metal-CO Bond Research Articles

The nature and degree of the cooperativity of (η5-C5H5)–metal and metal–CO bonds in half-sandwich complexes of groups 5, 7, 9, and 11 transition metals

It is shown that, the cooperativity always has the same quantitative effect on the interaction energies of two cooperated chemical bonds but may have different effects on their nature.

Insights into the Metal-CO Bond in O2M(η1-CO) (M = Cr, Mo, W, Nd, and U) Complexes.

Investigations on the structures and bonding properties of metal carbonyl compounds provide fundamental understandings on the origin of small-molecule activations. Herein, the geometry and bonding trends of a series of isovalent metal oxocarbonyl complexes O2M(η1-CO) (M = Cr, Mo, W, Nd, and U) were studied by combined matrix-isolation infrared spectroscopy and advanced quantum chemical calculations. The title complexes present red shift of C-O stretching bands in the range from 122 to 244 cm-1, indicating the difference of CO activation ability for the series of isovalent metal dioxides. Density functional theory calculations predict T-shaped structures with a C2v symmetry for all the title molecules. O2Nd(η1-CO) bears little resemblance to the other complexes in bonding characters because of the weak interactions between the NdO2 and CO moiety. For the other complexes, natural localized molecular orbital analysis reveals a gradual increase of covalent character in M-CO bonds along the metal series Cr → Mo → W→ U. Energy decomposition analysis with natural orbitals for chemical valence calculations demonstrates that the M-CO bonding patterns conform to the conventional Dewar-Chatt-Duncanson motif. The contributions from orbital interactions in total attractions increase from Cr (41.7%) to U (52.7%). The breakdown of the orbital term into pairwise interactions shows that contributions of the M ← CO σ donation decrease from Cr (59.2%) to U (28.4%), while the M → CO π* backdonation increases significantly from Cr (23.8%) to U (67.3%). The more effective overlap and the better energy matching of U 5f and U 6d valence orbitals with CO π* orbitals result in much stronger U → CO π backdonation than the other metal elements.

Metal-CO Bonding in Mononuclear Transition Metal Carbonyl Complexes.

DFT calculations have been carried out for coordinatively saturated neutral and charged carbonyl complexes [M(CO)n]q where M is a metal atom of groups 2–10. The model compounds M(CO)2 (M = Ca, Sr, Ba) and the experimentally observed [Ba(CO)]+ were also studied. The bonding situation has been analyzed with a variety of charge and energy partitioning approaches. It is shown that the Dewar–Chatt–Duncanson model in terms of M ← CO σ-donation and M → CO π-backdonation is a valid approach to explain the M–CO bonds and the trend of the CO stretching frequencies. The carbonyl ligands of the neutral complexes carry a negative charge, and the polarity of the M–CO bonds increases for the less electronegative metals, which is particularly strong for the group 4 and group 2 atoms. The NBO method delivers an unrealistic charge distribution in the carbonyl complexes, while the AIM approach gives physically reasonable partial charges that are consistent with the EDA-NOCV calculations and with the trend of the C–O stretching frequencies. The AdNDP method provides delocalized MOs which are very useful models for the carbonyl complexes. Deep insight into the nature of the metal–CO bonds and quantitative information about the strength of the [M] ← (CO)8 σ-donation and [M(d)] → (CO)8 π-backdonation visualized by the deformation densities are provided by the EDA-NOCV method. The large polarity of the M–CO π orbitals toward the CO end in the alkaline earth octacarbonyls M(CO)8 (M = Ca, Sr, Ba) leads to small values for the delocalization indices δ(M–C) and δ(M···O) and significant overlap between adjacent CO groups, but the origin of the charge migration and the associated red-shift of the C–O stretching frequencies is the [M(d)] → (CO)8 π-backdonation. The heavier alkaline earth metals calcium, strontium and barium use their s/d valence orbitals for covalent bonding. They are therefore to be assigned to the transition metals.

