Quantum Chemical Study of the Properties of Molecular Hydrogen

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J. Phys. Chem. 1996, 100, 6023-6031

6023

ARTICLES Quantum Chemical Study of the Properties of Molecular Hydrogen Complexes of Osmium(II): A Comparison of Density Functional and Conventional ab Initio Methods Ian Bytheway,† George B. Bacskay,† and Noel S. Hush*,†,‡ School of Chemistry and Department of Biochemistry, UniVersity of Sydney, Sydney, NSW 2006, Australia ReceiVed: August 8, 1995; In Final Form: December 1, 1995X

The geometries of [Os(NH3)4Lz(η2-H2)](z+2)+ complexes, where molecular hydrogen is trans to the Lz ligand, have been calculated using density functional theory (DFT) and compared with the results of MP2 calculations. The quality of agreement between the DFT and MP2 geometries is found to be dependent on the trans ligand Lz. When Lz ) acetone, water, acetate, and chloride, the agreement between the DFT and MP2 calculations is generally reasonable, and for the Lz ) acetate complex, the DFT and the MP2 predictions are in acceptable agreement with the experimental geometry. When Lz ) hydride, pyridine, acetonitrile, cyanide, hydroxylamine, and ammonia, the DFT calculations predict a much shorter H-H bond length and slightly longer Os-H distances when compared with the MP2 values. As the potential energy surfaces are very flat with respect to the H-H stretch, the differences between the DFT and MP2 geometries correspond to energy differences of approximately 3 kcal mol-1 when calculated at the same level of theory. The differences between the DFT and MP2 predictions appear to correlate with the properties of the trans ligand Lz, in particular its σ-donor and π-acceptor/donor properties. The DFT predictions of the Os-H2 interaction energy are consistently smaller by ∼25% than the corresponding MP2 values, but the agreement is much better in the case of the Os-Lz bond. Solvation by water, estimated by a self-consistent reaction field technique, is found to have little effect on the binding of H2, while significantly reducing the binding energies of the trans ligands, especially those that are charged. The integrated atomic charges for the dihydrogen ligand, obtained by the atoms in molecules method, are slightly negative, while Os varies between 1.01 and 1.81. The DFT calculations generally predict both species to be somewhat closer to neutral than those obtained at the MP2 level; this is consistent with the notion that DFT predicts stronger H-H but weaker Os-H bonding than MP2, i.e., less donation by Os into the antibonding σ* MO of H2.

Introduction Molecular hydrogen complexes represent a relatively new but rapidly expanding area of transition metal chemistry, and several useful reviews on the synthesis and properties1,2 as well as the theoretical interpretation3 of the binding of molecular hydrogen in such complexes have appeared. While in weakly bound complexes the H2 bond length is about 10% longer than in the free H2 molecule,1,2 in a series of osmium(II) complexes4 H2 appears to be remarkably stretched, with a bond length up to nearly twice that in the free molecule. Most synthetic work and the related experimental characterization of these η2-H2 osmium complexes have been carried out by Li and Taube,4 but thus far the H-H distance has been experimentally established for one complex only, namely, [Os(en)2CH3COO(η2-H2)]+ (en ) ethylenediamine), using X-ray5 and neutron diffraction6 methods. However, the series [Os(NH3)4Lz(η2-H2)](z+2)+, where Lz is a trans ligand (Lz ) (CH3)2CO, H2O, CH3COO-, Cl-, H-, C5H5N, and CH3CN), has been the subject of a careful quantum chemical study by Craw, Bacskay, and Hush7 (referred to as CBH hereafter) which addressed the problems of molecular geometries, binding energies of H2 in the complexes, and spin-spin coupling constants JHD, as well as elucidating the bonding mechanism. †

School of Chemistry. Department of Biochemistry. X Abstract published in AdVance ACS Abstracts, March 15, 1996. ‡

0022-3654/96/20100-6023$12.00/0

The calculations were carried out largely at the Hartree-Fock self-consistent field (SCF) and second order Møller-Plesset (MP2) levels of theory, yielding the result that electron correlation is of crucial importance in the description of the H2 geometry: the MP2 bond lengths were found to be 1.30-1.40 Å, in stark contrast with the SCF predictions of ∼0.8 Å. Given the size of these molecules, MP2 represents effectively the highest level of ab initio theory that could be currently used to optimize the geometries, even if effective core potentials (ecp) are used, as in the work of CBH. Although in that study it was verified, at least for one member of the series, Viz., Lz ) Cl-, by comparing MP2 with the averaged coupled pair functional (ACPF) approach,8 that MP2 is capable of yielding a reasonably accurate geometry, it is clearly desirable to test this contention more thoroughly. Density functional theory (DFT) represents an alternative, semiempirical approach that can be used to study the electronic structure and properties of molecules, with the proViso that the exchange-correlation functionals formulated thus far are sufficiently accurate and applicable to the system of interest. Given the remarkable sensitivity of the H-H bond length in the [Os(NH3)4Lz(η2-H2)](z+2)+ complexes to electron correlation effects as well as the unusual bonding (between molecular hydrogen and a transition metal), this series of molecules represent a class of molecules that could provide a demanding test of DFT in general and exchange-correlation functionals in particular. On © 1996 American Chemical Society

6024 J. Phys. Chem., Vol. 100, No. 15, 1996

Bytheway et al. Becke Exc ) A(ESlater ) + (1 - A)EHF + CELYP + x x + BEx c

(1) (1 - C)EVWN c

Figure 1. General stereochemistry of the [Os(NH3)4Lz(η2-H2)](z+2)+ complexes.

