Table of Contents
Journal of Quantum Chemistry
Volume 2014, Article ID 639851, 5 pages
Research Article

DFT Study on the Co-Xe Bond in the HCo(CO)Xe Adduct

MTA-TKI Research Group for Selective Chemical Syntheses, Department of Inorganic Chemistry and János Szentágothai Research Center, University of Pécs, Ifjúság Útja 6, Pécs 7624, Hungary

Received 1 August 2013; Revised 1 October 2013; Accepted 15 October 2013; Published 2 January 2014

Academic Editor: Yinghong Sheng

Copyright © 2014 Tamás Kégl. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The metal-xenon interaction has been studied in hydrido-cobalt-carbonyl complexes by means of density functional methods. The method of choice has been selected after testing various functionals including dispersion correction on the bond dissociation enthalpy of Xe in the Cr(CO)5Xe adduct. In general, the long range corrected versions of popular gradient-corrected functionals performed well. In particular, LC-mPWPW91 resulted in a perfect match with available experimental data; therefore this functional was selected for the computation of HCo(CO)3Xe adducts. For HCo(CO)3Xe two isomers have been located; the structure with CS symmetry has proved to be more stable by 5.3 kcal/mol than the C3V adduct in terms of free energy. The formation of HCo(CO)3Xe is, however, endergonic by 3.5 kcal/mol for the CS isomer.

1. Introduction

Hydroformylation of olefins is one of the most important applications of homogeneous catalysis in industry. The first precatalyst system containing Co2(CO)8 and HCo(CO)4 was applied originally by Roelen [1]. This catalytic system is still in application predominantly for hydroformylation of higher olefins. According to Heck and Breslow [2] the initial step of the reaction is the dissociation of one of the CO ligands from HCo(CO)4 resulting in HCo(CO)3 as the active catalyst.

It is known that the rate of cobalt-catalyzed hydroformylation of olefins can be significantly reduced by the addition of a seemingly inert gas component such as N2, Ar, or Xe to the reaction mixture [35]. The retarding effect can be explained by competitive coordination of the inert gas component, for example, the xenon to the catalytically active coordinatively unsaturated HCo(CO)3 complex:

Among the few examples of transition metal, noble gas adducts and the M(CO)5-Ng complexes (M = Group 6 metals; Ng = noble gas, such as argon, krypton, or xenon) are best examined. The experimental studies provided information about bond energies and infrared spectra [6, 7]; however, no structural information was obtained. The most comprehensive theoretical study on these types of complexes was completed by Ehlers et al. Optimized geometries and M-Ng bond energies were reported, which corresponded well with the experimental results [8].

Ono and Taketsugu investigated the binding of noble gas atoms to the coordinative highly unsaturated NiCO and CoCO species with density functional, multireference, and coupled-cluster methods [9, 10]. It was also shown that two Ng atoms can bind with Pt atom in linear geometry [11].

The aim of this work is to shed some light to the molecular and electronic structure and the bond dissociation energies of the isomers of HCo(CO)3Xe. The secondary objective is a survey on the available density functional methods including dispersion correction by calculating the Cr-Xe bond strength in Cr(CO)5Xe and comparing it with the experimental value.

2. Computational Details

All the structures have been fully optimized without using symmetry constraints employing the Gaussian 09 suite program [12]. The def2-TZVP basis set [13] was utilized for every atom with the corresponding pseudopotential for Xe. The absence of negative eigenvalues has been confirmed by frequency calculations on the optimized geometries. Single point calculations have been made with symmetry enabled on the respective point groups of each structure. The dissociation enthalpies for the metal-xenon bond have been counterpoise-corrected according to Boys and Bernardi [14]. NPA charges [15] and Wiberg bond indices (WBIs) on the NPA basis have been computed using the separate GENNBO 6.0 program because the NBO 3.1 version, implemented in Gaussian, results in highly erroneous natural atomic orbital occupancies. QTAIM (Quantum theory of atoms in molecules) calculations have been completed utilizing the AIMAll package [16]. For the charge decomposition analyses (CDA) the Multi.wfm program [17] has been employed.

