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

using relativistic ECPs and all-electron basis sets, where the relativistic effects have been estimated by direct perturbation theory (DPT) (59), by the quasirelativistic approximation using the Pauli Hamiltonian (PH) (60), and by the zero-order regular approximation (ZORA) (61). A comparison with the experimental bond lengths shows that the ECPs perform equally well as the more expensive all-electron calculations. The three methods—DPT, PH, and ZORA—give very similar results, with one notable exception. The calculated W–P(CH3)3 bond length at BP86(PH) is too short, and the theoretical value for the W–P(CH3)3 BDE at this level is much higher (75.7 kcal/mol) than predicted by the other three methods (43.5–45.5 kcal/mol). It has been pointed out that the PH scheme is problematic from a theoretical point of view, because the Pauli operator is not bounded from below, and nonphysical low energies may result from the variational treatment (53).

The failure of the PH method is disturbing, because it occurs for only one molecule [(CO)5WP(CH3)3], while the PH result for the related compound (CO)5WPH3 is in agreement with the other methods. A related situation has recently been reported by van Lenthe et al. (54a), who calculated the geometries and bond energies of the TM carbonyls W(CO)6, Os(CO)5, and Pt(CO)4 with the PH and ZORA approximations using different basis sets. It was found that the variational collapse of the PH method occurs when the basis set becomes very large. The FBDE of Os(CO)5 was predicted with the Pauli Hamiltonian and a triple-ζ basis set for oxygen and carbon to be 42.9 kcal/mol, which agrees with the results given by other methods. The bond energy becomes unrealistically high (191.5 kcal/mol) when a quadruple-ζ basis set is employed (54a). The unpredictability of cases where significant errors may occur makes the PH approach unsuitable for reliable calculation of TM compounds. The ZORA approach (61), which includes higher-order relativistic effects than the Pauli Hamiltonian, is clearly the better method for relativistic calculations.

As a final example of substituted carbonyl complexes we want to mention TM complexes with group-13 diyl ligands (CO)nTM-ER, where E is either B, Al, Ga, or In. This is a rather young class of compounds, for which the first examples of stable molecules have been synthesized only in the last couple of years (62). A review about theoretical work of group-13 diyl complexes has just been published (63). Table 11 shows calculated and experimental bond lengths and theoretically predicted bond dissociation energies at BP86. It becomes obvious that the theoretical bond lengths are in very good agreement with experimental values of related compounds. Table 11 shows also two examples of homoleptic group-13 diyl complexes that confirm the good performance of BP86. Reliable theoretical studies in this field are particularly important, because there is still not much known experimentally about the stabilities and properties of these compounds.

3.3.Complexes with TMDN and TMDP Triple Bonds

Transition-metal nitrido and phosphido complexes have been investigated by us in two theoretical studies (64,65). The results are interesting in the present context, because the calculated molecules have metal–ligand triple bonds. It is known that the MP2 method predicts bond lengths of multiple bonds between main group elements that are too long (66), and it is important to compare the performance of MP2 and DFT methods for calculating multiple bonds between a TM and a main group element. This has been done in Refs. 64 and 65.

Figure 2 shows the theoretically predicted structures of the rhenium nitrido complex Cl2(PH3)3ReN and the compounds where the nitrido ligand is bonded to different Lewis acids Cl2(PH3)3ReN–X (X BH3, BCl3, BBr3, AlH3, AlCl3, AlBr3, GaH3, GaCl3, GaBr3, O, S, Se, Te)(64). The geometries were optimized at the MP2 and B3LYP levels of theory using our standard basis set II (4). A comparison of the calculated interatomic distances shows that the MP2 values for all Re–PH3 and most Re–Cl bond lengths are slightly smaller than the B3LYP data, while MP2 calculates the TM–N multiple bond longer than at B3LYP. The MP2-calculated N–chalcogen bond lengths are shorter than for B3LYP, except for the N–O bond, which has the highest N–chalcogen double bond character according to the NBO analysis (64). It has been found by us in several investigations of TM compounds that MP2 tends to give slightly too long interatomic distances for TM–X shared-electron multiple bonds, while TM–X single bonds and donor–acceptor bonds are usually shorter than at the DFT (B3LYP and BP86) level (4). However, the differences are in most cases not very large, and both methods give geometries that are reasonably accurate.

Experimental values of three related compounds may be used to estimate the accuracy of the theoretical data given in Figure 2. The geometry of the parent nitrido complex, Cl2(PH3)3ReN, can be compared with the X-ray structure analysis of Cl2(PMe2Ph)3ReN (67). The most important bond lengths at B3LYP/II are

˚

Re–N bond length (1.703 A) is slightly too long. An X-ray structure analysis has also been reported for Cl2(PMe2Ph)3ReN–GaCl3, which shows that the Re–

˚

N distance becomes a little longer (1.68 A) than in the parent compounds (1.660

˚

A) (68). This is in agreement with the calculated data, which predict at both

˚

levels of theory that the Re–N bond of Cl2(PH3)3ReN–GaCl3 is ca. 0.02 A longer than in the parent compound (Fig. 2). The calculations show that the complexation of Cl2(PH3)3ReN by GaCl3 leads to a significant shortening of the Re–Cl