the practical level, since the computational requirements of DFT scale as those of SCF, it is a very much cheaper technique than the conventional methods based on the configuration interaction (CI) expansion of molecular wave functions. Indeed, DFT has been applied, of necessity, to the study of a variety of transition metal complexes,9 although comparisons with conventional ab initio results have only recently become common.10 The main aim of the work presented in this paper is to further the studies of CBH, by determining the equilibrium geometries of the above group of [Os(NH3)4Lz(η2-H2)](z+2)+ complexes using DFT, allowing detailed comparisons with the MP2 results to be made. Three new complexes that have not been synthesized as yet are also included in this study, where Lz ) NH3, NH2OH, and CN-. In addition to geometries, we study the energetics of complex formation, in particular the binding of molecular H2 and of the trans ligands to osmium in this series of compounds. The trends in the geometries and energies are correlated with the spectrochemical constants of the trans ligands.11 Such a correlation was already explored in the work of CBH; here, it is extended further. Indeed, the choice of CNand NH2OH as ligands was motivated by our wish to extend the range of spectrochemical constants spanned in our study. Theoretical Details As in the previous work by CBH, the calculations described in this study were performed using the effective core potentials (ecp) and basis sets of Stoll et al.12 to describe the heavy atoms. The osmium atom ecp was parametrized so as to allow for relativistic effects. For osmium the (valence) basis is a [5s4p3d] Gaussian set, to accommodate the valence ns, np, and nd (n ) 5) electrons, while for the carbon, nitrogen, oxygen, and chlorine atoms [2s,2p] Gaussian bases have been used. A double-ζ basis set has been chosen for the hydrogen atoms,13 augmented with a set of 2p polarization functions (ζ ) 0.8) for the molecular hydrogen and hydride ligands. The sensitivity of the predicted energetics to inclusion of polarization functions on the other ligands and on osmium was tested using the above bases enlarged by a single set of polarization functions on the heavy atoms (ζ3d(N) ) 0.7, ζ3d(Cl) ) 0.9, ζ4f(Os) ) 0.5). The density functional calculations reported are based on exchange-correlation functionals Exc[F] implemented in the GAUSSIAN92/DFT software package.14 They have the general form

where the first two terms correspond to the Slater and HartreeFock exchange functionals, the third term is the Becke gradient correction to the exchange functional,15 and the final terms are the Lee, Yang, Parr16 and the Vosko, Wilk, Nuisar17 correlation functionals, respectively. Two functionals were employed in this work: the BLYP functional,18 where A ) B ) C ) 1.0, and the B3LYP functional,19 in which A ) 0.80, B ) 0.72, and C ) 0.81. The general structure of the complexes studied is shown in Figure 1. Cs symmetry was assumed in the geometry optimizations. In contrast with the previous work, where only the H-H and Os-H distances were optimized at the correlated level, the geometries of the complexes studied were optimized, using analytic gradients, with respect to all geometric parameters, except those that define the intramolecular geometries of Lz and NH3 which were frozen at their respective optimized monomeric SCF values. In addition to geometries, the binding energies of molecular hydrogen and of the ligands Lz, in the osmium(II) complex, were calculated in various ways:

(a)∆E1(H2) is defined as the energy change that corresponds to the reaction [Os(NH3)4Lz](z+2)+ + H2 f [Os(NH3)4Lz(η2-H2)](z+2)+ (2) (b) ∆E2(H2) is the energy change associated with the reaction [Os(NH3)4]2+ + H2 f [Os(NH3)4(η2-H2)]2+

(3)

(c) ∆E1(L) is the energy change of the reaction [Os(NH3)4(η2-H2)]2+ + Lz f [Os(NH3)4Lz(η2-H2)](z+2)+ (4) (d) ∆E2(L) is the energy change of the reaction [Os(NH3)4]2+ + Lz f [Os(NH3)4Lz](z+2)+

(5)

Thus the binding energies of both H2 and Lz ligands in the complexes are calculated in the presence and absence of the other. The four sets of energies were obtained using both the BLYP and B3LYP functionals, and where the appropriate MP2 data were not already available from previous work, MP2 calculations were also carried out. In all cases the equilibrium energies of the various species were used in the calculation of the binding energies. The solvation energy Esolv of a given complex is calculated using self-consistent reaction field (SCRF) theory:

Esolv ) -

1

l

0 Mlm Flm ∑ ∑ 2 l m)-1

(6)

0 } are components of the solute's permanent multiwhere {Mlm pole moments (written in spherical tensor form) and {Flm} are the corresponding components of the reaction field, defined as

Flm ) glMlm

(7)

where {Mlm} are the multipole moments in the presence of the reaction field that models the solvent. The solute is assumed

Molecular Hydrogen Complexes of Osmium(II)

J. Phys. Chem., Vol. 100, No. 15, 1996 6025

TABLE 1: Calculated Geometrical Parameters for the [Os(NH3)4Lz(η2-H2)](z+2)+ Complexes (Bond Lengths, Å; Bond Angles, deg) r(H-H) L

z

(CH3)2CO H2O CH3COOClHC5H5N CH3CN CNNH2OH NH3

r(Os-Lz)

r(Os-H)

BLYP

B3LYP

MP2

BLYP

B3LYP

MP2

BLYP

B3LYP

MP2

1.249 1.250 1.316 1.314 0.978 0.998 0.985 0.953 1.031 1.057

1.133 1.135 1.213 1.243 0.936 0.944 0.940 0.920 0.961 0.969

1.380 1.350 1.389 1.400 1.330 1.300 1.330 1.293 1.256 1.252

1.612 1.613 1.635 1.630 1.751 1.689 1.691 1.746 1.670 1.659

1.615 1.616 1.630 1.622 1.752 1.693 1.692 1.742 1.679 1.672

1.596 1.590 1.580 1.600 1.630 1.616 1.580 1.614 1.582 1.581

2.292 2.279 2.146 2.532 1.691 2.179 2.079 2.028 2.238 2.288

2.244 2.243 2.120 2.508 1.678 2.166 2.078 2.024 2.216 2.253

2.218 2.200 2.159 2.551 1.707 2.279 2.244 2.114 2.270 2.308

to be in a spherical cavity of radius R0, in which case

gl )

(l + 1)( - 1) 1 [(l + 1) + l] R02l+1

(8)

where  is the dielectric constant of the solvent. The selfconsistent multipole moment reaction field (SCMMRF) technique20 is used to determine the components of the reaction field, which are obtained simply from the permanent moments and their polarizabilities, e.g.

µR ) µ0R + ∑RRβFβ + ...