Silylated silicon–carbonyl complexes as mimics of ubiquitous transition-metal carbonyls

Transition-metal-carbonyl complexes are common organometallic reagents that feature metal-CO bonds. These complexes have proven to be powerful catalysts for various applications. By contrast, silicon-carbonyl complexes, organosilicon reagents poised to be eco-friendly alternatives for transition-metal carbonyls, have remained largely elusive. They have mostly been explored theoretically and/or through low-temperature matrix isolation studies, but their instability had typically precluded isolation under ambient conditions. Here we present the synthesis, isolation and full characterization of stable silyl-substituted silicon-carbonyl complexes, along with bonding analysis. Initial reactivity investigations showed examples of CO liberation, which could be induced either thermally or photochemically, as well as substitution and functionalization of the CO moiety. Importantly, the complexes exhibit strong Si-CO bonding, with CO→Si σ-donation and Si→CO π-backbonding, which is reminiscent of transition-metal carbonyls. This similarity between the abundant semi-metal silicon and rare transition metals may provide new opportunities for the development of silicon-based catalysis.

Reply to the 'Comment on "Revisiting π backbonding: the influence of d orbitals on metal-CO bonds and ligand red shifts"' by G. Frenking and S. Pan, Phys. Chem. Chem. Phys., 2019, 22, DOI: 10.1039/C9CP05951B.

We respond to the comment by Pan and Frenking with regard to our investigation on transition and alkaline earth metal d orbital influence on their bonding to carbonyl ligands to clarify misconceptions. We do not consider the points raised in the comment as affecting our conclusions.

Molecular Bonding of Predissociative CO on Fe(100): Molecular Orbital Perspective.

On Fe(100), CO molecules can get activated efficiently so that CO bond breaking occurs with its transition state in close connection to the adsorbate. The CO bonding thus serves as a prototype model, nicely representing a balance of two simultaneous processes, namely, bond making with the surface and bond breaking within the adsorbate. Such unique configuration highlighting the interplay of two fundamental processes in one adsorption geometry, about which chemists have often fantasized, provides a viable solution to understand the very fundamental aspects of chemistry exemplified in a broad range of disciplines. Using density functional theory calculations, in this paper, we get a glimpse into how the CO bond activation is gestated and initiated in the adsorbate, wherein orbital cooperation in CO activation is evidenced by external CO bond making with the metal and internal CO bond breaking. We find that the symmetry breaking of occupied molecular orbitals in both 5σ and 1π symmetries marks efficient CO bond activation, which is reinforced by 1π → 2π excitations and 2π backdonation that are coupled with the symmetry transition of partially occupied 2π orbitals to a rotational symmetry. Our findings promote our knowledge of CO bond activation beyond the established picture of 5σ donation and 2π backdonation without symmetry breaking and may have insightful implications on orbital control of molecular activation, with further possible impact on elucidating the physical basis of heterogeneous catalysis.

Octacarbonyl Ion Complexes of Actinides [An(CO)8 ]+/- (An=Th, U) and the Role of f Orbitals in Metal-Ligand Bonding.

The octacarbonyl cation and anion complexes of actinide metals [An(CO)8]+/− (An=Th, U) are prepared in the gas phase and are studied by mass‐selected infrared photodissociation spectroscopy. Both the octacarbonyl cations and anions have been characterized to be saturated coordinated complexes. Quantum chemical calculations by using density functional theory show that the [Th(CO)8]+ and [Th(CO)8]− complexes have a distorted octahedral (D 4h) equilibrium geometry and a doublet electronic ground state. Both the [U(CO)8]+ cation and the [U(CO)8]− anion exhibit cubic structures (Oh) with a 6A1g ground state for the cation and a 4A1g ground state for the anion. The neutral species [Th(CO)8] (Oh; 1A1g) and [U(CO)8] (D 4h; 5B1u) have also been calculated. Analysis of their electronic structures with the help on an energy decomposition method reveals that, along with the dominating 6d valence orbitals, there are significant 5f orbital participation in both the [An]←CO σ donation and [An]→CO π back donation interactions in the cations and anions, for which the electronic reference state of An has both occupied and vacant 5f AOs. The trend of the valence orbital contribution to the metal–CO bonds has the order of 6d≫5f>7s≈7p, with the 5f orbitals of uranium being more important than the 5f orbitals of thorium.

Bonding in Binuclear Carbonyl Complexes M2(CO)9 (M = Fe, Ru, Os).