˚

bond trans to the nitrido ligand by 0.13 A. The experimentally observed Re–

˚

Cltrans bond length of Cl2(PMe2Ph)3ReN–GaCl3 is 0.15 A shorter than in the parent compound (68). The calculated RE–N–Ga bond angle is 162°, while the experimental value is 168°. A significant difference between theory and experiment is

2 Optimized geometries at B3LYP/II of the nitrido complex Cl2(PH3)3ReN and the nitrido adducts with various Lewis acids and chalcogen atoms. MP2/II values are shown in parentheses. Bond lengths are given in angstroms, bond angles in degrees. (From Ref. 64.)

found only for the N–Ga bond length. The X-ray structure analysis gives a value

˚ ˚

of 1.97 A, which is clearly shorter than the calculated values of 2.055 A (B3LYP/

˚

II) and 2.080 A (MP2/II). The disagreement between experiment and theory is probably not caused by an insufficient level of the calculation, but rather by intermolecular forces that lead to a shortening of bonds between Lewis acids and Lewis bases (52). The calculated structures of the N–chalcogen complexes show

˚

that the Re–N distances are significantly longer (1.767–1.745 A) than in the

FIGURE 2 Continued

˚

parent compound (1.668 A, Fig. 2). This is in agreement with the measured Re–

˚

N bond lengths for Cl(PMe2Ph)2(Et2dtc)ReNS (1.72(1) and 1.795(9) A), which are clearly longer than in parent nitrido complexes (69).

While the MP2 and B3LYP geometries of the complexes shown in Figure 2 are quite similar, there are larger differences between the theoretically predicted N–X bond dissociation energies. Table 12 gives the calculated results. The BDEs of the chalcogen complexes, where X O, S, Se, Te calculated at MP2 and B3LYP, are nearly the same. The MP2 values of the BDEs of the nitrido–group 13 complexes Cl2(PH3)3ReN–AY3 are clearly higher than the B3LYP data, except for the BH3 complex. MP2 predicts that BH3 is slightly stronger bonded to the nitrido ligand than BCl3, while B3LYP strongly favors BH3 over BCl3. The MP2

FIGURE 2 Continued

result is supported by the CCSD(T) calculations, which also give similar BDEs for the BH3 and BCl3 complexes.

Theoretical and experimental geometries of molybdenum and tungsten phosphido and phosphorous sulfide complexes are shown in Figure 3 (65). The geometry optimizations were carried out at the HF, MP2, and B3LYP levels of theory using our standard basis set II (4). Because the TM has the high oxidation state VI in the molecules it can be expected that the HF geometries should be in reasonable agreement with experiment. The results given in Figure 3 generally confirm the expectation. The HF, MP2, and B3LYP bond lengths and bond angles

FIGURE 2 Continued

are in most cases not very different from each other. Please note, however, that the TM P triple bond length is predicted to be too short at HF and too long at MP2, while the B3LYP value is in good agreement with the experimental values of the two compounds that have been reported (70,71).

Table 13 gives the calculated BDEs at HF, MP2, B3LYP, and CCSD(T) levels of the P–S bonds and the TM–NH3 bonds trans to the TM–P(S) ligand. The CCSD(T) energies were calculated using B3LYP optimized geometries. Since experimental values for the BDEs are not available, the CCSD(T) results may be used as reference data. The B3LYP BDEs of the P–S bonds are 8–10 kcal/ mol higher than the CCSD(T) values, but the trend is the same. MP2 and particu-

12 Dissociation Energies De and Zero-Point Energy Corrected Values D0 of the Rhenium Nitrido–Bridged Complexes Cl2(PH3)3ReN–X (kcal/mol) with Respect to Cl2(PH3)3ReN and X at the B3LYP and MP2 Levels Using Basis Set II

a Using B3LYP/II optimized geometries.

Source: Ref. 64. For the Cl2(PH3)3Re(N–X) chalcogen complexes the dissociation energies correspond to formation of Cl2(PH3)3ReN and X in its 3P state.

larly HF give P–S bond energies that are too low. MP2 even gives the wrong trend between the Mo and W complexes. MP2 performs better for the bond energies of the TM–NH3 donor–acceptor bond, where the calculated values exhibit good agreement with the CCSD(T) results. B3LYP gives similar TM–NH3 bond energies to HF, which are clearly too low.

3.4.Reaction Energies of Transition Metal–Catalyzed Processes

Quantum chemical calculations have become important tools for elucidating the reaction mechanisms of TM-catalyzed processes (99). Most of the recent studies have been carried out at the NL-DFT level of theory, which has clearly become the standard method in the field. There are very few studies of reaction profiles of catalytic reactions, however, where the results of DFT methods are compared with data that are predicted by ab initio methods. In the following we will give three examples where NL-DFT methods are compared with CCSD(T) and MP2.

FIGURE 3 Calculated and experimental geometries of phosphido complexes and phosphido-sulfur adducts. The experimental values for 1 and 8 are taken from substituted analogs that have been reported in Refs. 70 and 71, respectively. (From Ref. 65.)

FIGURE 3 Continued

Water–Gas Shift Reaction

A recent theoretical work by Torrent et al. (72) investigated gas-phase reactions of Fe(CO)5 with OH , which are relevant for the water–gas shift reaction (WGSR):

The WGSR can be catalyzed by TM compounds, and Fe(CO)5 is a promising candidate for a mononuclear catalyst (73). The mechanism of the reaction is