(9)

R,β

where {RRβ} are components of the dipole polarizability. In this work multipole moments up to hexadecapole are used in conjunction with the dipole polarizability R. The SCMMRF method, requiring only the permanent multipole moments of the solute and their polarizabilities, represents a simplification of conventional SCRF theory21,22 where the multipole moments {Mlm} are obtained by the self-consistent solution of the appropriate Schro¨dinger equation with the perturbed Hamiltonian

H ˆ )H ˆ0 - ∑

l

∑ Mˆ lmFlm

(10)

l m)-1

The SCMMRF method, where eqs 7 and 9 are solved iteratively, has been extensively tested for several molecules at different levels of theory, with a range of basis sets, and found to reproduce closely the results of the conventional approach.20 The total charge densities of the various osmium(II)dihydrogen complexes were examined using both the Mulliken population analysis and the atoms in molecules (AIM) technique of Bader and co-workers.23 The latter were carried out using the AIMPAC suite of programs.24 These analyses serve two purposes: firstly, as a means of understanding the results obtained by the various theoretical methods, i.e., MP2, BLYP, and B3LYP, and secondly, to obtain useful additional information about the nature of the osmium-hydrogen and hydrogenhydrogen bonding in these complexes. In the AIM analyses all-electron wave functions were used, where the occupied core MO’s were expanded in terms of Huzinaga’s minimal bases.25 The electronic structure calculations were performed using the GAUSSIAN92/DFT programs installed on HP700 and IBM RS6000/320 workstations. Geometries The key parameters that characterize the optimized (gas phase) geometries of the [Os(NH3)4Lz(η2H2)](z+2)+ complexes, obtained using the BLYP and B3LYP density functional

formalisms, are summarized in Table 1, where they are compared with the corresponding MP2 results. In general, the DFT geometries are quite similar to those obtained at the MP2 level, although DFT consistently predicts shorter H-H and longer Os-H bond lengths than MP2. The agreement in the case of other parameters such as the Os-N distance and LzOs-N angle (where N is the nitrogen atom of an ammonia ligand) is much closer. The DFT estimates of the Os-N distances are generally within ∼0.02 Å of the MP2 values,7 while the corresponding agreement in the Lz-Os-N angle is within ∼1°. The degree of difference between the DFT and MP2 geometries depends quite markedly, however, on the nature of the trans ligand Lz. The effects of constraining the geometry optimizations, as noted in the previous section, has been tested for the complexes with Lz as acetone. Performing full geometry optimizations at the BLYP level results in Os-H, Os-Lz, and H-H distances that are 0.002 Å smaller, 0.011 Å larger, and 0.016 Å larger, respectively, than those obtained in the constrained optimization, and quoted in Table 1. The most significant effects of the relaxation are with respect to the N-H distance in the NH3 ligand, which is 0.029 Å larger in the complex, resulting in a reduction of the Os-N distance by 0.012 Å in comparison with the value of 2.221 Å obtained in the constrained calculation. Consequently, freezing the intramolecular geometries of NH3 and Lz has an essentially negligible effect on the overall geometry of the complex, in particular on the important distances quoted in Table 1. The DFT and MP2 geometries agree best when Lz is either acetone, water, acetate, or chloridesthese will be referred to as class 1 ligands. The geometries of the complexes containing these ligands are characterized by large H-H separations that range from 1.13 to 1.31 Å, when calculated using DFT, and at most 0.16 Å shorter than those obtained at the MP2 level. In the case of the acetate complex it is possible to compare theory and experiment. The BLYP values for the H-H and Os-H distances of 1.316 and 1.635 Å, respectively, are in good agreement with the MP2 values of 1.389 and 1.58 Å and certainly consistent with the experimental distances of 1.34 and 1.60 Å.6 The B3LYP values of 1.213 and 1.630 Å are in somewhat poorer agreement with experiment. In the case of the other class 1 ligands (i.e., Lz ) acetone, water, and chloride) the MP2 H-H distances are all between 1.35 and 1.40 Å, while the BLYP and B3LYP methods predict them to be shorter, by 0.1-0.2 Å. Conversely the Os-H distances predicted by the two DFT formalisms are generally 0.02-0.06 Å longer than the MP2 values. It appears that this trend is fairly general and even more accentuated for the other ligands, suggesting that, in comparison with MP2, the DFT methods predict stronger H-H but weaker Os-H bonds. For the remaining complexes, where Lz ) hydride, pyridine,

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Bytheway et al.

acetonitrile, cyanide, hydroxylamine, and ammonia, referred to as class 2 ligands, the BLYP and B3LYP geometries are in closer agreement with each other but differ more from those obtained using MP2. The BLYP and B3LYP H-H distances are smaller, by as much as 0.39 Å, than at the MP2 level of theory. Nevertheless, DFT still predicts that H2 is significantly stretched. The shortest predicted H-H distance is 0.92 Å, when Lz ) CN-, i.e., ∼0.2 Å longer than in free H2,26 and longer than that found experimentally in many other η2-H2 complexes.27 Correspondingly, the Os-H distances from the BLYP and B3LYP calculations are longer than the MP2 values by as much as 0.12 Å, showing the same trend as that noted for the class 1 ligands. The differences in H-H and Os-H bond lengths constitute the major part of the disagreement between the geometries predicted by the DFT and MP2 methods, although qualitatively the predicted geometries can be said to agree. This is enforced in part by the constraints on the molecule during optimization. The level of consistency between the different methods has not been tested for other stereochemistries of the [Os(NH3)4Lz(η2H2)](z+2)+ complex, e.g., the cis isomer of this complex or one with formal seven coordination, with both H atoms acting as unidentate hydride ligands. The difference between the two classes of ligands is conveniently described and systematized in terms of their spectrochemical parameters f(L) that may be quantified Via the angular overlap (AO) model.28 According to the AO model the separation ∆0 between the metal dσ and dπ orbitals, brought about by the interaction between the metal and ligands, is given as

∆0 ) 3eσ - 4eπ

Figure 2. Correlation of the calculated H-H distances (Å) in the [Os(NH3)4Lz(η2-H2)](z+2)+ complexes with the spectrochemical parameter, f(L), of the trans ligand Lz. (A ) Cl-, B ) (CH3)2CO, C ) H2O, D ) CH3CN, E ) C5H5N, F ) NH3, G ) NH2OH, H ) CN-).