Quantum-chemical density functional theory calculations using the BP86 functional in conjunction with a triple-ζ basis set and dispersion correction by Grimme with Becke-Johnson damping D3(BJ) were performed for the title molecules. The nature of the bonding was examined with the quantum theory of atoms in molecules (QTAIM) and natural bond order (NBO) methods and with the energy decomposition analysis in conjunction with the natural orbital for chemical valence (EDA-NOCV) analysis. The energetically lowest-lying form of Fe2(CO)9 is the triply bridged D3 h structure, whereas the most stable structures of Ru2(CO)9 and Os2(CO)9 are singly bridged C2 species. The calculated reaction energies for the formation of the cyclic trinuclear carbonyls M3(CO)12 from the dinuclear carbonyls M2(CO)9 are in agreement with experiment, as the iron complex Fe2(CO)9 is thermodynamically stable in these reactions, but the heavier homologues Ru2(CO)9 and Os2(CO)9 are not. The metal-CO bond to the bridging CO ligands is stronger than the bonds to the terminal CO ligands. This holds for the triply bridged D3 h structures as well as for the singly bridged C2 or C2 v species. The analysis of the orbital interactions with the help of the EDA-NOCV method suggests that the overall M→CO π backdonation is always stronger than the M←CO σ donation. The bridging carbonyls are more strongly bonded than the terminal CO ligands, and they are engaged in stronger σ donation and π backdonation, but the formation of bridging carbonyls requires reorganization energy, which may or may not be compensated by the stronger metal-ligand interactions. The lower-lying D3 h form of Fe2(CO)9 and C2 structures of Ru2(CO)9 and Os2(CO)9 are due to a delicate balance of several forces.

Tuning CO sensing properties and magnetism of MoS2 monolayer through anchoring transition metal dopants

The CO sensing and magnetic properties of pristine and metal-doped MoS2 monolayers (defined as MoS2-M, where M=Pd, Co, and Fe) were investigated by anchoring CO onto 2D nanosheets with first-principles calculations. Pristine MoS2 exhibits weak physisorption to CO, whereas MoS2-M monolayers show enhanced interaction with CO by forming a metalCO bond, and narrow band gaps and spontaneous magnetization upon CO adsorption. MoS2-Co and MoS2-Fe systems are ferromagnetic (FM) half metals (HM), whereas MoS2-Pd is a nonmagnetic (NM) metal. After CO adsorption, MoS2-Fe coverts to NM metal to maintain the unchanged ground states. Results indicate that MoS2-M systems are promising candidates for future applications in designing novel gas sensors, nanoelectronics, and spintronics.

Hexacarbonyls of Mo, W, and Sg: Metal-CO Bonding Revisited.

Calculations of the first bond dissociation energies (FBDEs) and other molecular properties of M(CO)6, where M = Mo, W, and Sg, have been performed using a variety of nonrelativistic and relativistic methods, such as ZORA-DFT, X2c+AMFI-CCSD(T), and Dirac-Coulomb density functional theory. The aim of the study is to assist experiments on the measurements of the FBDE of Sg(CO)6. We have found that, different from the results published earlier, the metal-CO bond in Sg(CO)6 should be weaker than that in W(CO)6. A comparison of the relativistic and nonrelativistic FBDE values, as well as molecular orbital and vibrational frequency analyses within both the nonrelativistic and relativistic approaches, have shown that this is a relativistic, predominantly scalar, effect causing weaker d(M) → π(CO) back-bonding in Sg(CO)6 than in the lighter homologues. Good agreement between the calculated FBDEs in this work and the experimental FBDEs for the Mo and W compounds gives credit to the present FBDE of Sg(CO)6, which should serve as guidance for ongoing experiments.

Single Molecule Vibrational Spectroscopy: CO Bonding to Edge and Terrace Positions on Ag, Au, and Pd Islands on NiAl(110).

The vibrational properties of single CO molecules adsorbed on nanosized Ag, Au, and Pd islands on a NiAl(110) surface were studied with a scanning tunneling microscope. The sensitivity of single molecule vibrational spectroscopy to aspects of the local environment is demonstrated by comparative studies of CO-metal bond vibrations at island terrace and island edge sites. Vibrational spectra of single CO molecules adsorbed on Ag, Au, and Pd island terraces showed peaks at 27, 32, and 44 meV, respectively, which are assigned to the hindered rotational mode. CO molecules on Au and Pd island edges, on the other hand, showed blue-shifted hindered rotational modes at 34 and 46 meV, respectively. On Au islands, CO molecules showed a strong preference for adsorption on edges, while no such preference was observed on Pd.

