metallocenes as well as high-valent oligomeric metallocene clusters and polymeric metallocene chains. Half-sandwich metallocenes of Group 13 elements can be found in the gas phase, but exist as clusters and polymeric forms in the solid state. Schleyer calculated the CpE, E Be, B, C, and N, molecules at the SCF level and found the shortest C–C ring bond length in CpB (18). The