(11)

where eσ and eπ represent the σ-donor and π-acceptor strengths of a given ligand. Thus, while eσ is positive, eπ is positive for π-donor ligands, e.g., halides, but negative for ligands that are strong π-acceptors, e.g., acetonitrile or cyanide. Consequently, other things being equal, ∆0 is small for the π-acceptors but large for π-donor ligands. Similarly, strong σ-donor capacity results in increased splitting of ∆0. The spectrochemical parameter f(L) is then linked to these σ- and π-donor/acceptor properties by the expression

(12)

Figure 3. Correlation of the calculated Os-H and H-H distances (Å) for the various [Os(NH3)4Lz(η2-H2)](z+2)+ complexes.

where g(M) is a parameter that quantifies the contribution of the metal M to ∆0. Estimates, based on experimental data, are available for both f(L) and g(M).11 Given the dependence of the geometry on the class of a given trans ligand, as noted above, a convenient way to systematize the trends in the geometries, as well as other properties of the complexes, is to correlate them with the spectrochemical parameters of the trans ligands. Figure 2 contains a plot of the calculated H-H distances against the spectrochemical constants that graphically illustrates the overall variation of the H-H distance with the nature of the trans ligand, as well as the growing difference between the DFT and MP2 predictions as the ligands change from being π-donors to π-acceptors. (Our choice of CN- as a trans ligand was in fact motivated by its extremely large spectrochemical parameter.) The correlation between f(L) and the calculated H-H distances is reasonable, but while the MP2 distances appear to be fairly insensitive to variations in the nature of trans ligand, the DFT methods predict a considerably stronger dependence on f(L). The correlation between the H-H and Os-H distances, that has been remarked on above, is indicated in the plot in Figure

3. The DFT results span a considerable range of distances and fall into two fairly distinct groups corresponding to the ligand's class. By comparison, the MP2 results show very little variation, and any correlation between the H-H and Os-H distances is tenuous. In Figure 4 the differences between the DFT and MP2 H-H distances are plotted against f(L), showing clearly that agreement between the MP2 and DFT results is best when the trans ligand is a π-donor, resulting in stronger Os-H2 bonding and consequently longer H-H distances. As the trans ligand becomes a stronger π-acceptor, the Os-H2 bond becomes weaker with a concomitant shortening of the H-H bond, and this is where the difference between the MP2 and DFT predictions becomes larger, reaching a maximum of ∼0.3 Å. In terms of the AO model, the dependence of the H-H separation on the trans ligand can be thought of as arising from the amount of charge on the osmium atom that is available for back-bonding to the dihydrogen ligand. Thus, in the case of a trans ligand that is a π-donor, more electronic charge is placed on the osmium atom which is then available for back-bonding, resulting in longer H-H distances. Correspondingly, for

∆0 ) f(L) g(M)

Molecular Hydrogen Complexes of Osmium(II)

J. Phys. Chem., Vol. 100, No. 15, 1996 6027

Figure 4. Correlation of the difference in the MP2 and DFT calculated H-H bond lengths (Å) in the [Os(NH3)4Lz(η2-H2)](z+2)+ complexes with the values of the spectrochemical parameter f(L) of Lz. (The labels identifying Lz are as in Figure 2.)

Figure 5. Variation of energy (kcal mol-1) with H-H distance (Å) at the MP2 geometry for the [Os(NH3)4NH3(H2)]2+ complex relative to the energy at the MP2 equilibrium geometry, Viz., rH-H ) 1.252 Å.

TABLE 2: Difference in Energy, on the BLYP Potential Energy Surface, between the MP2 and the BLYP Equilibrium Geometries

Lz

E(BLYP//BLYP) E(BLYP//MP2) (kcal mol-1)

Lz

E(BLYP//BLYP) E(BLYP//MP2) (kcal mol-1)

(CH3)2CO H 2O CH3COOClH-

3.01 2.99 1.18 1.50 6.65

C5H5N CH3CN CNNH2OH NH3

1.92 1.82 3.94 2.57 2.88

π-acceptor ligands, the removal of charge from the osmium results in less back-bonding and hence smaller H-H distances. In order to obtain further information on the potential energy surface in the vicinity of the equilibrium geometries, we calculated energies using the BLYP method at the MP2 equilibrium geometries. The rise in energy, associated with the distortion of the BLYP equilibrium geometry, provides a measure of the sensitivity of the energy to such distortions, i.e., a measure of the force constants associated with a particular distortion. The results of such a calculation are summarized in Table 2. Somewhat surprisingly, the energy changes (calculated using the BLYP functional) corresponding to the geometry change BLYP f MP2 are, with the exception of the hydride, uniformly small. These results indicate not only that the potential energy surfaces are quite flat, but that those corresponding to the complexes with class 2 ligands are on average somewhat less sensitive to distortions in the geometry than the rest, i.e., have even flatter surfaces. Thus, although the differences between DFT and MP2 geometries are largest when the trans ligand belongs to class 2, as noted already, the corresponding energy differences are actually comparable. The question that arises, of course, is whether or not to prefer the MP2 geometries over those obtained using DFT; i.e., which method is the more reliable for the calculation of [Os(NH3)4Lz(η2-H2)](z+2)+ geometries? In an effort to answer this, we undertook a limited, pointwise study of the potential energy surface of the pentaamine complex, i.e., Lz ) NH3, at the MP4(SDQ) level of theory that includes contributions from single, double, and quadruple excitations. The pentaamine complex was chosen as a test case because of the large difference in the predicted MP2 and BLYP H-H distances. Using the MP2 and BLYP optimized geometries as reference, the H-H distance was varied and at each point the energy calculated at the MP2,

Figure 6. Variation of energy (kcal mol-1) with H-H distance (Å) at the BLYP geometry for the [Os(NH3)4NH3(H2)]2+ complex relative to the energy at the BLYP equilibrium geometry, Viz., rH-H ) 1.057 Å.