Interaction of CO with PtxAg1-x/Pt(111) surface alloys: More than dilution by Ag atoms

We have investigated CO adsorption on structurally well-defined PtxAg1-x/Pt(111) surface alloys, combining temperature-programmed desorption (TPD) and infrared reflection absorption spectroscopy (IRRAS) as well as density functional theory (DFT) based calculations. This is part of a systematic approach including previous studies of CO adsorption on closely related Pt(111)- and Pd(111)-based surface alloys. Following changes in the adsorption properties with increasing Ag content and correlating them with structural changes allow us to assign desorption features to specific adsorption sites/ensembles identified in previous scanning tunneling microscopy (STM) measurements, and thus to identify and separate contributions from different effects such as geometric ensemble effects and electronic ligand/strain effects. DFT calculations give further insight into the nature of the metal–CO bond on these bimetallic sites. Most prominently, the growth of a new CO desorption feature at higher temperature (~550K) in the TPD spectra of Ag-rich surface alloys, which is unique for the group of Pt(111)- and Pd(111)-based surface alloys, is attributed to CO adsorption on Pt atoms surrounded by a Ag-rich neighborhood. Adsorption on these sites manifests in an IR band down-shifted to significantly lower wave number. Systematic comparison of the present results with previous findings for CO adsorption on the related Pt(111)- and Pd(111)-based surface alloys gains a detailed insight into general trends in the adsorption behavior of bimetallic surfaces.

Influence of support morphology on the bonding of molecules to nanoparticles

Supported metal nanoparticles form the basis of heterogeneous catalysts. Above a certain nanoparticle size, it is generally assumed that adsorbates bond in an identical fashion as on a semiinfinite crystal. This assumption has allowed the database on metal single crystals accumulated over the past 40 years to be used to model heterogeneous catalysts. Using a surface science approach to CO adsorption on supported Pd nanoparticles, we show that this assumption may be flawed. Near-edge X-ray absorption fine structure measurements, isolated to one nanoparticle, show that CO bonds upright on the nanoparticle top facets as expected from single-crystal data. However, the CO lateral registry differs from the single crystal. Our calculations indicate that this is caused by the strain on the nanoparticle, induced by carpet growth across the substrate step edges. This strain also weakens the CO-metal bond, which will reduce the energy barrier for catalytic reactions, including CO oxidation.

Photodelivery of CO by designed PhotoCORMs: correlation between absorption in the visible region and metal-CO bond labilization in carbonyl complexes.

The therapeutic potential of photoactive CO-releasing molecules (photoCORMs) have called for close examination of the roles of the ligand(s) and the central metal atoms on the overall photochemical labilization of the metal-CO bonds. Along this line, we have synthesized four metal complexes, namely, [MnBr(azpy)(CO)3 ] (1), [Mn(azpy)(CO)3 (PPh3 )]ClO4 (2), [ReBr(azpy)(CO)3 ] (3), and [Re(azpy)(CO)3 (PPh3 )]ClO4 (4), derived from 2-phenylazopyridine. These complexes were characterized by spectroscopic and crystallographic studies. Although both 1 and 3 exhibit strong metal-to-ligand charge-transfer bands in the 500-600 nm region, only 1 photoreleases CO upon illumination with visible light. Results of theoretical studies were used to gain insight into this surprising difference. Strong spin-orbit coupling (prominent in heavy metals) appears to promote intersystem crossing to a triplet state in 3, a step that discourages CO release upon illumination with visible light. Slow release of CO from 2 and 4 also indicates that strong σ-donating ligands, such as Br(-) , accelerate the rate of CO photorelease relative to π-acid ligands, such as PPh3 .

Valence ionization spectra of group six metal hexacarbonyls studied by the symmetry-adapted cluster-configuration interaction method

The valence ionization spectra up to 20 eV of group six metal carbonyls, chromium hexacarbonyl, molybdenum hexacarbonyl, and tungsten hexacarbonyl were studied by the symmetry-adapted cluster-configuration interaction (SAC-CI) method. The assignments of the spectra are given based on reliable SAC-CI calculations. The relativistic effects including the spin-orbit effects are important for the ionization spectrum of W(CO)(6). The relation between the metal-CO distance and ionization energies was examined. The lowest ionization energies of the three metal carbonyls are approximately the same because of the energy dependence of the metal-CO length and relativistic effects. In Cr(CO)(6), the Cr-CO interaction significantly increases the lowest ionization energy in comparison with Mo(CO)(6) and W(CO)(6) because of the relatively short metal-CO bond length. The relativistic effect reduces the lowest ionization energy of W(CO)(6) because the effective core potential of 5d electrons is more efficiently screened as a result of the relativistic contraction of the inner electrons.