3. Results and Discussion

The accurate determination of the strengths of Xe-metal bonds is a real challenge because most DFT methods lead us to more or less erroneous results. However, the introduction of dispersion (or long range) corrected functionals seems to overcome this problem. Therefore a set of dispersion corrected functionals have been selected, and their accuracies have been validated by computing the BDE of the Cr-Xe bond in Cr(CO)5Xe, for which empirical data are available for comparison. Wells and Weitz reported 9.0 ± 1 kcal/mol by measuring the temperature dependence of the dissociation rate constant in gas phase [18]. The results are compiled in Table 1, along with the length of the Cr-Xe, which is anticipated to be indicative of the bond strength as well.

Table 1: Bond dissociation enthalpy (BDE) for the Cr-Xe bond in Cr(CO)5Xe, including BSSE correction, as well as the computed Cr-Xe equilibrium distance.

The set of functionals can be divided further into five groups: (i) original (uncorrected) GGA functionals frequently used for various studies, such as BP86, PBEPBE, OLYP, and mPW1PW91; (ii) their long range (LC) corrected versions developed by Ikura and coworkers [19]; (iii) standalone GGA functionals modified to handle weak interactions as well, such as B97D, VSXC, and M06L; (iv) hybrid functionals including dispersion correction, such as CAM-B3LYP and M06; and (v) uncorrected hybrid functionals.

In general, the hybrid functionals resulted in somewhat disappointing prediction for the BDE of Cr(CO)5Xe. The O3LYP functional predicts no Cr-Xe interaction at all, whereas fairly small interaction energy is predicted by B98, CAM-B3LYP, and mPW1PW91. Somewhat better agreement with the experimental data has been achieved by PBE0. Among the hybrid functionals M06 provided the best result with a BDE being only 1.5 kcal/mol smaller than the experimental value.

Comparing the pure GGA functionals, it is remarkable that OLYP predicted no Cr-Xe interaction similar to its hybrid counterpart. Difference is, however, the Cr-Xe distance, which is also very large (4.730 Å). The inclusion of long range correction dramatically improves the accuracy increasing the BDE to 6.5 kcal/mol. Similar BDE was obtained by B97D, somewhat better by M06L. The remaining three uncorrected functionals also gave BDEs in this range; however, the LC correction for them resulted in spectacularly accurate results. LC-BP86 now somewhat overestimates the bond strength by 1.3 kcal/mol, whereas LC-PBEPBE and especially LC-mPWPW91 resulted in excellent agreement with the experimental BDE. Finally, the VSXC functional drastically overestimates the strength of the Cr-Xe interaction (15.7 kcal/mol) and, strangely, this is not reflected with the equilibrium Cr-Xe bond distance, which is over 3.0 Å. Thus, among the training set of functionals LC-mPWPW91 is selected for further studies and all the structural and electronical data provided below are obtained at the LC-mPWPW91/def2-TZVP level of theory.

The structure of Cr(CO)5Xe as well as that of the unsaturated Cr(CO)5Xe are depicted in Figure 1.

Figure 1: Optimized structure of Cr(CO)5Xe and Cr(CO)5. Bond lengths are given in Å. The NPA charges are written in italics.

Upon coordination to chromium, the xenon atom loses some of its electron density, which is reflected by its positive NPA charge (0.230). As a light σ-donor, Xe also resulted in a minor elongation of the Cr-Ccarbonyl bond trans to Xe. On the other hand, the equatorial Cr-Ccarbonyl bonds have been contracted. The Cr-Xe distance is predicted to be 2.801 Å which is somewhat shorter than that reported by Ehlers and coworkers at the BP86 level [8].

Moving from the test complex to the cobalt-carbonyl complex, the structure of HCo(CO)3 has been examined at the def2-TZVP level of theory. According to Huo et al. [20] two possible structures of singlet HCo(CO)3 (with C2v and C3v symmetry) should be taken in account with an energy difference of 10.4 kcal/mol. The xenon coordination can take place on both structures resulting in a strongly distorted trigonal bipyramidal Cs complex (denoted by Cs) and a trigonal bipyramidal configuration in C3v symmetry (C3v), as illustrated in Scheme 1.