BLYP, and MP4(SDQ) levels of theory. The resulting H-H stretching potentials are shown in Figures 5 and 6, plotted relative to their respective values at the MP2 or BLYP geometry. Interestingly, at the MP2 geometry (Figure 5) the MP2 and BLYP H-H potentials are in close agreement, their minima being at ∼1.25 Å, while the MP4(SDQ) minimum is at ∼1.15 Å. At the BLYP geometry (Figure 6) the minima are 1.06, ∼1.15, and 1.25 Å, at the BLYP, MP4(SDQ), and MP2 levels of theory, respectively. Thus, MP4(SDQ) predicts a H-H separation that is longer than the BLYP value but shorter than what is obtained using MP2. This result is consistent with the findings of CBH, where an averaged coupled pair functional calculation for the complex with Lz ) Cl- also predicted a shorter H-H distance than the MP2 value, by ∼0.05 Å. The calculations of H-H potentials, as described above, also suggest that while MP2 and MP4 appear to produce H-H bond lengths that are not very sensitive to the choice of reference geometry, at the BLYP level a larger degree of coupling between the H-H stretch and the other vibrational modes, especially the Os-H stretch, seems to be present. In summary, it appears probable that the MP4(SDQ) H-H distance would be approximately midway between the BLYP and MP2 values. On the basis of past experience, we regard the MP4 method as the most reliable

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TABLE 3: Calculated Os-Lz Distances (Å) for the Various Fragments Obtained Using the BLYP, B3LYP, and MP2 Methods

(L), respectively, as defined by eqs 2 and 4, are given in Table 4. They are to be compared with the corresponding binding energies of H2 and Lz in the [Os(NH3)4(η2H2)]2+ and [Os(NH3)4Lz]2+ fragments, respectively, i.e., ∆E2(H2) and ∆E2(L), as defined by eqs 3 and 5, that are also listed in Table 4. The effect of hydration has been estimated by the SCMMRF technique, used in conjunction with the BLYP method. The (gas phase) BLYP and B3LYP binding energies are in close agreement but significantly lower in magnitude than those obtained at the MP2 level. As anticipated on the basis of the Os-H and Os-Lz bond lengths, H2 is more strongly bound in the absence of a trans ligand and, similarly, Lz is more strongly bound in the absence of H2. Where Lz is an ionic species its (gas phase) binding energy is very large due to the presence of a large Coulomb attraction. We note here that basis set effects, while not expected to be significant in the case of geometries, may be of some importance in the calculation of binding energies. Future work, therefore, will include the study of larger basis sets than those employed in this work. One such test calculation has already been carried out for the Lz ) Cl- complex, with the standard basis set enlarged by polarization functions on the heavy atoms of the NH3 and Cl- ligands as well as the Os atom (see Theoretical Details). The results, also shown in Table 4, indicate that the BLYP energies are quite stable to these changes in the basis; the binding energies of H2 change by ∼3 kcal mol-1 at most. The corresponding variation in the MP2 results is considerably larger. The energetic effects of the constraints that were imposed on the geometry optimizations are quite small, as one may expect on the basis of the small relaxation in geometry, noted above, for the test molecule with Lz ) acetone. The binding energies from the fully relaxed calculations, also given in Table 4, differ by 0.2-1.8 kcal mol-1 from those obtained from the constrained calculations. Solvation in water (at 298 K) appears to have a relatively small effect on the binding energies of H2, except in the case of Lz ) (CH3)2CO and CH3CN, where it results in a reduction in the binding energies by ∼10 kcal mol-1. The situation, however, is markedly different in the case of the trans ligands' binding energies, where the reduction is much more significant, especially in the case of charged ligands. We wish to emphasize though that the computed solvent effects are to be taken not as definitive, but only as a qualitative guide, owing to the inherent

r(Os-Lz) L

z

(CH3)2CO H2O CH3COOClHC5H5N CH3CN CNNH2OH NH3

BLYP

B3LYP

MP2

2.038 2.135 2.058 2.424 1.607 2.049 1.940 1.920 2.088 2.155

2.054 2.127 2.043 2.408 1.597 2.049 1.949 1.921 2.087 2.144

2.218 2.200 2.159 2.457 1.618 2.143 1.981 1.937 2.092 2.142

among the techniques used here, hence, we conclude that in the complexes studied in this work the true H-H distance is likely to be halfway between the BLYP and MP2 predictions. The calculation of the binding energies of H2 and Lz in the complexes also necessitated the optimization of the geometries of the [Os(NH3)4Lz](z+2)+, [Os(NH3)4(η2-H2)]2+ and [Os(NH3)4]2+, complexes, Viz., fragments. The important geometrical parameters for the [Os(NH3)4Lz](z+2)+ fragments are listed in Table 3. The Os-Lz distances are shorter by up to ∼0.2 Å than in the corresponding dihydrogen complexes, suggesting that the Os-Lz bonds are stronger in the fragments, i.e., there exists a synergistic coupling between the Os-Lz and Os-(η2-H2) interactions, Viz., trans influence. The overall agreement between the DFT and MP2 Os-Lz distances is quite good, the largest difference being ∼0.1 Å (for Lz ) pyridine). The level of agreement is in fact generally better than in the case of the dihydrogen complexes, and this too is consistent with the view that there is a reasonable degree of coupling between the Os-Lz and the Os-(η2-H2) bonds. For the [Os(NH3)4(η2-H2)]2+ fragment a long H-H distance is predicted along with a fairly short Os-H distance, indicative of a stronger Os-H bond than in the presence of a trans ligand. Furthermore, the agreement between the DFT and MP2 bond lengths is quite good, comparable with that noted for the complexes with class 1 trans ligands. Binding Energies of H2 and Lz The binding energies of both the dihydrogen and trans ligands Lz in the [Os(NH3)4Lz(η2H2)](z+2)+ complexes, ∆E1(H2) and ∆E1-

TABLE 4: Calculated Binding Energies of H2 and Lz in the [Os(NH3)4Lz(η2-H2)](z+2)+ Complexes (in kcal mol-1) -∆E1(H2)

-∆E1(L)

-∆E2(L)