Quantum-chemical study of donor-acceptor interactions in chelate dicarbonyl complexes of rhodium(I)

DFT calculations were used to analyze the electronic structures of 15 mono- and dicarbonyl rhodium(I) complexes with bidentate O,O-, N,N-, and N,O-donor ligands. The characteristics describing the metal-CO bond (bond length and spin-spin coupling constant J(CRh)) were found to depend on which of the donor atoms (N or O) is trans to the carbonyl group. Because of this, the trans-effect transmitted along the σ-bonds can be judged from the values of these characteristics. The characteristics whose values are determined by the populations of the π-antibonding orbitals of the CO groups primarily depend on the cis-partners in the coordination sphere.

Transition Metal−Carbon Complexes. A Theoretical Study

The equilibrium geometries and bond dissociation energies of 16VE and 18VE complexes of ruthenium and iron with a naked carbon ligand are reported using density functional theory at the BP86/TZ2P level. Bond energies were also calculated at CCSD(T) using TZ2P quality basis sets. The calculations of [Cl2(PMe3)2Ru(C)] (1Ru), [Cl2(PMe3)2Fe(C)] (1Fe), [(CO)2(PMe3)2Ru(C)] (2Ru), [(CO)2(PMe3)2Fe(C)] (2Fe), [(CO)4Ru(C)] (3Ru), and [(CO)4Fe(C)] (3Fe) show that 1Ru has a very strong Ru-C bond which is stronger than the Fe-C bond in 1Fe. The metal-carbon bonds in the 18VE complexes 2Ru-3Fe are weaker than those in the 16VE species. Calculations of the related carbonyl complexes [(PMe3)2Cl2Ru(CO)] (4Ru), [(PMe3)2Cl2Fe(CO)] (4Fe), [(PMe3)2Ru(CO)3] (5Ru), [(PMe3)2Fe(CO)3] (5Fe), [Ru(CO)5] (6Ru), and [Fe(CO)5] (6Fe) show that the metal-CO bonds are much weaker than the metal-C bonds. The 18VE iron complexes have a larger BDE than the 18VE ruthenium complexes, while the opposite trend is calculated for the 16VE compounds. Charge and energy decomposition analyses (EDA) have been carried out for the calculated compounds. The Ru-C and Fe-C bonds in 1Ru and 1Fe are best described in terms of two electron-sharing bonds with sigma and pi symmetry and one donor-acceptor pi bond. The bonding situation in the 18 VE complexes 2Ru-3Fe is better described in terms of closed shell donor-acceptor interactions in accordance with the Dewar-Chatt-Duncanson model. The bonding analysis clearly shows that the 16VE carbon complexes 1Ru and 1Fe are much more strongly stabilized by metal-C sigma interactions than the 18VE complexes which is probably the reason why the substituted homologue of 1Ru could become isolated. The EDA calculations show that the nature of the TM-C and TM-CO binding interactions resembles each other. The absolute values for the energy terms which contribute to Delta(Eint) are much larger for the carbon complexes than for the carbonyl complexes, but the relative strengths of the energy terms are not very different from each other. The pi bonding contribution to the orbital interactions in the carbon complexes is always stronger than sigma bonding. There is no particular bonding component which is responsible for the reversal of the relative bond dissociation energies of the Ru and Fe complexes when one goes from the 16VE complexes to the 18VE species. That the 18 VE compounds have longer and weaker TM-C and TM-CO bonds than the respective 16 VE compounds holds for all complexes. This is because the LUMO in the 16 VE species is a sigma-antibonding orbital which becomes occupied in the 18 VE species.