Scheme 1

The geometries of the initial coordinatively unsaturated complexes HCo(CO)3, as well as those for the adducts containing the coordinated xenon, are depicted in Figure 2. Unlike the B3LYP results, published by Beller et al., the LC-mPWPW91/def2-TZVP level resulted in a near planar structure with Cs symmetry. Similar structure was reported by Ziegler and co-workers [21], albeit, with notably smaller bond angle for the carbonyl ligands cis to H through cobalt. The energy difference between the C3v and Cs structures of HCo(CO)3 is 10.9 kcal/mol, which is very close to that given by Beller [20].

Figure 2: Computed structures of HCo(CO)3 and HCo(CO)3Xe isomers. Bond lengths are given in Å. The NPA charges are written in italics.

The coordination of Xe to cobalt results in a slight change in geometry for the Cs structure with smaller equatorial C-Co-C bond angles. The free energy difference between Cs and C3v is 5.3 kcal/mol in favor of the former isomer. Despite its lesser stability, the counterpoise-corrected BDE in C3v is 11.1 kcal/mol, as opposed to that of Cs which is 5.7 kcal/mol. According to the free energy change of the adduct formation; however, the formation of both structures are endergonic, with ΔG = 3.5 and 8.8 kcal/mol for Cs and for C3v, respectively.

According to the NBO analysis the xenon atom is positively charged in both isomers of HCo(CO)3Xe; that is, Xe loses some of its electron density when coordinating to the cobalt center. Its net charge increases from 0 to 0.115 and 0.187 in the case of Cs and C3v, respectively. As shown by CDA analysis, for the charge transfer mainly the binding HOMO-7 orbitals are responsible, which are shown in Figure 3. These are the only ones among the occupied orbitals where the p atomic orbitals of xenon (px of Cs and pz of C3v) overlap significantly with the d orbitals of cobalt forming a σ-type interaction. The increase of natural charge is in strong correspondence with the decrease of the natural atomic orbital occupancy of the most interacting p orbital of xenon. The Wiberg bond indices (WBI) on the NAO basis of the Co-Xe bond (0.119 for Csand 0.202 for C3v) are also in relationship with the natural charge of Xe. Thus, the greater degree of electron donation and hence the more positive partial charge of xenon, in the case of C3v, results in stronger bond to cobalt.

Figure 3: The HOMO-7 orbitals of Cs and C3v.

The nature of the Co-Xe bond was also examined by topological analysis of the electron density distribution evaluating the electron density in the Co-Xe bond critical point, as well as the delocalization index δ(A,B), which is introduced by Bader and Stephens [22] and describes the number of electron pairs delocalized between two atomic basins. The δ(A,B) is somewhat related to formal bond orders for an equally shared pair between two atoms in a polyatomic molecule; however, it is usually less than that due to delocalization over the other atoms in the molecule. For both structures bond path exists between Co and Xe, with a bond critical point. In contrast to the Wiberg bond indices, the electron density at the bond critical point is smaller for C3v than that for Cs, albeit, both values are rather small (0.0411 for C3v and 0.0415 for Cs). On the other hand, the delocalization index δ(Co, Xe) results in the same order of bond strengths as WBI (0.482 for C3v and 0.446 for Cs). The Laplacian distribution of the HCo(CO)3Xe isomers are depicted in Figure 4. showing no significant distortion in the electron distribution around the xenon atom.

Figure 4: Contour line diagram of the Laplacian distribution of the HCo (CO)3Xe isomers. Solid lines indicate charge depletion and dashed lines indicate charge concentration .

4. Conclusion

It can be concluded that xenon is able to coordinate to the coordinative unsaturated cobalt-catalyst under hydroformylation conditions; however, due to the endergonic formation of HCo(CO)3Xe it is probably not able to influence the rate of the reaction. The molecular orbital and the natural population analyses reveal that the Co-Xe bond may be characterized by the electron donation from one of the p atomic orbitals of xenon to cobalt. The survey on some commonly employed functionals show that in terms of BDE prediction the long range corrected LC-mPWPW91 functional very accurately describes the strength of the metal-xenon interaction.

Conflict of Interests

The author declares that there is no conflict of interests regarding the publication of this paper.


The author is thankful for the support of the Developing Competitiveness of Universities in the South Transdanubian Region (SROP-4.2.2/B-16-10/1-2010-0029) Project as well as the Supercomputer Center of the National Information Infrastructure Development (NIIF) Program.


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