Lz

BLYP

B3LYP

MP2

BLYP/Sa

BLYP

B3LYP

MP2

BLYP/Sa

BLYP

B3LYP

MP2

BLYP/Sa

(CH3)2CO

45.9 45.7b 49.7 44.5 45.0 42.1c 22.9 32.3 33.0 23.7 36.5 37.5

44.9

64.0

35.7

47.3

48.9

18.8

55.0

45.7

57.7 59.0 60.8 64.5c 40.2 46.7 46.7 40.5 48.2 49.1 43.3d

51.3 42.1 44.6

40.3 248.0 233.5

39.0 254.5 237.4 252.0c 303.0 62.6 51.3 256.0 53.1 51.8 50.5d

24.0 68.8 56.1

62.5 64.3b 52.6 264.1 253.0 260.3c 334.2 85.7 83.8 292.2 74.6 72.7

61.4

46.6 43.8 43.2

43.5 44.5b 37.4 243.8 232.8 238.9c 292.2 53.5 52.0 251.1 46.2 45.3

52.8 263.2 249.2

51.5 265.6 246.8 261.8c 332.6 85.8 74.4 285.3 74.7 71.5 69.9d

35.3 89.1 74.3

61.1 74.2c 63.0d

62.6

H2O CH3COOClHC5H5N CH3CN CNNH2OH NH3 -∆E2(H2)

64.9 65.6b 63.4c

22.8 32.6 33.4 24.9 35.8 36.3 65.9

23.2 37.4 24.6 21.8 40.9 39.5

294.4 55.6 55.9 251.2 51.4 48.6

107.8 30.8 34.4 73.9 28.6 35.6

330.7 85.1 81.5 285.4 74.5 71.4

147.7 55.5 64.0 112.7 59.1 62.6

a BLYP/S refers to BLYP energies in the presence of water as solvent at 298 K (dielectric constant  ) 78.54). b Energies calculated at unconstrained (fully optimized) geometries. c Energies calculated using the basis set including polarization functions on N, Cl, and Os. d Energies calculated at the MP4(SDQ) level using the MP2 optimized geometries.

Molecular Hydrogen Complexes of Osmium(II)

Figure 7. Correlation of the binding energy of H2 (∆E1(H2), in kcal mol-1) with calculated H-H bond length (Å) for the [Os(NH3)4Lz(η2H2)](z+2)+ complexes. (The labels identifying Lz are as in Figure 2; I ) CH3COO-, J ) H-).

inadaquacies of the continuum model that is used, especially where solvation involves substantial hydrogen bonding, e.g., in the case of trans ligands such as H2O, NH3, or indeed any of the charged ligands. Given the tentative nature of the calculated solvation effects, their study was restricted to one level of theory, Viz., using the BLYP functional. Comparative studies for the Lz ) Cl- showed, however, that the solvation energies using the BLYP functional are very close to those calculated at the MP2 level. The H-H distance in a given complex is expected to depend on the strength of the interaction of H2 with Os, and to test this, the (gas phase) binding energies ∆E1(H2) were plotted against the calculated H-H distances. The plot, shown in Figure 7, indicates that the more H2 is stretched, i.e., the more (di)hydride-like it is, the larger its binding energy becomes. Such a result was anticipated on the basis of a simple description of the osmium-dihydrogen bonding in these complexes:3 as the Os-(η2-H2) bond is best described as a dative bond, it is expected to be weaker than two polar-covalent-type bonds in an osmium dihydride complex. As shown already (Figure 2), the H-H bond lengths, especially when obtained using DFT, correlate fairly well with the spectrochemical constants of the trans ligands, f(L). Consequently, the binding energies ∆E1(H2) also correlate with f(L); i.e., the bonding between H2 and Os becomes weaker with increasing f(L). As the discrepancy between the DFT and MP2 predictions of the H-H bond length is largest for large f(L), a similar trend is expected in the case of the binding energies. This does appear to be the case, as the plot in Figure 8 shows. The ratio of the predicted DFT and MP2 binding energies varies between approximately 0.85 and 0.57, roughly inversely with f(L). Charge Distribution and Bonding The nature of charge distribution in the [Os(NH3)4Lz(η2H2)](z+2)+ complexes has been investigated in detail using the Mulliken and AIM methods. The results of Mulliken population analyses corresponding to the three different types of wave functions are presented in Tables S1 and S2 of the supplementary material to this paper. On the whole, the populations on the H2 moiety in the dihydrogen complexes are insensitive to the choice of the theoretical method, but the populations on the other ligands and especially on the Os atom are very method dependent. Both types of DFT calculations result in a negative

J. Phys. Chem., Vol. 100, No. 15, 1996 6029

Figure 8. Correlation of the ratio of the MP2 and DFT binding energies (∆E1(H2)) with the spectrochemical constant f(L) of Lz in the [Os(NH3)4Lz(η2-H2)](z+2)+ complexes. (The labels identifying Lz are as in Figure 2.)

Mulliken charge on the Os atom, while the trans and ammonia ligands are predicted to be more positive than those obtained in the MP2 calculations. Similar trends are evident in the populations of the [Os(NH3)4Lz](z+2)+ fragment molecules, where the Os atom is consistently predicted to be more negative than at the MP2 level, with the opposite trend noted for the ligands. While the actual populations depend strongly on the level of theory, as one may expect,29 the differences between the complex and fragment populations are quite similar. Upon removal of the dihydrogen ligand both the Os and Lz moieties become more positive, while the ammonia ligands become more negative. It appears, however, that the Mulliken populations do not display any systematic variation that may be correlated with the changing trans ligand. As discussed in detail elsewhere,7 the dominant contributions to the Os-H2 bond are σ donation by H2 and dπ f σ* backdonation by Os. The Mullikan populations suggest that the amount of charge donated by H2 is generally larger than, or nearly equal to, the back-donated charge. However, as noted in our previous work,7 a density difference plot suggested that there was a net increase in electronic charge on the dihydrogen ligand, as a given [Os(NH3)4Lz(η2-H2)](z+2)+ complex was formed from stretched H2 and the [Os(NH3)4Lz](z+2)+ fragment, seemingly contradicting the results of the Mulliken analysis. In an effort to resolve this problem, integrated atomic charges, as defined in the theory of AIM, were also calculated for Os and all of the ligands, from the BLYP and MP2 charge densities. The resulting atomic charges and densities at the H-H and Os-H bond critical points are compared in Table 5. We note first that, in contrast with the Mulliken analysis, the AIM method does predict H2 to be negative while Os is consistently positive, its net atomic charge varying between 1.02 and 1.89 e. While the charge on H2 is relatively insensitive to the choice of method, BLYP consistently predicts Os to be considerably less positive than at the MP2 level, especially in the case of the class 2 trans ligands, where, significantly, BLYP predicts H2 to be also closer to neutral. These trends are consistent with the idea that in comparison with MP2 the DFT calculations result in weaker Os-H2 but stronger H-H bonds, since Os donates less charge into the σ* molecular orbital of H2. Bond critical points24 were sought between the atoms of the H2 molecule and between Os and H atoms, since the charge density at such a point is also a useful probe of chemical