Metal-benzene and metal-CO bond energies in neutral and ionic C6H6Cr(CO)3 studied by threshold photoelectron-photoion coincidence spectroscopy and density functional theory.

photoelectron-photoion coincidence spectroscopy and density functional theory calculations have been used to investigate the dissociation kinetics of the benzene chromium tricarbonyl ion, BzCr(CO)3+ (Bz = C6H6). The dissociation of the BzCr(CO)3+ ion proceeds by the sequential loss of three CO and benzene ligands. The first and third CO and the benzene loss reactions were associated with metastable precursor ions (lifetimes in the microsecond range). By simulating the resulting asymmetric time-of-flight peak shapes and breakdown diagram, the 0 K appearance energies of the four product ions were determined to be 8.33 +/- 0.05, 8.93 +/- 0.05, 9.97 +/- 0.06, and 11.71 +/- 0.06 eV, respectively. Combined with the ionization energy of BzCr(CO)3, 7.30 +/- 0.05 eV, the three successive Cr-CO bond energies in the BzCr(CO)3+ were found to alternate, with values of 1.03 +/- 0.05, 0.60 +/- 0.05, and 1.04 +/- 0.05 eV, respectively, and the Bz-Cr bond energy in BzCr+ is 1.74 +/- 0.05 eV, a trend confirmed by the density functional theory (DFT) calculations. Using the heats of formation of the fully dissociated products, C6H6, Cr+, and CO, the 298 K heats of formation the ionic BzCr(CO)n+ (n = 03) species were determined. By scaling the DFT calculated bond energies for the neutral molecules, the heats of formation of the neutral BzCr(CO)n (n = 03) were also obtained.

Potential-dependent chemisorption of carbon monoxide on platinum electrodes: new insight from quantum-chemical calculations combined with vibrational spectroscopy

Abstract Density functional theory (DFT) using the finite cluster approach is utilized to compute binding energies, bond geometries, and vibrational properties of carbon monoxide adsorbed on Pt(111) as a function of the external interfacial field, focusing attention on the metal–CO bond itself. Comparison with electrode potential-dependent frequencies for the metal–CO ( ν M–CO ) as well as the much-studied intramolecular CO ( ν CO ) vibration, as measured by in-situ Raman and infrared spectroscopy, facilitate their interpretation in terms of metal-chemisorbate bonding for this archetypal electrochemical system. Decomposing the calculated metal–CO binding energy and vibrational frequencies into individual orbital and steric repulsion components enables the role of such quantum-chemical interactions to the field- (and hence potential-) dependent bonding to be assessed. No simple relationship between the field( F )-dependent binding energies and the ν M–CO frequencies is evident. While the DFT ν M–CO – F slopes are negative at positive and small–moderate negative fields, reflecting the prevailing influence of back-donation, a ν M–CO – F maximum is obtained at larger negative fields for atop CO, and a plateau for hollow-site CO. This Stark-tuning behavior reflects largely offsetting field-dependent contributions from π and σ surface bonding, and can also be rationalized on the basis of changes in the electrostatic component of ν M–CO from increasing M–CO charge polarization. A rough correlation between the field-dependent ν M–CO frequencies and the corresponding bond distances, r M–CO , is observed for hollow and atop CO in that r M–CO shortens towards less positive fields, but becomes near-constant at moderate–large negative fields. A more quantitative correlation between the field-dependent CO frequencies and bond lengths is also evident. In harmony with earlier findings (and unlike the ν M–CO – F behavior), the ν CO – F dependence is due chiefly to changes in the back-donation bonding component. The overall vibrational frequency-field behavior predicted by DFT is also in semi-quantitative concordance with experimental potential-dependent spectra.

Theoretical studies of CO interaction on Rh3 cluster

Geometries and energy separations of 27-low-lying electronic states of Rh3CO with different structures have been investigated. Atop, bridged, and threefold CO orientations with Rh3 were considered. Complete active space multiconfiguration self-consistent field method (CASMCSCF) followed by large scale multireference singles and doubles configuration interaction (MRSDCI) computations that included up to 2.1 million configurations were used. Three nearly degenerate electronic states were found for the threefold structure around the minimum energy region. At the highest level of theory, the A22 state prevailed to be the ground state. The assignment of minimum energy states for the atop and bridged structures are unambiguous. The B42 and B41 electronic states were found to be the most stable states for these two respective geometries. The nature of the metal–CO bond formation in different states is discussed, and the difference density maps of Rh3CO with respect to Rh3 and COs are presented. The dissociation energies and CO vibrational frequencies have been computed and the results are compared with the available experimental data.