6030 J. Phys. Chem., Vol. 100, No. 15, 1996

Bytheway et al.

TABLE 5: Atomic Chargesa (e) and the Electron Density G (ea0-3) at the H-H and Os-H Bond Critical Points Obtained from the AIM Analysis of the BLYP and MP2 Charge Densities q(Os)b

q(H2) L

z

(CH3)2CO H2O CH3COOClHC5H5N CH3CN CNNH2OH NH3

q(Lz)

q(NH3)

F(H-H)c,d

F(Os-H)

BLYP

MP2

BLYP

MP2

BLYP

MP2

BLYP

MP2

BLYP

MP2

BLYP

MP2

-0.116 -0.111 -0.261 -0.235 -0.208 -0.097 -0.081 -0.158 -0.086 -0.093

-0.122 -0.102 -0.256 -0.218 -0.298 -0.109 -0.109 -0.220 -0.087 -0.089

1.128 1.099 1.142 1.710 0.886 1.122 1.122 1.063 1.015 1.033

1.382 1.351 1.443 1.810 1.224 1.336 1.351 1.333 1.275 1.295

0.079 0.086 -0.716 -1.267 -0.364 0.151 0.059 -0.669 0.152 0.185

0.064 0.062 -0.839 -1.180 -0.483 0.136 0.081 -0.736 0.108 0.124

0.227 0.232 0.209 0.197 0.172 0.206 0.225 0.191 0.230 0.219

0.169 0.172 0.163 0.147 0.139 0.159 0.169 0.156 0.176 0.167

0.102 0.102 0.090 0.091 0.160* 0.158* 0.163* 0.170* 0.149* 0.144*

0.091 0.096 0.090 0.091 0.092 0.101 0.099 0.107* 0.110 0.111

0.154 0.154 0.146 0.147 0.105 0.123 0.122 0.106 0.130 0.134

0.164 0.165 0.168 0.166 0.146 0.153 0.168 0.151 0.164 0.164

a The electronic charge associated with an atom in a given molecule, N(Ω), was obtained by integration of the electron density F over the basin of the atom. The corresponding net charge (e) q(Ω) ) Z(Ω) - N(Ω), where Z(Ω) is the nuclear charge. b The charge on the Os atom was obtained from the other integrated values by subtraction. c F(H-H) calculated midway between H atoms when no bond critical point found (unstarred entries). d Presence/absence of asterisk indicates presence/absence of H-H bond critical point.

bonding. In the case of the H2 ligand, bond critical points were found only in the complexes with class 2 trans ligands and then only for the corresponding BLYP densities (and geometries). These results appear to suggest that the coordinated dihydrogen ligand in these complexes, where the H-H distances are unusually long, may well be better described as two separate hydrogen ligands. Of course, the “existence” or otherwise of “bonds” is a matter of interpretation and what these negative results imply is that in these highly stretched molecules with shallow stretching potentials the interaction between the hydrogen atoms is very weak, especially in comparison with the Os-H interaction. Nevertheless, these results, obtained at the equilibrium geometries, are consistent with the hypothesis that the H-H interaction is predicted to be stronger by the DFT methods than by MP2, especially in the case of complexes with class 2 trans ligands. The values of the charge density at the Os-H bond critical points further strengthen this argument,23 inasmuch as these are larger for the complexes with class 1 ligands, indicative of stronger Os-H bonds. Moreover, the BLYP charge densities (at the Os-H bond critical points) are consistently lower than those obtained at the MP2 level. Conclusions When comparing the results of MP2, BLYP, and B3LYP calculations on the [Os(NH3)4Lz(η2-H2)](z+2)+ complexes, the most obvious conclusion is that qualitatively similar results are predicted by all three methods. The bond lengths of the dihydrogen ligands are unusually long, ranging from 1.0 to 1.4 Å, depending on the trans ligand but also on the method of calculation. The DFT calculations consistently result in geometries with shorter H-H and longer Os-H distances than those calculated at the MP2 level. The H-H distance in a given complex depends on the type of trans ligand Lz as does the difference between the DFT and MP2 predictions. When Lz is a strong π-donor, the DFT and MP2 calculations predict H-H distances that are ∼1.3 Å and agree with each other to within ∼0.1 Å. However, when Lz is a π-acceptor, the DFT methods predict H-H distances that are ∼1.0 Å and differ by ∼0.3 Å from the MP2 values. The limited MP4(SDQ) studies that were carried out favor distances approximately halfway between DFT and MP2. We emphasize, however, that as the potential energy surfaces are very flat with respect to the H-H stretch, the energy differences between DFT and MP2 geometries are very small, ∼3 kcal mol-1. The binding energies of the dihydrogen ligand ∆E1(H2) to the complex, when computed by DFT methods, are uniformly smaller than the MP2 values. This result, along with the

analogous differences in the calculated geometries, suggests that for these complexes the two methods differ largely in the relative emphasis they place on the H-H and Os-H bonding. By contrast, the ligand binding energies ∆E1(L) and ∆E2(L) are quite insensitive to the method used, suggesting that the methods are fairly consistent in their treatment of the rest of the complex. Solvation is found to significantly reduce the binding energies of the trans ligands, but not the binding of dihydrogen. The Mulliken population analyses assign a net positive charge to the dihydrogen ligand in the complexes as well as predict Os to have a low positive or even negative charge, depending on the method of calculation, Viz., DFT or MP2. The AIM integrated atomic charges appear to be more reasonable chemically, inasmuch as the charge on Os ranges from ∼0.9 to 1.8 e, while the H2 ligand is negative, confirming our previous prediction.7 Acknowledgment. We wish to thank Dr T.-X. Lu¨ for the use of his SCMMRF program. Financial support by the Australian Research Council is gratefully acknowledged. Supporting Information Available: Tables of Mulliken populations (2 pages). This material is contained in many libraries on microfiche, immediately follows this article in the microfilm version of the journal, and can be ordered from the ACS; see any current masthead page for ordering information. References and Notes (1) Heinekey, D. M.; Oldham, W. J., Jr. Chem. ReV. 1993, 93, 913. (2) Jessop, P. G.; Morris, R. H. Coord. Chem. ReV. 1992, 121, 155. (3) Lin. Z.; Hall, M. B. Coord. Chem. ReV. 1994, 135/136, 845. (4) (a) Li, Z.-W.; Taube, H. J. Am. Chem. Soc. 1991, 113, 8946. (b) Li. Z.-W.; Taube, H. J. Am. Chem. Soc. 1994, 116, 9506. (c) Li. Z.-W.; Taube, H. J. Am. Chem. Soc. 1994, 116, 11584. (5) Taube, H. Private communication, 1993. (6) Hasegawa, T.; Koetzle, T. J.; Li, Z.; Parkin, S.; McMullan, R.; Taube, H. 29th International Conference on Coordination Chemistry, Lausane, Switzerland, 1992. (7) (a) Craw, J. S.; Bacskay, G. B.; Hush. N. S. Inorg. Chem. 1993, 32, 2230. (b) Craw, J. S.; Bacskay, G. B.; Hush. N. S. J. Am. Chem. Soc. 1994, 116, 5937. (8) Gdanitz, R. J.; Ahlrichs, R. Chem. Phys. Lett. 1988, 143, 413. (9) (a) Ziegler, T. Chem. ReV. 1991, 91, 651. (b) Ziegler, T. Can. J. Chem. 1995, 73, 743. (10) (a) Li, J.; Schreckenbach, G.; Ziegler, T. J. Phys. Chem. 1994, 98, 4838. (b) Li, J.; Schreckenbach, G.; Ziegler, T. J. Am. Chem. Soc. 1995, 117, 486. (c) Ricca, A.; Bauschlicher, C. W., Jr. J. Phys. Chem. 1995, 99, 5922. (d) Russo, T. V.; Martin, R. L.; Hay, P. J. J. Chem. Phys. 1995, 102, 8023. (e) Maitre, P.; Bauschlicher, C. W., Jr. J. Phys. Chem. 1995, 99, 6836. (11) Lever, A. B. P. Inorganic Electronic Spectroscopy; Elsevier: Amsterdam, 1984.

Molecular Hydrogen Complexes of Osmium(II) (12) (a) Igel-Mann, G.; Stoll, H.; Preuss, H. Mol. Phys. 1988, 65, 1321. (b) Andrae, D.; Ha¨ussermann, U.; Dolg, M.; Stoll, H.; Preuss, H. Theor. Chem. Acta 1990, 77, 123. (13) Huzinaga, S. J. Chem. Phys. 1965, 42, 1293. (14) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A.; Head-Gordon, M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Pople, J. A. Gaussian 92/DFT, Revision G.1, Gaussian Inc.: Pittsburgh, PA, 1993. (15) (a) Becke, A. D. Phys. ReV. A 1988, 38, 3098. (b) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (16) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (17) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys 1980, 58, 1200. (18) (a) Johnson, B. G.; Gill, P. M. W.; Pople, J. A. J. Chem. Phys. 1993, 98, 5612. (b) Laming, G. J.; Termath, V.; Handy, N. C. J. Chem. Phys. 1993, 99, 8765. (19) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (20) Lu¨, T.-X.; Bacskay, G. B.; Haymet, A. D. J. Mol. Phys., in press. (21) Wong, M. W.; Frisch, M. J.; Wiberg, K. B. J. Am. Chem. Soc. 1991, 113, 4776.

J. Phys. Chem., Vol. 100, No. 15, 1996 6031 (22) Dillet, V.; Rinaldi, D.; Rivail, J.-L. J. Phys. Chem. 1994, 98, 5034. (23) (a) Bader, R. F. W. Atoms in Molecules: A Quantum Theory, Oxford University Press: Oxford, U.K., 1990. (b) Bader, R. F. W.; Popelier, P. L. A.; Keith, T. A. Angew. Chem., Int. Ed. Engl. 1994, 33, 620. (24) Biegler-Ko¨nig, F. W.; Bader, R. F. W.; Tang, T.-H. J. Comput. Chem. 1982, 3, 317. (25) Huzinaga S.; Andzelm, J.; Klobukowski, M.; Radzio-Andelm, E.; Sakai, Y.; Tatewaki, H. Gaussian Basis Sets for Molecular Calculations; Elsevier: Amsterdam, 1984. (26) Equilibrium bond lengths of H2 calculated by these methods using the same hydrogen basis set as in the calculations of the complexes are as follows: BLYP, r(H-H) ) 0.766 Å; B3LYP, r(H-H) ) 0.760 Å (c.f. MP2, r(H-H) ) 0.752 Å). (27) Known H-H distances obtained from neutron diffraction experiments are tabulated in: Klooster, W.; Koetzle, T. F.; Jiu, G.; Fong, T. P.; Morris, R. H.; Albinati, A. J. Am. Chem. Soc. 1994, 116, 7677. (28) Gerloch, M.; Slade, R. C. Ligand Field Parameters; Cambridge University Press: Cambridge, U.K., 1973. (29) Wiberg, K.; Rablen, P. R. J. Comput. Chem. 1993, 14, 1504.

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